Release 0.5.0.

.github/workflows/nodejs.yml

@@ -13,6 +13,5 @@ jobs:
         node-version: 18
     - run: npm install
     - run: npm run build --if-present
-    - run: cd curve-definitions; npm install; npm run build --if-present
-    - run: npm test
     - run: npm run lint --if-present
+    - run: npm test

README.md

@@ -1,71 +1,427 @@
 # noble-curves
 
-Minimal, zero-dependency JS implementation of elliptic curve cryptography.
+Minimal, auditable JS implementation of elliptic curve cryptography.
 
-Implements Short Weierstrass curves with ECDSA signature scheme.
+- Short Weierstrass, Edwards, Montgomery curves
+- ECDSA, EdDSA, Schnorr, BLS signature schemes, ECDH key agreement
+- [hash to curve](https://datatracker.ietf.org/doc/draft-irtf-cfrg-hash-to-curve/)
+  for encoding or hashing an arbitrary string to a point on an elliptic curve
+- Auditable, [fast](#speed)
+- 🔻 Tree-shaking-friendly: there is no entry point, which ensures small size of your app
+- 🔍 Unique tests ensure correctness. Wycheproof vectors included
 
-To keep the package minimal, no curve definitions are provided out-of-box.
-Main reason for that is the fact hashing library is usually required for full functionality. Use separate package that defines popular curves: `micro-curve-definitions` for P192, P224, P256, P384, P521, secp256k1, stark curve, bn254, pasta (pallas/vesta) - it depends on `@noble/hashes`.
+There are two parts of the package:
 
-Future plans:
+1. `abstract/` directory specifies zero-dependency EC algorithms
+2. root directory utilizes one dependency `@noble/hashes` and provides ready-to-use:
+   - NIST curves secp192r1/P192, secp224r1/P224, secp256r1/P256, secp384r1/P384, secp521r1/P521
+   - SECG curve secp256k1
+   - pairing-friendly curves bls12-381, bn254
+   - ed25519/curve25519/x25519/ristretto, edwards448/curve448/x448 RFC7748 / RFC8032 / ZIP215 stuff
 
-- Edwards, Twisted Edwards & Montgomery curves
-- hash-to-curve standard
-- pairings
+Curves incorporate work from previous noble packages
+([secp256k1](https://github.com/paulmillr/noble-secp256k1),
+[ed25519](https://github.com/paulmillr/noble-ed25519),
+[bls12-381](https://github.com/paulmillr/noble-bls12-381)),
+which had security audits and were developed from 2019 to 2022.
+The goal is to replace them with lean UMD builds based on single-codebase noble-curves.
 
 ### This library belongs to _noble_ crypto
 
 > **noble-crypto** — high-security, easily auditable set of contained cryptographic libraries and tools.
 
-- No dependencies, small files
+- Minimal dependencies, small files
 - Easily auditable TypeScript/JS code
 - Supported in all major browsers and stable node.js versions
 - All releases are signed with PGP keys
 - Check out [homepage](https://paulmillr.com/noble/) & all libraries:
-  [secp256k1](https://github.com/paulmillr/noble-secp256k1),
+  [curves](https://github.com/paulmillr/noble-curves) ([secp256k1](https://github.com/paulmillr/noble-secp256k1),
   [ed25519](https://github.com/paulmillr/noble-ed25519),
-  [bls12-381](https://github.com/paulmillr/noble-bls12-381),
-  [hashes](https://github.com/paulmillr/noble-hashes),
-  [curves](https://github.com/paulmillr/noble-curves)
+  [bls12-381](https://github.com/paulmillr/noble-bls12-381)),
+  [hashes](https://github.com/paulmillr/noble-hashes)
 
 ## Usage
 
 Use NPM in node.js / browser, or include single file from
 [GitHub's releases page](https://github.com/paulmillr/noble-curves/releases):
 
-## Usage
+> npm install @noble/curves
 
-```sh
-npm install @noble/curves
-```
+The library does not have an entry point. It allows you to select specific primitives and drop everything else. If you only want to use secp256k1, just use the library with rollup or other bundlers. This is done to make your bundles tiny.
 
 ```ts
-// Short Weierstrass curve
-import shortw from '@noble/curves/shortw';
+// Common.js and ECMAScript Modules (ESM)
+import { secp256k1 } from '@noble/curves/secp256k1';
+
+const key = secp256k1.utils.randomPrivateKey();
+const pub = secp256k1.getPublicKey(key);
+const msg = new Uint8Array(32).fill(1);
+const sig = secp256k1.sign(msg, key);
+secp256k1.verify(sig, msg, pub) === true;
+sig.recoverPublicKey(msg) === pub;
+const someonesPub = secp256k1.getPublicKey(secp256k1.utils.randomPrivateKey());
+const shared = secp256k1.getSharedSecret(key, someonesPub);
+```
+
+All curves:
+
+```ts
+import { secp256k1 } from '@noble/curves/secp256k1';
+import { ed25519, ed25519ph, ed25519ctx, x25519, RistrettoPoint } from '@noble/curves/ed25519';
+import { ed448, ed448ph, ed448ctx, x448 } from '@noble/curves/ed448';
+import { p256 } from '@noble/curves/p256';
+import { p384 } from '@noble/curves/p384';
+import { p521 } from '@noble/curves/p521';
+import { pallas, vesta } from '@noble/curves/pasta';
+import * as stark from '@noble/curves/stark';
+import { bls12_381 } from '@noble/curves/bls12-381';
+import { bn254 } from '@noble/curves/bn';
+import { jubjub } from '@noble/curves/jubjub';
+```
+
+To define a custom curve, check out API below.
+
+## API
+
+- [Overview](#overview)
+- [abstract/edwards: Twisted Edwards curve](#abstract/edwards-twisted-edwards-curve)
+- [abstract/montgomery: Montgomery curve](#abstract/montgomery-montgomery-curve)
+- [abstract/weierstrass: Short Weierstrass curve](#abstract/weierstrass-short-weierstrass-curve)
+- [abstract/modular](#abstract/modular)
+- [abstract/utils](#abstract/utils)
+
+### Overview
+
+There are following zero-dependency abstract algorithms:
+
+```ts
+import { bls } from '@noble/curves/abstract/bls';
+import { twistedEdwards } from '@noble/curves/abstract/edwards';
+import { montgomery } from '@noble/curves/abstract/montgomery';
+import { weierstrass } from '@noble/curves/abstract/weierstrass';
+import * as mod from '@noble/curves/abstract/modular';
+import * as utils from '@noble/curves/abstract/utils';
+```
+
+They allow to define a new curve in a few lines of code:
+
+```ts
+import { Fp } from '@noble/curves/abstract/modular';
+import { weierstrass } from '@noble/curves/abstract/weierstrass';
+import { hmac } from '@noble/hashes/hmac';
+import { sha256 } from '@noble/hashes/sha256';
+import { concatBytes, randomBytes } from '@noble/hashes/utils';
+
+const secp256k1 = weierstrass({
+  a: 0n,
+  b: 7n,
+  Fp: Fp(2n ** 256n - 2n ** 32n - 2n ** 9n - 2n ** 8n - 2n ** 7n - 2n ** 6n - 2n ** 4n - 1n),
+  n: 2n ** 256n - 432420386565659656852420866394968145599n,
+  Gx: 55066263022277343669578718895168534326250603453777594175500187360389116729240n,
+  Gy: 32670510020758816978083085130507043184471273380659243275938904335757337482424n,
+  hash: sha256,
+  hmac: (key: Uint8Array, ...msgs: Uint8Array[]) => hmac(sha256, key, concatBytes(...msgs)),
+  randomBytes,
+});
+```
+
+- To initialize new curve, you must specify its variables, order (number of points on curve), field prime (over which the modular division would be done)
+- All curves expose same generic interface:
+  - `getPublicKey()`, `sign()`, `verify()` functions
+  - `Point` conforming to `Group` interface with add/multiply/double/negate/add/equals methods
+  - `CURVE` object with curve variables like `Gx`, `Gy`, `Fp` (field), `n` (order)
+  - `utils` object with `randomPrivateKey()`, `mod()`, `invert()` methods (`mod CURVE.P`)
+- All arithmetics is done with JS bigints over finite fields, which is defined from `modular` sub-module
+- Many features require hashing, which is not provided. `@noble/hashes` can be used for this purpose.
+  Any other library must conform to the CHash interface:
+  ```ts
+  export type CHash = {
+    (message: Uint8Array): Uint8Array;
+    blockLen: number;
+    outputLen: number;
+    create(): any;
+  };
+  ```
+- w-ary non-adjacent form (wNAF) method with constant-time adjustments is used for point multiplication.
+  It is possible to enable precomputes for edwards & weierstrass curves.
+  Precomputes are calculated once (takes ~20-40ms), after that most `G` base point multiplications:
+  for example, `getPublicKey()`, `sign()` and similar methods - would be much faster.
+  Use `curve.utils.precompute()` to adjust precomputation window size
+- You could use optional special params to tune performance:
+  - `Fp({sqrt})` square root calculation, used for point decompression
+  - `endo` endomorphism options for Koblitz curves
+
+### abstract/edwards: Twisted Edwards curve
+
+Twisted Edwards curve's formula is: ax² + y² = 1 + dx²y².
+
+- You must specify curve params `a`, `d`, field `Fp`, order `n`, cofactor `h` and coordinates `Gx`, `Gy` of generator point
+- For EdDSA signatures, params `hash` is also required. `adjustScalarBytes` which instructs how to change private scalars could be specified
+
+```typescript
+import { twistedEdwards } from '@noble/curves/abstract/edwards';
+import { div } from '@noble/curves/abstract/modular';
+import { sha512 } from '@noble/hashes/sha512';
+
+const ed25519 = twistedEdwards({
+  a: -1n,
+  d: div(-121665n, 121666n, 2n ** 255n - 19n), // -121665n/121666n
+  P: 2n ** 255n - 19n,
+  n: 2n ** 252n + 27742317777372353535851937790883648493n,
+  h: 8n,
+  Gx: 15112221349535400772501151409588531511454012693041857206046113283949847762202n,
+  Gy: 46316835694926478169428394003475163141307993866256225615783033603165251855960n,
+  hash: sha512,
+  randomBytes,
+  adjustScalarBytes(bytes) {
+    // optional in general, mandatory in ed25519
+    bytes[0] &= 248;
+    bytes[31] &= 127;
+    bytes[31] |= 64;
+    return bytes;
+  },
+} as const);
+const key = ed25519.utils.randomPrivateKey();
+const pub = ed25519.getPublicKey(key);
+const msg = new TextEncoder().encode('hello world'); // strings not accepted, must be Uint8Array
+const sig = ed25519.sign(msg, key);
+ed25519.verify(sig, msg, pub) === true;
+```
+
+`twistedEdwards()` returns `CurveFn` of following type:
+
+```ts
+export type CurveFn = {
+  CURVE: ReturnType<typeof validateOpts>;
+  getPublicKey: (privateKey: PrivKey, isCompressed?: boolean) => Uint8Array;
+  sign: (message: Hex, privateKey: Hex) => Uint8Array;
+  verify: (sig: SigType, message: Hex, publicKey: PubKey) => boolean;
+  Point: PointConstructor;
+  ExtendedPoint: ExtendedPointConstructor;
+  Signature: SignatureConstructor;
+  utils: {
+    mod: (a: bigint, b?: bigint) => bigint;
+    invert: (number: bigint, modulo?: bigint) => bigint;
+    randomPrivateKey: () => Uint8Array;
+    getExtendedPublicKey: (key: PrivKey) => {
+      head: Uint8Array;
+      prefix: Uint8Array;
+      scalar: bigint;
+      point: PointType;
+      pointBytes: Uint8Array;
+    };
+  };
+};
+```
+
+### abstract/montgomery: Montgomery curve
+
+For now the module only contains methods for x-only ECDH on Curve25519 / Curve448 from RFC7748.
+
+Proper Elliptic Curve Points are not implemented yet.
+
+You must specify curve field, `a24` special variable, `montgomeryBits`, `nByteLength`, and coordinate `u` of generator point.
+
+```typescript
+import { montgomery } from '@noble/curves/abstract/montgomery';
+
+const x25519 = montgomery({
+  P: 2n ** 255n - 19n,
+  a24: 121665n, // TODO: change to a
+  montgomeryBits: 255,
+  nByteLength: 32,
+  Gu: '0900000000000000000000000000000000000000000000000000000000000000',
+
+  // Optional params
+  powPminus2: (x: bigint): bigint => {
+    return mod.pow(x, P - 2, P);
+  },
+  adjustScalarBytes(bytes) {
+    bytes[0] &= 248;
+    bytes[31] &= 127;
+    bytes[31] |= 64;
+    return bytes;
+  },
+});
+```
+
+### abstract/weierstrass: Short Weierstrass curve
+
+Short Weierstrass curve's formula is: y² = x³ + ax + b. Uses deterministic ECDSA from RFC6979. You can also specify `extraEntropy` in `sign()`.
+
+- You must specify curve params: `a`, `b`, field `Fp`, order `n`, cofactor `h` and coordinates `Gx`, `Gy` of generator point
+- For ECDSA, you must specify `hash`, `hmac`. It is also possible to recover keys from signatures
+- For ECDH, use `getSharedSecret(privKeyA, pubKeyB)`
+- Optional params are `lowS` (default value) and `endo` (endomorphism)
+
+```typescript
+import { Fp } from '@noble/curves/abstract/modular';
+import { weierstrass } from '@noble/curves/abstract/weierstrass'; // Short Weierstrass curve
 import { sha256 } from '@noble/hashes/sha256';
 import { hmac } from '@noble/hashes/hmac';
 import { concatBytes, randomBytes } from '@noble/hashes/utils';
 
-export const secp256k1 = shortw({
+const secp256k1 = weierstrass({
   a: 0n,
   b: 7n,
-  // Field over which we'll do calculations
-  P: 2n ** 256n - 2n ** 32n - 2n ** 9n - 2n ** 8n - 2n ** 7n - 2n ** 6n - 2n ** 4n - 1n,
-  // Curve order, total count of valid points in the field
-  n: 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141n,
-  // Base point (x, y) aka generator point
+  Fp: Fp(2n ** 256n - 2n ** 32n - 2n ** 9n - 2n ** 8n - 2n ** 7n - 2n ** 6n - 2n ** 4n - 1n),
+  n: 2n ** 256n - 432420386565659656852420866394968145599n,
   Gx: 55066263022277343669578718895168534326250603453777594175500187360389116729240n,
   Gy: 32670510020758816978083085130507043184471273380659243275938904335757337482424n,
   hash: sha256,
   hmac: (k: Uint8Array, ...msgs: Uint8Array[]) => hmac(sha256, key, concatBytes(...msgs)),
-  randomBytes: randomBytes
+  randomBytes,
+
+  // Optional params
+  h: 1n, // Cofactor
+  lowS: true, // Allow only low-S signatures by default in sign() and verify()
+  endo: {
+    // Endomorphism options for Koblitz curve
+    // Beta param
+    beta: 0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501een,
+    // Split scalar k into k1, k2
+    splitScalar: (k: bigint) => {
+      // return { k1neg: true, k1: 512n, k2neg: false, k2: 448n };
+    },
+  },
 });
 
-// secp256k1.getPublicKey(priv)
-// secp256k1.sign(msg, priv)
-// secp256k1.verify(sig, msg, pub)
+// Usage
+const key = secp256k1.utils.randomPrivateKey();
+const pub = secp256k1.getPublicKey(key);
+const msg = randomBytes(32);
+const sig = secp256k1.sign(msg, key);
+secp256k1.verify(sig, msg, pub); // true
+sig.recoverPublicKey(msg); // == pub
+const someonesPubkey = secp256k1.getPublicKey(secp256k1.utils.randomPrivateKey());
+const shared = secp256k1.getSharedSecret(key, someonesPubkey);
 ```
 
+`weierstrass()` returns `CurveFn`:
+
+```ts
+export type CurveFn = {
+  CURVE: ReturnType<typeof validateOpts>;
+  getPublicKey: (privateKey: PrivKey, isCompressed?: boolean) => Uint8Array;
+  getSharedSecret: (privateA: PrivKey, publicB: PubKey, isCompressed?: boolean) => Uint8Array;
+  sign: (msgHash: Hex, privKey: PrivKey, opts?: SignOpts) => SignatureType;
+  verify: (
+    signature: Hex | SignatureType,
+    msgHash: Hex,
+    publicKey: PubKey,
+    opts?: { lowS?: boolean }
+  ) => boolean;
+  Point: PointConstructor;
+  ProjectivePoint: ProjectivePointConstructor;
+  Signature: SignatureConstructor;
+  utils: {
+    mod: (a: bigint) => bigint;
+    invert: (number: bigint) => bigint;
+    isValidPrivateKey(privateKey: PrivKey): boolean;
+    hashToPrivateKey: (hash: Hex) => Uint8Array;
+    randomPrivateKey: () => Uint8Array;
+  };
+};
+```
+
+### abstract/modular
+
+Modular arithmetics utilities.
+
+```typescript
+import { mod, invert, div, invertBatch, sqrt, Fp } from '@noble/curves/abstract/modular';
+mod(21n, 10n); // 21 mod 10 == 1n; fixed version of 21 % 10
+invert(17n, 10n); // invert(17) mod 10; modular multiplicative inverse
+div(5n, 17n, 10n); // 5/17 mod 10 == 5 * invert(17) mod 10; division
+invertBatch([1n, 2n, 4n], 21n); // => [1n, 11n, 16n] in one inversion
+sqrt(21n, 73n); // √21 mod 73; square root
+const fp = Fp(2n ** 255n - 19n); // Finite field over 2^255-19
+fp.mul(591n, 932n);
+fp.pow(481n, 11024858120n);
+```
+
+### abstract/utils
+
+```typescript
+import * as utils from '@noble/curves/abstract/utils';
+
+utils.bytesToHex(Uint8Array.from([0xde, 0xad, 0xbe, 0xef]));
+utils.hexToBytes('deadbeef');
+utils.hexToNumber();
+utils.bytesToNumberBE(Uint8Array.from([0xde, 0xad, 0xbe, 0xef]));
+utils.bytesToNumberLE(Uint8Array.from([0xde, 0xad, 0xbe, 0xef]));
+utils.numberToBytesBE(123n);
+utils.numberToBytesLE(123n);
+utils.numberToHexUnpadded(123n);
+utils.concatBytes(Uint8Array.from([0xde, 0xad]), Uint8Array.from([0xbe, 0xef]));
+utils.nLength(255n);
+utils.hashToPrivateScalar(sha512_of_something, secp256r1.n);
+utils.equalBytes(Uint8Array.from([0xde]), Uint8Array.from([0xde]));
+```
+
+## Security
+
+The library had no prior security audit.
+
+[Timing attack](https://en.wikipedia.org/wiki/Timing_attack) considerations: _JIT-compiler_ and _Garbage Collector_ make "constant time" extremely hard to achieve in a scripting language. Which means _any other JS library can't have constant-timeness_. Even statically typed Rust, a language without GC, [makes it harder to achieve constant-time](https://www.chosenplaintext.ca/open-source/rust-timing-shield/security) for some cases. If your goal is absolute security, don't use any JS lib — including bindings to native ones. Use low-level libraries & languages. Nonetheless we're targetting algorithmic constant time.
+
+We consider infrastructure attacks like rogue NPM modules very important; that's why it's crucial to minimize the amount of 3rd-party dependencies & native bindings. If your app uses 500 dependencies, any dep could get hacked and you'll be downloading malware with every `npm install`. Our goal is to minimize this attack vector.
+
+## Speed
+
+Benchmark results on Apple M2 with node v18.10:
+
+```
+getPublicKey
+  secp256k1 x 5,241 ops/sec @ 190μs/op
+  P256 x 7,993 ops/sec @ 125μs/op
+  P384 x 3,819 ops/sec @ 261μs/op
+  P521 x 2,074 ops/sec @ 481μs/op
+  ed25519 x 8,390 ops/sec @ 119μs/op
+  ed448 x 3,224 ops/sec @ 310μs/op
+sign
+  secp256k1 x 3,934 ops/sec @ 254μs/op
+  P256 x 5,327 ops/sec @ 187μs/op
+  P384 x 2,728 ops/sec @ 366μs/op
+  P521 x 1,594 ops/sec @ 626μs/op
+  ed25519 x 4,233 ops/sec @ 236μs/op
+  ed448 x 1,561 ops/sec @ 640μs/op
+verify
+  secp256k1 x 731 ops/sec @ 1ms/op
+  P256 x 806 ops/sec @ 1ms/op
+  P384 x 353 ops/sec @ 2ms/op
+  P521 x 171 ops/sec @ 5ms/op
+  ed25519 x 860 ops/sec @ 1ms/op
+  ed448 x 313 ops/sec @ 3ms/op
+getSharedSecret
+  secp256k1 x 445 ops/sec @ 2ms/op
+recoverPublicKey
+  secp256k1 x 732 ops/sec @ 1ms/op
+==== bls12-381 ====
+getPublicKey x 817 ops/sec @ 1ms/op
+sign x 50 ops/sec @ 19ms/op
+verify x 34 ops/sec @ 28ms/op
+pairing x 89 ops/sec @ 11ms/op
+==== stark ====
+pedersen
+  old x 85 ops/sec @ 11ms/op
+  noble x 1,216 ops/sec @ 822μs/op
+verify
+  old x 302 ops/sec @ 3ms/op
+  noble x 698 ops/sec @ 1ms/op
+```
+
+## Contributing & testing
+
+1. Clone the repository
+2. `npm install` to install build dependencies like TypeScript
+3. `npm run build` to compile TypeScript code
+4. `npm run test` will execute all main tests
+
 ## License
 
-MIT (c) Paul Miller [(https://paulmillr.com)](https://paulmillr.com), see LICENSE file.
+The MIT License (MIT)
+
+Copyright (c) 2022 Paul Miller [(https://paulmillr.com)](https://paulmillr.com)
+
+See LICENSE file.

SECURITY.md

@@ -0,0 +1,18 @@
+# Security Policy
+
+## Supported Versions
+
+| Version | Supported          |
+| ------- | ------------------ |
+| >=0.5.0   | :white_check_mark: |
+| <0.5.0   | :x:                |
+
+## Reporting a Vulnerability
+
+Use maintainer's email specified at https://github.com/paulmillr.
+
+It's preferred that you use
+PGP key from [pgp proof](https://paulmillr.com/pgp_proof.txt) (current is [697079DA6878B89B](https://paulmillr.com/pgp_proof.txt)).
+Ensure the pgp proof page has maintainer's site/github specified.
+
+You will get an update as soon as the email is read; a "Security vulnerability" phrase in email's title would help.

benchmark/index.js

@@ -0,0 +1,398 @@
+import * as bench from 'micro-bmark';
+const { run, mark } = bench; // or bench.mark
+import { readFileSync } from 'fs';
+
+// Curves
+import { secp256k1 } from '../lib/secp256k1.js';
+import { P256 } from '../lib/p256.js';
+import { P384 } from '../lib/p384.js';
+import { P521 } from '../lib/p521.js';
+import { ed25519 } from '../lib/ed25519.js';
+import { ed448 } from '../lib/ed448.js';
+import { bls12_381 as bls } from '../lib/bls12-381.js';
+
+// Others
+import { hmac } from '@noble/hashes/hmac';
+import { sha256 } from '@noble/hashes/sha256';
+import { sha512 } from '@noble/hashes/sha512';
+
+import * as old_secp from '@noble/secp256k1';
+import * as old_bls from '@noble/bls12-381';
+import { concatBytes, hexToBytes } from '@noble/hashes/utils';
+
+import * as starkwareCrypto from '@starkware-industries/starkware-crypto-utils';
+import * as stark from '../lib/stark.js';
+
+old_secp.utils.sha256Sync = (...msgs) =>
+  sha256
+    .create()
+    .update(concatBytes(...msgs))
+    .digest();
+old_secp.utils.hmacSha256Sync = (key, ...msgs) =>
+  hmac
+    .create(sha256, key)
+    .update(concatBytes(...msgs))
+    .digest();
+import * as noble_ed25519 from '@noble/ed25519';
+noble_ed25519.utils.sha512Sync = (...m) => sha512(concatBytes(...m));
+
+// BLS
+const G2_VECTORS = readFileSync('../test/bls12-381/bls12-381-g2-test-vectors.txt', 'utf-8')
+  .trim()
+  .split('\n')
+  .map((l) => l.split(':'));
+let p1, p2, oldp1, oldp2;
+// /BLS
+
+for (let item of [secp256k1, ed25519, ed448, P256, P384, P521, old_secp, noble_ed25519]) {
+  item.utils.precompute(8);
+}
+
+const ONLY_NOBLE = process.argv[2] === 'noble';
+
+function generateData(namespace) {
+  const priv = namespace.utils.randomPrivateKey();
+  const pub = namespace.getPublicKey(priv);
+  const msg = namespace.utils.randomPrivateKey();
+  const sig = namespace.sign(msg, priv);
+  return { priv, pub, msg, sig };
+}
+
+export const CURVES = {
+  secp256k1: {
+    data: () => {
+      return generateData(secp256k1);
+    },
+    getPublicKey1: {
+      samples: 10000,
+      secp256k1_old: () => old_secp.getPublicKey(3n),
+      secp256k1: () => secp256k1.getPublicKey(3n),
+    },
+    getPublicKey255: {
+      samples: 10000,
+      secp256k1_old: () => old_secp.getPublicKey(2n ** 255n - 1n),
+      secp256k1: () => secp256k1.getPublicKey(2n ** 255n - 1n),
+    },
+    sign: {
+      samples: 5000,
+      secp256k1_old: ({ msg, priv }) => old_secp.signSync(msg, priv),
+      secp256k1: ({ msg, priv }) => secp256k1.sign(msg, priv),
+    },
+    verify: {
+      samples: 1000,
+      secp256k1_old: ({ sig, msg, pub }) => {
+        return old_secp.verify(new old_secp.Signature(sig.r, sig.s), msg, pub);
+      },
+      secp256k1: ({ sig, msg, pub }) => secp256k1.verify(sig, msg, pub),
+    },
+    getSharedSecret: {
+      samples: 1000,
+      secp256k1_old: ({ pub, priv }) => old_secp.getSharedSecret(priv, pub),
+      secp256k1: ({ pub, priv }) => secp256k1.getSharedSecret(priv, pub),
+    },
+    recoverPublicKey: {
+      samples: 1000,
+      secp256k1_old: ({ sig, msg }) =>
+        old_secp.recoverPublicKey(msg, new old_secp.Signature(sig.r, sig.s), sig.recovery),
+      secp256k1: ({ sig, msg }) => sig.recoverPublicKey(msg),
+    },
+  },
+  ed25519: {
+    data: () => {
+      function to32Bytes(numOrStr) {
+        const hex = typeof numOrStr === 'string' ? numOrStr : numOrStr.toString(16);
+        return hexToBytes(hex.padStart(64, '0'));
+      }
+      const priv = to32Bytes(0x9d61b19deffd5a60ba844af492ec2cc44449c5697b326919703bac031cae7f60n);
+      const pub = noble_ed25519.sync.getPublicKey(priv);
+      const msg = to32Bytes('deadbeefdeadbeefdeadbeefdeadbeefdeadbeef');
+      const sig = noble_ed25519.sync.sign(msg, priv);
+      return { pub, priv, msg, sig };
+    },
+    getPublicKey: {
+      samples: 10000,
+      old: () => noble_ed25519.sync.getPublicKey(noble_ed25519.utils.randomPrivateKey()),
+      noble: () => ed25519.getPublicKey(ed25519.utils.randomPrivateKey()),
+    },
+    sign: {
+      samples: 5000,
+      old: ({ msg, priv }) => noble_ed25519.sync.sign(msg, priv),
+      noble: ({ msg, priv }) => ed25519.sign(msg, priv),
+    },
+    verify: {
+      samples: 1000,
+      old: ({ sig, msg, pub }) => noble_ed25519.sync.verify(sig, msg, pub),
+      noble: ({ sig, msg, pub }) => ed25519.verify(sig, msg, pub),
+    },
+  },
+  ed448: {
+    data: () => {
+      const priv = ed448.utils.randomPrivateKey();
+      const pub = ed448.getPublicKey(priv);
+      const msg = ed448.utils.randomPrivateKey();
+      const sig = ed448.sign(msg, priv);
+      return { priv, pub, msg, sig };
+    },
+    getPublicKey: {
+      samples: 5000,
+      noble: () => ed448.getPublicKey(ed448.utils.randomPrivateKey()),
+    },
+    sign: {
+      samples: 2500,
+      noble: ({ msg, priv }) => ed448.sign(msg, priv),
+    },
+    verify: {
+      samples: 500,
+      noble: ({ sig, msg, pub }) => ed448.verify(sig, msg, pub),
+    },
+  },
+  nist: {
+    data: () => {
+      return { p256: generateData(P256), p384: generateData(P384), p521: generateData(P521) };
+    },
+    getPublicKey: {
+      samples: 2500,
+      P256: () => P256.getPublicKey(P256.utils.randomPrivateKey()),
+      P384: () => P384.getPublicKey(P384.utils.randomPrivateKey()),
+      P521: () => P521.getPublicKey(P521.utils.randomPrivateKey()),
+    },
+    sign: {
+      samples: 1000,
+      P256: ({ p256: { msg, priv } }) => P256.sign(msg, priv),
+      P384: ({ p384: { msg, priv } }) => P384.sign(msg, priv),
+      P521: ({ p521: { msg, priv } }) => P521.sign(msg, priv),
+    },
+    verify: {
+      samples: 250,
+      P256: ({ p256: { sig, msg, pub } }) => P256.verify(sig, msg, pub),
+      P384: ({ p384: { sig, msg, pub } }) => P384.verify(sig, msg, pub),
+      P521: ({ p521: { sig, msg, pub } }) => P521.verify(sig, msg, pub),
+    },
+  },
+  stark: {
+    data: () => {
+      const priv = '2dccce1da22003777062ee0870e9881b460a8b7eca276870f57c601f182136c';
+      const msg = 'c465dd6b1bbffdb05442eb17f5ca38ad1aa78a6f56bf4415bdee219114a47';
+      const pub = stark.getPublicKey(priv);
+      const sig = stark.sign(msg, priv);
+
+      const privateKey = '2dccce1da22003777062ee0870e9881b460a8b7eca276870f57c601f182136c';
+      const msgHash = 'c465dd6b1bbffdb05442eb17f5ca38ad1aa78a6f56bf4415bdee219114a47';
+      const keyPair = starkwareCrypto.default.ec.keyFromPrivate(privateKey, 'hex');
+      const publicKeyStark = starkwareCrypto.default.ec.keyFromPublic(
+        keyPair.getPublic(true, 'hex'),
+        'hex'
+      );
+
+      return { priv, sig, msg, pub, publicKeyStark, msgHash, keyPair };
+    },
+    pedersen: {
+      samples: 500,
+      old: () => {
+        return starkwareCrypto.default.pedersen([
+          '3d937c035c878245caf64531a5756109c53068da139362728feb561405371cb',
+          '208a0a10250e382e1e4bbe2880906c2791bf6275695e02fbbc6aeff9cd8b31a',
+        ]);
+      },
+      noble: () => {
+        return stark.pedersen(
+          '3d937c035c878245caf64531a5756109c53068da139362728feb561405371cb',
+          '208a0a10250e382e1e4bbe2880906c2791bf6275695e02fbbc6aeff9cd8b31a'
+        );
+      },
+    },
+    verify: {
+      samples: 500,
+      old: ({ publicKeyStark, msgHash, keyPair }) => {
+        return starkwareCrypto.default.verify(
+          publicKeyStark,
+          msgHash,
+          starkwareCrypto.default.sign(keyPair, msgHash)
+        );
+      },
+      noble: ({ priv, msg, pub }) => {
+        return stark.verify(stark.sign(msg, priv), msg, pub);
+      },
+    },
+  },
+  'bls12-381': {
+    data: async () => {
+      const priv = '28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4c';
+      const pubs = G2_VECTORS.map((v) => bls.getPublicKey(v[0]));
+      const sigs = G2_VECTORS.map((v) => v[2]);
+      const pub = bls.getPublicKey(priv);
+      const pub512 = pubs.slice(0, 512); // .map(bls.PointG1.fromHex)
+      const pub32 = pub512.slice(0, 32);
+      const pub128 = pub512.slice(0, 128);
+      const pub2048 = pub512.concat(pub512, pub512, pub512);
+      const sig512 = sigs.slice(0, 512); // .map(bls.PointG2.fromSignature);
+      const sig32 = sig512.slice(0, 32);
+      const sig128 = sig512.slice(0, 128);
+      const sig2048 = sig512.concat(sig512, sig512, sig512);
+      return {
+        priv,
+        pubs,
+        sigs,
+        pub,
+        pub512,
+        pub32,
+        pub128,
+        pub2048,
+        sig32,
+        sig128,
+        sig512,
+        sig2048,
+      };
+    },
+    init: {
+      samples: 1,
+      old: () => {
+        oldp1 =
+          old_bls.PointG1.BASE.multiply(
+            0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4cn
+          );
+        oldp2 =
+          old_bls.PointG2.BASE.multiply(
+            0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4dn
+          );
+        old_bls.pairing(oldp1, oldp2);
+      },
+      noble: () => {
+        p1 =
+          bls.G1.Point.BASE.multiply(
+            0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4cn
+          );
+        p2 =
+          bls.G2.Point.BASE.multiply(
+            0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4dn
+          );
+        bls.pairing(p1, p2);
+      },
+    },
+    'getPublicKey (1-bit)': {
+      samples: 1000,
+      old: () => old_bls.getPublicKey('2'.padStart(64, '0')),
+      noble: () => bls.getPublicKey('2'.padStart(64, '0')),
+    },
+    getPublicKey: {
+      samples: 1000,
+      old: ({ priv }) => old_bls.getPublicKey(priv),
+      noble: ({ priv }) => bls.getPublicKey(priv),
+    },
+    sign: {
+      samples: 50,
+      old: ({ priv }) => old_bls.sign('09', priv),
+      noble: ({ priv }) => bls.sign('09', priv),
+    },
+    verify: {
+      samples: 50,
+      old: ({ pub }) =>
+        old_bls.verify(
+          '8647aa9680cd0cdf065b94e818ff2bb948cc97838bcee987b9bc1b76d0a0a6e0d85db4e9d75aaedfc79d4ea2733a21ae0579014de7636dd2943d45b87c82b1c66a289006b0b9767921bb8edd3f6c5c5dec0d54cd65f61513113c50cc977849e5',
+          '09',
+          pub
+        ),
+      noble: ({ pub }) =>
+        bls.verify(
+          '8647aa9680cd0cdf065b94e818ff2bb948cc97838bcee987b9bc1b76d0a0a6e0d85db4e9d75aaedfc79d4ea2733a21ae0579014de7636dd2943d45b87c82b1c66a289006b0b9767921bb8edd3f6c5c5dec0d54cd65f61513113c50cc977849e5',
+          '09',
+          pub
+        ),
+    },
+    pairing: {
+      samples: 100,
+      old: () => old_bls.pairing(oldp1, oldp2),
+      noble: () => bls.pairing(p1, p2),
+    },
+    'hashToCurve/G1': {
+      samples: 500,
+      old: () => old_bls.PointG1.hashToCurve('abcd'),
+      noble: () => bls.G1.Point.hashToCurve('abcd'),
+    },
+    'hashToCurve/G2': {
+      samples: 200,
+      old: () => old_bls.PointG2.hashToCurve('abcd'),
+      noble: () => bls.G2.Point.hashToCurve('abcd'),
+    },
+    // SLOW PART
+    // Requires points which we cannot init before (data fn same for all)
+    // await mark('sign/nc', 30, () => bls.sign(msgp, priv));
+    // await mark('verify/nc', 30, () => bls.verify(sigp, msgp, pubp));
+    'aggregatePublicKeys/8': {
+      samples: 100,
+      old: ({ pubs }) => old_bls.aggregatePublicKeys(pubs.slice(0, 8)),
+      noble: ({ pubs }) => bls.aggregatePublicKeys(pubs.slice(0, 8)),
+    },
+    'aggregatePublicKeys/32': {
+      samples: 50,
+      old: ({ pub32 }) => old_bls.aggregatePublicKeys(pub32.map(old_bls.PointG1.fromHex)),
+      noble: ({ pub32 }) => bls.aggregatePublicKeys(pub32.map(bls.G1.Point.fromHex)),
+    },
+    'aggregatePublicKeys/128': {
+      samples: 20,
+      old: ({ pub128 }) => old_bls.aggregatePublicKeys(pub128.map(old_bls.PointG1.fromHex)),
+      noble: ({ pub128 }) => bls.aggregatePublicKeys(pub128.map(bls.G1.Point.fromHex)),
+    },
+    'aggregatePublicKeys/512': {
+      samples: 10,
+      old: ({ pub512 }) => old_bls.aggregatePublicKeys(pub512.map(old_bls.PointG1.fromHex)),
+      noble: ({ pub512 }) => bls.aggregatePublicKeys(pub512.map(bls.G1.Point.fromHex)),
+    },
+    'aggregatePublicKeys/2048': {
+      samples: 5,
+      old: ({ pub2048 }) => old_bls.aggregatePublicKeys(pub2048.map(old_bls.PointG1.fromHex)),
+      noble: ({ pub2048 }) => bls.aggregatePublicKeys(pub2048.map(bls.G1.Point.fromHex)),
+    },
+    'aggregateSignatures/8': {
+      samples: 50,
+      old: ({ sigs }) => old_bls.aggregateSignatures(sigs.slice(0, 8)),
+      noble: ({ sigs }) => bls.aggregateSignatures(sigs.slice(0, 8)),
+    },
+    'aggregateSignatures/32': {
+      samples: 10,
+      old: ({ sig32 }) => old_bls.aggregateSignatures(sig32.map(old_bls.PointG2.fromSignature)),
+      noble: ({ sig32 }) => bls.aggregateSignatures(sig32.map(bls.Signature.decode)),
+    },
+    'aggregateSignatures/128': {
+      samples: 5,
+      old: ({ sig128 }) => old_bls.aggregateSignatures(sig128.map(old_bls.PointG2.fromSignature)),
+      noble: ({ sig128 }) => bls.aggregateSignatures(sig128.map(bls.Signature.decode)),
+    },
+    'aggregateSignatures/512': {
+      samples: 3,
+      old: ({ sig512 }) => old_bls.aggregateSignatures(sig512.map(old_bls.PointG2.fromSignature)),
+      noble: ({ sig512 }) => bls.aggregateSignatures(sig512.map(bls.Signature.decode)),
+    },
+    'aggregateSignatures/2048': {
+      samples: 2,
+      old: ({ sig2048 }) => old_bls.aggregateSignatures(sig2048.map(old_bls.PointG2.fromSignature)),
+      noble: ({ sig2048 }) => bls.aggregateSignatures(sig2048.map(bls.Signature.decode)),
+    },
+  },
+};
+
+const main = () =>
+  run(async () => {
+    for (const [name, curve] of Object.entries(CURVES)) {
+      console.log(`==== ${name} ====`);
+      const data = await curve.data();
+      for (const [fnName, libs] of Object.entries(curve)) {
+        if (fnName === 'data') continue;
+        const samples = libs.samples;
+        console.log(`  - ${fnName} (samples: ${samples})`);
+        for (const [lib, fn] of Object.entries(libs)) {
+          if (lib === 'samples') continue;
+          if (ONLY_NOBLE && lib !== 'noble') continue;
+          await mark(`    ${lib}`, samples, () => fn(data));
+        }
+      }
+    }
+    // Log current RAM
+    bench.logMem();
+  });
+
+// ESM is broken.
+import url from 'url';
+if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
+  main();
+}

benchmark/package.json

@@ -0,0 +1,24 @@
+{
+    "name": "benchmark",
+    "private": true,
+    "version": "0.1.0",
+    "description": "benchmarks",
+    "main": "index.js",
+    "type": "module",
+    "scripts": {
+        "bench": "node index.js"
+    },
+    "keywords": [],
+    "author": "",
+    "license": "MIT",
+    "devDependencies": {
+        "micro-bmark": "0.2.0"
+    },
+    "dependencies": {
+        "@noble/bls12-381": "^1.4.0",
+        "@noble/ed25519": "^1.7.1",
+        "@noble/hashes": "^1.1.5",
+        "@noble/secp256k1": "^1.7.0",
+        "@starkware-industries/starkware-crypto-utils": "^0.0.2"
+    }
+}

curve-definitions/LICENSE

@@ -1,21 +0,0 @@
-The MIT License (MIT)
-
-Copyright (c) 2022 Paul Miller (https://paulmillr.com)
-
-Permission is hereby granted, free of charge, to any person obtaining a copy
-of this software and associated documentation files (the “Software”), to deal
-in the Software without restriction, including without limitation the rights
-to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-copies of the Software, and to permit persons to whom the Software is
-furnished to do so, subject to the following conditions:
-
-The above copyright notice and this permission notice shall be included in
-all copies or substantial portions of the Software.
-
-THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
-THE SOFTWARE.

curve-definitions/README.md

@@ -1,28 +0,0 @@
-# micro-curve-definitions
-
-Elliptic curves implementations. `@noble/curves` is zero-dependency library for internal arithmetics.
-
-`micro-curve-definitions` is the actual implementations. Current functionality:
-
-- NIST curves: P192, P224, P256, P384, P521 (ECDSA)
-- secp256k1 (ECDSA, without Schnorr)
-- stark curve
-- bn254
-
-Pairings are not implemented.
-
-## Usage
-
-```sh
-npm install micro-curve-definitions
-```
-
-```ts
-import * as nist from 'micro-curve-definitions';
-
-// P192, P224, P256, P384, P521, bn254
-```
-
-## License
-
-MIT (c) Paul Miller [(https://paulmillr.com)](https://paulmillr.com), see LICENSE file.

curve-definitions/package.json

@@ -1,62 +0,0 @@
-{
-  "name": "micro-curve-definitions",
-  "version": "0.1.0",
-  "description": "Curve definitions for @noble/curves",
-  "files": [
-    "index.js",
-    "index.d.ts",
-    "index.d.ts.map",
-    "index.ts"
-  ],
-  "type": "module",
-  "main": "index.js",
-  "module": "index.js",
-  "types": "index.d.ts",
-  "dependencies": {
-    "@noble/curves": "~0.1.0",
-    "@noble/hashes": "1.1.4"
-  },
-  "devDependencies": {
-    "@scure/base": "~1.1.0",
-    "@scure/bip32": "^1.1.1",
-    "@scure/bip39": "^1.1.0",
-    "@types/node": "^18.11.3",
-    "fast-check": "3.0.0",
-    "micro-should": "0.2.0",
-    "prettier": "2.6.2",
-    "typescript": "4.7.3"
-  },
-  "author": "Paul Miller (https://paulmillr.com)",
-  "license": "MIT",
-  "homepage": "https://github.com/paulmillr/noble-curves",
-  "repository": {
-    "type": "git",
-    "url": "git+https://github.com/paulmillr/noble-curves.git"
-  },
-  "scripts": {
-    "build": "tsc",
-    "lint": "prettier --check index.ts",
-    "test": "node test/index.test.js"
-  },
-  "keywords": [
-    "secp192r1",
-    "secp224r1",
-    "secp256r1",
-    "secp384r1",
-    "secp521r1",
-    "NIST P192",
-    "NIST P224",
-    "NIST P256",
-    "NIST P384",
-    "NIST P521",
-    "NIST curves",
-    "EC",
-    "elliptic curves"
-  ],
-  "funding": [
-    {
-      "type": "individual",
-      "url": "https://paulmillr.com/funding/"
-    }
-  ]
-}

curve-definitions/src/bn.ts

@@ -1,25 +0,0 @@
-/*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-import { weierstrass, CHash } from '@noble/curves/shortw';
-import { concatBytes, randomBytes } from '@noble/hashes/utils';
-import { hmac } from '@noble/hashes/hmac';
-import { sha256 } from '@noble/hashes/sha256';
-
-function getHash(hash: CHash) {
-  return {
-    hash,
-    hmac: (key: Uint8Array, ...msgs: Uint8Array[]) => hmac(hash, key, concatBytes(...msgs)),
-    randomBytes,
-  };
-}
-
-// Was known as alt_bn128 when it had 128-bit security. Now that it's much lower, the naming
-// has been changed to its prime bit count.
-export const bn254 = weierstrass({
-  a: 0n,
-  b: 3n,
-  P: 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47n,
-  n: 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001n,
-  Gx: 1n,
-  Gy: 2n,
-  ...getHash(sha256),
-});

curve-definitions/src/nist.ts

@@ -1,190 +0,0 @@
-/*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-import { hmac } from '@noble/hashes/hmac';
-import { sha256 } from '@noble/hashes/sha256';
-import { sha384, sha512 } from '@noble/hashes/sha512';
-import { concatBytes, randomBytes } from '@noble/hashes/utils';
-import { weierstrass, CHash } from '@noble/curves/shortw';
-import { mod, pow2 } from '@noble/curves/modular';
-
-function getHash(hash: CHash) {
-  return {
-    hash,
-    hmac: (key: Uint8Array, ...msgs: Uint8Array[]) => hmac(hash, key, concatBytes(...msgs)),
-    randomBytes,
-  };
-}
-
-// https://www.secg.org/sec2-v2.pdf
-// https://neuromancer.sk/std/secg/secp192r1
-export const P192 = weierstrass({
-  // Params: a, b
-  a: BigInt('0xfffffffffffffffffffffffffffffffefffffffffffffffc'),
-  b: BigInt('0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1'),
-  // Field over which we'll do calculations. Verify with: 2n ** 192n - 2n ** 64n - 1n
-  P: BigInt('0xfffffffffffffffffffffffffffffffeffffffffffffffff'),
-  // Curve order, total count of valid points in the field. Verify with:
-  n: BigInt('0xffffffffffffffffffffffff99def836146bc9b1b4d22831'),
-  // Base point (x, y) aka generator point
-  Gx: BigInt('0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012'),
-  Gy: BigInt('0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811'),
-  lowS: false,
-  // Default options
-  ...getHash(sha256),
-} as const);
-export const secp192r1 = P192;
-// https://neuromancer.sk/std/nist/P-224
-export const P224 = weierstrass({
-  // Params: a, b
-  a: BigInt('0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe'),
-  b: BigInt('0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4'),
-  // Field over which we'll do calculations. Verify with:
-  P: 2n ** 224n - 2n ** 96n + 1n,
-  // Curve order, total count of valid points in the field. Verify with:
-  n: BigInt('0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d'),
-  // Base point (x, y) aka generator point
-  Gx: BigInt('0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21'),
-  Gy: BigInt('0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34'),
-  lowS: false,
-  // Default options
-  ...getHash(sha256),
-} as const);
-export const secp224r1 = P224;
-// https://neuromancer.sk/std/nist/P-256
-export const P256 = weierstrass({
-  // Params: a, b
-  a: BigInt('0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc'),
-  b: BigInt('0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b'),
-  // Field over which we'll do calculations. Verify with:
-  // 2n ** 224n * (2n ** 32n - 1n) + 2n ** 192n + 2n ** 96n - 1n,
-  P: BigInt('0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff'),
-  // Curve order, total count of valid points in the field. Verify with:
-  n: BigInt('0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551'),
-  // Base point (x, y) aka generator point
-  Gx: BigInt('0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296'),
-  Gy: BigInt('0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5'),
-  lowS: false,
-  // Default options
-  ...getHash(sha256),
-} as const);
-export const secp256r1 = P256;
-// https://neuromancer.sk/std/nist/P-384
-// prettier-ignore
-export const P384 = weierstrass({
-  // Params: a, b
-  a: BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc'),
-  b: BigInt('0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef'),
-  // Field over which we'll do calculations. Verify with:
-  // 2n ** 384n - 2n ** 128n - 2n ** 96n + 2n ** 32n - 1n
-  P: BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff'),
-  // Curve order, total count of valid points in the field. Verify with:
-  n: BigInt('0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973'),
-  // Base point (x, y) aka generator point
-  Gx: BigInt('0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7'),
-  Gy: BigInt('0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f'),
-  lowS: false,
-  // Default options
-  ...getHash(sha384),
-} as const);
-export const secp384r1 = P384;
-// https://neuromancer.sk/std/nist/P-521
-// prettier-ignore
-export const P521 = weierstrass({
-  // Params: a, b
-  a: BigInt('0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc'),
-  b: BigInt('0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00'),
-  // Field over which we'll do calculations. Verify with:
-  // 2n ** 521n - 1n,
-  P: BigInt('0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff'),
-  // Curve order, total count of valid points in the field. Verify with:
-  n: BigInt('0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409'),
-  // Base point (x, y) aka generator point
-  Gx: BigInt('0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66'),
-  Gy: BigInt('0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650'),
-  lowS: false,
-  // Default options
-  ...getHash(sha512),
-} as const);
-export const secp521r1 = P521;
-
-/**
- * secp256k1 definition with efficient square root and endomorphism.
- * Endomorphism works only for Koblitz curves with a == 0.
- * It improves efficiency:
- * Uses 2x less RAM, speeds up precomputation by 2x and ECDH / sign key recovery by 20%.
- * Should always be used for Jacobian's double-and-add multiplication.
- * For affines cached multiplication, it trades off 1/2 init time & 1/3 ram for 20% perf hit.
- * https://gist.github.com/paulmillr/eb670806793e84df628a7c434a873066
- */
-const secp256k1P = BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f');
-const secp256k1N = BigInt('0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141');
-const _1n = BigInt(1);
-const _2n = BigInt(2);
-const divNearest = (a: bigint, b: bigint) => (a + b / _2n) / b;
-export const secp256k1 = weierstrass({
-  a: 0n,
-  b: 7n,
-  // Field over which we'll do calculations. Verify with:
-  // 2n ** 256n - 2n ** 32n - 2n ** 9n - 2n ** 8n - 2n ** 7n - 2n ** 6n - 2n ** 4n - 1n
-  P: secp256k1P,
-  // Curve order, total count of valid points in the field. Verify with:
-  n: secp256k1N,
-  // Base point (x, y) aka generator point
-  Gx: BigInt('55066263022277343669578718895168534326250603453777594175500187360389116729240'),
-  Gy: BigInt('32670510020758816978083085130507043184471273380659243275938904335757337482424'),
-  ...getHash(sha256),
-  // noble-secp256k1 compat
-  lowS: true,
-  // Used to calculate y - the square root of y².
-  // Exponentiates it to very big number (P+1)/4.
-  // We are unwrapping the loop because it's 2x faster.
-  // (P+1n/4n).toString(2) would produce bits [223x 1, 0, 22x 1, 4x 0, 11, 00]
-  // We are multiplying it bit-by-bit
-  sqrtMod: (x: bigint): bigint => {
-    const P = secp256k1P;
-    const _3n = BigInt(3);
-    const _6n = BigInt(6);
-    const _11n = BigInt(11);
-    const _22n = BigInt(22);
-    const _23n = BigInt(23);
-    const _44n = BigInt(44);
-    const _88n = BigInt(88);
-    const b2 = (x * x * x) % P; // x^3, 11
-    const b3 = (b2 * b2 * x) % P; // x^7
-    const b6 = (pow2(b3, _3n, P) * b3) % P;
-    const b9 = (pow2(b6, _3n, P) * b3) % P;
-    const b11 = (pow2(b9, _2n, P) * b2) % P;
-    const b22 = (pow2(b11, _11n, P) * b11) % P;
-    const b44 = (pow2(b22, _22n, P) * b22) % P;
-    const b88 = (pow2(b44, _44n, P) * b44) % P;
-    const b176 = (pow2(b88, _88n, P) * b88) % P;
-    const b220 = (pow2(b176, _44n, P) * b44) % P;
-    const b223 = (pow2(b220, _3n, P) * b3) % P;
-    const t1 = (pow2(b223, _23n, P) * b22) % P;
-    const t2 = (pow2(t1, _6n, P) * b2) % P;
-    return pow2(t2, _2n, P);
-  },
-  endo: {
-    beta: BigInt('0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee'),
-    splitScalar: (k: bigint) => {
-      const n = secp256k1N;
-      const a1 = BigInt('0x3086d221a7d46bcde86c90e49284eb15');
-      const b1 = -_1n * BigInt('0xe4437ed6010e88286f547fa90abfe4c3');
-      const a2 = BigInt('0x114ca50f7a8e2f3f657c1108d9d44cfd8');
-      const b2 = a1;
-      const POW_2_128 = BigInt('0x100000000000000000000000000000000');
-
-      const c1 = divNearest(b2 * k, n);
-      const c2 = divNearest(-b1 * k, n);
-      let k1 = mod(k - c1 * a1 - c2 * a2, n);
-      let k2 = mod(-c1 * b1 - c2 * b2, n);
-      const k1neg = k1 > POW_2_128;
-      const k2neg = k2 > POW_2_128;
-      if (k1neg) k1 = n - k1;
-      if (k2neg) k2 = n - k2;
-      if (k1 > POW_2_128 || k2 > POW_2_128) {
-        throw new Error('splitScalar: Endomorphism failed, k=' + k);
-      }
-      return { k1neg, k1, k2neg, k2 };
-    },
-  },
-});

curve-definitions/src/pasta.ts

@@ -1,35 +0,0 @@
-/*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-import { hmac } from '@noble/hashes/hmac';
-import { sha256 } from '@noble/hashes/sha256';
-import { concatBytes, randomBytes } from '@noble/hashes/utils';
-import { weierstrass, CHash } from '@noble/curves/shortw';
-
-function getHash(hash: CHash) {
-  return {
-    hash,
-    hmac: (key: Uint8Array, ...msgs: Uint8Array[]) => hmac(hash, key, concatBytes(...msgs)),
-    randomBytes,
-  };
-}
-const p = BigInt('0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001');
-const q = BigInt('0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001');
-
-export const pallas = weierstrass({
-  a: BigInt(0),
-  b: BigInt(5),
-  P: p,
-  n: q,
-  Gx: BigInt(-1),
-  Gy: BigInt(2),
-  ...getHash(sha256),
-});
-
-export const vesta = weierstrass({
-  a: BigInt(0),
-  b: BigInt(5),
-  P: q,
-  n: p,
-  Gx: BigInt(-1),
-  Gy: BigInt(2),
-  ...getHash(sha256),
-});

curve-definitions/test/basic.test.js

@@ -1,97 +0,0 @@
-import { deepStrictEqual, throws } from 'assert';
-import { should } from 'micro-should';
-import * as nist from '../lib/nist.js';
-import { hexToBytes } from '@noble/curves/utils';
-import { default as ecdsa } from './fixtures/ecdsa_test.json' assert { type: 'json' };
-import { default as ecdh } from './fixtures/ecdh_test.json' assert { type: 'json' };
-
-// import { hexToBytes } from '@noble/curves';
-
-should('Curve Fields', () => {
-  const vectors = {
-    secp192r1: 0xfffffffffffffffffffffffffffffffeffffffffffffffffn,
-    secp224r1: 0xffffffffffffffffffffffffffffffff000000000000000000000001n,
-    secp256r1: 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffffn,
-    secp256k1: 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2fn,
-    secp384r1:
-      0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffffn,
-    secp521r1:
-      0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffn,
-  };
-  for (const n in vectors) deepStrictEqual(nist[n].CURVE.P, vectors[n]);
-});
-
-should('wychenproof ECDSA vectors', () => {
-  for (const group of ecdsa.testGroups) {
-    // Tested in secp256k1.test.js
-    if (group.key.curve === 'secp256k1') continue;
-    // We don't have SHA-224
-    if (group.key.curve === 'secp224r1' && group.sha === 'SHA-224') continue;
-    const CURVE = nist[group.key.curve];
-    if (!CURVE) continue;
-    const pubKey = CURVE.Point.fromHex(group.key.uncompressed);
-    deepStrictEqual(pubKey.x, BigInt(`0x${group.key.wx}`));
-    deepStrictEqual(pubKey.y, BigInt(`0x${group.key.wy}`));
-    for (const test of group.tests) {
-      if (['Hash weaker than DL-group'].includes(test.comment)) {
-        continue;
-      }
-      const m = CURVE.CURVE.hash(hexToBytes(test.msg));
-      if (test.result === 'valid' || test.result === 'acceptable') {
-        try {
-          CURVE.Signature.fromDER(test.sig);
-        } catch (e) {
-          // Some test has invalid signature which we don't accept
-          if (e.message.includes('Invalid signature: incorrect length')) continue;
-          throw e;
-        }
-        const verified = CURVE.verify(test.sig, m, pubKey);
-        deepStrictEqual(verified, true, 'valid');
-      } else if (test.result === 'invalid') {
-        let failed = false;
-        try {
-          failed = !CURVE.verify(test.sig, m, pubKey);
-        } catch (error) {
-          failed = true;
-        }
-        deepStrictEqual(failed, true, 'invalid');
-      } else throw new Error('unknown test result');
-    }
-  }
-});
-
-should('wychenproof ECDH vectors', () => {
-  for (const group of ecdh.testGroups) {
-    // // Tested in secp256k1.test.js
-    // if (group.key.curve === 'secp256k1') continue;
-    // We don't have SHA-224
-    const CURVE = nist[group.curve];
-    if (!CURVE) continue;
-    for (const test of group.tests) {
-      if (test.result === 'valid' || test.result === 'acceptable') {
-        try {
-          const pub = CURVE.Point.fromHex(test.public);
-        } catch (e) {
-          if (e.message.includes('Point.fromHex: received invalid point.')) continue;
-          throw e;
-        }
-        const shared = CURVE.getSharedSecret(test.private, test.public);
-        deepStrictEqual(shared, test.shared, 'valid');
-      } else if (test.result === 'invalid') {
-        let failed = false;
-        try {
-          CURVE.getSharedSecret(test.private, test.public);
-        } catch (error) {
-          failed = true;
-        }
-        deepStrictEqual(failed, true, 'invalid');
-      } else throw new Error('unknown test result');
-    }
-  }
-});
-
-// ESM is broken.
-import url from 'url';
-if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
-  should.run();
-}

curve-definitions/test/index.test.js

@@ -1,8 +0,0 @@
-import { should } from 'micro-should';
-
-import './basic.test.js';
-import './rfc6979.test.js';
-import './secp256k1.test.js';
-import './starknet/starknet.test.js';
-
-should.run();

curve-definitions/test/rfc6979.test.js

@@ -1,33 +0,0 @@
-import { deepStrictEqual } from 'assert';
-import { should } from 'micro-should';
-import * as nist from '../lib/nist.js';
-import { default as rfc6979 } from './fixtures/rfc6979.json' assert { type: 'json' };
-function hexToBigint(hex) {
-  return BigInt('0x' + hex)
-}
-
-should('RFC6979', () => {
-  for (const v of rfc6979) {
-    const curve = nist[v.curve];
-    deepStrictEqual(curve.CURVE.n, hexToBigint(v.q));
-    const pubKey = curve.getPublicKey(v.private);
-    const pubPoint = curve.Point.fromHex(pubKey);
-    deepStrictEqual(pubPoint.x, hexToBigint(v.Ux));
-    deepStrictEqual(pubPoint.y, hexToBigint(v.Uy));
-    for (const c of v.cases) {
-      const h = curve.CURVE.hash(c.message);
-      const sigObj = curve.sign(h, v.private);
-      // const sigObj = curve.Signature.fromDER(sig);
-      deepStrictEqual(sigObj.r, hexToBigint(c.r), 'R');
-      deepStrictEqual(sigObj.s, hexToBigint(c.s), 'S');
-      deepStrictEqual(curve.verify(sigObj.toDERRawBytes(), h, pubKey), true, 'verify(1)');
-      deepStrictEqual(curve.verify(sigObj, h, pubKey), true, 'verify(2)');
-    }
-  }
-});
-
-// ESM is broken.
-import url from 'url';
-if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
-  should.run();
-}

curve-definitions/tsconfig.json

@@ -1,25 +0,0 @@
-{
-  "compilerOptions": {
-    "strict": true,
-    "declaration": true,
-    "declarationMap": true,
-    "target": "es2020",
-    "lib": [
-      "es2020",
-      "dom"
-    ],
-    "module": "es6",
-    "moduleResolution": "node16",
-    "outDir": "lib",
-    "noImplicitAny": true,
-    "preserveConstEnums": true,
-    "baseUrl": ".",
-  },
-  "include": [
-    "src",
-  ],
-  "exclude": [
-    "node_modules",
-    "lib"
-  ]
-}

index.js

@@ -1 +0,0 @@
-throw new Error('Incorrect usage. Import submodules instead');

package.json

@@ -1,19 +1,17 @@
 {
   "name": "@noble/curves",
-  "version": "0.1.0",
-  "description": "Minimal, zero-dependency JS implementation of elliptic curve cryptography",
+  "version": "0.5.0",
+  "description": "Minimal, auditable JS implementation of elliptic curve cryptography",
   "files": [
-    "index.js",
-    "lib",
-    "lib/esm"
+    "lib"
   ],
   "scripts": {
-    "bench": "node test/benchmark/index.js",
+    "bench": "node benchmark/index.js",
     "build": "tsc && tsc -p tsconfig.esm.json",
     "build:release": "rollup -c rollup.config.js",
-    "lint": "prettier --check 'src/**/*.{js,ts}' 'curve-definitions/src/**/*.{js,ts}'",
-    "format": "prettier --write 'src/**/*.{js,ts}' 'curve-definitions/src/**/*.{js,ts}'",
-    "test": "cd curve-definitions; node test/index.test.js"
+    "lint": "prettier --check 'src/**/*.{js,ts}' 'test/*.js'",
+    "format": "prettier --write 'src/**/*.{js,ts}' 'test/*.js'",
+    "test": "node test/index.test.js"
   },
   "author": "Paul Miller (https://paulmillr.com)",
   "homepage": "https://paulmillr.com/noble/",
@@ -22,8 +20,16 @@
     "url": "https://github.com/paulmillr/noble-curves.git"
   },
   "license": "MIT",
+  "dependencies": {
+    "@noble/hashes": "1.1.5"
+  },
   "devDependencies": {
     "@rollup/plugin-node-resolve": "13.3.0",
+    "@scure/base": "~1.1.1",
+    "@scure/bip32": "~1.1.1",
+    "@scure/bip39": "~1.1.0",
+    "@types/node": "18.11.3",
+    "fast-check": "3.0.0",
     "micro-bmark": "0.2.0",
     "micro-should": "0.2.0",
     "prettier": "2.6.2",
@@ -32,35 +38,146 @@
   },
   "main": "index.js",
   "exports": {
-    "./modular": {
-      "types": "./lib/modular.d.ts",
-      "import": "./lib/esm/modular.js",
-      "default": "./lib/modular.js"
+    ".": {
+      "types": "./lib/index.d.ts",
+      "import": "./lib/esm/index.js",
+      "default": "./lib/index.js"
     },
-    "./shortw": {
-      "types": "./lib/shortw.d.ts",
-      "import": "./lib/esm/shortw.js",
-      "default": "./lib/shortw.js"
+    "./abstract/edwards": {
+      "types": "./lib/abstract/edwards.d.ts",
+      "import": "./lib/esm/abstract/edwards.js",
+      "default": "./lib/abstract/edwards.js"
     },
-    "./utils": {
-      "types": "./lib/utils.d.ts",
-      "import": "./lib/esm/utils.js",
-      "default": "./lib/utils.js"
+    "./abstract/modular": {
+      "types": "./lib/abstract/modular.d.ts",
+      "import": "./lib/esm/abstract/modular.js",
+      "default": "./lib/abstract/modular.js"
+    },
+    "./abstract/montgomery": {
+      "types": "./lib/abstract/montgomery.d.ts",
+      "import": "./lib/esm/abstract/montgomery.js",
+      "default": "./lib/abstract/montgomery.js"
+    },
+    "./abstract/weierstrass": {
+      "types": "./lib/abstract/weierstrass.d.ts",
+      "import": "./lib/esm/abstract/weierstrass.js",
+      "default": "./lib/abstract/weierstrass.js"
+    },
+    "./abstract/bls": {
+      "types": "./lib/abstract/bls.d.ts",
+      "import": "./lib/esm/abstract/bls.js",
+      "default": "./lib/abstract/bls.js"
+    },
+    "./abstract/hash-to-curve": {
+      "types": "./lib/abstract/hash-to-curve.d.ts",
+      "import": "./lib/esm/abstract/hash-to-curve.js",
+      "default": "./lib/abstract/hash-to-curve.js"
+    },
+    "./abstract/group": {
+      "types": "./lib/abstract/group.d.ts",
+      "import": "./lib/esm/abstract/group.js",
+      "default": "./lib/abstract/group.js"
+    },
+    "./abstract/utils": {
+      "types": "./lib/abstract/utils.d.ts",
+      "import": "./lib/esm/abstract/utils.js",
+      "default": "./lib/abstract/utils.js"
+    },
+    "./_shortw_utils": {
+      "types": "./lib/_shortw_utils.d.ts",
+      "import": "./lib/esm/_shortw_utils.js",
+      "default": "./lib/_shortw_utils.js"
+    },
+    "./bls12-381": {
+      "types": "./lib/bls12-381.d.ts",
+      "import": "./lib/esm/bls12-381.js",
+      "default": "./lib/bls12-381.js"
+    },
+    "./bn": {
+      "types": "./lib/bn.d.ts",
+      "import": "./lib/esm/bn.js",
+      "default": "./lib/bn.js"
+    },
+    "./ed25519": {
+      "types": "./lib/ed25519.d.ts",
+      "import": "./lib/esm/ed25519.js",
+      "default": "./lib/ed25519.js"
+    },
+    "./ed448": {
+      "types": "./lib/ed448.d.ts",
+      "import": "./lib/esm/ed448.js",
+      "default": "./lib/ed448.js"
+    },
+    "./index": {
+      "types": "./lib/index.d.ts",
+      "import": "./lib/esm/index.js",
+      "default": "./lib/index.js"
+    },
+    "./jubjub": {
+      "types": "./lib/jubjub.d.ts",
+      "import": "./lib/esm/jubjub.js",
+      "default": "./lib/jubjub.js"
+    },
+    "./p192": {
+      "types": "./lib/p192.d.ts",
+      "import": "./lib/esm/p192.js",
+      "default": "./lib/p192.js"
+    },
+    "./p224": {
+      "types": "./lib/p224.d.ts",
+      "import": "./lib/esm/p224.js",
+      "default": "./lib/p224.js"
+    },
+    "./p256": {
+      "types": "./lib/p256.d.ts",
+      "import": "./lib/esm/p256.js",
+      "default": "./lib/p256.js"
+    },
+    "./p384": {
+      "types": "./lib/p384.d.ts",
+      "import": "./lib/esm/p384.js",
+      "default": "./lib/p384.js"
+    },
+    "./p521": {
+      "types": "./lib/p521.d.ts",
+      "import": "./lib/esm/p521.js",
+      "default": "./lib/p521.js"
+    },
+    "./pasta": {
+      "types": "./lib/pasta.d.ts",
+      "import": "./lib/esm/pasta.js",
+      "default": "./lib/pasta.js"
+    },
+    "./secp256k1": {
+      "types": "./lib/secp256k1.d.ts",
+      "import": "./lib/esm/secp256k1.js",
+      "default": "./lib/secp256k1.js"
+    },
+    "./stark": {
+      "types": "./lib/stark.d.ts",
+      "import": "./lib/esm/stark.js",
+      "default": "./lib/stark.js"
     }
   },
   "keywords": [
     "elliptic",
     "curve",
     "cryptography",
-    "hyperelliptic",
+    "weierstrass",
+    "montgomery",
+    "edwards",
     "p256",
     "p384",
     "p521",
+    "secp256r1",
+    "secp256k1",
+    "ed25519",
+    "ed448",
+    "bls12-381",
+    "bn254",
+    "pasta",
+    "bls",
     "nist",
-    "weierstrass",
-    "edwards",
-    "montgomery",
-    "hashes",
     "ecc",
     "ecdsa",
     "eddsa",

src/_shortw_utils.ts

@@ -0,0 +1,19 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+import { hmac } from '@noble/hashes/hmac';
+import { concatBytes, randomBytes } from '@noble/hashes/utils';
+import { weierstrass, CurveType } from './abstract/weierstrass.js';
+import { CHash } from './abstract/utils.js';
+
+export function getHash(hash: CHash) {
+  return {
+    hash,
+    hmac: (key: Uint8Array, ...msgs: Uint8Array[]) => hmac(hash, key, concatBytes(...msgs)),
+    randomBytes,
+  };
+}
+// Same API as @noble/hashes, with ability to create curve with custom hash
+type CurveDef = Readonly<Omit<CurveType, 'hash' | 'hmac' | 'randomBytes'>>;
+export function createCurve(curveDef: CurveDef, defHash: CHash) {
+  const create = (hash: CHash) => weierstrass({ ...curveDef, ...getHash(hash) });
+  return Object.freeze({ ...create(defHash), create });
+}

src/abstract/bls.ts

@@ -0,0 +1,419 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+// Barreto-Lynn-Scott Curves. A family of pairing friendly curves, with embedding degree = 12 or 24
+// NOTE: only 12 supported for now
+// Constructed from pair of weierstrass curves, based pairing logic
+import * as mod from './modular.js';
+import { ensureBytes, numberToBytesBE, bytesToNumberBE, bitLen, bitGet } from './utils.js';
+import * as utils from './utils.js';
+// Types
+import { hexToBytes, bytesToHex, Hex, PrivKey } from './utils.js';
+import { htfOpts, stringToBytes, hash_to_field, expand_message_xmd } from './hash-to-curve.js';
+import { CurvePointsType, PointType, CurvePointsRes, weierstrassPoints } from './weierstrass.js';
+
+type Fp = bigint; // Can be different field?
+
+export type SignatureCoder<Fp2> = {
+  decode(hex: Hex): PointType<Fp2>;
+  encode(point: PointType<Fp2>): Uint8Array;
+};
+
+export type CurveType<Fp, Fp2, Fp6, Fp12> = {
+  r: bigint;
+  G1: Omit<CurvePointsType<Fp>, 'n'>;
+  G2: Omit<CurvePointsType<Fp2>, 'n'> & {
+    Signature: SignatureCoder<Fp2>;
+  };
+  x: bigint;
+  Fp: mod.Field<Fp>;
+  Fr: mod.Field<bigint>;
+  Fp2: mod.Field<Fp2> & {
+    reim: (num: Fp2) => { re: bigint; im: bigint };
+    multiplyByB: (num: Fp2) => Fp2;
+    frobeniusMap(num: Fp2, power: number): Fp2;
+  };
+  Fp6: mod.Field<Fp6>;
+  Fp12: mod.Field<Fp12> & {
+    frobeniusMap(num: Fp12, power: number): Fp12;
+    multiplyBy014(num: Fp12, o0: Fp2, o1: Fp2, o4: Fp2): Fp12;
+    conjugate(num: Fp12): Fp12;
+    finalExponentiate(num: Fp12): Fp12;
+  };
+  htfDefaults: htfOpts;
+  hash: utils.CHash; // Because we need outputLen for DRBG
+  randomBytes: (bytesLength?: number) => Uint8Array;
+};
+
+export type CurveFn<Fp, Fp2, Fp6, Fp12> = {
+  CURVE: CurveType<Fp, Fp2, Fp6, Fp12>;
+  Fr: mod.Field<bigint>;
+  Fp: mod.Field<Fp>;
+  Fp2: mod.Field<Fp2>;
+  Fp6: mod.Field<Fp6>;
+  Fp12: mod.Field<Fp12>;
+  G1: CurvePointsRes<Fp>;
+  G2: CurvePointsRes<Fp2>;
+  Signature: SignatureCoder<Fp2>;
+  millerLoop: (ell: [Fp2, Fp2, Fp2][], g1: [Fp, Fp]) => Fp12;
+  calcPairingPrecomputes: (x: Fp2, y: Fp2) => [Fp2, Fp2, Fp2][];
+  pairing: (P: PointType<Fp>, Q: PointType<Fp2>, withFinalExponent?: boolean) => Fp12;
+  getPublicKey: (privateKey: PrivKey) => Uint8Array;
+  sign: {
+    (message: Hex, privateKey: PrivKey): Uint8Array;
+    (message: PointType<Fp2>, privateKey: PrivKey): PointType<Fp2>;
+  };
+  verify: (
+    signature: Hex | PointType<Fp2>,
+    message: Hex | PointType<Fp2>,
+    publicKey: Hex | PointType<Fp>
+  ) => boolean;
+  aggregatePublicKeys: {
+    (publicKeys: Hex[]): Uint8Array;
+    (publicKeys: PointType<Fp>[]): PointType<Fp>;
+  };
+  aggregateSignatures: {
+    (signatures: Hex[]): Uint8Array;
+    (signatures: PointType<Fp2>[]): PointType<Fp2>;
+  };
+  verifyBatch: (
+    signature: Hex | PointType<Fp2>,
+    messages: (Hex | PointType<Fp2>)[],
+    publicKeys: (Hex | PointType<Fp>)[]
+  ) => boolean;
+  utils: {
+    bytesToHex: typeof utils.bytesToHex;
+    hexToBytes: typeof utils.hexToBytes;
+    stringToBytes: typeof stringToBytes;
+    hashToField: typeof hash_to_field;
+    expandMessageXMD: typeof expand_message_xmd;
+    mod: typeof mod.mod;
+    getDSTLabel: () => string;
+    setDSTLabel(newLabel: string): void;
+  };
+};
+
+export function bls<Fp2, Fp6, Fp12>(
+  CURVE: CurveType<Fp, Fp2, Fp6, Fp12>
+): CurveFn<Fp, Fp2, Fp6, Fp12> {
+  // Fields looks pretty specific for curve, so for now we need to pass them with options
+  const Fp = CURVE.Fp;
+  const Fr = CURVE.Fr;
+  const Fp2 = CURVE.Fp2;
+  const Fp6 = CURVE.Fp6;
+  const Fp12 = CURVE.Fp12;
+  const BLS_X_LEN = bitLen(CURVE.x);
+
+  // Pre-compute coefficients for sparse multiplication
+  // Point addition and point double calculations is reused for coefficients
+  function calcPairingPrecomputes(x: Fp2, y: Fp2) {
+    // prettier-ignore
+    const Qx = x, Qy = y, Qz = Fp2.ONE;
+    // prettier-ignore
+    let Rx = Qx, Ry = Qy, Rz = Qz;
+    let ell_coeff: [Fp2, Fp2, Fp2][] = [];
+    for (let i = BLS_X_LEN - 2; i >= 0; i--) {
+      // Double
+      let t0 = Fp2.square(Ry); // Ry²
+      let t1 = Fp2.square(Rz); // Rz²
+      let t2 = Fp2.multiplyByB(Fp2.mul(t1, 3n)); // 3 * T1 * B
+      let t3 = Fp2.mul(t2, 3n); // 3 * T2
+      let t4 = Fp2.sub(Fp2.sub(Fp2.square(Fp2.add(Ry, Rz)), t1), t0); // (Ry + Rz)² - T1 - T0
+      ell_coeff.push([
+        Fp2.sub(t2, t0), // T2 - T0
+        Fp2.mul(Fp2.square(Rx), 3n), // 3 * Rx²
+        Fp2.negate(t4), // -T4
+      ]);
+      Rx = Fp2.div(Fp2.mul(Fp2.mul(Fp2.sub(t0, t3), Rx), Ry), 2n); // ((T0 - T3) * Rx * Ry) / 2
+      Ry = Fp2.sub(Fp2.square(Fp2.div(Fp2.add(t0, t3), 2n)), Fp2.mul(Fp2.square(t2), 3n)); // ((T0 + T3) / 2)² - 3 * T2²
+      Rz = Fp2.mul(t0, t4); // T0 * T4
+      if (bitGet(CURVE.x, i)) {
+        // Addition
+        let t0 = Fp2.sub(Ry, Fp2.mul(Qy, Rz)); // Ry - Qy * Rz
+        let t1 = Fp2.sub(Rx, Fp2.mul(Qx, Rz)); // Rx - Qx * Rz
+        ell_coeff.push([
+          Fp2.sub(Fp2.mul(t0, Qx), Fp2.mul(t1, Qy)), // T0 * Qx - T1 * Qy
+          Fp2.negate(t0), // -T0
+          t1, // T1
+        ]);
+        let t2 = Fp2.square(t1); // T1²
+        let t3 = Fp2.mul(t2, t1); // T2 * T1
+        let t4 = Fp2.mul(t2, Rx); // T2 * Rx
+        let t5 = Fp2.add(Fp2.sub(t3, Fp2.mul(t4, 2n)), Fp2.mul(Fp2.square(t0), Rz)); // T3 - 2 * T4 + T0² * Rz
+        Rx = Fp2.mul(t1, t5); // T1 * T5
+        Ry = Fp2.sub(Fp2.mul(Fp2.sub(t4, t5), t0), Fp2.mul(t3, Ry)); // (T4 - T5) * T0 - T3 * Ry
+        Rz = Fp2.mul(Rz, t3); // Rz * T3
+      }
+    }
+    return ell_coeff;
+  }
+
+  function millerLoop(ell: [Fp2, Fp2, Fp2][], g1: [Fp, Fp]): Fp12 {
+    const Px = g1[0];
+    const Py = g1[1];
+    let f12 = Fp12.ONE;
+    for (let j = 0, i = BLS_X_LEN - 2; i >= 0; i--, j++) {
+      const E = ell[j];
+      f12 = Fp12.multiplyBy014(f12, E[0], Fp2.mul(E[1], Px), Fp2.mul(E[2], Py));
+      if (bitGet(CURVE.x, i)) {
+        j += 1;
+        const F = ell[j];
+        f12 = Fp12.multiplyBy014(f12, F[0], Fp2.mul(F[1], Px), Fp2.mul(F[2], Py));
+      }
+      if (i !== 0) f12 = Fp12.square(f12);
+    }
+    return Fp12.conjugate(f12);
+  }
+
+  // bls12-381 is a construction of two curves:
+  // 1. Fp: (x, y)
+  // 2. Fp₂: ((x₁, x₂+i), (y₁, y₂+i)) - (complex numbers)
+  //
+  // Bilinear Pairing (ate pairing) is used to combine both elements into a paired one:
+  //   Fp₁₂ = e(Fp, Fp2)
+  //   where Fp₁₂ = 12-degree polynomial
+  // Pairing is used to verify signatures.
+  //
+  // We are using Fp for private keys (shorter) and Fp2 for signatures (longer).
+  // Some projects may prefer to swap this relation, it is not supported for now.
+
+  const htfDefaults = { ...CURVE.htfDefaults };
+
+  function isWithinCurveOrder(num: bigint): boolean {
+    return 0 < num && num < CURVE.r;
+  }
+
+  const utils = {
+    hexToBytes: hexToBytes,
+    bytesToHex: bytesToHex,
+    mod: mod.mod,
+    stringToBytes,
+    // TODO: do we need to export it here?
+    hashToField: (msg: Uint8Array, count: number, options: Partial<typeof htfDefaults> = {}) =>
+      hash_to_field(msg, count, { ...CURVE.htfDefaults, ...options }),
+    expandMessageXMD: (msg: Uint8Array, DST: Uint8Array, lenInBytes: number, H = CURVE.hash) =>
+      expand_message_xmd(msg, DST, lenInBytes, H),
+
+    /**
+     * Can take 40 or more bytes of uniform input e.g. from CSPRNG or KDF
+     * and convert them into private key, with the modulo bias being negligible.
+     * As per FIPS 186 B.1.1.
+     * https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
+     * @param hash hash output from sha512, or a similar function
+     * @returns valid private key
+     */
+    hashToPrivateKey: (hash: Hex): Uint8Array => {
+      hash = ensureBytes(hash);
+      if (hash.length < 40 || hash.length > 1024)
+        throw new Error('Expected 40-1024 bytes of private key as per FIPS 186');
+      //     hashToPrivateScalar(hash, CURVE.r)
+      // NOTE: doesn't add +/-1
+      const num = mod.mod(bytesToNumberBE(hash), CURVE.r);
+      // This should never happen
+      if (num === 0n || num === 1n) throw new Error('Invalid private key');
+      return numberToBytesBE(num, 32);
+    },
+
+    randomBytes: (bytesLength: number = 32): Uint8Array => CURVE.randomBytes(bytesLength),
+    // NIST SP 800-56A rev 3, section 5.6.1.2.2
+    // https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
+    randomPrivateKey: (): Uint8Array => utils.hashToPrivateKey(utils.randomBytes(40)),
+    getDSTLabel: () => htfDefaults.DST,
+    setDSTLabel(newLabel: string) {
+      // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-3.1
+      if (typeof newLabel !== 'string' || newLabel.length > 2048 || newLabel.length === 0) {
+        throw new TypeError('Invalid DST');
+      }
+      htfDefaults.DST = newLabel;
+    },
+  };
+
+  function normalizePrivKey(key: PrivKey): bigint {
+    let int: bigint;
+    if (key instanceof Uint8Array && key.length === 32) int = bytesToNumberBE(key);
+    else if (typeof key === 'string' && key.length === 64) int = BigInt(`0x${key}`);
+    else if (typeof key === 'number' && key > 0 && Number.isSafeInteger(key)) int = BigInt(key);
+    else if (typeof key === 'bigint' && key > 0n) int = key;
+    else throw new TypeError('Expected valid private key');
+    int = mod.mod(int, CURVE.r);
+    if (!isWithinCurveOrder(int)) throw new Error('Private key must be 0 < key < CURVE.r');
+    return int;
+  }
+
+  // Point on G1 curve: (x, y)
+  const G1 = weierstrassPoints({
+    n: Fr.ORDER,
+    ...CURVE.G1,
+  });
+
+  // Sparse multiplication against precomputed coefficients
+  // TODO: replace with weakmap?
+  type withPairingPrecomputes = { _PPRECOMPUTES: [Fp2, Fp2, Fp2][] | undefined };
+  function pairingPrecomputes(point: G2): [Fp2, Fp2, Fp2][] {
+    const p = point as G2 & withPairingPrecomputes;
+    if (p._PPRECOMPUTES) return p._PPRECOMPUTES;
+    p._PPRECOMPUTES = calcPairingPrecomputes(p.x, p.y);
+    return p._PPRECOMPUTES;
+  }
+
+  function clearPairingPrecomputes(point: G2) {
+    const p = point as G2 & withPairingPrecomputes;
+    p._PPRECOMPUTES = undefined;
+  }
+  clearPairingPrecomputes;
+
+  function millerLoopG1(Q: G1, P: G2): Fp12 {
+    return millerLoop(pairingPrecomputes(P), [Q.x, Q.y]);
+  }
+
+  // Point on G2 curve (complex numbers): (x₁, x₂+i), (y₁, y₂+i)
+  const G2 = weierstrassPoints({
+    n: Fr.ORDER,
+    ...CURVE.G2,
+  });
+  const { Signature } = CURVE.G2;
+
+  // Calculates bilinear pairing
+  function pairing(P: G1, Q: G2, withFinalExponent: boolean = true): Fp12 {
+    if (P.equals(G1.Point.ZERO) || Q.equals(G2.Point.ZERO))
+      throw new Error('No pairings at point of Infinity');
+    P.assertValidity();
+    Q.assertValidity();
+    // Performance: 9ms for millerLoop and ~14ms for exp.
+    const looped = millerLoopG1(P, Q);
+    return withFinalExponent ? Fp12.finalExponentiate(looped) : looped;
+  }
+  type G1 = typeof G1.Point.BASE;
+  type G2 = typeof G2.Point.BASE;
+
+  type G1Hex = Hex | G1;
+  type G2Hex = Hex | G2;
+  function normP1(point: G1Hex): G1 {
+    return point instanceof G1.Point ? (point as G1) : G1.Point.fromHex(point);
+  }
+  function normP2(point: G2Hex): G2 {
+    return point instanceof G2.Point ? point : Signature.decode(point);
+  }
+  function normP2Hash(point: G2Hex): G2 {
+    return point instanceof G2.Point ? point : G2.Point.hashToCurve(point);
+  }
+
+  // Multiplies generator by private key.
+  // P = pk x G
+  function getPublicKey(privateKey: PrivKey): Uint8Array {
+    return G1.Point.fromPrivateKey(privateKey).toRawBytes(true);
+  }
+
+  // Executes `hashToCurve` on the message and then multiplies the result by private key.
+  // S = pk x H(m)
+  function sign(message: Hex, privateKey: PrivKey): Uint8Array;
+  function sign(message: G2, privateKey: PrivKey): G2;
+  function sign(message: G2Hex, privateKey: PrivKey): Uint8Array | G2 {
+    const msgPoint = normP2Hash(message);
+    msgPoint.assertValidity();
+    const sigPoint = msgPoint.multiply(normalizePrivKey(privateKey));
+    if (message instanceof G2.Point) return sigPoint;
+    return Signature.encode(sigPoint);
+  }
+
+  // Checks if pairing of public key & hash is equal to pairing of generator & signature.
+  // e(P, H(m)) == e(G, S)
+  function verify(signature: G2Hex, message: G2Hex, publicKey: G1Hex): boolean {
+    const P = normP1(publicKey);
+    const Hm = normP2Hash(message);
+    const G = G1.Point.BASE;
+    const S = normP2(signature);
+    // Instead of doing 2 exponentiations, we use property of billinear maps
+    // and do one exp after multiplying 2 points.
+    const ePHm = pairing(P.negate(), Hm, false);
+    const eGS = pairing(G, S, false);
+    const exp = Fp12.finalExponentiate(Fp12.mul(eGS, ePHm));
+    return Fp12.equals(exp, Fp12.ONE);
+  }
+
+  // Adds a bunch of public key points together.
+  // pk1 + pk2 + pk3 = pkA
+  function aggregatePublicKeys(publicKeys: Hex[]): Uint8Array;
+  function aggregatePublicKeys(publicKeys: G1[]): G1;
+  function aggregatePublicKeys(publicKeys: G1Hex[]): Uint8Array | G1 {
+    if (!publicKeys.length) throw new Error('Expected non-empty array');
+    const agg = publicKeys
+      .map(normP1)
+      .reduce((sum, p) => sum.add(G1.ProjectivePoint.fromAffine(p)), G1.ProjectivePoint.ZERO);
+    const aggAffine = agg.toAffine();
+    if (publicKeys[0] instanceof G1.Point) {
+      aggAffine.assertValidity();
+      return aggAffine;
+    }
+    // toRawBytes ensures point validity
+    return aggAffine.toRawBytes(true);
+  }
+
+  // Adds a bunch of signature points together.
+  function aggregateSignatures(signatures: Hex[]): Uint8Array;
+  function aggregateSignatures(signatures: G2[]): G2;
+  function aggregateSignatures(signatures: G2Hex[]): Uint8Array | G2 {
+    if (!signatures.length) throw new Error('Expected non-empty array');
+    const agg = signatures
+      .map(normP2)
+      .reduce((sum, s) => sum.add(G2.ProjectivePoint.fromAffine(s)), G2.ProjectivePoint.ZERO);
+    const aggAffine = agg.toAffine();
+    if (signatures[0] instanceof G2.Point) {
+      aggAffine.assertValidity();
+      return aggAffine;
+    }
+    return Signature.encode(aggAffine);
+  }
+
+  // https://ethresear.ch/t/fast-verification-of-multiple-bls-signatures/5407
+  // e(G, S) = e(G, SUM(n)(Si)) = MUL(n)(e(G, Si))
+  function verifyBatch(signature: G2Hex, messages: G2Hex[], publicKeys: G1Hex[]): boolean {
+    if (!messages.length) throw new Error('Expected non-empty messages array');
+    if (publicKeys.length !== messages.length)
+      throw new Error('Pubkey count should equal msg count');
+    const sig = normP2(signature);
+    const nMessages = messages.map(normP2Hash);
+    const nPublicKeys = publicKeys.map(normP1);
+    try {
+      const paired = [];
+      for (const message of new Set(nMessages)) {
+        const groupPublicKey = nMessages.reduce(
+          (groupPublicKey, subMessage, i) =>
+            subMessage === message ? groupPublicKey.add(nPublicKeys[i]) : groupPublicKey,
+          G1.Point.ZERO
+        );
+        // const msg = message instanceof PointG2 ? message : await PointG2.hashToCurve(message);
+        // Possible to batch pairing for same msg with different groupPublicKey here
+        paired.push(pairing(groupPublicKey, message, false));
+      }
+      paired.push(pairing(G1.Point.BASE.negate(), sig, false));
+      const product = paired.reduce((a, b) => Fp12.mul(a, b), Fp12.ONE);
+      const exp = Fp12.finalExponentiate(product);
+      return Fp12.equals(exp, Fp12.ONE);
+    } catch {
+      return false;
+    }
+  }
+
+  // Pre-compute points. Refer to README.
+  G1.Point.BASE._setWindowSize(4);
+  return {
+    CURVE,
+    Fr,
+    Fp,
+    Fp2,
+    Fp6,
+    Fp12,
+    G1,
+    G2,
+    Signature,
+    millerLoop,
+    calcPairingPrecomputes,
+    pairing,
+    getPublicKey,
+    sign,
+    verify,
+    aggregatePublicKeys,
+    aggregateSignatures,
+    verifyBatch,
+    utils,
+  };
+}

src/abstract/edwards.ts

@@ -0,0 +1,727 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+// Twisted Edwards curve. The formula is: ax² + y² = 1 + dx²y²
+
+// Differences from @noble/ed25519 1.7:
+// 1. Different field element lengths in ed448:
+//   EDDSA (RFC8032) is 456 bits / 57 bytes, ECDH (RFC7748) is 448 bits / 56 bytes
+// 2. Different addition formula (doubling is same)
+// 3. uvRatio differs between curves (half-expected, not only pow fn changes)
+// 4. Point decompression code is different too (unexpected), now using generalized formula
+// 5. Domain function was no-op for ed25519, but adds some data even with empty context for ed448
+
+import * as mod from './modular.js';
+import {
+  bytesToHex,
+  concatBytes,
+  ensureBytes,
+  numberToBytesLE,
+  bytesToNumberLE,
+  hashToPrivateScalar,
+  BasicCurve,
+  validateOpts as utilOpts,
+  Hex,
+  PrivKey,
+} from './utils.js'; // TODO: import * as u from './utils.js'?
+import { Group, GroupConstructor, wNAF } from './group.js';
+import { hash_to_field, htfOpts, validateHTFOpts } from './hash-to-curve.js';
+
+// Be friendly to bad ECMAScript parsers by not using bigint literals like 123n
+const _0n = BigInt(0);
+const _1n = BigInt(1);
+const _2n = BigInt(2);
+const _8n = BigInt(8);
+
+export type CHash = {
+  (message: Uint8Array | string): Uint8Array;
+  blockLen: number;
+  outputLen: number;
+  create(): any;
+};
+
+export type CurveType = BasicCurve<bigint> & {
+  // Params: a, d
+  a: bigint;
+  d: bigint;
+  // Hashes
+  hash: CHash; // Because we need outputLen for DRBG
+  randomBytes: (bytesLength?: number) => Uint8Array;
+  adjustScalarBytes?: (bytes: Uint8Array) => Uint8Array;
+  domain?: (data: Uint8Array, ctx: Uint8Array, phflag: boolean) => Uint8Array;
+  uvRatio?: (u: bigint, v: bigint) => { isValid: boolean; value: bigint };
+  preHash?: CHash;
+  clearCofactor?: (c: ExtendedPointConstructor, point: ExtendedPointType) => ExtendedPointType;
+  // Hash to field opts
+  htfDefaults?: htfOpts;
+  mapToCurve?: (scalar: bigint[]) => { x: bigint; y: bigint };
+};
+
+// Should be separate from overrides, since overrides can use information about curve (for example nBits)
+function validateOpts(curve: CurveType) {
+  const opts = utilOpts(curve);
+  if (typeof opts.hash !== 'function' || !Number.isSafeInteger(opts.hash.outputLen))
+    throw new Error('Invalid hash function');
+  for (const i of ['a', 'd'] as const) {
+    if (typeof opts[i] !== 'bigint')
+      throw new Error(`Invalid curve param ${i}=${opts[i]} (${typeof opts[i]})`);
+  }
+  for (const fn of ['randomBytes'] as const) {
+    if (typeof opts[fn] !== 'function') throw new Error(`Invalid ${fn} function`);
+  }
+  for (const fn of [
+    'adjustScalarBytes',
+    'domain',
+    'uvRatio',
+    'mapToCurve',
+    'clearCofactor',
+  ] as const) {
+    if (opts[fn] === undefined) continue; // Optional
+    if (typeof opts[fn] !== 'function') throw new Error(`Invalid ${fn} function`);
+  }
+  if (opts.htfDefaults !== undefined) validateHTFOpts(opts.htfDefaults);
+  // Set defaults
+  return Object.freeze({ ...opts } as const);
+}
+
+// Instance
+export interface SignatureType {
+  readonly r: PointType;
+  readonly s: bigint;
+  assertValidity(): SignatureType;
+  toRawBytes(): Uint8Array;
+  toHex(): string;
+}
+// Static methods
+export type SignatureConstructor = {
+  new (r: PointType, s: bigint): SignatureType;
+  fromHex(hex: Hex): SignatureType;
+};
+
+// Instance
+export interface ExtendedPointType extends Group<ExtendedPointType> {
+  readonly x: bigint;
+  readonly y: bigint;
+  readonly z: bigint;
+  readonly t: bigint;
+  multiply(scalar: number | bigint, affinePoint?: PointType): ExtendedPointType;
+  multiplyUnsafe(scalar: number | bigint): ExtendedPointType;
+  isSmallOrder(): boolean;
+  isTorsionFree(): boolean;
+  toAffine(invZ?: bigint): PointType;
+  clearCofactor(): ExtendedPointType;
+}
+// Static methods
+export interface ExtendedPointConstructor extends GroupConstructor<ExtendedPointType> {
+  new (x: bigint, y: bigint, z: bigint, t: bigint): ExtendedPointType;
+  fromAffine(p: PointType): ExtendedPointType;
+  toAffineBatch(points: ExtendedPointType[]): PointType[];
+  normalizeZ(points: ExtendedPointType[]): ExtendedPointType[];
+}
+
+// Instance
+export interface PointType extends Group<PointType> {
+  readonly x: bigint;
+  readonly y: bigint;
+  _setWindowSize(windowSize: number): void;
+  toRawBytes(isCompressed?: boolean): Uint8Array;
+  toHex(isCompressed?: boolean): string;
+  isTorsionFree(): boolean;
+  clearCofactor(): PointType;
+}
+// Static methods
+export interface PointConstructor extends GroupConstructor<PointType> {
+  new (x: bigint, y: bigint): PointType;
+  fromHex(hex: Hex): PointType;
+  fromPrivateKey(privateKey: PrivKey): PointType;
+  hashToCurve(msg: Hex, options?: Partial<htfOpts>): PointType;
+  encodeToCurve(msg: Hex, options?: Partial<htfOpts>): PointType;
+}
+
+export type PubKey = Hex | PointType;
+export type SigType = Hex | SignatureType;
+
+export type CurveFn = {
+  CURVE: ReturnType<typeof validateOpts>;
+  getPublicKey: (privateKey: PrivKey, isCompressed?: boolean) => Uint8Array;
+  sign: (message: Hex, privateKey: Hex) => Uint8Array;
+  verify: (sig: SigType, message: Hex, publicKey: PubKey) => boolean;
+  Point: PointConstructor;
+  ExtendedPoint: ExtendedPointConstructor;
+  Signature: SignatureConstructor;
+  utils: {
+    mod: (a: bigint) => bigint;
+    invert: (number: bigint) => bigint;
+    randomPrivateKey: () => Uint8Array;
+    getExtendedPublicKey: (key: PrivKey) => {
+      head: Uint8Array;
+      prefix: Uint8Array;
+      scalar: bigint;
+      point: PointType;
+      pointBytes: Uint8Array;
+    };
+  };
+};
+
+// NOTE: it is not generic twisted curve for now, but ed25519/ed448 generic implementation
+export function twistedEdwards(curveDef: CurveType): CurveFn {
+  const CURVE = validateOpts(curveDef) as ReturnType<typeof validateOpts>;
+  const Fp = CURVE.Fp as mod.Field<bigint>;
+  const CURVE_ORDER = CURVE.n;
+  const fieldLen = Fp.BYTES; // 32 (length of one field element)
+  if (fieldLen > 2048) throw new Error('Field lengths over 2048 are not supported');
+  const groupLen = CURVE.nByteLength;
+  // (2n ** 256n).toString(16);
+  const maxGroupElement = _2n ** BigInt(groupLen * 8); // previous POW_2_256
+
+  // Function overrides
+  const { randomBytes } = CURVE;
+  const modP = Fp.create;
+
+  // sqrt(u/v)
+  function _uvRatio(u: bigint, v: bigint) {
+    try {
+      const value = Fp.sqrt(u * Fp.invert(v));
+      return { isValid: true, value };
+    } catch (e) {
+      return { isValid: false, value: _0n };
+    }
+  }
+  const uvRatio = CURVE.uvRatio || _uvRatio;
+
+  const _adjustScalarBytes = (bytes: Uint8Array) => bytes; // NOOP
+  const adjustScalarBytes = CURVE.adjustScalarBytes || _adjustScalarBytes;
+  function _domain(data: Uint8Array, ctx: Uint8Array, phflag: boolean) {
+    if (ctx.length || phflag) throw new Error('Contexts/pre-hash are not supported');
+    return data;
+  }
+  const domain = CURVE.domain || _domain; // NOOP
+
+  /**
+   * Extended Point works in extended coordinates: (x, y, z, t) ∋ (x=x/z, y=y/z, t=xy).
+   * Default Point works in affine coordinates: (x, y)
+   * https://en.wikipedia.org/wiki/Twisted_Edwards_curve#Extended_coordinates
+   */
+  class ExtendedPoint implements ExtendedPointType {
+    constructor(readonly x: bigint, readonly y: bigint, readonly z: bigint, readonly t: bigint) {}
+
+    static BASE = new ExtendedPoint(CURVE.Gx, CURVE.Gy, _1n, modP(CURVE.Gx * CURVE.Gy));
+    static ZERO = new ExtendedPoint(_0n, _1n, _1n, _0n);
+    static fromAffine(p: Point): ExtendedPoint {
+      if (!(p instanceof Point)) {
+        throw new TypeError('ExtendedPoint#fromAffine: expected Point');
+      }
+      if (p.equals(Point.ZERO)) return ExtendedPoint.ZERO;
+      return new ExtendedPoint(p.x, p.y, _1n, modP(p.x * p.y));
+    }
+    // Takes a bunch of Jacobian Points but executes only one
+    // invert on all of them. invert is very slow operation,
+    // so this improves performance massively.
+    static toAffineBatch(points: ExtendedPoint[]): Point[] {
+      const toInv = Fp.invertBatch(points.map((p) => p.z));
+      return points.map((p, i) => p.toAffine(toInv[i]));
+    }
+
+    static normalizeZ(points: ExtendedPoint[]): ExtendedPoint[] {
+      return this.toAffineBatch(points).map(this.fromAffine);
+    }
+
+    // Compare one point to another.
+    equals(other: ExtendedPoint): boolean {
+      assertExtPoint(other);
+      const { x: X1, y: Y1, z: Z1 } = this;
+      const { x: X2, y: Y2, z: Z2 } = other;
+      const X1Z2 = modP(X1 * Z2);
+      const X2Z1 = modP(X2 * Z1);
+      const Y1Z2 = modP(Y1 * Z2);
+      const Y2Z1 = modP(Y2 * Z1);
+      return X1Z2 === X2Z1 && Y1Z2 === Y2Z1;
+    }
+
+    // Inverses point to one corresponding to (x, -y) in Affine coordinates.
+    negate(): ExtendedPoint {
+      return new ExtendedPoint(modP(-this.x), this.y, this.z, modP(-this.t));
+    }
+
+    // Fast algo for doubling Extended Point.
+    // https://hyperelliptic.org/EFD/g1p/auto-twisted-extended.html#doubling-dbl-2008-hwcd
+    // Cost: 4M + 4S + 1*a + 6add + 1*2.
+    double(): ExtendedPoint {
+      const { a } = CURVE;
+      const { x: X1, y: Y1, z: Z1 } = this;
+      const A = modP(X1 * X1); // A = X12
+      const B = modP(Y1 * Y1); // B = Y12
+      const C = modP(_2n * modP(Z1 * Z1)); // C = 2*Z12
+      const D = modP(a * A); // D = a*A
+      const x1y1 = X1 + Y1;
+      const E = modP(modP(x1y1 * x1y1) - A - B); // E = (X1+Y1)2-A-B
+      const G = D + B; // G = D+B
+      const F = G - C; // F = G-C
+      const H = D - B; // H = D-B
+      const X3 = modP(E * F); // X3 = E*F
+      const Y3 = modP(G * H); // Y3 = G*H
+      const T3 = modP(E * H); // T3 = E*H
+      const Z3 = modP(F * G); // Z3 = F*G
+      return new ExtendedPoint(X3, Y3, Z3, T3);
+    }
+
+    // Fast algo for adding 2 Extended Points.
+    // https://hyperelliptic.org/EFD/g1p/auto-twisted-extended.html#addition-add-2008-hwcd
+    // Cost: 9M + 1*a + 1*d + 7add.
+    add(other: ExtendedPoint) {
+      assertExtPoint(other);
+      const { a, d } = CURVE;
+      const { x: X1, y: Y1, z: Z1, t: T1 } = this;
+      const { x: X2, y: Y2, z: Z2, t: T2 } = other;
+      // Faster algo for adding 2 Extended Points when curve's a=-1.
+      // http://hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#addition-add-2008-hwcd-4
+      // Cost: 8M + 8add + 2*2.
+      // Note: It does not check whether the `other` point is valid.
+      if (a === BigInt(-1)) {
+        const A = modP((Y1 - X1) * (Y2 + X2));
+        const B = modP((Y1 + X1) * (Y2 - X2));
+        const F = modP(B - A);
+        if (F === _0n) return this.double(); // Same point. Tests say it doesn't affect timing
+        const C = modP(Z1 * _2n * T2);
+        const D = modP(T1 * _2n * Z2);
+        const E = D + C;
+        const G = B + A;
+        const H = D - C;
+        const X3 = modP(E * F);
+        const Y3 = modP(G * H);
+        const T3 = modP(E * H);
+        const Z3 = modP(F * G);
+        return new ExtendedPoint(X3, Y3, Z3, T3);
+      }
+      const A = modP(X1 * X2); // A = X1*X2
+      const B = modP(Y1 * Y2); // B = Y1*Y2
+      const C = modP(T1 * d * T2); // C = T1*d*T2
+      const D = modP(Z1 * Z2); // D = Z1*Z2
+      const E = modP((X1 + Y1) * (X2 + Y2) - A - B); // E = (X1+Y1)*(X2+Y2)-A-B
+      const F = D - C; // F = D-C
+      const G = D + C; // G = D+C
+      const H = modP(B - a * A); // H = B-a*A
+      const X3 = modP(E * F); // X3 = E*F
+      const Y3 = modP(G * H); // Y3 = G*H
+      const T3 = modP(E * H); // T3 = E*H
+      const Z3 = modP(F * G); // Z3 = F*G
+
+      return new ExtendedPoint(X3, Y3, Z3, T3);
+    }
+
+    subtract(other: ExtendedPoint): ExtendedPoint {
+      return this.add(other.negate());
+    }
+
+    private wNAF(n: bigint, affinePoint?: Point): ExtendedPoint {
+      if (!affinePoint && this.equals(ExtendedPoint.BASE)) affinePoint = Point.BASE;
+      const W = (affinePoint && affinePoint._WINDOW_SIZE) || 1;
+      let precomputes = affinePoint && pointPrecomputes.get(affinePoint);
+      if (!precomputes) {
+        precomputes = wnaf.precomputeWindow(this, W) as ExtendedPoint[];
+        if (affinePoint && W !== 1) {
+          precomputes = ExtendedPoint.normalizeZ(precomputes);
+          pointPrecomputes.set(affinePoint, precomputes);
+        }
+      }
+      const { p, f } = wnaf.wNAF(W, precomputes, n);
+      return ExtendedPoint.normalizeZ([p, f])[0];
+    }
+
+    // Constant time multiplication.
+    // Uses wNAF method. Windowed method may be 10% faster,
+    // but takes 2x longer to generate and consumes 2x memory.
+    multiply(scalar: number | bigint, affinePoint?: Point): ExtendedPoint {
+      return this.wNAF(normalizeScalar(scalar, CURVE_ORDER), affinePoint);
+    }
+
+    // Non-constant-time multiplication. Uses double-and-add algorithm.
+    // It's faster, but should only be used when you don't care about
+    // an exposed private key e.g. sig verification.
+    // Allows scalar bigger than curve order, but less than 2^256
+    multiplyUnsafe(scalar: number | bigint): ExtendedPoint {
+      let n = normalizeScalar(scalar, CURVE_ORDER, false);
+      const G = ExtendedPoint.BASE;
+      const P0 = ExtendedPoint.ZERO;
+      if (n === _0n) return P0;
+      if (this.equals(P0) || n === _1n) return this;
+      if (this.equals(G)) return this.wNAF(n);
+      return wnaf.unsafeLadder(this, n);
+    }
+
+    // Multiplies point by cofactor and checks if the result is 0.
+    isSmallOrder(): boolean {
+      return this.multiplyUnsafe(CURVE.h).equals(ExtendedPoint.ZERO);
+    }
+
+    // Multiplies point by a very big scalar n and checks if the result is 0.
+    isTorsionFree(): boolean {
+      return this.multiplyUnsafe(CURVE_ORDER).equals(ExtendedPoint.ZERO);
+    }
+
+    // Converts Extended point to default (x, y) coordinates.
+    // Can accept precomputed Z^-1 - for example, from invertBatch.
+    toAffine(invZ?: bigint): Point {
+      const { x, y, z } = this;
+      const is0 = this.equals(ExtendedPoint.ZERO);
+      if (invZ == null) invZ = is0 ? _8n : (Fp.invert(z) as bigint); // 8 was chosen arbitrarily
+      const ax = modP(x * invZ);
+      const ay = modP(y * invZ);
+      const zz = modP(z * invZ);
+      if (is0) return Point.ZERO;
+      if (zz !== _1n) throw new Error('invZ was invalid');
+      return new Point(ax, ay);
+    }
+    clearCofactor(): ExtendedPoint {
+      if (CURVE.h === _1n) return this; // Fast-path
+      // clear_cofactor(P) := h_eff * P
+      // hEff = h for ed25519/ed448. Maybe worth moving to params?
+      if (CURVE.clearCofactor) return CURVE.clearCofactor(ExtendedPoint, this) as ExtendedPoint;
+      return this.multiplyUnsafe(CURVE.h);
+    }
+  }
+  const wnaf = wNAF(ExtendedPoint, groupLen * 8);
+
+  function assertExtPoint(other: unknown) {
+    if (!(other instanceof ExtendedPoint)) throw new TypeError('ExtendedPoint expected');
+  }
+  // Stores precomputed values for points.
+  const pointPrecomputes = new WeakMap<Point, ExtendedPoint[]>();
+
+  /**
+   * Default Point works in affine coordinates: (x, y)
+   */
+  class Point implements PointType {
+    // Base point aka generator
+    // public_key = Point.BASE * private_key
+    static BASE: Point = new Point(CURVE.Gx, CURVE.Gy);
+    // Identity point aka point at infinity
+    // point = point + zero_point
+    static ZERO: Point = new Point(_0n, _1n);
+    // We calculate precomputes for elliptic curve point multiplication
+    // using windowed method. This specifies window size and
+    // stores precomputed values. Usually only base point would be precomputed.
+    _WINDOW_SIZE?: number;
+
+    constructor(readonly x: bigint, readonly y: bigint) {}
+
+    // "Private method", don't use it directly.
+    _setWindowSize(windowSize: number) {
+      this._WINDOW_SIZE = windowSize;
+      pointPrecomputes.delete(this);
+    }
+
+    // Converts hash string or Uint8Array to Point.
+    // Uses algo from RFC8032 5.1.3.
+    static fromHex(hex: Hex, strict = true) {
+      const { d, a } = CURVE;
+      hex = ensureBytes(hex, fieldLen);
+      // 1.  First, interpret the string as an integer in little-endian
+      // representation. Bit 255 of this number is the least significant
+      // bit of the x-coordinate and denote this value x_0.  The
+      // y-coordinate is recovered simply by clearing this bit.  If the
+      // resulting value is >= p, decoding fails.
+      const normed = hex.slice();
+      const lastByte = hex[fieldLen - 1];
+      normed[fieldLen - 1] = lastByte & ~0x80;
+      const y = bytesToNumberLE(normed);
+
+      if (strict && y >= Fp.ORDER) throw new Error('Expected 0 < hex < P');
+      if (!strict && y >= maxGroupElement) throw new Error('Expected 0 < hex < 2**256');
+
+      // 2.  To recover the x-coordinate, the curve equation implies
+      // Ed25519: x² = (y² - 1) / (d y² + 1) (mod p).
+      // Ed448: x² = (y² - 1) / (d y² - 1) (mod p).
+      // For generic case:
+      // a*x²+y²=1+d*x²*y²
+      // -> y²-1 = d*x²*y²-a*x²
+      // -> y²-1 = x² (d*y²-a)
+      // -> x² = (y²-1) / (d*y²-a)
+
+      // The denominator is always non-zero mod p.  Let u = y² - 1 and v = d y² + 1.
+      const y2 = modP(y * y);
+      const u = modP(y2 - _1n);
+      const v = modP(d * y2 - a);
+      let { isValid, value: x } = uvRatio(u, v);
+      if (!isValid) throw new Error('Point.fromHex: invalid y coordinate');
+      // 4.  Finally, use the x_0 bit to select the right square root.  If
+      // x = 0, and x_0 = 1, decoding fails.  Otherwise, if x_0 != x mod
+      // 2, set x <-- p - x.  Return the decoded point (x,y).
+      const isXOdd = (x & _1n) === _1n;
+      const isLastByteOdd = (lastByte & 0x80) !== 0;
+      if (isLastByteOdd !== isXOdd) x = modP(-x);
+      return new Point(x, y);
+    }
+
+    static fromPrivateKey(privateKey: PrivKey) {
+      return getExtendedPublicKey(privateKey).point;
+    }
+
+    // There can always be only two x values (x, -x) for any y
+    // When compressing point, it's enough to only store its y coordinate
+    // and use the last byte to encode sign of x.
+    toRawBytes(): Uint8Array {
+      const bytes = numberToBytesLE(this.y, fieldLen);
+      bytes[fieldLen - 1] |= this.x & _1n ? 0x80 : 0;
+      return bytes;
+    }
+
+    // Same as toRawBytes, but returns string.
+    toHex(): string {
+      return bytesToHex(this.toRawBytes());
+    }
+
+    isTorsionFree(): boolean {
+      return ExtendedPoint.fromAffine(this).isTorsionFree();
+    }
+
+    equals(other: Point): boolean {
+      if (!(other instanceof Point)) throw new TypeError('Point#equals: expected Point');
+      return this.x === other.x && this.y === other.y;
+    }
+
+    negate(): Point {
+      return new Point(modP(-this.x), this.y);
+    }
+
+    double(): Point {
+      return ExtendedPoint.fromAffine(this).double().toAffine();
+    }
+
+    add(other: Point) {
+      return ExtendedPoint.fromAffine(this).add(ExtendedPoint.fromAffine(other)).toAffine();
+    }
+
+    subtract(other: Point) {
+      return this.add(other.negate());
+    }
+
+    /**
+     * Constant time multiplication.
+     * @param scalar Big-Endian number
+     * @returns new point
+     */
+    multiply(scalar: number | bigint): Point {
+      return ExtendedPoint.fromAffine(this).multiply(scalar, this).toAffine();
+    }
+
+    clearCofactor() {
+      return ExtendedPoint.fromAffine(this).clearCofactor().toAffine();
+    }
+    // Encodes byte string to elliptic curve
+    // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-3
+    static hashToCurve(msg: Hex, options?: Partial<htfOpts>) {
+      if (!CURVE.mapToCurve) throw new Error('No mapToCurve defined for curve');
+      msg = ensureBytes(msg);
+      const u = hash_to_field(msg, 2, { ...CURVE.htfDefaults, ...options } as htfOpts);
+      const { x: x0, y: y0 } = CURVE.mapToCurve(u[0]);
+      const { x: x1, y: y1 } = CURVE.mapToCurve(u[1]);
+      const p = new Point(x0, y0).add(new Point(x1, y1)).clearCofactor();
+      return p;
+    }
+    // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16#section-3
+    static encodeToCurve(msg: Hex, options?: Partial<htfOpts>) {
+      if (!CURVE.mapToCurve) throw new Error('No mapToCurve defined for curve');
+      msg = ensureBytes(msg);
+      const u = hash_to_field(msg, 1, { ...CURVE.htfDefaults, ...options } as htfOpts);
+      const { x, y } = CURVE.mapToCurve(u[0]);
+      return new Point(x, y).clearCofactor();
+    }
+  }
+
+  /**
+   * EDDSA signature.
+   */
+  class Signature implements SignatureType {
+    constructor(readonly r: Point, readonly s: bigint) {
+      this.assertValidity();
+    }
+
+    static fromHex(hex: Hex) {
+      const bytes = ensureBytes(hex, 2 * fieldLen);
+      const r = Point.fromHex(bytes.slice(0, fieldLen), false);
+      const s = bytesToNumberLE(bytes.slice(fieldLen, 2 * fieldLen));
+      return new Signature(r, s);
+    }
+
+    assertValidity() {
+      const { r, s } = this;
+      if (!(r instanceof Point)) throw new Error('Expected Point instance');
+      // 0 <= s < l
+      normalizeScalar(s, CURVE_ORDER, false);
+      return this;
+    }
+
+    toRawBytes() {
+      return concatBytes(this.r.toRawBytes(), numberToBytesLE(this.s, fieldLen));
+    }
+
+    toHex() {
+      return bytesToHex(this.toRawBytes());
+    }
+  }
+
+  // Little-endian SHA512 with modulo n
+  function modlLE(hash: Uint8Array): bigint {
+    return mod.mod(bytesToNumberLE(hash), CURVE_ORDER);
+  }
+
+  /**
+   * Checks for num to be in range:
+   * For strict == true:  `0 <  num < max`.
+   * For strict == false: `0 <= num < max`.
+   * Converts non-float safe numbers to bigints.
+   */
+  function normalizeScalar(num: number | bigint, max: bigint, strict = true): bigint {
+    if (!max) throw new TypeError('Specify max value');
+    if (typeof num === 'number' && Number.isSafeInteger(num)) num = BigInt(num);
+    if (typeof num === 'bigint' && num < max) {
+      if (strict) {
+        if (_0n < num) return num;
+      } else {
+        if (_0n <= num) return num;
+      }
+    }
+    throw new TypeError('Expected valid scalar: 0 < scalar < max');
+  }
+
+  function checkPrivateKey(key: PrivKey) {
+    // Normalize bigint / number / string to Uint8Array
+    key =
+      typeof key === 'bigint' || typeof key === 'number'
+        ? numberToBytesLE(normalizeScalar(key, maxGroupElement), groupLen)
+        : ensureBytes(key);
+    if (key.length !== groupLen) throw new Error(`Expected ${groupLen} bytes, got ${key.length}`);
+    return key;
+  }
+
+  // Takes 64 bytes
+  function getKeyFromHash(hashed: Uint8Array) {
+    // First 32 bytes of 64b uniformingly random input are taken,
+    // clears 3 bits of it to produce a random field element.
+    const head = adjustScalarBytes(hashed.slice(0, groupLen));
+    // Second 32 bytes is called key prefix (5.1.6)
+    const prefix = hashed.slice(groupLen, 2 * groupLen);
+    // The actual private scalar
+    const scalar = modlLE(head);
+    // Point on Edwards curve aka public key
+    const point = Point.BASE.multiply(scalar);
+    const pointBytes = point.toRawBytes();
+    return { head, prefix, scalar, point, pointBytes };
+  }
+
+  /** Convenience method that creates public key and other stuff. RFC8032 5.1.5 */
+  function getExtendedPublicKey(key: PrivKey) {
+    return getKeyFromHash(CURVE.hash(checkPrivateKey(key)));
+  }
+
+  /**
+   * Calculates ed25519 public key. RFC8032 5.1.5
+   * 1. private key is hashed with sha512, then first 32 bytes are taken from the hash
+   * 2. 3 least significant bits of the first byte are cleared
+   */
+  function getPublicKey(privateKey: PrivKey): Uint8Array {
+    return getExtendedPublicKey(privateKey).pointBytes;
+  }
+
+  const EMPTY = new Uint8Array();
+  function hashDomainToScalar(message: Uint8Array, context: Hex = EMPTY) {
+    context = ensureBytes(context);
+    return modlLE(CURVE.hash(domain(message, context, !!CURVE.preHash)));
+  }
+
+  /** Signs message with privateKey. RFC8032 5.1.6 */
+  function sign(message: Hex, privateKey: Hex, context?: Hex): Uint8Array {
+    message = ensureBytes(message);
+    if (CURVE.preHash) message = CURVE.preHash(message);
+    const { prefix, scalar, pointBytes } = getExtendedPublicKey(privateKey);
+    const r = hashDomainToScalar(concatBytes(prefix, message), context);
+    const R = Point.BASE.multiply(r); // R = rG
+    const k = hashDomainToScalar(concatBytes(R.toRawBytes(), pointBytes, message), context); // k = hash(R+P+msg)
+    const s = mod.mod(r + k * scalar, CURVE_ORDER); // s = r + kp
+    return new Signature(R, s).toRawBytes();
+  }
+
+  /**
+   * Verifies EdDSA signature against message and public key.
+   * An extended group equation is checked.
+   * RFC8032 5.1.7
+   * Compliant with ZIP215:
+   * 0 <= sig.R/publicKey < 2**256 (can be >= curve.P)
+   * 0 <= sig.s < l
+   * Not compliant with RFC8032: it's not possible to comply to both ZIP & RFC at the same time.
+   */
+  function verify(sig: SigType, message: Hex, publicKey: PubKey, context?: Hex): boolean {
+    message = ensureBytes(message);
+    if (CURVE.preHash) message = CURVE.preHash(message);
+    // When hex is passed, we check public key fully.
+    // When Point instance is passed, we assume it has already been checked, for performance.
+    // If user passes Point/Sig instance, we assume it has been already verified.
+    // We don't check its equations for performance. We do check for valid bounds for s though
+    // We always check for: a) s bounds. b) hex validity
+    if (publicKey instanceof Point) {
+      // ignore
+    } else if (publicKey instanceof Uint8Array || typeof publicKey === 'string') {
+      publicKey = Point.fromHex(publicKey, false);
+    } else {
+      throw new Error(`Invalid publicKey: ${publicKey}`);
+    }
+
+    if (sig instanceof Signature) sig.assertValidity();
+    else if (sig instanceof Uint8Array || typeof sig === 'string') sig = Signature.fromHex(sig);
+    else throw new Error(`Wrong signature: ${sig}`);
+
+    const { r, s } = sig;
+    const SB = ExtendedPoint.BASE.multiplyUnsafe(s);
+    const k = hashDomainToScalar(
+      concatBytes(r.toRawBytes(), publicKey.toRawBytes(), message),
+      context
+    );
+    const kA = ExtendedPoint.fromAffine(publicKey).multiplyUnsafe(k);
+    const RkA = ExtendedPoint.fromAffine(r).add(kA);
+    // [8][S]B = [8]R + [8][k]A'
+    return RkA.subtract(SB).multiplyUnsafe(CURVE.h).equals(ExtendedPoint.ZERO);
+  }
+
+  // Enable precomputes. Slows down first publicKey computation by 20ms.
+  Point.BASE._setWindowSize(8);
+
+  const utils = {
+    getExtendedPublicKey,
+    mod: modP,
+    invert: Fp.invert,
+
+    /**
+     * Not needed for ed25519 private keys. Needed if you use scalars directly (rare).
+     */
+    hashToPrivateScalar: (hash: Hex): bigint => hashToPrivateScalar(hash, CURVE_ORDER, true),
+
+    /**
+     * ed25519 private keys are uniform 32-bit strings. We do not need to check for
+     * modulo bias like we do in secp256k1 randomPrivateKey()
+     */
+    randomPrivateKey: (): Uint8Array => randomBytes(fieldLen),
+
+    /**
+     * We're doing scalar multiplication (used in getPublicKey etc) with precomputed BASE_POINT
+     * values. This slows down first getPublicKey() by milliseconds (see Speed section),
+     * but allows to speed-up subsequent getPublicKey() calls up to 20x.
+     * @param windowSize 2, 4, 8, 16
+     */
+    precompute(windowSize = 8, point = Point.BASE): Point {
+      const cached = point.equals(Point.BASE) ? point : new Point(point.x, point.y);
+      cached._setWindowSize(windowSize);
+      cached.multiply(_2n);
+      return cached;
+    },
+  };
+
+  return {
+    CURVE,
+    getPublicKey,
+    sign,
+    verify,
+    ExtendedPoint,
+    Point,
+    Signature,
+    utils,
+  };
+}

src/abstract/group.ts

@@ -0,0 +1,129 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+// Abelian group utilities
+const _0n = BigInt(0);
+const _1n = BigInt(1);
+
+export interface Group<T extends Group<T>> {
+  double(): T;
+  negate(): T;
+  add(other: T): T;
+  subtract(other: T): T;
+  equals(other: T): boolean;
+  multiply(scalar: number | bigint): T;
+}
+
+export type GroupConstructor<T> = {
+  BASE: T;
+  ZERO: T;
+};
+// Not big, but pretty complex and it is easy to break stuff. To avoid too much copy paste
+export function wNAF<T extends Group<T>>(c: GroupConstructor<T>, bits: number) {
+  const constTimeNegate = (condition: boolean, item: T): T => {
+    const neg = item.negate();
+    return condition ? neg : item;
+  };
+  const opts = (W: number) => {
+    const windows = Math.ceil(bits / W) + 1; // +1, because
+    const windowSize = 2 ** (W - 1); // -1 because we skip zero
+    return { windows, windowSize };
+  };
+  return {
+    constTimeNegate,
+    // non-const time multiplication ladder
+    unsafeLadder(elm: T, n: bigint) {
+      let p = c.ZERO;
+      let d: T = elm;
+      while (n > _0n) {
+        if (n & _1n) p = p.add(d);
+        d = d.double();
+        n >>= _1n;
+      }
+      return p;
+    },
+
+    /**
+     * Creates a wNAF precomputation window. Used for caching.
+     * Default window size is set by `utils.precompute()` and is equal to 8.
+     * Which means we are caching 65536 points: 256 points for every bit from 0 to 256.
+     * @returns 65K precomputed points, depending on W
+     */
+    precomputeWindow(elm: T, W: number): Group<T>[] {
+      const { windows, windowSize } = opts(W);
+      const points: T[] = [];
+      let p: T = elm;
+      let base = p;
+      for (let window = 0; window < windows; window++) {
+        base = p;
+        points.push(base);
+        // =1, because we skip zero
+        for (let i = 1; i < windowSize; i++) {
+          base = base.add(p);
+          points.push(base);
+        }
+        p = base.double();
+      }
+      return points;
+    },
+
+    /**
+     * Implements w-ary non-adjacent form for calculating ec multiplication.
+     * @param W window size
+     * @param affinePoint optional 2d point to save cached precompute windows on it.
+     * @param n bits
+     * @returns real and fake (for const-time) points
+     */
+    wNAF(W: number, precomputes: T[], n: bigint): { p: T; f: T } {
+      // TODO: maybe check that scalar is less than group order? wNAF will fail otherwise
+      // But need to carefully remove other checks before wNAF. ORDER == bits here
+      const { windows, windowSize } = opts(W);
+
+      let p = c.ZERO;
+      let f = c.BASE;
+
+      const mask = BigInt(2 ** W - 1); // Create mask with W ones: 0b1111 for W=4 etc.
+      const maxNumber = 2 ** W;
+      const shiftBy = BigInt(W);
+
+      for (let window = 0; window < windows; window++) {
+        const offset = window * windowSize;
+        // Extract W bits.
+        let wbits = Number(n & mask);
+
+        // Shift number by W bits.
+        n >>= shiftBy;
+
+        // If the bits are bigger than max size, we'll split those.
+        // +224 => 256 - 32
+        if (wbits > windowSize) {
+          wbits -= maxNumber;
+          n += _1n;
+        }
+
+        // This code was first written with assumption that 'f' and 'p' will never be infinity point:
+        // since each addition is multiplied by 2 ** W, it cannot cancel each other. However,
+        // there is negate now: it is possible that negated element from low value
+        // would be the same as high element, which will create carry into next window.
+        // It's not obvious how this can fail, but still worth investigating later.
+
+        // Check if we're onto Zero point.
+        // Add random point inside current window to f.
+        const offset1 = offset;
+        const offset2 = offset + Math.abs(wbits) - 1; // -1 because we skip zero
+        const cond1 = window % 2 !== 0;
+        const cond2 = wbits < 0;
+        if (wbits === 0) {
+          // The most important part for const-time getPublicKey
+          f = f.add(constTimeNegate(cond1, precomputes[offset1]));
+        } else {
+          p = p.add(constTimeNegate(cond2, precomputes[offset2]));
+        }
+      }
+      // JIT-compiler should not eliminate f here, since it will later be used in normalizeZ()
+      // Even if the variable is still unused, there are some checks which will
+      // throw an exception, so compiler needs to prove they won't happen, which is hard.
+      // At this point there is a way to F be infinity-point even if p is not,
+      // which makes it less const-time: around 1 bigint multiply.
+      return { p, f };
+    },
+  };
+}

src/abstract/hash-to-curve.ts

@@ -0,0 +1,146 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+import { CHash, concatBytes } from './utils.js';
+import * as mod from './modular.js';
+
+export type htfOpts = {
+  // DST: a domain separation tag
+  // defined in section 2.2.5
+  DST: string;
+  // p: the characteristic of F
+  //    where F is a finite field of characteristic p and order q = p^m
+  p: bigint;
+  // m: the extension degree of F, m >= 1
+  //     where F is a finite field of characteristic p and order q = p^m
+  m: number;
+  // k: the target security level for the suite in bits
+  // defined in section 5.1
+  k: number;
+  // option to use a message that has already been processed by
+  // expand_message_xmd
+  expand: boolean;
+  // Hash functions for: expand_message_xmd is appropriate for use with a
+  // wide range of hash functions, including SHA-2, SHA-3, BLAKE2, and others.
+  // BBS+ uses blake2: https://github.com/hyperledger/aries-framework-go/issues/2247
+  hash: CHash;
+};
+
+export function validateHTFOpts(opts: htfOpts) {
+  if (typeof opts.DST !== 'string') throw new Error('Invalid htf/DST');
+  if (typeof opts.p !== 'bigint') throw new Error('Invalid htf/p');
+  if (typeof opts.m !== 'number') throw new Error('Invalid htf/m');
+  if (typeof opts.k !== 'number') throw new Error('Invalid htf/k');
+  if (typeof opts.expand !== 'boolean') throw new Error('Invalid htf/expand');
+  if (typeof opts.hash !== 'function' || !Number.isSafeInteger(opts.hash.outputLen))
+    throw new Error('Invalid htf/hash function');
+}
+
+// UTF8 to ui8a
+// TODO: looks broken, ASCII only, why not TextEncoder/TextDecoder? it is in hashes anyway
+export function stringToBytes(str: string) {
+  const bytes = new Uint8Array(str.length);
+  for (let i = 0; i < str.length; i++) bytes[i] = str.charCodeAt(i);
+  return bytes;
+}
+
+// Octet Stream to Integer (bytesToNumberBE)
+function os2ip(bytes: Uint8Array): bigint {
+  let result = 0n;
+  for (let i = 0; i < bytes.length; i++) {
+    result <<= 8n;
+    result += BigInt(bytes[i]);
+  }
+  return result;
+}
+
+// Integer to Octet Stream
+function i2osp(value: number, length: number): Uint8Array {
+  if (value < 0 || value >= 1 << (8 * length)) {
+    throw new Error(`bad I2OSP call: value=${value} length=${length}`);
+  }
+  const res = Array.from({ length }).fill(0) as number[];
+  for (let i = length - 1; i >= 0; i--) {
+    res[i] = value & 0xff;
+    value >>>= 8;
+  }
+  return new Uint8Array(res);
+}
+
+function strxor(a: Uint8Array, b: Uint8Array): Uint8Array {
+  const arr = new Uint8Array(a.length);
+  for (let i = 0; i < a.length; i++) {
+    arr[i] = a[i] ^ b[i];
+  }
+  return arr;
+}
+
+// Produces a uniformly random byte string using a cryptographic hash function H that outputs b bits
+// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-5.4.1
+export function expand_message_xmd(
+  msg: Uint8Array,
+  DST: Uint8Array,
+  lenInBytes: number,
+  H: CHash
+): Uint8Array {
+  // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16#section-5.3.3
+  if (DST.length > 255) DST = H(concatBytes(stringToBytes('H2C-OVERSIZE-DST-'), DST));
+  const b_in_bytes = H.outputLen;
+  const r_in_bytes = H.blockLen;
+  const ell = Math.ceil(lenInBytes / b_in_bytes);
+  if (ell > 255) throw new Error('Invalid xmd length');
+  const DST_prime = concatBytes(DST, i2osp(DST.length, 1));
+  const Z_pad = i2osp(0, r_in_bytes);
+  const l_i_b_str = i2osp(lenInBytes, 2);
+  const b = new Array<Uint8Array>(ell);
+  const b_0 = H(concatBytes(Z_pad, msg, l_i_b_str, i2osp(0, 1), DST_prime));
+  b[0] = H(concatBytes(b_0, i2osp(1, 1), DST_prime));
+  for (let i = 1; i <= ell; i++) {
+    const args = [strxor(b_0, b[i - 1]), i2osp(i + 1, 1), DST_prime];
+    b[i] = H(concatBytes(...args));
+  }
+  const pseudo_random_bytes = concatBytes(...b);
+  return pseudo_random_bytes.slice(0, lenInBytes);
+}
+
+// hashes arbitrary-length byte strings to a list of one or more elements of a finite field F
+// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-5.3
+// Inputs:
+// msg - a byte string containing the message to hash.
+// count - the number of elements of F to output.
+// Outputs:
+// [u_0, ..., u_(count - 1)], a list of field elements.
+export function hash_to_field(msg: Uint8Array, count: number, options: htfOpts): bigint[][] {
+  // if options is provided but incomplete, fill any missing fields with the
+  // value in hftDefaults (ie hash to G2).
+  const log2p = options.p.toString(2).length;
+  const L = Math.ceil((log2p + options.k) / 8); // section 5.1 of ietf draft link above
+  const len_in_bytes = count * options.m * L;
+  const DST = stringToBytes(options.DST);
+  let pseudo_random_bytes = msg;
+  if (options.expand) {
+    pseudo_random_bytes = expand_message_xmd(msg, DST, len_in_bytes, options.hash);
+  }
+  const u = new Array(count);
+  for (let i = 0; i < count; i++) {
+    const e = new Array(options.m);
+    for (let j = 0; j < options.m; j++) {
+      const elm_offset = L * (j + i * options.m);
+      const tv = pseudo_random_bytes.subarray(elm_offset, elm_offset + L);
+      e[j] = mod.mod(os2ip(tv), options.p);
+    }
+    u[i] = e;
+  }
+  return u;
+}
+
+export function isogenyMap<T, F extends mod.Field<T>>(field: F, map: [T[], T[], T[], T[]]) {
+  // Make same order as in spec
+  const COEFF = map.map((i) => Array.from(i).reverse());
+  return (x: T, y: T) => {
+    const [xNum, xDen, yNum, yDen] = COEFF.map((val) =>
+      val.reduce((acc, i) => field.add(field.mul(acc, x), i))
+    );
+    x = field.div(xNum, xDen); // xNum / xDen
+    y = field.mul(y, field.div(yNum, yDen)); // y * (yNum / yDev)
+    return { x, y };
+  };
+}

src/abstract/modular.ts

@@ -0,0 +1,391 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+import * as utils from './utils.js';
+// Utilities for modular arithmetics and finite fields
+// prettier-ignore
+const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);
+// prettier-ignore
+const _4n = BigInt(4), _5n = BigInt(5), _7n = BigInt(7), _8n = BigInt(8);
+// prettier-ignore
+const _9n = BigInt(9), _16n = BigInt(16);
+
+// Calculates a modulo b
+export function mod(a: bigint, b: bigint): bigint {
+  const result = a % b;
+  return result >= _0n ? result : b + result;
+}
+/**
+ * Efficiently exponentiate num to power and do modular division.
+ * Unsafe in some contexts: uses ladder, so can expose bigint bits.
+ * @example
+ * powMod(2n, 6n, 11n) // 64n % 11n == 9n
+ */
+// TODO: use field version && remove
+export function pow(num: bigint, power: bigint, modulo: bigint): bigint {
+  if (modulo <= _0n || power < _0n) throw new Error('Expected power/modulo > 0');
+  if (modulo === _1n) return _0n;
+  let res = _1n;
+  while (power > _0n) {
+    if (power & _1n) res = (res * num) % modulo;
+    num = (num * num) % modulo;
+    power >>= _1n;
+  }
+  return res;
+}
+
+// Does x ^ (2 ^ power) mod p. pow2(30, 4) == 30 ^ (2 ^ 4)
+// TODO: Fp version?
+export function pow2(x: bigint, power: bigint, modulo: bigint): bigint {
+  let res = x;
+  while (power-- > _0n) {
+    res *= res;
+    res %= modulo;
+  }
+  return res;
+}
+
+// Inverses number over modulo
+export function invert(number: bigint, modulo: bigint): bigint {
+  if (number === _0n || modulo <= _0n) {
+    throw new Error(`invert: expected positive integers, got n=${number} mod=${modulo}`);
+  }
+  // Eucledian GCD https://brilliant.org/wiki/extended-euclidean-algorithm/
+  let a = mod(number, modulo);
+  let b = modulo;
+  // prettier-ignore
+  let x = _0n, y = _1n, u = _1n, v = _0n;
+  while (a !== _0n) {
+    const q = b / a;
+    const r = b % a;
+    const m = x - u * q;
+    const n = y - v * q;
+    // prettier-ignore
+    b = a, a = r, x = u, y = v, u = m, v = n;
+  }
+  const gcd = b;
+  if (gcd !== _1n) throw new Error('invert: does not exist');
+  return mod(x, modulo);
+}
+
+/**
+ * Calculates Legendre symbol (a | p), which denotes the value of a^((p-1)/2) (mod p).
+ * * (a | p) ≡ 1    if a is a square (mod p)
+ * * (a | p) ≡ -1   if a is not a square (mod p)
+ * * (a | p) ≡ 0    if a ≡ 0 (mod p)
+ */
+export function legendre(num: bigint, fieldPrime: bigint): bigint {
+  return pow(num, (fieldPrime - _1n) / _2n, fieldPrime);
+}
+
+/**
+ * Calculates square root of a number in a finite field.
+ * √a mod P
+ */
+// TODO: rewrite as generic Fp function && remove bls versions
+export function sqrt(number: bigint, modulo: bigint): bigint {
+  // prettier-ignore
+  const n = number;
+  const P = modulo;
+  const p1div4 = (P + _1n) / _4n;
+
+  // P ≡ 3 (mod 4)
+  // √n = n^((P+1)/4)
+  if (P % _4n === _3n) {
+    // Not all roots possible!
+    // const ORDER =
+    //   0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaabn;
+    // const NUM = 72057594037927816n;
+    // TODO: fix sqrtMod in secp256k1
+    const root = pow(n, p1div4, P);
+    if (mod(root * root, modulo) !== number) throw new Error('Cannot find square root');
+    return root;
+  }
+
+  // P ≡ 5 (mod 8)
+  if (P % _8n === _5n) {
+    const n2 = mod(n * _2n, P);
+    const v = pow(n2, (P - _5n) / _8n, P);
+    const nv = mod(n * v, P);
+    const i = mod(_2n * nv * v, P);
+    const r = mod(nv * (i - _1n), P);
+    return r;
+  }
+
+  // Other cases: Tonelli-Shanks algorithm
+  if (legendre(n, P) !== _1n) throw new Error('Cannot find square root');
+  let q: bigint, s: number, z: bigint;
+  for (q = P - _1n, s = 0; q % _2n === _0n; q /= _2n, s++);
+  if (s === 1) return pow(n, p1div4, P);
+  for (z = _2n; z < P && legendre(z, P) !== P - _1n; z++);
+
+  let c = pow(z, q, P);
+  let r = pow(n, (q + _1n) / _2n, P);
+  let t = pow(n, q, P);
+
+  let t2 = _0n;
+  while (mod(t - _1n, P) !== _0n) {
+    t2 = mod(t * t, P);
+    let i;
+    for (i = 1; i < s; i++) {
+      if (mod(t2 - _1n, P) === _0n) break;
+      t2 = mod(t2 * t2, P);
+    }
+    let b = pow(c, BigInt(1 << (s - i - 1)), P);
+    r = mod(r * b, P);
+    c = mod(b * b, P);
+    t = mod(t * c, P);
+    s = i;
+  }
+  return r;
+}
+
+// Little-endian check for first LE bit (last BE bit);
+export const isNegativeLE = (num: bigint, modulo: bigint) => (mod(num, modulo) & _1n) === _1n;
+
+// Currently completly inconsistent naming:
+// - readable: add, mul, sqr, sqrt, inv, div, pow, eq, sub
+// - unreadable mess: addition, multiply, square, squareRoot, inversion, divide, power, equals, subtract
+
+// Field is not always over prime, Fp2 for example has ORDER(q)=p^m
+export interface Field<T> {
+  ORDER: bigint;
+  BYTES: number;
+  BITS: number;
+  MASK: bigint;
+  ZERO: T;
+  ONE: T;
+  // 1-arg
+  create: (num: T) => T;
+  isValid: (num: T) => boolean;
+  isZero: (num: T) => boolean;
+  negate(num: T): T;
+  invert(num: T): T;
+  sqrt(num: T): T;
+  square(num: T): T;
+  // 2-args
+  equals(lhs: T, rhs: T): boolean;
+  add(lhs: T, rhs: T): T;
+  sub(lhs: T, rhs: T): T;
+  mul(lhs: T, rhs: T | bigint): T;
+  pow(lhs: T, power: bigint): T;
+  div(lhs: T, rhs: T | bigint): T;
+  // N for NonNormalized (for now)
+  addN(lhs: T, rhs: T): T;
+  subN(lhs: T, rhs: T): T;
+  mulN(lhs: T, rhs: T | bigint): T;
+  squareN(num: T): T;
+
+  // Optional
+  // Should be same as sgn0 function in https://datatracker.ietf.org/doc/draft-irtf-cfrg-hash-to-curve/
+  isOdd?(num: T): boolean; // Odd instead of even since we have it for Fp2
+  legendre?(num: T): T;
+  pow(lhs: T, power: bigint): T;
+  invertBatch: (lst: T[]) => T[];
+  toBytes(num: T): Uint8Array;
+  fromBytes(bytes: Uint8Array): T;
+  // If c is False, CMOV returns a, otherwise it returns b.
+  cmov(a: T, b: T, c: boolean): T;
+}
+// prettier-ignore
+const FIELD_FIELDS = [
+  'create', 'isValid', 'isZero', 'negate', 'invert', 'sqrt', 'square',
+  'equals', 'add', 'sub', 'mul', 'pow', 'div',
+  'addN', 'subN', 'mulN', 'squareN'
+] as const;
+export function validateField<T>(field: Field<T>) {
+  for (const i of ['ORDER', 'MASK'] as const) {
+    if (typeof field[i] !== 'bigint')
+      throw new Error(`Invalid field param ${i}=${field[i]} (${typeof field[i]})`);
+  }
+  for (const i of ['BYTES', 'BITS'] as const) {
+    if (typeof field[i] !== 'number')
+      throw new Error(`Invalid field param ${i}=${field[i]} (${typeof field[i]})`);
+  }
+  for (const i of FIELD_FIELDS) {
+    if (typeof field[i] !== 'function')
+      throw new Error(`Invalid field param ${i}=${field[i]} (${typeof field[i]})`);
+  }
+}
+
+// Generic field functions
+export function FpPow<T>(f: Field<T>, num: T, power: bigint): T {
+  // Should have same speed as pow for bigints
+  // TODO: benchmark!
+  if (power < _0n) throw new Error('Expected power > 0');
+  if (power === _0n) return f.ONE;
+  if (power === _1n) return num;
+  let p = f.ONE;
+  let d = num;
+  while (power > _0n) {
+    if (power & _1n) p = f.mul(p, d);
+    d = f.square(d);
+    power >>= 1n;
+  }
+  return p;
+}
+
+export function FpInvertBatch<T>(f: Field<T>, nums: T[]): T[] {
+  const tmp = new Array(nums.length);
+  // Walk from first to last, multiply them by each other MOD p
+  const lastMultiplied = nums.reduce((acc, num, i) => {
+    if (f.isZero(num)) return acc;
+    tmp[i] = acc;
+    return f.mul(acc, num);
+  }, f.ONE);
+  // Invert last element
+  const inverted = f.invert(lastMultiplied);
+  // Walk from last to first, multiply them by inverted each other MOD p
+  nums.reduceRight((acc, num, i) => {
+    if (f.isZero(num)) return acc;
+    tmp[i] = f.mul(acc, tmp[i]);
+    return f.mul(acc, num);
+  }, inverted);
+  return tmp;
+}
+
+export function FpDiv<T>(f: Field<T>, lhs: T, rhs: T | bigint): T {
+  return f.mul(lhs, typeof rhs === 'bigint' ? invert(rhs, f.ORDER) : f.invert(rhs));
+}
+
+// NOTE: very fragile, always bench. Major performance points:
+// - NonNormalized ops
+// - Object.freeze
+// - same shape of object (don't add/remove keys)
+export function Fp(
+  ORDER: bigint,
+  bitLen?: number,
+  isLE = false,
+  redef: Partial<Field<bigint>> = {}
+): Readonly<Field<bigint>> {
+  if (ORDER <= _0n) throw new Error(`Expected Fp ORDER > 0, got ${ORDER}`);
+  const { nBitLength: BITS, nByteLength: BYTES } = utils.nLength(ORDER, bitLen);
+  if (BYTES > 2048) throw new Error('Field lengths over 2048 bytes are not supported');
+  const sqrtP = (num: bigint) => sqrt(num, ORDER);
+  const f: Field<bigint> = Object.freeze({
+    ORDER,
+    BITS,
+    BYTES,
+    MASK: utils.bitMask(BITS),
+    ZERO: _0n,
+    ONE: _1n,
+    create: (num) => mod(num, ORDER),
+    isValid: (num) => {
+      if (typeof num !== 'bigint')
+        throw new Error(`Invalid field element: expected bigint, got ${typeof num}`);
+      return _0n <= num && num < ORDER;
+    },
+    isZero: (num) => num === _0n,
+    isOdd: (num) => (num & _1n) === _1n,
+    negate: (num) => mod(-num, ORDER),
+    equals: (lhs, rhs) => lhs === rhs,
+
+    square: (num) => mod(num * num, ORDER),
+    add: (lhs, rhs) => mod(lhs + rhs, ORDER),
+    sub: (lhs, rhs) => mod(lhs - rhs, ORDER),
+    mul: (lhs, rhs) => mod(lhs * rhs, ORDER),
+    pow: (num, power) => FpPow(f, num, power),
+    div: (lhs, rhs) => mod(lhs * invert(rhs, ORDER), ORDER),
+
+    // Same as above, but doesn't normalize
+    squareN: (num) => num * num,
+    addN: (lhs, rhs) => lhs + rhs,
+    subN: (lhs, rhs) => lhs - rhs,
+    mulN: (lhs, rhs) => lhs * rhs,
+
+    invert: (num) => invert(num, ORDER),
+    sqrt: redef.sqrt || sqrtP,
+    invertBatch: (lst) => FpInvertBatch(f, lst),
+    // TODO: do we really need constant cmov?
+    // We don't have const-time bigints anyway, so probably will be not very useful
+    cmov: (a, b, c) => (c ? b : a),
+    toBytes: (num) =>
+      isLE ? utils.numberToBytesLE(num, BYTES) : utils.numberToBytesBE(num, BYTES),
+
+    fromBytes: (bytes) => {
+      if (bytes.length !== BYTES)
+        throw new Error(`Fp.fromBytes: expected ${BYTES}, got ${bytes.length}`);
+      return isLE ? utils.bytesToNumberLE(bytes) : utils.bytesToNumberBE(bytes);
+    },
+  } as Field<bigint>);
+  return Object.freeze(f);
+}
+
+// TODO: re-use in bls/generic sqrt for field/etc?
+// Something like sqrtUnsafe which always returns value, but sqrt throws exception if non-square
+// From draft-irtf-cfrg-hash-to-curve-16
+export function FpSqrt<T>(Fp: Field<T>) {
+  // NOTE: it requires another sqrt for constant precomputes, but no need for roots of unity,
+  // probably we can simply bls code using it
+  const q = Fp.ORDER;
+  const squareConst = (q - _1n) / _2n;
+  // is_square(x) := { True,  if x^((q - 1) / 2) is 0 or 1 in F;
+  //                 { False, otherwise.
+  let isSquare: (x: T) => boolean = (x) => {
+    const p = Fp.pow(x, squareConst);
+    return Fp.equals(p, Fp.ZERO) || Fp.equals(p, Fp.ONE);
+  };
+  // Constant-time Tonelli-Shanks algorithm
+  let l = _0n;
+  for (let o = q - _1n; o % _2n === _0n; o /= _2n) l += _1n;
+  const c1 = l; // 1. c1, the largest integer such that 2^c1 divides q - 1.
+  const c2 = (q - _1n) / _2n ** c1; // 2. c2 = (q - 1) / (2^c1)        # Integer arithmetic
+  const c3 = (c2 - _1n) / _2n; // 3. c3 = (c2 - 1) / 2            # Integer arithmetic
+  //  4. c4, a non-square value in F
+  //  5. c5 = c4^c2 in F
+  let c4 = Fp.ONE;
+  while (isSquare(c4)) c4 = Fp.add(c4, Fp.ONE);
+  const c5 = Fp.pow(c4, c2);
+
+  let sqrt: (x: T) => T = (x) => {
+    let z = Fp.pow(x, c3); // 1.  z = x^c3
+    let t = Fp.square(z); // 2.  t = z * z
+    t = Fp.mul(t, x); // 3.  t = t * x
+    z = Fp.mul(z, x); // 4.  z = z * x
+    let b = t; // 5.  b = t
+    let c = c5; // 6.  c = c5
+    // 7.  for i in (c1, c1 - 1, ..., 2):
+    for (let i = c1; i > 1; i--) {
+      // 8.    for j in (1, 2, ..., i - 2):
+      // 9.      b = b * b
+      for (let j = _1n; j < i - _1n; i++) b = Fp.square(b);
+      const e = Fp.equals(b, Fp.ONE); // 10.   e = b == 1
+      const zt = Fp.mul(z, c); // 11.   zt = z * c
+      z = Fp.cmov(zt, z, e); // 12.   z = CMOV(zt, z, e)
+      c = Fp.square(c); // 13.   c = c * c
+      let tt = Fp.mul(t, c); // 14.   tt = t * c
+      t = Fp.cmov(tt, t, e); // 15.   t = CMOV(tt, t, e)
+      b = t; // 16.   b = t
+    }
+    return z; // 17. return z
+  };
+  if (q % _4n === _3n) {
+    const c1 = (q + _1n) / _4n; // 1. c1 = (q + 1) / 4     # Integer arithmetic
+    sqrt = (x) => Fp.pow(x, c1);
+  } else if (q % _8n === _5n) {
+    const c1 = Fp.sqrt(Fp.negate(Fp.ONE)); //  1. c1 = sqrt(-1) in F, i.e., (c1^2) == -1 in F
+    const c2 = (q + _3n) / _8n; //  2. c2 = (q + 3) / 8     # Integer arithmetic
+    sqrt = (x) => {
+      let tv1 = Fp.pow(x, c2); //  1. tv1 = x^c2
+      let tv2 = Fp.mul(tv1, c1); //  2. tv2 = tv1 * c1
+      let e = Fp.equals(Fp.square(tv1), x); //  3.   e = (tv1^2) == x
+      return Fp.cmov(tv2, tv1, e); //  4.   z = CMOV(tv2, tv1, e)
+    };
+  } else if (Fp.ORDER % _16n === _9n) {
+    const c1 = Fp.sqrt(Fp.negate(Fp.ONE)); //  1. c1 = sqrt(-1) in F, i.e., (c1^2) == -1 in F
+    const c2 = Fp.sqrt(c1); //  2. c2 = sqrt(c1) in F, i.e., (c2^2) == c1 in F
+    const c3 = Fp.sqrt(Fp.negate(c1)); //  3. c3 = sqrt(-c1) in F, i.e., (c3^2) == -c1 in F
+    const c4 = (Fp.ORDER + _7n) / _16n; //  4. c4 = (q + 7) / 16         # Integer arithmetic
+    sqrt = (x) => {
+      let tv1 = Fp.pow(x, c4); //  1. tv1 = x^c4
+      let tv2 = Fp.mul(c1, tv1); //  2. tv2 = c1 * tv1
+      const tv3 = Fp.mul(c2, tv1); //  3. tv3 = c2 * tv1
+      let tv4 = Fp.mul(c3, tv1); //  4. tv4 = c3 * tv1
+      const e1 = Fp.equals(Fp.square(tv2), x); //  5.  e1 = (tv2^2) == x
+      const e2 = Fp.equals(Fp.square(tv3), x); //  6.  e2 = (tv3^2) == x
+      tv1 = Fp.cmov(tv1, tv2, e1); //  7. tv1 = CMOV(tv1, tv2, e1)  # Select tv2 if (tv2^2) == x
+      tv2 = Fp.cmov(tv4, tv3, e2); //  8. tv2 = CMOV(tv4, tv3, e2)  # Select tv3 if (tv3^2) == x
+      const e3 = Fp.equals(Fp.square(tv2), x); //  9.  e3 = (tv2^2) == x
+      return Fp.cmov(tv1, tv2, e3); //  10.  z = CMOV(tv1, tv2, e3)  # Select the sqrt from tv1 and tv2
+    };
+  }
+  return { sqrt, isSquare };
+}

src/abstract/montgomery.ts

@@ -0,0 +1,223 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+import * as mod from './modular.js';
+import {
+  ensureBytes,
+  numberToBytesLE,
+  bytesToNumberLE,
+  // nLength,
+} from './utils.js';
+
+const _0n = BigInt(0);
+const _1n = BigInt(1);
+type Hex = string | Uint8Array;
+
+export type CurveType = {
+  // Field over which we'll do calculations. Verify with:
+  P: bigint;
+  nByteLength: number;
+  adjustScalarBytes?: (bytes: Uint8Array) => Uint8Array;
+  domain?: (data: Uint8Array, ctx: Uint8Array, phflag: boolean) => Uint8Array;
+  a24: bigint; // Related to d, but cannot be derived from it
+  montgomeryBits: number;
+  powPminus2?: (x: bigint) => bigint;
+  xyToU?: (x: bigint, y: bigint) => bigint;
+  Gu: string;
+};
+export type CurveFn = {
+  scalarMult: (scalar: Hex, u: Hex) => Uint8Array;
+  scalarMultBase: (scalar: Hex) => Uint8Array;
+  getSharedSecret: (privateKeyA: Hex, publicKeyB: Hex) => Uint8Array;
+  getPublicKey: (privateKey: Hex) => Uint8Array;
+  Gu: string;
+};
+
+function validateOpts(curve: CurveType) {
+  for (const i of ['a24'] as const) {
+    if (typeof curve[i] !== 'bigint')
+      throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
+  }
+  for (const i of ['montgomeryBits', 'nByteLength'] as const) {
+    if (curve[i] === undefined) continue; // Optional
+    if (!Number.isSafeInteger(curve[i]))
+      throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
+  }
+  for (const fn of ['adjustScalarBytes', 'domain', 'powPminus2'] as const) {
+    if (curve[fn] === undefined) continue; // Optional
+    if (typeof curve[fn] !== 'function') throw new Error(`Invalid ${fn} function`);
+  }
+  for (const i of ['Gu'] as const) {
+    if (curve[i] === undefined) continue; // Optional
+    if (typeof curve[i] !== 'string')
+      throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
+  }
+  // Set defaults
+  // ...nLength(curve.n, curve.nBitLength),
+  return Object.freeze({ ...curve } as const);
+}
+
+// NOTE: not really montgomery curve, just bunch of very specific methods for X25519/X448 (RFC 7748, https://www.rfc-editor.org/rfc/rfc7748)
+// Uses only one coordinate instead of two
+export function montgomery(curveDef: CurveType): CurveFn {
+  const CURVE = validateOpts(curveDef);
+  const { P } = CURVE;
+  const modP = (a: bigint) => mod.mod(a, P);
+  const montgomeryBits = CURVE.montgomeryBits;
+  const montgomeryBytes = Math.ceil(montgomeryBits / 8);
+  const fieldLen = CURVE.nByteLength;
+  const adjustScalarBytes = CURVE.adjustScalarBytes || ((bytes: Uint8Array) => bytes);
+  const powPminus2 = CURVE.powPminus2 || ((x: bigint) => mod.pow(x, P - BigInt(2), P));
+
+  /**
+   * Checks for num to be in range:
+   * For strict == true:  `0 <  num < max`.
+   * For strict == false: `0 <= num < max`.
+   * Converts non-float safe numbers to bigints.
+   */
+  function normalizeScalar(num: number | bigint, max: bigint, strict = true): bigint {
+    if (!max) throw new TypeError('Specify max value');
+    if (typeof num === 'number' && Number.isSafeInteger(num)) num = BigInt(num);
+    if (typeof num === 'bigint' && num < max) {
+      if (strict) {
+        if (_0n < num) return num;
+      } else {
+        if (_0n <= num) return num;
+      }
+    }
+    throw new TypeError('Expected valid scalar: 0 < scalar < max');
+  }
+
+  // cswap from RFC7748
+  // NOTE: cswap is not from RFC7748!
+  /*
+    cswap(swap, x_2, x_3):
+         dummy = mask(swap) AND (x_2 XOR x_3)
+         x_2 = x_2 XOR dummy
+         x_3 = x_3 XOR dummy
+         Return (x_2, x_3)
+  Where mask(swap) is the all-1 or all-0 word of the same length as x_2
+   and x_3, computed, e.g., as mask(swap) = 0 - swap.
+  */
+  function cswap(swap: bigint, x_2: bigint, x_3: bigint): [bigint, bigint] {
+    const dummy = modP(swap * (x_2 - x_3));
+    x_2 = modP(x_2 - dummy);
+    x_3 = modP(x_3 + dummy);
+    return [x_2, x_3];
+  }
+
+  // x25519 from 4
+  /**
+   *
+   * @param pointU u coordinate (x) on Montgomery Curve 25519
+   * @param scalar by which the point would be multiplied
+   * @returns new Point on Montgomery curve
+   */
+  function montgomeryLadder(pointU: bigint, scalar: bigint): bigint {
+    const { P } = CURVE;
+    const u = normalizeScalar(pointU, P);
+    // Section 5: Implementations MUST accept non-canonical values and process them as
+    // if they had been reduced modulo the field prime.
+    const k = normalizeScalar(scalar, P);
+    // The constant a24 is (486662 - 2) / 4 = 121665 for curve25519/X25519
+    const a24 = CURVE.a24;
+    const x_1 = u;
+    let x_2 = _1n;
+    let z_2 = _0n;
+    let x_3 = u;
+    let z_3 = _1n;
+    let swap = _0n;
+    let sw: [bigint, bigint];
+    for (let t = BigInt(montgomeryBits - 1); t >= _0n; t--) {
+      const k_t = (k >> t) & _1n;
+      swap ^= k_t;
+      sw = cswap(swap, x_2, x_3);
+      x_2 = sw[0];
+      x_3 = sw[1];
+      sw = cswap(swap, z_2, z_3);
+      z_2 = sw[0];
+      z_3 = sw[1];
+      swap = k_t;
+
+      const A = x_2 + z_2;
+      const AA = modP(A * A);
+      const B = x_2 - z_2;
+      const BB = modP(B * B);
+      const E = AA - BB;
+      const C = x_3 + z_3;
+      const D = x_3 - z_3;
+      const DA = modP(D * A);
+      const CB = modP(C * B);
+      const dacb = DA + CB;
+      const da_cb = DA - CB;
+      x_3 = modP(dacb * dacb);
+      z_3 = modP(x_1 * modP(da_cb * da_cb));
+      x_2 = modP(AA * BB);
+      z_2 = modP(E * (AA + modP(a24 * E)));
+    }
+    // (x_2, x_3) = cswap(swap, x_2, x_3)
+    sw = cswap(swap, x_2, x_3);
+    x_2 = sw[0];
+    x_3 = sw[1];
+    // (z_2, z_3) = cswap(swap, z_2, z_3)
+    sw = cswap(swap, z_2, z_3);
+    z_2 = sw[0];
+    z_3 = sw[1];
+    // z_2^(p - 2)
+    const z2 = powPminus2(z_2);
+    // Return x_2 * (z_2^(p - 2))
+    return modP(x_2 * z2);
+  }
+
+  function encodeUCoordinate(u: bigint): Uint8Array {
+    return numberToBytesLE(modP(u), montgomeryBytes);
+  }
+
+  function decodeUCoordinate(uEnc: Hex): bigint {
+    const u = ensureBytes(uEnc, montgomeryBytes);
+    // Section 5: When receiving such an array, implementations of X25519
+    // MUST mask the most significant bit in the final byte.
+    // This is very ugly way, but it works because fieldLen-1 is outside of bounds for X448, so this becomes NOOP
+    // fieldLen - scalaryBytes = 1 for X448 and = 0 for X25519
+    u[fieldLen - 1] &= 127; // 0b0111_1111
+    return bytesToNumberLE(u);
+  }
+
+  function decodeScalar(n: Hex): bigint {
+    const bytes = ensureBytes(n);
+    if (bytes.length !== montgomeryBytes && bytes.length !== fieldLen)
+      throw new Error(`Expected ${montgomeryBytes} or ${fieldLen} bytes, got ${bytes.length}`);
+    return bytesToNumberLE(adjustScalarBytes(bytes));
+  }
+  /**
+   * Computes shared secret between private key "scalar" and public key's "u" (x) coordinate.
+   * We can get 'y' coordinate from 'u',
+   * but Point.fromHex also wants 'x' coordinate oddity flag,
+   * and we cannot get 'x' without knowing 'v'.
+   * Need to add generic conversion between twisted edwards and complimentary curve for JubJub.
+   */
+  function scalarMult(scalar: Hex, u: Hex): Uint8Array {
+    const pointU = decodeUCoordinate(u);
+    const _scalar = decodeScalar(scalar);
+    const pu = montgomeryLadder(pointU, _scalar);
+    // The result was not contributory
+    // https://cr.yp.to/ecdh.html#validate
+    if (pu === _0n) throw new Error('Invalid private or public key received');
+    return encodeUCoordinate(pu);
+  }
+  /**
+   * Computes public key from private.
+   * Executes scalar multiplication of curve's base point by scalar.
+   * @param scalar private key
+   * @returns new public key
+   */
+  function scalarMultBase(scalar: Hex): Uint8Array {
+    return scalarMult(scalar, CURVE.Gu);
+  }
+
+  return {
+    scalarMult,
+    scalarMultBase,
+    getSharedSecret: (privateKey: Hex, publicKey: Hex) => scalarMult(privateKey, publicKey),
+    getPublicKey: (privateKey: Hex): Uint8Array => scalarMultBase(privateKey),
+    Gu: CURVE.Gu,
+  };
+}

src/abstract/utils.ts

@@ -0,0 +1,187 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+import * as mod from './modular.js';
+const _0n = BigInt(0);
+const _1n = BigInt(1);
+const _2n = BigInt(2);
+
+// We accept hex strings besides Uint8Array for simplicity
+export type Hex = Uint8Array | string;
+// Very few implementations accept numbers, we do it to ease learning curve
+export type PrivKey = Hex | bigint | number;
+export type CHash = {
+  (message: Uint8Array | string): Uint8Array;
+  blockLen: number;
+  outputLen: number;
+  create(): any;
+};
+
+// NOTE: these are generic, even if curve is on some polynominal field (bls), it will still have P/n/h
+// But generator can be different (Fp2/Fp6 for bls?)
+export type BasicCurve<T> = {
+  // Field over which we'll do calculations (Fp)
+  Fp: mod.Field<T>;
+  // Curve order, total count of valid points in the field
+  n: bigint;
+  // Bit/byte length of curve order
+  nBitLength?: number;
+  nByteLength?: number;
+  // Cofactor
+  // NOTE: we can assign default value of 1, but then users will just ignore it, without validating with spec
+  // Has not use for now, but nice to have in API
+  h: bigint;
+  hEff?: bigint; // Number to multiply to clear cofactor
+  // Base point (x, y) aka generator point
+  Gx: T;
+  Gy: T;
+  // Wrap private key by curve order (% CURVE.n instead of throwing error)
+  wrapPrivateKey?: boolean;
+  // Point at infinity is perfectly valid point, but not valid public key.
+  // Disabled by default because of compatibility reasons with @noble/secp256k1
+  allowInfinityPoint?: boolean;
+};
+
+export function validateOpts<FP, T>(curve: BasicCurve<FP> & T) {
+  mod.validateField(curve.Fp);
+  for (const i of ['n', 'h'] as const) {
+    if (typeof curve[i] !== 'bigint')
+      throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
+  }
+  if (!curve.Fp.isValid(curve.Gx)) throw new Error('Invalid generator X coordinate Fp element');
+  if (!curve.Fp.isValid(curve.Gy)) throw new Error('Invalid generator Y coordinate Fp element');
+
+  for (const i of ['nBitLength', 'nByteLength'] as const) {
+    if (curve[i] === undefined) continue; // Optional
+    if (!Number.isSafeInteger(curve[i]))
+      throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
+  }
+  // Set defaults
+  return Object.freeze({ ...nLength(curve.n, curve.nBitLength), ...curve } as const);
+}
+
+const hexes = Array.from({ length: 256 }, (v, i) => i.toString(16).padStart(2, '0'));
+export function bytesToHex(uint8a: Uint8Array): string {
+  if (!(uint8a instanceof Uint8Array)) throw new Error('Expected Uint8Array');
+  // pre-caching improves the speed 6x
+  let hex = '';
+  for (let i = 0; i < uint8a.length; i++) {
+    hex += hexes[uint8a[i]];
+  }
+  return hex;
+}
+
+export function numberToHexUnpadded(num: number | bigint): string {
+  const hex = num.toString(16);
+  return hex.length & 1 ? `0${hex}` : hex;
+}
+
+export function hexToNumber(hex: string): bigint {
+  if (typeof hex !== 'string') {
+    throw new TypeError('hexToNumber: expected string, got ' + typeof hex);
+  }
+  // Big Endian
+  return BigInt(`0x${hex}`);
+}
+
+// Caching slows it down 2-3x
+export function hexToBytes(hex: string): Uint8Array {
+  if (typeof hex !== 'string') {
+    throw new TypeError('hexToBytes: expected string, got ' + typeof hex);
+  }
+  if (hex.length % 2) throw new Error('hexToBytes: received invalid unpadded hex ' + hex.length);
+  const array = new Uint8Array(hex.length / 2);
+  for (let i = 0; i < array.length; i++) {
+    const j = i * 2;
+    const hexByte = hex.slice(j, j + 2);
+    const byte = Number.parseInt(hexByte, 16);
+    if (Number.isNaN(byte) || byte < 0) throw new Error('Invalid byte sequence');
+    array[i] = byte;
+  }
+  return array;
+}
+
+// Big Endian
+export function bytesToNumberBE(bytes: Uint8Array): bigint {
+  return hexToNumber(bytesToHex(bytes));
+}
+export function bytesToNumberLE(uint8a: Uint8Array): bigint {
+  if (!(uint8a instanceof Uint8Array)) throw new Error('Expected Uint8Array');
+  return BigInt('0x' + bytesToHex(Uint8Array.from(uint8a).reverse()));
+}
+
+export const numberToBytesBE = (n: bigint, len: number) =>
+  hexToBytes(n.toString(16).padStart(len * 2, '0'));
+export const numberToBytesLE = (n: bigint, len: number) => numberToBytesBE(n, len).reverse();
+
+export function ensureBytes(hex: Hex, expectedLength?: number): Uint8Array {
+  // Uint8Array.from() instead of hash.slice() because node.js Buffer
+  // is instance of Uint8Array, and its slice() creates **mutable** copy
+  const bytes = hex instanceof Uint8Array ? Uint8Array.from(hex) : hexToBytes(hex);
+  if (typeof expectedLength === 'number' && bytes.length !== expectedLength)
+    throw new Error(`Expected ${expectedLength} bytes`);
+  return bytes;
+}
+
+// Copies several Uint8Arrays into one.
+export function concatBytes(...arrays: Uint8Array[]): Uint8Array {
+  if (!arrays.every((b) => b instanceof Uint8Array)) throw new Error('Uint8Array list expected');
+  if (arrays.length === 1) return arrays[0];
+  const length = arrays.reduce((a, arr) => a + arr.length, 0);
+  const result = new Uint8Array(length);
+  for (let i = 0, pad = 0; i < arrays.length; i++) {
+    const arr = arrays[i];
+    result.set(arr, pad);
+    pad += arr.length;
+  }
+  return result;
+}
+
+// CURVE.n lengths
+export function nLength(n: bigint, nBitLength?: number) {
+  // Bit size, byte size of CURVE.n
+  const _nBitLength = nBitLength !== undefined ? nBitLength : n.toString(2).length;
+  const nByteLength = Math.ceil(_nBitLength / 8);
+  return { nBitLength: _nBitLength, nByteLength };
+}
+
+/**
+ * Can take (n+8) or more bytes of uniform input e.g. from CSPRNG or KDF
+ * and convert them into private scalar, with the modulo bias being neglible.
+ * As per FIPS 186 B.4.1.
+ * https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
+ * @param hash hash output from sha512, or a similar function
+ * @returns valid private scalar
+ */
+export function hashToPrivateScalar(hash: Hex, CURVE_ORDER: bigint, isLE = false): bigint {
+  hash = ensureBytes(hash);
+  const orderLen = nLength(CURVE_ORDER).nByteLength;
+  const minLen = orderLen + 8;
+  if (orderLen < 16 || hash.length < minLen || hash.length > 1024)
+    throw new Error('Expected valid bytes of private key as per FIPS 186');
+  const num = isLE ? bytesToNumberLE(hash) : bytesToNumberBE(hash);
+  return mod.mod(num, CURVE_ORDER - _1n) + _1n;
+}
+
+export function equalBytes(b1: Uint8Array, b2: Uint8Array) {
+  // We don't care about timing attacks here
+  if (b1.length !== b2.length) return false;
+  for (let i = 0; i < b1.length; i++) if (b1[i] !== b2[i]) return false;
+  return true;
+}
+
+// Bit operations
+
+// Amount of bits inside bigint (Same as n.toString(2).length)
+export function bitLen(n: bigint) {
+  let len;
+  for (len = 0; n > 0n; n >>= _1n, len += 1);
+  return len;
+}
+// Gets single bit at position. NOTE: first bit position is 0 (same as arrays)
+// Same as !!+Array.from(n.toString(2)).reverse()[pos]
+export const bitGet = (n: bigint, pos: number) => (n >> BigInt(pos)) & 1n;
+// Sets single bit at position
+export const bitSet = (n: bigint, pos: number, value: boolean) =>
+  n | ((value ? _1n : _0n) << BigInt(pos));
+// Return mask for N bits (Same as BigInt(`0b${Array(i).fill('1').join('')}`))
+// Not using ** operator with bigints for old engines.
+export const bitMask = (n: number) => (_2n << BigInt(n - 1)) - _1n;

src/bn.ts

@@ -0,0 +1,21 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+import { weierstrass } from './abstract/weierstrass.js';
+import { sha256 } from '@noble/hashes/sha256';
+import { getHash } from './_shortw_utils.js';
+import { Fp } from './abstract/modular.js';
+/**
+ * bn254 pairing-friendly curve.
+ * Previously known as alt_bn_128, when it had 128-bit security.
+ * Recent research shown it's weaker, the naming has been adjusted to its prime bit count.
+ * https://github.com/zcash/zcash/issues/2502
+ */
+export const bn254 = weierstrass({
+  a: BigInt(0),
+  b: BigInt(3),
+  Fp: Fp(BigInt('0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47')),
+  n: BigInt('0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001'),
+  Gx: BigInt(1),
+  Gy: BigInt(2),
+  h: BigInt(1),
+  ...getHash(sha256),
+});

src/ed25519.ts

@@ -0,0 +1,353 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+import { sha512 } from '@noble/hashes/sha512';
+import { concatBytes, randomBytes, utf8ToBytes } from '@noble/hashes/utils';
+import { twistedEdwards, ExtendedPointType } from './abstract/edwards.js';
+import { montgomery } from './abstract/montgomery.js';
+import { mod, pow2, isNegativeLE, Fp as Field } from './abstract/modular.js';
+import {
+  ensureBytes,
+  equalBytes,
+  bytesToHex,
+  bytesToNumberLE,
+  numberToBytesLE,
+  Hex,
+} from './abstract/utils.js';
+
+/**
+ * ed25519 Twisted Edwards curve with following addons:
+ * - X25519 ECDH
+ * - Ristretto cofactor elimination
+ * - Elligator hash-to-group / point indistinguishability
+ */
+
+const ED25519_P = BigInt(
+  '57896044618658097711785492504343953926634992332820282019728792003956564819949'
+);
+// √(-1) aka √(a) aka 2^((p-1)/4)
+const ED25519_SQRT_M1 = BigInt(
+  '19681161376707505956807079304988542015446066515923890162744021073123829784752'
+);
+
+// prettier-ignore
+const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _5n = BigInt(5);
+// prettier-ignore
+const _10n = BigInt(10), _20n = BigInt(20), _40n = BigInt(40), _80n = BigInt(80);
+function ed25519_pow_2_252_3(x: bigint) {
+  const P = ED25519_P;
+  const x2 = (x * x) % P;
+  const b2 = (x2 * x) % P; // x^3, 11
+  const b4 = (pow2(b2, _2n, P) * b2) % P; // x^15, 1111
+  const b5 = (pow2(b4, _1n, P) * x) % P; // x^31
+  const b10 = (pow2(b5, _5n, P) * b5) % P;
+  const b20 = (pow2(b10, _10n, P) * b10) % P;
+  const b40 = (pow2(b20, _20n, P) * b20) % P;
+  const b80 = (pow2(b40, _40n, P) * b40) % P;
+  const b160 = (pow2(b80, _80n, P) * b80) % P;
+  const b240 = (pow2(b160, _80n, P) * b80) % P;
+  const b250 = (pow2(b240, _10n, P) * b10) % P;
+  const pow_p_5_8 = (pow2(b250, _2n, P) * x) % P;
+  // ^ To pow to (p+3)/8, multiply it by x.
+  return { pow_p_5_8, b2 };
+}
+function adjustScalarBytes(bytes: Uint8Array): Uint8Array {
+  // Section 5: For X25519, in order to decode 32 random bytes as an integer scalar,
+  // set the three least significant bits of the first byte
+  bytes[0] &= 248; // 0b1111_1000
+  // and the most significant bit of the last to zero,
+  bytes[31] &= 127; // 0b0111_1111
+  // set the second most significant bit of the last byte to 1
+  bytes[31] |= 64; // 0b0100_0000
+  return bytes;
+}
+// sqrt(u/v)
+function uvRatio(u: bigint, v: bigint): { isValid: boolean; value: bigint } {
+  const P = ED25519_P;
+  const v3 = mod(v * v * v, P); // v³
+  const v7 = mod(v3 * v3 * v, P); // v⁷
+  // (p+3)/8 and (p-5)/8
+  const pow = ed25519_pow_2_252_3(u * v7).pow_p_5_8;
+  let x = mod(u * v3 * pow, P); // (uv³)(uv⁷)^(p-5)/8
+  const vx2 = mod(v * x * x, P); // vx²
+  const root1 = x; // First root candidate
+  const root2 = mod(x * ED25519_SQRT_M1, P); // Second root candidate
+  const useRoot1 = vx2 === u; // If vx² = u (mod p), x is a square root
+  const useRoot2 = vx2 === mod(-u, P); // If vx² = -u, set x <-- x * 2^((p-1)/4)
+  const noRoot = vx2 === mod(-u * ED25519_SQRT_M1, P); // There is no valid root, vx² = -u√(-1)
+  if (useRoot1) x = root1;
+  if (useRoot2 || noRoot) x = root2; // We return root2 anyway, for const-time
+  if (isNegativeLE(x, P)) x = mod(-x, P);
+  return { isValid: useRoot1 || useRoot2, value: x };
+}
+
+// Just in case
+export const ED25519_TORSION_SUBGROUP = [
+  '0100000000000000000000000000000000000000000000000000000000000000',
+  'c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac037a',
+  '0000000000000000000000000000000000000000000000000000000000000080',
+  '26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc05',
+  'ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f',
+  '26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc85',
+  '0000000000000000000000000000000000000000000000000000000000000000',
+  'c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa',
+];
+
+const Fp = Field(ED25519_P);
+
+const ED25519_DEF = {
+  // Param: a
+  a: BigInt(-1),
+  // Equal to -121665/121666 over finite field.
+  // Negative number is P - number, and division is invert(number, P)
+  d: BigInt('37095705934669439343138083508754565189542113879843219016388785533085940283555'),
+  // Finite field 𝔽p over which we'll do calculations; 2n ** 255n - 19n
+  Fp,
+  // Subgroup order: how many points ed25519 has
+  // 2n ** 252n + 27742317777372353535851937790883648493n;
+  n: BigInt('7237005577332262213973186563042994240857116359379907606001950938285454250989'),
+  // Cofactor
+  h: BigInt(8),
+  // Base point (x, y) aka generator point
+  Gx: BigInt('15112221349535400772501151409588531511454012693041857206046113283949847762202'),
+  Gy: BigInt('46316835694926478169428394003475163141307993866256225615783033603165251855960'),
+  hash: sha512,
+  randomBytes,
+  adjustScalarBytes,
+  // dom2
+  // Ratio of u to v. Allows us to combine inversion and square root. Uses algo from RFC8032 5.1.3.
+  // Constant-time, u/√v
+  uvRatio,
+  htfDefaults: {
+    DST: 'edwards25519_XMD:SHA-512_ELL2_RO_',
+    p: Fp.ORDER,
+    m: 1,
+    k: 128,
+    expand: true,
+    hash: sha512,
+  },
+  mapToCurve: (scalars: bigint[]): { x: bigint; y: bigint } => {
+    throw new Error('Not supported yet');
+    // const { x, y } = calcElligatorRistrettoMap(scalars[0]).toAffine();
+    // return { x, y };
+  },
+} as const;
+
+export const ed25519 = twistedEdwards(ED25519_DEF);
+function ed25519_domain(data: Uint8Array, ctx: Uint8Array, phflag: boolean) {
+  if (ctx.length > 255) throw new Error('Context is too big');
+  return concatBytes(
+    utf8ToBytes('SigEd25519 no Ed25519 collisions'),
+    new Uint8Array([phflag ? 1 : 0, ctx.length]),
+    ctx,
+    data
+  );
+}
+export const ed25519ctx = twistedEdwards({ ...ED25519_DEF, domain: ed25519_domain });
+export const ed25519ph = twistedEdwards({
+  ...ED25519_DEF,
+  domain: ed25519_domain,
+  preHash: sha512,
+});
+
+export const x25519 = montgomery({
+  P: ED25519_P,
+  a24: BigInt('121665'),
+  montgomeryBits: 255, // n is 253 bits
+  nByteLength: 32,
+  Gu: '0900000000000000000000000000000000000000000000000000000000000000',
+  powPminus2: (x: bigint): bigint => {
+    const P = ED25519_P;
+    // x^(p-2) aka x^(2^255-21)
+    const { pow_p_5_8, b2 } = ed25519_pow_2_252_3(x);
+    return mod(pow2(pow_p_5_8, BigInt(3), P) * b2, P);
+  },
+  adjustScalarBytes,
+});
+
+function assertRstPoint(other: unknown) {
+  if (!(other instanceof RistrettoPoint)) throw new TypeError('RistrettoPoint expected');
+}
+// √(-1) aka √(a) aka 2^((p-1)/4)
+const SQRT_M1 = BigInt(
+  '19681161376707505956807079304988542015446066515923890162744021073123829784752'
+);
+// √(ad - 1)
+const SQRT_AD_MINUS_ONE = BigInt(
+  '25063068953384623474111414158702152701244531502492656460079210482610430750235'
+);
+// 1 / √(a-d)
+const INVSQRT_A_MINUS_D = BigInt(
+  '54469307008909316920995813868745141605393597292927456921205312896311721017578'
+);
+// 1-d²
+const ONE_MINUS_D_SQ = BigInt(
+  '1159843021668779879193775521855586647937357759715417654439879720876111806838'
+);
+// (d-1)²
+const D_MINUS_ONE_SQ = BigInt(
+  '40440834346308536858101042469323190826248399146238708352240133220865137265952'
+);
+// Calculates 1/√(number)
+const invertSqrt = (number: bigint) => uvRatio(_1n, number);
+
+const MAX_255B = BigInt('0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff');
+const bytes255ToNumberLE = (bytes: Uint8Array) =>
+  ed25519.utils.mod(bytesToNumberLE(bytes) & MAX_255B);
+
+type ExtendedPoint = ExtendedPointType;
+
+// Computes Elligator map for Ristretto
+// https://ristretto.group/formulas/elligator.html
+function calcElligatorRistrettoMap(r0: bigint): ExtendedPoint {
+  const { d } = ed25519.CURVE;
+  const P = ed25519.CURVE.Fp.ORDER;
+  const { mod } = ed25519.utils;
+  const r = mod(SQRT_M1 * r0 * r0); // 1
+  const Ns = mod((r + _1n) * ONE_MINUS_D_SQ); // 2
+  let c = BigInt(-1); // 3
+  const D = mod((c - d * r) * mod(r + d)); // 4
+  let { isValid: Ns_D_is_sq, value: s } = uvRatio(Ns, D); // 5
+  let s_ = mod(s * r0); // 6
+  if (!isNegativeLE(s_, P)) s_ = mod(-s_);
+  if (!Ns_D_is_sq) s = s_; // 7
+  if (!Ns_D_is_sq) c = r; // 8
+  const Nt = mod(c * (r - _1n) * D_MINUS_ONE_SQ - D); // 9
+  const s2 = s * s;
+  const W0 = mod((s + s) * D); // 10
+  const W1 = mod(Nt * SQRT_AD_MINUS_ONE); // 11
+  const W2 = mod(_1n - s2); // 12
+  const W3 = mod(_1n + s2); // 13
+  return new ed25519.ExtendedPoint(mod(W0 * W3), mod(W2 * W1), mod(W1 * W3), mod(W0 * W2));
+}
+
+/**
+ * Each ed25519/ExtendedPoint has 8 different equivalent points. This can be
+ * a source of bugs for protocols like ring signatures. Ristretto was created to solve this.
+ * Ristretto point operates in X:Y:Z:T extended coordinates like ExtendedPoint,
+ * but it should work in its own namespace: do not combine those two.
+ * https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-ristretto255-decaf448
+ */
+export class RistrettoPoint {
+  static BASE = new RistrettoPoint(ed25519.ExtendedPoint.BASE);
+  static ZERO = new RistrettoPoint(ed25519.ExtendedPoint.ZERO);
+
+  // Private property to discourage combining ExtendedPoint + RistrettoPoint
+  // Always use Ristretto encoding/decoding instead.
+  constructor(private readonly ep: ExtendedPoint) {}
+  /**
+   * Takes uniform output of 64-bit hash function like sha512 and converts it to `RistrettoPoint`.
+   * The hash-to-group operation applies Elligator twice and adds the results.
+   * **Note:** this is one-way map, there is no conversion from point to hash.
+   * https://ristretto.group/formulas/elligator.html
+   * @param hex 64-bit output of a hash function
+   */
+  static hashToCurve(hex: Hex): RistrettoPoint {
+    hex = ensureBytes(hex, 64);
+    const r1 = bytes255ToNumberLE(hex.slice(0, 32));
+    const R1 = calcElligatorRistrettoMap(r1);
+    const r2 = bytes255ToNumberLE(hex.slice(32, 64));
+    const R2 = calcElligatorRistrettoMap(r2);
+    return new RistrettoPoint(R1.add(R2));
+  }
+
+  /**
+   * Converts ristretto-encoded string to ristretto point.
+   * https://ristretto.group/formulas/decoding.html
+   * @param hex Ristretto-encoded 32 bytes. Not every 32-byte string is valid ristretto encoding
+   */
+  static fromHex(hex: Hex): RistrettoPoint {
+    hex = ensureBytes(hex, 32);
+    const { a, d } = ed25519.CURVE;
+    const P = ed25519.CURVE.Fp.ORDER;
+    const { mod } = ed25519.utils;
+    const emsg = 'RistrettoPoint.fromHex: the hex is not valid encoding of RistrettoPoint';
+    const s = bytes255ToNumberLE(hex);
+    // 1. Check that s_bytes is the canonical encoding of a field element, or else abort.
+    // 3. Check that s is non-negative, or else abort
+    if (!equalBytes(numberToBytesLE(s, 32), hex) || isNegativeLE(s, P)) throw new Error(emsg);
+    const s2 = mod(s * s);
+    const u1 = mod(_1n + a * s2); // 4 (a is -1)
+    const u2 = mod(_1n - a * s2); // 5
+    const u1_2 = mod(u1 * u1);
+    const u2_2 = mod(u2 * u2);
+    const v = mod(a * d * u1_2 - u2_2); // 6
+    const { isValid, value: I } = invertSqrt(mod(v * u2_2)); // 7
+    const Dx = mod(I * u2); // 8
+    const Dy = mod(I * Dx * v); // 9
+    let x = mod((s + s) * Dx); // 10
+    if (isNegativeLE(x, P)) x = mod(-x); // 10
+    const y = mod(u1 * Dy); // 11
+    const t = mod(x * y); // 12
+    if (!isValid || isNegativeLE(t, P) || y === _0n) throw new Error(emsg);
+    return new RistrettoPoint(new ed25519.ExtendedPoint(x, y, _1n, t));
+  }
+
+  /**
+   * Encodes ristretto point to Uint8Array.
+   * https://ristretto.group/formulas/encoding.html
+   */
+  toRawBytes(): Uint8Array {
+    let { x, y, z, t } = this.ep;
+    const P = ed25519.CURVE.Fp.ORDER;
+    const { mod } = ed25519.utils;
+    const u1 = mod(mod(z + y) * mod(z - y)); // 1
+    const u2 = mod(x * y); // 2
+    // Square root always exists
+    const u2sq = mod(u2 * u2);
+    const { value: invsqrt } = invertSqrt(mod(u1 * u2sq)); // 3
+    const D1 = mod(invsqrt * u1); // 4
+    const D2 = mod(invsqrt * u2); // 5
+    const zInv = mod(D1 * D2 * t); // 6
+    let D: bigint; // 7
+    if (isNegativeLE(t * zInv, P)) {
+      let _x = mod(y * SQRT_M1);
+      let _y = mod(x * SQRT_M1);
+      x = _x;
+      y = _y;
+      D = mod(D1 * INVSQRT_A_MINUS_D);
+    } else {
+      D = D2; // 8
+    }
+    if (isNegativeLE(x * zInv, P)) y = mod(-y); // 9
+    let s = mod((z - y) * D); // 10 (check footer's note, no sqrt(-a))
+    if (isNegativeLE(s, P)) s = mod(-s);
+    return numberToBytesLE(s, 32); // 11
+  }
+
+  toHex(): string {
+    return bytesToHex(this.toRawBytes());
+  }
+
+  toString(): string {
+    return this.toHex();
+  }
+
+  // Compare one point to another.
+  equals(other: RistrettoPoint): boolean {
+    assertRstPoint(other);
+    const a = this.ep;
+    const b = other.ep;
+    const { mod } = ed25519.utils;
+    // (x1 * y2 == y1 * x2) | (y1 * y2 == x1 * x2)
+    const one = mod(a.x * b.y) === mod(a.y * b.x);
+    const two = mod(a.y * b.y) === mod(a.x * b.x);
+    return one || two;
+  }
+
+  add(other: RistrettoPoint): RistrettoPoint {
+    assertRstPoint(other);
+    return new RistrettoPoint(this.ep.add(other.ep));
+  }
+
+  subtract(other: RistrettoPoint): RistrettoPoint {
+    assertRstPoint(other);
+    return new RistrettoPoint(this.ep.subtract(other.ep));
+  }
+
+  multiply(scalar: number | bigint): RistrettoPoint {
+    return new RistrettoPoint(this.ep.multiply(scalar));
+  }
+
+  multiplyUnsafe(scalar: number | bigint): RistrettoPoint {
+    return new RistrettoPoint(this.ep.multiplyUnsafe(scalar));
+  }
+}

src/ed448.ts

@@ -0,0 +1,147 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+import { shake256 } from '@noble/hashes/sha3';
+import { concatBytes, randomBytes, utf8ToBytes, wrapConstructor } from '@noble/hashes/utils';
+import { twistedEdwards } from './abstract/edwards.js';
+import { mod, pow2, Fp } from './abstract/modular.js';
+import { montgomery } from './abstract/montgomery.js';
+
+/**
+ * Edwards448 (not Ed448-Goldilocks) curve with following addons:
+ * * X448 ECDH
+ * Conforms to RFC 8032 https://www.rfc-editor.org/rfc/rfc8032.html#section-5.2
+ */
+
+const shake256_114 = wrapConstructor(() => shake256.create({ dkLen: 114 }));
+const shake256_64 = wrapConstructor(() => shake256.create({ dkLen: 64 }));
+const ed448P = BigInt(
+  '726838724295606890549323807888004534353641360687318060281490199180612328166730772686396383698676545930088884461843637361053498018365439'
+);
+
+// powPminus3div4 calculates z = x^k mod p, where k = (p-3)/4.
+// Used for efficient square root calculation.
+// ((P-3)/4).toString(2) would produce bits [223x 1, 0, 222x 1]
+function ed448_pow_Pminus3div4(x: bigint): bigint {
+  const P = ed448P;
+  // prettier-ignore
+  const _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3), _11n = BigInt(11);
+  // prettier-ignore
+  const _22n = BigInt(22), _44n = BigInt(44), _88n = BigInt(88), _223n = BigInt(223);
+  const b2 = (x * x * x) % P;
+  const b3 = (b2 * b2 * x) % P;
+  const b6 = (pow2(b3, _3n, P) * b3) % P;
+  const b9 = (pow2(b6, _3n, P) * b3) % P;
+  const b11 = (pow2(b9, _2n, P) * b2) % P;
+  const b22 = (pow2(b11, _11n, P) * b11) % P;
+  const b44 = (pow2(b22, _22n, P) * b22) % P;
+  const b88 = (pow2(b44, _44n, P) * b44) % P;
+  const b176 = (pow2(b88, _88n, P) * b88) % P;
+  const b220 = (pow2(b176, _44n, P) * b44) % P;
+  const b222 = (pow2(b220, _2n, P) * b2) % P;
+  const b223 = (pow2(b222, _1n, P) * x) % P;
+  return (pow2(b223, _223n, P) * b222) % P;
+}
+
+function adjustScalarBytes(bytes: Uint8Array): Uint8Array {
+  // Section 5: Likewise, for X448, set the two least significant bits of the first byte to 0, and the most
+  // significant bit of the last byte to 1.
+  bytes[0] &= 252; // 0b11111100
+  // and the most significant bit of the last byte to 1.
+  bytes[55] |= 128; // 0b10000000
+  // NOTE: is is NOOP for 56 bytes scalars (X25519/X448)
+  bytes[56] = 0; // Byte outside of group (456 buts vs 448 bits)
+  return bytes;
+}
+
+const ED448_DEF = {
+  // Param: a
+  a: BigInt(1),
+  // -39081. Negative number is P - number
+  d: BigInt(
+    '726838724295606890549323807888004534353641360687318060281490199180612328166730772686396383698676545930088884461843637361053498018326358'
+  ),
+  // Finite field 𝔽p over which we'll do calculations; 2n ** 448n - 2n ** 224n - 1n
+  Fp: Fp(ed448P, 456),
+  // Subgroup order: how many points ed448 has; 2n**446n - 13818066809895115352007386748515426880336692474882178609894547503885n
+  n: BigInt(
+    '181709681073901722637330951972001133588410340171829515070372549795146003961539585716195755291692375963310293709091662304773755859649779'
+  ),
+  nBitLength: 456,
+  // Cofactor
+  h: BigInt(4),
+  // Base point (x, y) aka generator point
+  Gx: BigInt(
+    '224580040295924300187604334099896036246789641632564134246125461686950415467406032909029192869357953282578032075146446173674602635247710'
+  ),
+  Gy: BigInt(
+    '298819210078481492676017930443930673437544040154080242095928241372331506189835876003536878655418784733982303233503462500531545062832660'
+  ),
+  // SHAKE256(dom4(phflag,context)||x, 114)
+  hash: shake256_114,
+  randomBytes,
+  adjustScalarBytes,
+  // dom4
+  domain: (data: Uint8Array, ctx: Uint8Array, phflag: boolean) => {
+    if (ctx.length > 255) throw new Error(`Context is too big: ${ctx.length}`);
+    return concatBytes(
+      utf8ToBytes('SigEd448'),
+      new Uint8Array([phflag ? 1 : 0, ctx.length]),
+      ctx,
+      data
+    );
+  },
+
+  // Constant-time ratio of u to v. Allows to combine inversion and square root u/√v.
+  // Uses algo from RFC8032 5.1.3.
+  uvRatio: (u: bigint, v: bigint): { isValid: boolean; value: bigint } => {
+    const P = ed448P;
+    // https://datatracker.ietf.org/doc/html/rfc8032#section-5.2.3
+    // To compute the square root of (u/v), the first step is to compute the
+    //   candidate root x = (u/v)^((p+1)/4).  This can be done using the
+    // following trick, to use a single modular powering for both the
+    // inversion of v and the square root:
+    // x = (u/v)^((p+1)/4)   = u³v(u⁵v³)^((p-3)/4)   (mod p)
+    const u2v = mod(u * u * v, P); // u²v
+    const u3v = mod(u2v * u, P); // u³v
+    const u5v3 = mod(u3v * u2v * v, P); // u⁵v³
+    const root = ed448_pow_Pminus3div4(u5v3);
+    const x = mod(u3v * root, P);
+    // Verify that root is exists
+    const x2 = mod(x * x, P); // x²
+    // If vx² = u, the recovered x-coordinate is x.  Otherwise, no
+    // square root exists, and the decoding fails.
+    return { isValid: mod(x2 * v, P) === u, value: x };
+  },
+} as const;
+
+export const ed448 = twistedEdwards(ED448_DEF);
+// NOTE: there is no ed448ctx, since ed448 supports ctx by default
+export const ed448ph = twistedEdwards({ ...ED448_DEF, preHash: shake256_64 });
+
+export const x448 = montgomery({
+  a24: BigInt(39081),
+  montgomeryBits: 448,
+  nByteLength: 57,
+  P: ed448P,
+  Gu: '0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000',
+  powPminus2: (x: bigint): bigint => {
+    const P = ed448P;
+    const Pminus3div4 = ed448_pow_Pminus3div4(x);
+    const Pminus3 = pow2(Pminus3div4, BigInt(2), P);
+    return mod(Pminus3 * x, P); // Pminus3 * x = Pminus2
+  },
+  adjustScalarBytes,
+  // The 4-isogeny maps between the Montgomery curve and this Edwards
+  // curve are:
+  //   (u, v) = (y^2/x^2, (2 - x^2 - y^2)*y/x^3)
+  //   (x, y) = (4*v*(u^2 - 1)/(u^4 - 2*u^2 + 4*v^2 + 1),
+  //             -(u^5 - 2*u^3 - 4*u*v^2 + u)/
+  //             (u^5 - 2*u^2*v^2 - 2*u^3 - 2*v^2 + u))
+  // xyToU: (p: PointType) => {
+  //   const P = ed448P;
+  //   const { x, y } = p;
+  //   if (x === _0n) throw new Error(`Point with x=0 doesn't have mapping`);
+  //   const invX = invert(x * x, P); // x^2
+  //   const u = mod(y * y * invX, P); // (y^2/x^2)
+  //   return numberToBytesLE(u, 56);
+  // },
+});

src/index.ts

@@ -0,0 +1 @@
+throw new Error('Incorrect usage. Import submodules instead');

src/jubjub.ts

@@ -0,0 +1,57 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+import { sha256 } from '@noble/hashes/sha256';
+import { concatBytes, randomBytes, utf8ToBytes } from '@noble/hashes/utils';
+import { twistedEdwards } from './abstract/edwards.js';
+import { blake2s } from '@noble/hashes/blake2s';
+import { Fp } from './abstract/modular.js';
+
+/**
+ * jubjub Twisted Edwards curve.
+ * https://neuromancer.sk/std/other/JubJub
+ */
+
+export const jubjub = twistedEdwards({
+  // Params: a, d
+  a: BigInt('0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000000'),
+  d: BigInt('0x2a9318e74bfa2b48f5fd9207e6bd7fd4292d7f6d37579d2601065fd6d6343eb1'),
+  // Finite field 𝔽p over which we'll do calculations
+  Fp: Fp(BigInt('0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001')),
+  // Subgroup order: how many points ed25519 has
+  // 2n ** 252n + 27742317777372353535851937790883648493n;
+  n: BigInt('0xe7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7'),
+  // Cofactor
+  h: BigInt(8),
+  // Base point (x, y) aka generator point
+  Gx: BigInt('0x11dafe5d23e1218086a365b99fbf3d3be72f6afd7d1f72623e6b071492d1122b'),
+  Gy: BigInt('0x1d523cf1ddab1a1793132e78c866c0c33e26ba5cc220fed7cc3f870e59d292aa'),
+  hash: sha256,
+  randomBytes,
+} as const);
+
+const GH_FIRST_BLOCK = utf8ToBytes(
+  '096b36a5804bfacef1691e173c366a47ff5ba84a44f26ddd7e8d9f79d5b42df0'
+);
+
+// Returns point at JubJub curve which is prime order and not zero
+export function groupHash(tag: Uint8Array, personalization: Uint8Array) {
+  const h = blake2s.create({ personalization, dkLen: 32 });
+  h.update(GH_FIRST_BLOCK);
+  h.update(tag);
+  // NOTE: returns ExtendedPoint, in case it will be multiplied later
+  let p = jubjub.ExtendedPoint.fromAffine(jubjub.Point.fromHex(h.digest()));
+  // NOTE: cannot replace with isSmallOrder, returns Point*8
+  p = p.multiply(jubjub.CURVE.h);
+  if (p.equals(jubjub.ExtendedPoint.ZERO)) throw new Error('Point has small order');
+  return p;
+}
+
+export function findGroupHash(m: Uint8Array, personalization: Uint8Array) {
+  const tag = concatBytes(m, new Uint8Array([0]));
+  for (let i = 0; i < 256; i++) {
+    tag[tag.length - 1] = i;
+    try {
+      return groupHash(tag, personalization);
+    } catch (e) {}
+  }
+  throw new Error('findGroupHash tag overflow');
+}

src/modular.ts

@@ -1,146 +0,0 @@
-/*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-const _0n = BigInt(0);
-const _1n = BigInt(1);
-const _2n = BigInt(2);
-const _3n = BigInt(3);
-const _4n = BigInt(4);
-const _5n = BigInt(5);
-const _8n = BigInt(8);
-
-// Calculates a modulo b
-export function mod(a: bigint, b: bigint): bigint {
-  const result = a % b;
-  return result >= _0n ? result : b + result;
-}
-/**
- * Efficiently exponentiate num to power and do modular division.
- * @example
- * powMod(2n, 6n, 11n) // 64n % 11n == 9n
- */
-export function pow(num: bigint, power: bigint, modulo: bigint): bigint {
-  if (modulo <= _0n || power < _0n) throw new Error('Expected power/modulo > 0');
-  if (modulo === _1n) return _0n;
-  let res = _1n;
-  while (power > _0n) {
-    if (power & _1n) res = (res * num) % modulo;
-    num = (num * num) % modulo;
-    power >>= _1n;
-  }
-  return res;
-}
-
-// Does x ^ (2 ^ power) mod p. pow2(30, 4) == 30 ^ (2 ^ 4)
-export function pow2(x: bigint, power: bigint, modulo: bigint): bigint {
-  let res = x;
-  while (power-- > _0n) {
-    res *= res;
-    res %= modulo;
-  }
-  return res;
-}
-
-// Inverses number over modulo
-export function invert(number: bigint, modulo: bigint): bigint {
-  if (number === _0n || modulo <= _0n) {
-    throw new Error(`invert: expected positive integers, got n=${number} mod=${modulo}`);
-  }
-  // Eucledian GCD https://brilliant.org/wiki/extended-euclidean-algorithm/
-  let a = mod(number, modulo);
-  let b = modulo;
-  // prettier-ignore
-  let x = _0n, y = _1n, u = _1n, v = _0n;
-  while (a !== _0n) {
-    const q = b / a;
-    const r = b % a;
-    const m = x - u * q;
-    const n = y - v * q;
-    // prettier-ignore
-    b = a, a = r, x = u, y = v, u = m, v = n;
-  }
-  const gcd = b;
-  if (gcd !== _1n) throw new Error('invert: does not exist');
-  return mod(x, modulo);
-}
-
-/**
- * Takes a list of numbers, efficiently inverts all of them.
- * @param nums list of bigints
- * @param p modulo
- * @returns list of inverted bigints
- * @example
- * invertBatch([1n, 2n, 4n], 21n);
- * // => [1n, 11n, 16n]
- */
-export function invertBatch(nums: bigint[], modulo: bigint): bigint[] {
-  const scratch = new Array(nums.length);
-  // Walk from first to last, multiply them by each other MOD p
-  const lastMultiplied = nums.reduce((acc, num, i) => {
-    if (num === _0n) return acc;
-    scratch[i] = acc;
-    return mod(acc * num, modulo);
-  }, _1n);
-  // Invert last element
-  const inverted = invert(lastMultiplied, modulo);
-  // Walk from last to first, multiply them by inverted each other MOD p
-  nums.reduceRight((acc, num, i) => {
-    if (num === _0n) return acc;
-    scratch[i] = mod(acc * scratch[i], modulo);
-    return mod(acc * num, modulo);
-  }, inverted);
-  return scratch;
-}
-
-// Calculates Legendre symbol: num^((P-1)/2)
-export function legendre(num: bigint, fieldPrime: bigint): bigint {
-  return pow(num, (fieldPrime - _1n) / _2n, fieldPrime);
-}
-
-/**
- * Calculates square root of a number in a finite field.
- * Used to calculate y - the square root of y².
- */
-export function sqrt(number: bigint, modulo: bigint): bigint {
-  const n = number;
-  const P = modulo;
-  const p1div4 = (P + _1n) / _4n;
-
-  // P = 3 (mod 4)
-  // sqrt n = n^((P+1)/4)
-  if (P % _4n === _3n) return pow(n, p1div4, P);
-  // P = 5 (mod 8)
-  if (P % _8n === _5n) {
-    const n2 = mod(n * _2n, P);
-    const v = pow(n2, (P - _5n) / _8n, P);
-    const nv = mod(n * v, P);
-    const i = mod(_2n * nv * v, P);
-    const r = mod(nv * (i - _1n), P);
-    return r;
-  }
-
-  // Other cases: Tonelli-Shanks algorithm
-  if (legendre(n, P) !== _1n) throw new Error('Cannot find square root');
-  let q: bigint, s: number, z: bigint;
-  for (q = P - _1n, s = 0; q % _2n === _0n; q /= _2n, s++);
-  if (s === 1) return pow(n, p1div4, P);
-  for (z = _2n; z < P && legendre(z, P) !== P - _1n; z++);
-
-  let c = pow(z, q, P);
-  let r = pow(n, (q + _1n) / _2n, P);
-  let t = pow(n, q, P);
-
-  let t2 = _0n;
-  while (mod(t - _1n, P) !== _0n) {
-    t2 = mod(t * t, P);
-    let i;
-    for (i = 1; i < s; i++) {
-      if (mod(t2 - _1n, P) === _0n) break;
-      t2 = mod(t2 * t2, P);
-    }
-    let b = pow(c, BigInt(1 << (s - i - 1)), P);
-    r = mod(r * b, P);
-    c = mod(b * b, P);
-    t = mod(t * c, P);
-    s = i;
-  }
-  return r;
-}

src/p192.ts

@@ -0,0 +1,25 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+import { createCurve } from './_shortw_utils.js';
+import { sha256 } from '@noble/hashes/sha256';
+import { Fp } from './abstract/modular.js';
+
+// NIST secp192r1 aka P192
+// https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/secg/secp192r1
+export const P192 = createCurve(
+  {
+    // Params: a, b
+    a: BigInt('0xfffffffffffffffffffffffffffffffefffffffffffffffc'),
+    b: BigInt('0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1'),
+    // Field over which we'll do calculations; 2n ** 192n - 2n ** 64n - 1n
+    Fp: Fp(BigInt('0xfffffffffffffffffffffffffffffffeffffffffffffffff')),
+    // Curve order, total count of valid points in the field.
+    n: BigInt('0xffffffffffffffffffffffff99def836146bc9b1b4d22831'),
+    // Base point (x, y) aka generator point
+    Gx: BigInt('0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012'),
+    Gy: BigInt('0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811'),
+    h: BigInt(1),
+    lowS: false,
+  } as const,
+  sha256
+);
+export const secp192r1 = P192;

src/p224.ts

@@ -0,0 +1,25 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+import { createCurve } from './_shortw_utils.js';
+import { sha224 } from '@noble/hashes/sha256';
+import { Fp } from './abstract/modular.js';
+
+// NIST secp224r1 aka P224
+// https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-224
+export const P224 = createCurve(
+  {
+    // Params: a, b
+    a: BigInt('0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe'),
+    b: BigInt('0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4'),
+    // Field over which we'll do calculations; 2n**224n - 2n**96n + 1n
+    Fp: Fp(BigInt('0xffffffffffffffffffffffffffffffff000000000000000000000001')),
+    // Curve order, total count of valid points in the field
+    n: BigInt('0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d'),
+    // Base point (x, y) aka generator point
+    Gx: BigInt('0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21'),
+    Gy: BigInt('0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34'),
+    h: BigInt(1),
+    lowS: false,
+  } as const,
+  sha224
+);
+export const secp224r1 = P224;

src/p256.ts

@@ -0,0 +1,46 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+import { createCurve } from './_shortw_utils.js';
+import { sha256 } from '@noble/hashes/sha256';
+import { Fp as Field } from './abstract/modular.js';
+import { mapToCurveSimpleSWU } from './abstract/weierstrass.js';
+
+// NIST secp256r1 aka P256
+// https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-256
+
+// Field over which we'll do calculations; 2n**224n * (2n**32n-1n) + 2n**192n + 2n**96n-1n
+const Fp = Field(BigInt('0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff'));
+const CURVE_A = Fp.create(BigInt('-3'));
+const CURVE_B = BigInt('0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b');
+
+const mapSWU = mapToCurveSimpleSWU(Fp, {
+  A: CURVE_A,
+  B: CURVE_B,
+  Z: Fp.create(BigInt('-10')),
+});
+
+export const P256 = createCurve(
+  {
+    // Params: a, b
+    a: CURVE_A,
+    b: CURVE_B,
+    Fp,
+    // Curve order, total count of valid points in the field
+    n: BigInt('0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551'),
+    // Base point (x, y) aka generator point
+    Gx: BigInt('0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296'),
+    Gy: BigInt('0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5'),
+    h: BigInt(1),
+    lowS: false,
+    mapToCurve: (scalars: bigint[]) => mapSWU(scalars[0]),
+    htfDefaults: {
+      DST: 'P256_XMD:SHA-256_SSWU_RO_',
+      p: Fp.ORDER,
+      m: 1,
+      k: 128,
+      expand: true,
+      hash: sha256,
+    },
+  } as const,
+  sha256
+);
+export const secp256r1 = P256;

src/p384.ts

@@ -0,0 +1,50 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+import { createCurve } from './_shortw_utils.js';
+import { sha384 } from '@noble/hashes/sha512';
+import { Fp as Field } from './abstract/modular.js';
+import { mapToCurveSimpleSWU } from './abstract/weierstrass.js';
+
+// NIST secp384r1 aka P384
+// https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-384
+
+// Field over which we'll do calculations. 2n**384n - 2n**128n - 2n**96n + 2n**32n - 1n
+// prettier-ignore
+const P = BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff');
+const Fp = Field(P);
+const CURVE_A = Fp.create(BigInt('-3'));
+// prettier-ignore
+const CURVE_B = BigInt('0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef');
+
+const mapSWU = mapToCurveSimpleSWU(Fp, {
+  A: CURVE_A,
+  B: CURVE_B,
+  Z: Fp.create(BigInt('-12')),
+});
+
+// prettier-ignore
+export const P384 = createCurve({
+    // Params: a, b
+    a: CURVE_A,
+    b: CURVE_B,
+    // Field over which we'll do calculations. 2n**384n - 2n**128n - 2n**96n + 2n**32n - 1n
+    Fp,
+    // Curve order, total count of valid points in the field.
+    n: BigInt('0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973'),
+    // Base point (x, y) aka generator point
+    Gx: BigInt('0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7'),
+    Gy: BigInt('0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f'),
+    h: BigInt(1),
+    lowS: false,
+    mapToCurve: (scalars: bigint[]) => mapSWU(scalars[0]),
+    htfDefaults: {
+      DST: 'P384_XMD:SHA-384_SSWU_RO_',
+      p: Fp.ORDER,
+      m: 1,
+      k: 192,
+      expand: true,
+      hash: sha384,
+    },
+  } as const,
+  sha384
+);
+export const secp384r1 = P384;

src/p521.ts

@@ -0,0 +1,61 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+import { createCurve } from './_shortw_utils.js';
+import { sha512 } from '@noble/hashes/sha512';
+import { bytesToHex, PrivKey } from './abstract/utils.js';
+import { Fp as Field } from './abstract/modular.js';
+import { mapToCurveSimpleSWU } from './abstract/weierstrass.js';
+
+// NIST secp521r1 aka P521
+// Note that it's 521, which differs from 512 of its hash function.
+// https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-521
+
+// Field over which we'll do calculations; 2n**521n - 1n
+// prettier-ignore
+const P = BigInt('0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff');
+const Fp = Field(P);
+
+const CURVE_A = Fp.create(BigInt('-3'));
+// prettier-ignore
+const CURVE_B = BigInt('0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00');
+
+const mapSWU = mapToCurveSimpleSWU(Fp, {
+  A: CURVE_A,
+  B: CURVE_B,
+  Z: Fp.create(BigInt('-4')),
+});
+
+// prettier-ignore
+export const P521 = createCurve({
+  // Params: a, b
+  a: CURVE_A,
+  b: CURVE_B,
+  Fp,
+  // Curve order, total count of valid points in the field
+  n: BigInt('0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409'),
+  // Base point (x, y) aka generator point
+  Gx: BigInt('0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66'),
+  Gy: BigInt('0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650'),
+  h: BigInt(1),
+  lowS: false,
+  // P521 keys could be 130, 131, 132 bytes - which doesn't play nicely.
+  // We ensure all keys are 132 bytes.
+  // Does not replace validation; invalid keys would still be rejected.
+  normalizePrivateKey(key: PrivKey) {
+    if (typeof key === 'bigint') return key;
+    if (key instanceof Uint8Array) key = bytesToHex(key);
+    if (typeof key !== 'string' || !([130, 131, 132].includes(key.length))) {
+      throw new Error('Invalid key');
+    }
+    return key.padStart(66 * 2, '0');
+  },
+  mapToCurve: (scalars: bigint[]) => mapSWU(scalars[0]),
+  htfDefaults: {
+    DST: 'P521_XMD:SHA-512_SSWU_RO_',
+    p: Fp.ORDER,
+    m: 1,
+    k: 256,
+    expand: true,
+    hash: sha512,
+  },
+} as const, sha512);
+export const secp521r1 = P521;

src/pasta.ts

@@ -0,0 +1,31 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+import { sha256 } from '@noble/hashes/sha256';
+import { weierstrass } from './abstract/weierstrass.js';
+import { getHash } from './_shortw_utils.js';
+import * as mod from './abstract/modular.js';
+
+export const p = BigInt('0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001');
+export const q = BigInt('0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001');
+
+// https://neuromancer.sk/std/other/Pallas
+export const pallas = weierstrass({
+  a: BigInt(0),
+  b: BigInt(5),
+  Fp: mod.Fp(p),
+  n: q,
+  Gx: mod.mod(BigInt(-1), p),
+  Gy: BigInt(2),
+  h: BigInt(1),
+  ...getHash(sha256),
+});
+// https://neuromancer.sk/std/other/Vesta
+export const vesta = weierstrass({
+  a: BigInt(0),
+  b: BigInt(5),
+  Fp: mod.Fp(q),
+  n: p,
+  Gx: mod.mod(BigInt(-1), q),
+  Gy: BigInt(2),
+  h: BigInt(1),
+  ...getHash(sha256),
+});

src/secp256k1.ts

@@ -0,0 +1,317 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+import { sha256 } from '@noble/hashes/sha256';
+import { Fp as Field, mod, pow2 } from './abstract/modular.js';
+import { createCurve } from './_shortw_utils.js';
+import { PointType, mapToCurveSimpleSWU } from './abstract/weierstrass.js';
+import {
+  ensureBytes,
+  concatBytes,
+  Hex,
+  hexToBytes,
+  bytesToNumberBE,
+  PrivKey,
+} from './abstract/utils.js';
+import { randomBytes } from '@noble/hashes/utils';
+import { isogenyMap } from './abstract/hash-to-curve.js';
+
+/**
+ * secp256k1 belongs to Koblitz curves: it has
+ * efficiently computable Frobenius endomorphism.
+ * Endomorphism improves efficiency:
+ * Uses 2x less RAM, speeds up precomputation by 2x and ECDH / sign key recovery by 20%.
+ * Should always be used for Projective's double-and-add multiplication.
+ * For affines cached multiplication, it trades off 1/2 init time & 1/3 ram for 20% perf hit.
+ * https://gist.github.com/paulmillr/eb670806793e84df628a7c434a873066
+ */
+
+const secp256k1P = BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f');
+const secp256k1N = BigInt('0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141');
+const _1n = BigInt(1);
+const _2n = BigInt(2);
+const divNearest = (a: bigint, b: bigint) => (a + b / _2n) / b;
+
+/**
+ * Allows to compute square root √y 2x faster.
+ * To calculate √y, we need to exponentiate it to a very big number:
+ * `y² = x³ + ax + b; y = y² ^ (p+1)/4`
+ * We are unwrapping the loop and multiplying it bit-by-bit.
+ * (P+1n/4n).toString(2) would produce bits [223x 1, 0, 22x 1, 4x 0, 11, 00]
+ */
+function sqrtMod(y: bigint): bigint {
+  const P = secp256k1P;
+  // prettier-ignore
+  const _3n = BigInt(3), _6n = BigInt(6), _11n = BigInt(11), _22n = BigInt(22);
+  // prettier-ignore
+  const _23n = BigInt(23), _44n = BigInt(44), _88n = BigInt(88);
+  const b2 = (y * y * y) % P; // x^3, 11
+  const b3 = (b2 * b2 * y) % P; // x^7
+  const b6 = (pow2(b3, _3n, P) * b3) % P;
+  const b9 = (pow2(b6, _3n, P) * b3) % P;
+  const b11 = (pow2(b9, _2n, P) * b2) % P;
+  const b22 = (pow2(b11, _11n, P) * b11) % P;
+  const b44 = (pow2(b22, _22n, P) * b22) % P;
+  const b88 = (pow2(b44, _44n, P) * b44) % P;
+  const b176 = (pow2(b88, _88n, P) * b88) % P;
+  const b220 = (pow2(b176, _44n, P) * b44) % P;
+  const b223 = (pow2(b220, _3n, P) * b3) % P;
+  const t1 = (pow2(b223, _23n, P) * b22) % P;
+  const t2 = (pow2(t1, _6n, P) * b2) % P;
+  return pow2(t2, _2n, P);
+}
+
+const Fp = Field(secp256k1P, undefined, undefined, { sqrt: sqrtMod });
+type Fp = bigint;
+
+const isoMap = isogenyMap(
+  Fp,
+  [
+    // xNum
+    [
+      '0x8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa8c7',
+      '0x7d3d4c80bc321d5b9f315cea7fd44c5d595d2fc0bf63b92dfff1044f17c6581',
+      '0x534c328d23f234e6e2a413deca25caece4506144037c40314ecbd0b53d9dd262',
+      '0x8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa88c',
+    ],
+    // xDen
+    [
+      '0xd35771193d94918a9ca34ccbb7b640dd86cd409542f8487d9fe6b745781eb49b',
+      '0xedadc6f64383dc1df7c4b2d51b54225406d36b641f5e41bbc52a56612a8c6d14',
+      '0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1
+    ],
+    // yNum
+    [
+      '0x4bda12f684bda12f684bda12f684bda12f684bda12f684bda12f684b8e38e23c',
+      '0xc75e0c32d5cb7c0fa9d0a54b12a0a6d5647ab046d686da6fdffc90fc201d71a3',
+      '0x29a6194691f91a73715209ef6512e576722830a201be2018a765e85a9ecee931',
+      '0x2f684bda12f684bda12f684bda12f684bda12f684bda12f684bda12f38e38d84',
+    ],
+    // yDen
+    [
+      '0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffff93b',
+      '0x7a06534bb8bdb49fd5e9e6632722c2989467c1bfc8e8d978dfb425d2685c2573',
+      '0x6484aa716545ca2cf3a70c3fa8fe337e0a3d21162f0d6299a7bf8192bfd2a76f',
+      '0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1
+    ],
+  ].map((i) => i.map((j) => BigInt(j))) as [Fp[], Fp[], Fp[], Fp[]]
+);
+
+const mapSWU = mapToCurveSimpleSWU(Fp, {
+  A: BigInt('0x3f8731abdd661adca08a5558f0f5d272e953d363cb6f0e5d405447c01a444533'),
+  B: BigInt('1771'),
+  Z: Fp.create(BigInt('-11')),
+});
+
+export const secp256k1 = createCurve(
+  {
+    // Params: a, b
+    // Seem to be rigid https://bitcointalk.org/index.php?topic=289795.msg3183975#msg3183975
+    a: BigInt(0),
+    b: BigInt(7),
+    // Field over which we'll do calculations;
+    // 2n**256n - 2n**32n - 2n**9n - 2n**8n - 2n**7n - 2n**6n - 2n**4n - 1n
+    Fp,
+    // Curve order, total count of valid points in the field
+    n: secp256k1N,
+    // Base point (x, y) aka generator point
+    Gx: BigInt('55066263022277343669578718895168534326250603453777594175500187360389116729240'),
+    Gy: BigInt('32670510020758816978083085130507043184471273380659243275938904335757337482424'),
+    h: BigInt(1),
+    // Alllow only low-S signatures by default in sign() and verify()
+    lowS: true,
+    endo: {
+      // Params taken from https://gist.github.com/paulmillr/eb670806793e84df628a7c434a873066
+      beta: BigInt('0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee'),
+      splitScalar: (k: bigint) => {
+        const n = secp256k1N;
+        const a1 = BigInt('0x3086d221a7d46bcde86c90e49284eb15');
+        const b1 = -_1n * BigInt('0xe4437ed6010e88286f547fa90abfe4c3');
+        const a2 = BigInt('0x114ca50f7a8e2f3f657c1108d9d44cfd8');
+        const b2 = a1;
+        const POW_2_128 = BigInt('0x100000000000000000000000000000000');
+
+        const c1 = divNearest(b2 * k, n);
+        const c2 = divNearest(-b1 * k, n);
+        let k1 = mod(k - c1 * a1 - c2 * a2, n);
+        let k2 = mod(-c1 * b1 - c2 * b2, n);
+        const k1neg = k1 > POW_2_128;
+        const k2neg = k2 > POW_2_128;
+        if (k1neg) k1 = n - k1;
+        if (k2neg) k2 = n - k2;
+        if (k1 > POW_2_128 || k2 > POW_2_128) {
+          throw new Error('splitScalar: Endomorphism failed, k=' + k);
+        }
+        return { k1neg, k1, k2neg, k2 };
+      },
+    },
+    mapToCurve: (scalars: bigint[]) => {
+      const { x, y } = mapSWU(Fp.create(scalars[0]));
+      return isoMap(x, y);
+    },
+    htfDefaults: {
+      DST: 'secp256k1_XMD:SHA-256_SSWU_RO_',
+      p: Fp.ORDER,
+      m: 1,
+      k: 128,
+      expand: true,
+      hash: sha256,
+    },
+  },
+  sha256
+);
+
+// Schnorr
+const _0n = BigInt(0);
+const numTo32b = secp256k1.utils._bigintToBytes;
+const numTo32bStr = secp256k1.utils._bigintToString;
+const normalizePrivateKey = secp256k1.utils._normalizePrivateKey;
+
+// TODO: export?
+function normalizePublicKey(publicKey: Hex | PointType<bigint>): PointType<bigint> {
+  if (publicKey instanceof secp256k1.Point) {
+    publicKey.assertValidity();
+    return publicKey;
+  } else {
+    const bytes = ensureBytes(publicKey);
+    // Schnorr is 32 bytes
+    if (bytes.length === 32) {
+      const x = bytesToNumberBE(bytes);
+      if (!isValidFieldElement(x)) throw new Error('Point is not on curve');
+      const y2 = secp256k1.utils._weierstrassEquation(x); // y² = x³ + ax + b
+      let y = sqrtMod(y2); // y = y² ^ (p+1)/4
+      const isYOdd = (y & _1n) === _1n;
+      // Schnorr
+      if (isYOdd) y = secp256k1.CURVE.Fp.negate(y);
+      const point = new secp256k1.Point(x, y);
+      point.assertValidity();
+      return point;
+    }
+    // Do we need that in schnorr at all?
+    return secp256k1.Point.fromHex(publicKey);
+  }
+}
+
+const isWithinCurveOrder = secp256k1.utils._isWithinCurveOrder;
+const isValidFieldElement = secp256k1.utils._isValidFieldElement;
+
+const TAGS = {
+  challenge: 'BIP0340/challenge',
+  aux: 'BIP0340/aux',
+  nonce: 'BIP0340/nonce',
+} as const;
+
+/** An object mapping tags to their tagged hash prefix of [SHA256(tag) | SHA256(tag)] */
+const TAGGED_HASH_PREFIXES: { [tag: string]: Uint8Array } = {};
+export function taggedHash(tag: string, ...messages: Uint8Array[]): Uint8Array {
+  let tagP = TAGGED_HASH_PREFIXES[tag];
+  if (tagP === undefined) {
+    const tagH = sha256(Uint8Array.from(tag, (c) => c.charCodeAt(0)));
+    tagP = concatBytes(tagH, tagH);
+    TAGGED_HASH_PREFIXES[tag] = tagP;
+  }
+  return sha256(concatBytes(tagP, ...messages));
+}
+
+const toRawX = (point: PointType<bigint>) => point.toRawBytes(true).slice(1);
+
+// Schnorr signatures are superior to ECDSA from above.
+// Below is Schnorr-specific code as per BIP0340.
+function schnorrChallengeFinalize(ch: Uint8Array): bigint {
+  return mod(bytesToNumberBE(ch), secp256k1.CURVE.n);
+}
+// Do we need this at all for Schnorr?
+class SchnorrSignature {
+  constructor(readonly r: bigint, readonly s: bigint) {
+    this.assertValidity();
+  }
+  static fromHex(hex: Hex) {
+    const bytes = ensureBytes(hex);
+    if (bytes.length !== 64)
+      throw new TypeError(`SchnorrSignature.fromHex: expected 64 bytes, not ${bytes.length}`);
+    const r = bytesToNumberBE(bytes.subarray(0, 32));
+    const s = bytesToNumberBE(bytes.subarray(32, 64));
+    return new SchnorrSignature(r, s);
+  }
+  assertValidity() {
+    const { r, s } = this;
+    if (!isValidFieldElement(r) || !isWithinCurveOrder(s)) throw new Error('Invalid signature');
+  }
+  toHex(): string {
+    return numTo32bStr(this.r) + numTo32bStr(this.s);
+  }
+  toRawBytes(): Uint8Array {
+    return hexToBytes(this.toHex());
+  }
+}
+
+function schnorrGetScalar(priv: bigint) {
+  const point = secp256k1.Point.fromPrivateKey(priv);
+  const scalar = point.hasEvenY() ? priv : secp256k1.CURVE.n - priv;
+  return { point, scalar, x: toRawX(point) };
+}
+/**
+ * Synchronously creates Schnorr signature. Improved security: verifies itself before
+ * producing an output.
+ * @param msg message (not message hash)
+ * @param privateKey private key
+ * @param auxRand random bytes that would be added to k. Bad RNG won't break it.
+ */
+function schnorrSign(
+  message: Hex,
+  privateKey: PrivKey,
+  auxRand: Hex = randomBytes(32)
+): Uint8Array {
+  if (message == null) throw new TypeError(`sign: Expected valid message, not "${message}"`);
+  const m = ensureBytes(message);
+  // checks for isWithinCurveOrder
+  const { x: px, scalar: d } = schnorrGetScalar(normalizePrivateKey(privateKey));
+  const rand = ensureBytes(auxRand);
+  if (rand.length !== 32) throw new TypeError('sign: Expected 32 bytes of aux randomness');
+  const tag = taggedHash;
+  const t0h = tag(TAGS.aux, rand);
+  const t = numTo32b(d ^ bytesToNumberBE(t0h));
+  const k0h = tag(TAGS.nonce, t, px, m);
+  const k0 = mod(bytesToNumberBE(k0h), secp256k1.CURVE.n);
+  if (k0 === _0n) throw new Error('sign: Creation of signature failed. k is zero');
+  const { point: R, x: rx, scalar: k } = schnorrGetScalar(k0);
+  const e = schnorrChallengeFinalize(tag(TAGS.challenge, rx, px, m));
+  const sig = new SchnorrSignature(R.x, mod(k + e * d, secp256k1.CURVE.n)).toRawBytes();
+  if (!schnorrVerify(sig, m, px)) throw new Error('sign: Invalid signature produced');
+  return sig;
+}
+
+/**
+ * Verifies Schnorr signature synchronously.
+ */
+function schnorrVerify(signature: Hex, message: Hex, publicKey: Hex): boolean {
+  try {
+    const raw = signature instanceof SchnorrSignature;
+    const sig: SchnorrSignature = raw ? signature : SchnorrSignature.fromHex(signature);
+    if (raw) sig.assertValidity(); // just in case
+
+    const { r, s } = sig;
+    const m = ensureBytes(message);
+    const P = normalizePublicKey(publicKey);
+    const e = schnorrChallengeFinalize(taggedHash(TAGS.challenge, numTo32b(r), toRawX(P), m));
+    // Finalize
+    // R = s⋅G - e⋅P
+    // -eP == (n-e)P
+    const R = secp256k1.Point.BASE.multiplyAndAddUnsafe(
+      P,
+      normalizePrivateKey(s),
+      mod(-e, secp256k1.CURVE.n)
+    );
+    if (!R || !R.hasEvenY() || R.x !== r) return false;
+    return true;
+  } catch (error) {
+    return false;
+  }
+}
+
+export const schnorr = {
+  Signature: SchnorrSignature,
+  // Schnorr's pubkey is just `x` of Point (BIP340)
+  getPublicKey: (privateKey: PrivKey): Uint8Array =>
+    toRawX(secp256k1.Point.fromPrivateKey(privateKey)),
+  sign: schnorrSign,
+  verify: schnorrVerify,
+};

src/stark.ts

@@ -1,35 +1,33 @@
-/*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
 import { keccak_256 } from '@noble/hashes/sha3';
 import { sha256 } from '@noble/hashes/sha256';
-import { hmac } from '@noble/hashes/hmac';
-import { concatBytes, randomBytes } from '@noble/hashes/utils';
-import { weierstrass, CHash, JacobianPointType } from '@noble/curves/shortw';
-import * as cutils from '@noble/curves/utils';
+import { weierstrass, ProjectivePointType } from './abstract/weierstrass.js';
+import * as cutils from './abstract/utils.js';
+import { Fp } from './abstract/modular.js';
+import { getHash } from './_shortw_utils.js';
 
-function getHash(hash: CHash) {
-  return {
-    hash,
-    hmac: (key: Uint8Array, ...msgs: Uint8Array[]) => hmac(hash, key, concatBytes(...msgs)),
-    randomBytes,
-  };
-}
-
-const CURVE_N = 3618502788666131213697322783095070105526743751716087489154079457884512865583n;
-const nBitLength = 252;
+type ProjectivePoint = ProjectivePointType<bigint>;
+// Stark-friendly elliptic curve
 // https://docs.starkware.co/starkex/stark-curve.html
+
+const CURVE_N = BigInt(
+  '3618502788666131213697322783095070105526743751716087489154079457884512865583'
+);
+const nBitLength = 252;
 export const starkCurve = weierstrass({
   // Params: a, b
-  a: 1n,
-  b: 3141592653589793238462643383279502884197169399375105820974944592307816406665n,
-  // Field over which we'll do calculations. Verify with:
-  // NOTE: there is no efficient sqrt for field (P%4==1)
-  P: 2n ** 251n + 17n * 2n ** 192n + 1n,
-  // Curve order, total count of valid points in the field. Verify with:
+  a: BigInt(1),
+  b: BigInt('3141592653589793238462643383279502884197169399375105820974944592307816406665'),
+  // Field over which we'll do calculations; 2n**251n + 17n * 2n**192n + 1n
+  // There is no efficient sqrt for field (P%4==1)
+  Fp: Fp(BigInt('0x800000000000011000000000000000000000000000000000000000000000001')),
+  // Curve order, total count of valid points in the field.
   n: CURVE_N,
   nBitLength: nBitLength, // len(bin(N).replace('0b',''))
   // Base point (x, y) aka generator point
-  Gx: 874739451078007766457464989774322083649278607533249481151382481072868806602n,
-  Gy: 152666792071518830868575557812948353041420400780739481342941381225525861407n,
+  Gx: BigInt('874739451078007766457464989774322083649278607533249481151382481072868806602'),
+  Gy: BigInt('152666792071518830868575557812948353041420400780739481342941381225525861407'),
+  h: BigInt(1),
   // Default options
   lowS: false,
   ...getHash(sha256),
@@ -89,23 +87,34 @@ function ensureBytes0x(hex: Hex): Uint8Array {
   return hex instanceof Uint8Array ? Uint8Array.from(hex) : hexToBytes0x(hex);
 }
 
+function normalizePrivateKey(privKey: Hex) {
+  return cutils.bytesToHex(ensureBytes0x(privKey)).padStart(32 * 2, '0');
+}
+function getPublicKey0x(privKey: Hex, isCompressed?: boolean) {
+  return starkCurve.getPublicKey(normalizePrivateKey(privKey), isCompressed);
+}
+function getSharedSecret0x(privKeyA: Hex, pubKeyB: Hex) {
+  return starkCurve.getSharedSecret(normalizePrivateKey(privKeyA), pubKeyB);
+}
+
 function sign0x(msgHash: Hex, privKey: Hex, opts: any) {
-  return starkCurve.sign(ensureBytes0x(msgHash), ensureBytes0x(privKey), opts);
+  if (typeof privKey === 'string') privKey = strip0x(privKey).padStart(64, '0');
+  return starkCurve.sign(ensureBytes0x(msgHash), normalizePrivateKey(privKey), opts);
 }
 function verify0x(signature: Hex, msgHash: Hex, pubKey: Hex) {
   const sig = signature instanceof Signature ? signature : ensureBytes0x(signature);
   return starkCurve.verify(sig, ensureBytes0x(msgHash), ensureBytes0x(pubKey));
 }
 
-const { CURVE, Point, JacobianPoint, Signature, getPublicKey, getSharedSecret } = starkCurve;
+const { CURVE, Point, ProjectivePoint, Signature } = starkCurve;
 export const utils = starkCurve.utils;
 export {
   CURVE,
   Point,
   Signature,
-  JacobianPoint,
-  getPublicKey,
-  getSharedSecret,
+  ProjectivePoint,
+  getPublicKey0x as getPublicKey,
+  getSharedSecret0x as getSharedSecret,
   sign0x as sign,
   verify0x as verify,
 };
@@ -138,8 +147,7 @@ export function grindKey(seed: Hex) {
 }
 
 export function getStarkKey(privateKey: Hex) {
-  const priv = typeof privateKey === 'string' ? strip0x(privateKey) : privateKey;
-  return bytesToHexEth(Point.fromPrivateKey(priv).toRawBytes(true).slice(1));
+  return bytesToHexEth(getPublicKey0x(privateKey, true).slice(1));
 }
 
 export function ethSigToPrivate(signature: string) {
@@ -163,7 +171,7 @@ export function getAccountPath(
 }
 
 // https://docs.starkware.co/starkex/pedersen-hash-function.html
-const PEDERSEN_POINTS = [
+const PEDERSEN_POINTS_AFFINE = [
   new Point(
     2089986280348253421170679821480865132823066470938446095505822317253594081284n,
     1713931329540660377023406109199410414810705867260802078187082345529207694986n
@@ -186,10 +194,10 @@ const PEDERSEN_POINTS = [
   ),
 ];
 // for (const p of PEDERSEN_POINTS) p._setWindowSize(8);
-const PEDERSEN_POINTS_JACOBIAN = PEDERSEN_POINTS.map(JacobianPoint.fromAffine);
+const PEDERSEN_POINTS = PEDERSEN_POINTS_AFFINE.map(ProjectivePoint.fromAffine);
 
-function pedersenPrecompute(p1: JacobianPointType, p2: JacobianPointType): JacobianPointType[] {
-  const out: JacobianPointType[] = [];
+function pedersenPrecompute(p1: ProjectivePoint, p2: ProjectivePoint): ProjectivePoint[] {
+  const out: ProjectivePoint[] = [];
   let p = p1;
   for (let i = 0; i < 248; i++) {
     out.push(p);
@@ -202,14 +210,8 @@ function pedersenPrecompute(p1: JacobianPointType, p2: JacobianPointType): Jacob
   }
   return out;
 }
-const PEDERSEN_POINTS1 = pedersenPrecompute(
-  PEDERSEN_POINTS_JACOBIAN[1],
-  PEDERSEN_POINTS_JACOBIAN[2]
-);
-const PEDERSEN_POINTS2 = pedersenPrecompute(
-  PEDERSEN_POINTS_JACOBIAN[3],
-  PEDERSEN_POINTS_JACOBIAN[4]
-);
+const PEDERSEN_POINTS1 = pedersenPrecompute(PEDERSEN_POINTS[1], PEDERSEN_POINTS[2]);
+const PEDERSEN_POINTS2 = pedersenPrecompute(PEDERSEN_POINTS[3], PEDERSEN_POINTS[4]);
 
 type PedersenArg = Hex | bigint | number;
 function pedersenArg(arg: PedersenArg): bigint {
@@ -220,16 +222,12 @@ function pedersenArg(arg: PedersenArg): bigint {
     value = BigInt(arg);
   } else value = bytesToNumber0x(ensureBytes0x(arg));
   // [0..Fp)
-  if (!(0n <= value && value < starkCurve.CURVE.P))
+  if (!(0n <= value && value < starkCurve.CURVE.Fp.ORDER))
     throw new Error(`PedersenArg should be 0 <= value < CURVE.P: ${value}`);
   return value;
 }
 
-function pedersenSingle(
-  point: JacobianPointType,
-  value: PedersenArg,
-  constants: JacobianPointType[]
-) {
+function pedersenSingle(point: ProjectivePoint, value: PedersenArg, constants: ProjectivePoint[]) {
   let x = pedersenArg(value);
   for (let j = 0; j < 252; j++) {
     const pt = constants[j];
@@ -242,7 +240,7 @@ function pedersenSingle(
 
 // shift_point + x_low * P_0 + x_high * P1 + y_low * P2  + y_high * P3
 export function pedersen(x: PedersenArg, y: PedersenArg) {
-  let point: JacobianPointType = PEDERSEN_POINTS_JACOBIAN[0];
+  let point: ProjectivePoint = PEDERSEN_POINTS[0];
   point = pedersenSingle(point, x, PEDERSEN_POINTS1);
   point = pedersenSingle(point, y, PEDERSEN_POINTS2);
   return bytesToHexEth(point.toAffine().toRawBytes(true).slice(1));

src/utils.ts

@@ -1,69 +0,0 @@
-/*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-// Convert between types
-// ---------------------
-
-const hexes = Array.from({ length: 256 }, (v, i) => i.toString(16).padStart(2, '0'));
-export function bytesToHex(uint8a: Uint8Array): string {
-  if (!(uint8a instanceof Uint8Array)) throw new Error('Expected Uint8Array');
-  // pre-caching improves the speed 6x
-  let hex = '';
-  for (let i = 0; i < uint8a.length; i++) {
-    hex += hexes[uint8a[i]];
-  }
-  return hex;
-}
-
-export function numberToHexUnpadded(num: number | bigint): string {
-  const hex = num.toString(16);
-  return hex.length & 1 ? `0${hex}` : hex;
-}
-
-export function hexToNumber(hex: string): bigint {
-  if (typeof hex !== 'string') {
-    throw new TypeError('hexToNumber: expected string, got ' + typeof hex);
-  }
-  // Big Endian
-  return BigInt(`0x${hex}`);
-}
-
-// Caching slows it down 2-3x
-export function hexToBytes(hex: string): Uint8Array {
-  if (typeof hex !== 'string') {
-    throw new TypeError('hexToBytes: expected string, got ' + typeof hex);
-  }
-  if (hex.length % 2) throw new Error('hexToBytes: received invalid unpadded hex ' + hex.length);
-  const array = new Uint8Array(hex.length / 2);
-  for (let i = 0; i < array.length; i++) {
-    const j = i * 2;
-    const hexByte = hex.slice(j, j + 2);
-    const byte = Number.parseInt(hexByte, 16);
-    if (Number.isNaN(byte) || byte < 0) throw new Error('Invalid byte sequence');
-    array[i] = byte;
-  }
-  return array;
-}
-
-// Big Endian
-export function bytesToNumber(bytes: Uint8Array): bigint {
-  return hexToNumber(bytesToHex(bytes));
-}
-
-export function ensureBytes(hex: string | Uint8Array): Uint8Array {
-  // Uint8Array.from() instead of hash.slice() because node.js Buffer
-  // is instance of Uint8Array, and its slice() creates **mutable** copy
-  return hex instanceof Uint8Array ? Uint8Array.from(hex) : hexToBytes(hex);
-}
-
-// Copies several Uint8Arrays into one.
-export function concatBytes(...arrays: Uint8Array[]): Uint8Array {
-  if (!arrays.every((b) => b instanceof Uint8Array)) throw new Error('Uint8Array list expected');
-  if (arrays.length === 1) return arrays[0];
-  const length = arrays.reduce((a, arr) => a + arr.length, 0);
-  const result = new Uint8Array(length);
-  for (let i = 0, pad = 0; i < arrays.length; i++) {
-    const arr = arrays[i];
-    result.set(arr, pad);
-    pad += arr.length;
-  }
-  return result;
-}

test/basic.test.js

@@ -0,0 +1,316 @@
+import { deepStrictEqual, throws } from 'assert';
+import { should } from 'micro-should';
+import * as fc from 'fast-check';
+import * as mod from '../lib/esm/abstract/modular.js';
+// Generic tests for all curves in package
+import { secp192r1 } from '../lib/esm/p192.js';
+import { secp224r1 } from '../lib/esm/p224.js';
+import { secp256r1 } from '../lib/esm/p256.js';
+import { secp384r1 } from '../lib/esm/p384.js';
+import { secp521r1 } from '../lib/esm/p521.js';
+import { secp256k1 } from '../lib/esm/secp256k1.js';
+import { ed25519, ed25519ctx, ed25519ph } from '../lib/esm/ed25519.js';
+import { ed448, ed448ph } from '../lib/esm/ed448.js';
+import { starkCurve } from '../lib/esm/stark.js';
+import { pallas, vesta } from '../lib/esm/pasta.js';
+import { bn254 } from '../lib/esm/bn.js';
+import { jubjub } from '../lib/esm/jubjub.js';
+
+// prettier-ignore
+const CURVES = {
+  secp192r1, secp224r1, secp256r1, secp384r1, secp521r1,
+  secp256k1,
+  ed25519, ed25519ctx, ed25519ph,
+  ed448, ed448ph,
+  starkCurve,
+  pallas, vesta,
+  bn254,
+  jubjub,
+};
+
+const NUM_RUNS = 5;
+const getXY = (p) => ({ x: p.x, y: p.y });
+
+function equal(a, b, comment) {
+  deepStrictEqual(a.equals(b), true, `eq(${comment})`);
+  if (a.toAffine && b.toAffine) {
+    deepStrictEqual(getXY(a.toAffine()), getXY(b.toAffine()), `eqToAffine(${comment})`);
+  } else if (!a.toAffine && !b.toAffine) {
+    // Already affine
+    deepStrictEqual(getXY(a), getXY(b), `eqAffine(${comment})`);
+  } else throw new Error('Different point types');
+}
+
+for (const name in CURVES) {
+  const C = CURVES[name];
+  const CURVE_ORDER = C.CURVE.n;
+  const FC_BIGINT = fc.bigInt(1n + 1n, CURVE_ORDER - 1n);
+
+  // Check that curve doesn't accept points from other curves
+  const O = name === 'secp256k1' ? secp256r1 : secp256k1;
+  const POINTS = {};
+  const OTHER_POINTS = {};
+  for (const name of ['Point', 'ProjectivePoint', 'ExtendedPoint', 'ProjectivePoint']) {
+    POINTS[name] = C[name];
+    OTHER_POINTS[name] = O[name];
+  }
+
+  for (const pointName in POINTS) {
+    const p = POINTS[pointName];
+    const o = OTHER_POINTS[pointName];
+    if (!p) continue;
+
+    const G = [p.ZERO, p.BASE];
+    for (let i = 2; i < 10; i++) G.push(G[1].multiply(i));
+    // Here we check basic group laws, to verify that points works as group
+    should(`${name}/${pointName}/Basic group laws (zero)`, () => {
+      equal(G[0].double(), G[0], '(0*G).double() = 0');
+      equal(G[0].add(G[0]), G[0], '0*G + 0*G = 0');
+      equal(G[0].subtract(G[0]), G[0], '0*G - 0*G = 0');
+      equal(G[0].negate(), G[0], '-0 = 0');
+      for (let i = 0; i < G.length; i++) {
+        const p = G[i];
+        equal(p, p.add(G[0]), `${i}*G + 0 = ${i}*G`);
+        equal(G[0].multiply(i + 1), G[0], `${i + 1}*0 = 0`);
+      }
+    });
+    should(`${name}/${pointName}/Basic group laws (one)`, () => {
+      equal(G[1].double(), G[2], '(1*G).double() = 2*G');
+      equal(G[1].subtract(G[1]), G[0], '1*G - 1*G = 0');
+      equal(G[1].add(G[1]), G[2], '1*G + 1*G = 2*G');
+    });
+    should(`${name}/${pointName}/Basic group laws (sanity tests)`, () => {
+      equal(G[2].double(), G[4], `(2*G).double() = 4*G`);
+      equal(G[2].add(G[2]), G[4], `2*G + 2*G = 4*G`);
+      equal(G[7].add(G[3].negate()), G[4], `7*G - 3*G = 4*G`);
+    });
+    should(`${name}/${pointName}/Basic group laws (addition commutativity)`, () => {
+      equal(G[4].add(G[3]), G[3].add(G[4]), `4*G + 3*G = 3*G + 4*G`);
+      equal(G[4].add(G[3]), G[3].add(G[2]).add(G[2]), `4*G + 3*G = 3*G + 2*G + 2*G`);
+    });
+    should(`${name}/${pointName}/Basic group laws (double)`, () => {
+      equal(G[3].double(), G[6], '(3*G).double() = 6*G');
+    });
+    should(`${name}/${pointName}/Basic group laws (multiply)`, () => {
+      equal(G[2].multiply(3), G[6], '(2*G).multiply(3) = 6*G');
+    });
+    should(`${name}/${pointName}/Basic group laws (same point addition)`, () => {
+      equal(G[3].add(G[3]), G[6], `3*G + 3*G = 6*G`);
+    });
+    should(`${name}/${pointName}/Basic group laws (same point (negative) addition)`, () => {
+      equal(G[3].add(G[3].negate()), G[0], '3*G + (- 3*G) = 0*G');
+      equal(G[3].subtract(G[3]), G[0], '3*G - 3*G = 0*G');
+    });
+    should(`${name}/${pointName}/Basic group laws (curve order)`, () => {
+      equal(G[1].multiply(CURVE_ORDER - 1n).add(G[1]), G[0], '(N-1)*G + G = 0');
+      equal(G[1].multiply(CURVE_ORDER - 1n).add(G[2]), G[1], '(N-1)*G + 2*G = 1*G');
+      equal(G[1].multiply(CURVE_ORDER - 2n).add(G[2]), G[0], '(N-2)*G + 2*G = 0');
+      const half = CURVE_ORDER / 2n;
+      const carry = CURVE_ORDER % 2n === 1n ? G[1] : G[0];
+      equal(G[1].multiply(half).double().add(carry), G[0], '((N/2) * G).double() = 0');
+    });
+    should(`${name}/${pointName}/Basic group laws (inversion)`, () => {
+      const a = 1234n;
+      const b = 5678n;
+      const c = a * b;
+      equal(G[1].multiply(a).multiply(b), G[1].multiply(c), 'a*b*G = c*G');
+      const inv = mod.invert(b, CURVE_ORDER);
+      equal(G[1].multiply(c).multiply(inv), G[1].multiply(a), 'c*G * (1/b)*G = a*G');
+    });
+    should(`${name}/${pointName}/Basic group laws (multiply, rand)`, () =>
+      fc.assert(
+        fc.property(FC_BIGINT, FC_BIGINT, (a, b) => {
+          const c = mod.mod(a + b, CURVE_ORDER);
+          if (c === CURVE_ORDER || c < 1n) return;
+          const pA = G[1].multiply(a);
+          const pB = G[1].multiply(b);
+          const pC = G[1].multiply(c);
+          equal(pA.add(pB), pB.add(pA), `pA + pB = pB + pA`);
+          equal(pA.add(pB), pC, `pA + pB = pC`);
+        }),
+        { numRuns: NUM_RUNS }
+      )
+    );
+    should(`${name}/${pointName}/Basic group laws (multiply2, rand)`, () =>
+      fc.assert(
+        fc.property(FC_BIGINT, FC_BIGINT, (a, b) => {
+          const c = mod.mod(a * b, CURVE_ORDER);
+          const pA = G[1].multiply(a);
+          const pB = G[1].multiply(b);
+          equal(pA.multiply(b), pB.multiply(a), `b*pA = a*pB`);
+          equal(pA.multiply(b), G[1].multiply(c), `b*pA = c*G`);
+        }),
+        { numRuns: NUM_RUNS }
+      )
+    );
+
+    for (const op of ['add', 'subtract']) {
+      should(`${name}/${pointName}/${op} type check`, () => {
+        throws(() => G[1][op](0), '0');
+        throws(() => G[1][op](0n), '0n');
+        G[1][op](G[2]);
+        throws(() => G[1][op](CURVE_ORDER), 'CURVE_ORDER');
+        throws(() => G[1][op](123.456), '123.456');
+        throws(() => G[1][op](true), 'true');
+        throws(() => G[1][op]('1'), "'1'");
+        throws(() => G[1][op]({ x: 1n, y: 1n, z: 1n, t: 1n }), '{ x: 1n, y: 1n, z: 1n, t: 1n }');
+        throws(() => G[1][op](new Uint8Array([])), 'ui8a([])');
+        throws(() => G[1][op](new Uint8Array([0])), 'ui8a([0])');
+        throws(() => G[1][op](new Uint8Array([1])), 'ui8a([1])');
+        throws(() => G[1][op](new Uint8Array(4096).fill(1)), 'ui8a(4096*[1])');
+        if (G[1].toAffine) throws(() => G[1][op](C.Point.BASE), `Point ${op} ${pointName}`);
+        throws(() => G[1][op](o.BASE), `${op}/other curve point`);
+      });
+    }
+
+    should(`${name}/${pointName}/equals type check`, () => {
+      throws(() => G[1].equals(0), '0');
+      throws(() => G[1].equals(0n), '0n');
+      deepStrictEqual(G[1].equals(G[2]), false, '1*G != 2*G');
+      deepStrictEqual(G[1].equals(G[1]), true, '1*G == 1*G');
+      deepStrictEqual(G[2].equals(G[2]), true, '2*G == 2*G');
+      throws(() => G[1].equals(CURVE_ORDER), 'CURVE_ORDER');
+      throws(() => G[1].equals(123.456), '123.456');
+      throws(() => G[1].equals(true), 'true');
+      throws(() => G[1].equals('1'), "'1'");
+      throws(() => G[1].equals({ x: 1n, y: 1n, z: 1n, t: 1n }), '{ x: 1n, y: 1n, z: 1n, t: 1n }');
+      throws(() => G[1].equals(new Uint8Array([])), 'ui8a([])');
+      throws(() => G[1].equals(new Uint8Array([0])), 'ui8a([0])');
+      throws(() => G[1].equals(new Uint8Array([1])), 'ui8a([1])');
+      throws(() => G[1].equals(new Uint8Array(4096).fill(1)), 'ui8a(4096*[1])');
+      if (G[1].toAffine) throws(() => G[1].equals(C.Point.BASE), `Point.equals(${pointName})`);
+      throws(() => G[1].equals(o.BASE), 'other curve point');
+    });
+
+    for (const op of ['multiply', 'multiplyUnsafe']) {
+      if (!p.BASE[op]) continue;
+      should(`${name}/${pointName}/${op} type check`, () => {
+        if (op !== 'multiplyUnsafe') {
+          throws(() => G[1][op](0), '0');
+          throws(() => G[1][op](0n), '0n');
+        }
+        G[1][op](1n);
+        G[1][op](CURVE_ORDER - 1n);
+        throws(() => G[1][op](G[2]), 'G[2]');
+        throws(() => G[1][op](CURVE_ORDER), 'CURVE_ORDER');
+        throws(() => G[1][op](CURVE_ORDER + 1n), 'CURVE_ORDER+1');
+        throws(() => G[1][op](123.456), '123.456');
+        throws(() => G[1][op](true), 'true');
+        throws(() => G[1][op]('1'), '1');
+        throws(() => G[1][op](new Uint8Array([])), 'ui8a([])');
+        throws(() => G[1][op](new Uint8Array([0])), 'ui8a([0])');
+        throws(() => G[1][op](new Uint8Array([1])), 'ui8a([1])');
+        throws(() => G[1][op](new Uint8Array(4096).fill(1)), 'ui8a(4096*[1])');
+        throws(() => G[1][op](o.BASE), 'other curve point');
+      });
+    }
+    // Complex point (Extended/Jacobian/Projective?)
+    if (p.BASE.toAffine) {
+      should(`${name}/${pointName}/toAffine()`, () => {
+        equal(p.ZERO.toAffine(), C.Point.ZERO, `0 = 0`);
+        equal(p.BASE.toAffine(), C.Point.BASE, `1 = 1`);
+      });
+    }
+    if (p.fromAffine) {
+      should(`${name}/${pointName}/fromAffine()`, () => {
+        equal(p.ZERO, p.fromAffine(C.Point.ZERO), `0 = 0`);
+        equal(p.BASE, p.fromAffine(C.Point.BASE), `1 = 1`);
+      });
+    }
+    // toHex/fromHex (if available)
+    if (p.fromHex && p.BASE.toHex) {
+      should(`${name}/${pointName}/fromHex(toHex()) roundtrip`, () => {
+        fc.assert(
+          fc.property(FC_BIGINT, (x) => {
+            const hex = p.BASE.multiply(x).toHex();
+            deepStrictEqual(p.fromHex(hex).toHex(), hex);
+          })
+        );
+      });
+    }
+  }
+  // Generic complex things (getPublicKey/sign/verify/getSharedSecret)
+  should(`${name}/getPublicKey type check`, () => {
+    throws(() => C.getPublicKey(0), '0');
+    throws(() => C.getPublicKey(0n), '0n');
+    throws(() => C.getPublicKey(false), 'false');
+    throws(() => C.getPublicKey(123.456), '123.456');
+    throws(() => C.getPublicKey(true), 'true');
+    throws(() => C.getPublicKey(''), "''");
+    // NOTE: passes because of disabled hex padding checks for starknet, maybe enable?
+    //throws(() => C.getPublicKey('1'), "'1'");
+    throws(() => C.getPublicKey('key'), "'key'");
+    throws(() => C.getPublicKey(new Uint8Array([])));
+    throws(() => C.getPublicKey(new Uint8Array([0])));
+    throws(() => C.getPublicKey(new Uint8Array([1])));
+    throws(() => C.getPublicKey(new Uint8Array(4096).fill(1)));
+  });
+  should(`${name}.verify()/should verify random signatures`, () =>
+    fc.assert(
+      fc.property(fc.hexaString({ minLength: 64, maxLength: 64 }), (msg) => {
+        const priv = C.utils.randomPrivateKey();
+        const pub = C.getPublicKey(priv);
+        const sig = C.sign(msg, priv);
+        deepStrictEqual(C.verify(sig, msg, pub), true);
+      }),
+      { numRuns: NUM_RUNS }
+    )
+  );
+  should(`${name}.sign()/edge cases`, () => {
+    throws(() => C.sign());
+    throws(() => C.sign(''));
+  });
+
+  should(`${name}.verify()/should not verify signature with wrong hash`, () => {
+    const MSG = '01'.repeat(32);
+    const PRIV_KEY = 0x2n;
+    const WRONG_MSG = '11'.repeat(32);
+    const signature = C.sign(MSG, PRIV_KEY);
+    const publicKey = C.getPublicKey(PRIV_KEY);
+    deepStrictEqual(C.verify(signature, WRONG_MSG, publicKey), false);
+  });
+  // NOTE: fails for ed, because of empty message. Since we convert it to scalar,
+  // need to check what other implementations do. Empty message != new Uint8Array([0]), but what scalar should be in that case?
+  // should(`${name}/should not verify signature with wrong message`, () => {
+  //   fc.assert(
+  //     fc.property(
+  //       fc.array(fc.integer({ min: 0x00, max: 0xff })),
+  //       fc.array(fc.integer({ min: 0x00, max: 0xff })),
+  //       (bytes, wrongBytes) => {
+  //         const privKey = C.utils.randomPrivateKey();
+  //         const message = new Uint8Array(bytes);
+  //         const wrongMessage = new Uint8Array(wrongBytes);
+  //         const publicKey = C.getPublicKey(privKey);
+  //         const signature = C.sign(message, privKey);
+  //         deepStrictEqual(
+  //           C.verify(signature, wrongMessage, publicKey),
+  //           bytes.toString() === wrongBytes.toString()
+  //         );
+  //       }
+  //     ),
+  //     { numRuns: NUM_RUNS }
+  //   );
+  // });
+
+  if (C.getSharedSecret) {
+    should(`${name}/getSharedSecret() should be commutative`, () => {
+      for (let i = 0; i < NUM_RUNS; i++) {
+        const asec = C.utils.randomPrivateKey();
+        const apub = C.getPublicKey(asec);
+        const bsec = C.utils.randomPrivateKey();
+        const bpub = C.getPublicKey(bsec);
+        try {
+          deepStrictEqual(C.getSharedSecret(asec, bpub), C.getSharedSecret(bsec, apub));
+        } catch (error) {
+          console.error('not commutative', { asec, apub, bsec, bpub });
+          throw error;
+        }
+      }
+    });
+  }
+}
+// ESM is broken.
+import url from 'url';
+if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
+  should.run();
+}

test/bls12-381/bls12-381-g2-test-vectors.txt

@@ -0,0 +1,559 @@
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+ea697bc01540c1b708f03c9369d2ad84ac0e2ff087a17bf9c868b64d6076c6c0:f7a40db556:8151b87961f1f4f6a33993469131fa7d02f40ea3d7191fc72aee115a8bf8454e57f12b7c67fa4b56fcfb9767276c2c66017a25f362b59067a313a61fac44e6940bc82e445befb85e20f51f1444e54e353d641537b21e6d6fb2a865228b58edd1
+fda3cf7385cf4bb164645966281a68f0447a0fdcd1ec7e29bf7313860f4a3394:03d67ac13cee:a81fd948bd75d7fb1b9744bd12a83288d1794bce09a8d7a63cb39758b090296356c6290e3cd63d4cb1ebbd169bdfe1991063d3d323bf87af7c469cb5947a93870400518b1a48d96f98456211b706be4073a34f0af9bfeb86c2adccb64a005656
+b382e373ff8da48348d38447ef337570a9bafd91fab84c2a439f71880ea5e480:c89dc4de1fbc:8d3a93cbf8bce107c2dce15ddac3252792dfe2e9e9050e99100aae4d42ca1687b1a72abb372da6e01c761e7f37b6c6790ec1260c4e8052c3b21fc21c8a79fff22dbced49349f554f8efb34a20bc1aab0f252660eca89ece65a67097622e7e547
+d15ae5df8ca3c5e64b38d24653fc9bf809534e98f3c7162623b65d9e70d8d2c5:0ae955dfad3573:8ecfa5cd8164188ddbad47d4f7600751116c6ac96d5bf74cd8feccdd59366ceba5bceaba2241f0b4355b9ca7b3963e54076b31e58f38d9a8dbf8ef3c887514fec83bf2f3a82fa2d2bffced10fe7113388c86d9d441867b499caed7e2e45cd98e
+bdb098850c669ddde2018c5cea8b9f9a356c317868ddfc61ebf120d2ee9b6627:477405798be816:8108bdda52459a367f5ee6d2fb92a62144d2134cbf6755cc6c6ae4fde35f3d8c5a1ac6b5feb86290a76ffe5972cba95118dd0d095473e8d2e2027f9f10c67a388b4802f190ef8900eaef3246b26e2ab642c317a66f9571f339744dda641b9248
+f62d28e6fc14fb70610228ee1f4f7d2e065e05caaf18b766892eeabf7c05f924:06097228065d18c0:b82649d765a3fff1d72ee15b7906579c4f0a608fd03adb53c6214de0e5095383ea00b66d75b6a12b8c433251af517a61053d69cf3dfeebdd929275984d9d3b1f8eaadd308824fffb9bb4e5437539a2f3d68330dbb021524a1d0d4523e5adc34a
+27826e51f6e6446065e32c5b8e60aaf0109008d4eb9c2336a437ecb6fe415618:4f77125824409934:894e75525f6c5067b5274b52f39f3d0991ef27b9396ead5555f0dac07d07a962f3cc00b20e8324b69873abff1f8285d904428f93fc42354bb1cc50d95149014dd25b7000b161c4dbaaae54a90bcbde7e8c99c2111181e4e1e08648b4bec81cb4
+984cfc344dd7da98dc2dcbcb8427e0195989e6b06380dd7dde4d73e289e1013c:093906e014849826bb:b74fbc224468498a680c923e1e9e8b90e7e55e44ffcb7cf1d2cf5bcbac1964e238025e30565325f2a1854244fa4ab233091c298fb9d5ba2525620f900960819e21f2e3d364eeac93f82c1303a141b883d29bbf4de2796daeb41f20cc05f0cd48
+ac47cf8395c7858c34896e1501c77b1028bb00f15721d92b4208a13cad2fbdac:3c65e5bd83d0464de9:9414a283286bb2eebde7e00e5510e406e96750a3595a104b0a003fa181ca8022eb688d6ed5363711b59d86f3f0cc696d08ee7c6939b9d7ec44a8d597880e15700d6cdff0fdd76ff814797b7b928f123a8dc22425333064821992559baf7f4b4c

test/bls12-381/bls12-381-scalar-test-vectors.txt

@@ -0,0 +1,3 @@
+:0000000000000000000000000000000000000000000000000000000000000000
+aaaaaabbbbbbccccccddddddeeeeeeffffffgggggghhhhhh:2228450bf55d8fe62395161bd3677ff6fc28e45b89bc87e02a818eda11a8c5da
+111111222222333333444444555555666666777777888888:4aa543cbd2f0c8f37f8a375ce2e383eb343e7e3405f61e438b0a15fb8899d1ae

test/bls12-381/go_pairing_vectors/go.mod

@@ -0,0 +1,8 @@
+module blstests
+
+go 1.19
+
+require (
+	github.com/kilic/bls12-381 v0.1.0 // indirect
+	golang.org/x/sys v0.0.0-20201101102859-da207088b7d1 // indirect
+)

test/bls12-381/go_pairing_vectors/go.sum

@@ -0,0 +1,4 @@
+github.com/kilic/bls12-381 v0.1.0 h1:encrdjqKMEvabVQ7qYOKu1OvhqpK4s47wDYtNiPtlp4=
+github.com/kilic/bls12-381 v0.1.0/go.mod h1:vDTTHJONJ6G+P2R74EhnyotQDTliQDnFEwhdmfzw1ig=
+golang.org/x/sys v0.0.0-20201101102859-da207088b7d1 h1:a/mKvvZr9Jcc8oKfcmgzyp7OwF73JPWsQLvH1z2Kxck=
+golang.org/x/sys v0.0.0-20201101102859-da207088b7d1/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=

test/bls12-381/go_pairing_vectors/t.go

@@ -0,0 +1,29 @@
+package main
+
+import (
+	"encoding/hex"
+	"encoding/json"
+	"fmt"
+
+	kilic "github.com/kilic/bls12-381"
+)
+
+func main() {
+	g1 := kilic.NewG1()
+	g2 := kilic.NewG2()
+	gt := kilic.NewGT()
+	p1 := g1.One()
+	p2 := g2.One()
+	bls := kilic.NewEngine()
+	out := []string{}
+	for i := 0; i < 1000; i++ {
+		res := bls.AddPair(p1, p2).Result()
+		out = append(out, hex.EncodeToString(gt.ToBytes(res)))
+		g1.Add(p1, p1, g1.One())
+		g2.Add(p2, p2, g2.One())
+
+	}
+	bytes, _ := json.Marshal(out)
+	fmt.Println(string(bytes))
+
+}

test/bls12-381/zkcrypto/convert.js

@@ -0,0 +1,25 @@
+// This can be done inside of tests, but ESM is broken, jest doesn't want to work with it,
+// and ESM itself contaminates everything it touches
+
+(async () => {
+  const P = await import('micro-packed');
+  const { readFileSync } = require('fs');
+
+  const CompresedG1 = P.array(null, P.hex(48));
+  const UncompresedG1 = P.array(null, P.hex(2 * 48));
+  const CompresedG2 = P.array(null, P.hex(2 * 48));
+  const UncompresedG2 = P.array(null, P.hex(4 * 48));
+
+  const out = {
+    G1_Compressed: CompresedG1.decode(readFileSync('./g1_compressed_valid_test_vectors.dat')),
+    G1_Uncompressed: UncompresedG1.decode(readFileSync('./g1_uncompressed_valid_test_vectors.dat')),
+    G2_Compressed: CompresedG2.decode(readFileSync('./g2_compressed_valid_test_vectors.dat')),
+    G2_Uncompressed: UncompresedG2.decode(readFileSync('./g2_uncompressed_valid_test_vectors.dat')),
+  };
+  // Should be 1000
+  // console.log(
+  //   'T',
+  //   Object.values(out).map((i) => i.length)
+  // );
+  console.log(JSON.stringify(out));
+})();

test/ed25519.test.js

@@ -0,0 +1,657 @@
+import { deepStrictEqual, throws } from 'assert';
+import { should } from 'micro-should';
+import * as fc from 'fast-check';
+import { ed25519, ed25519ctx, ed25519ph, x25519, RistrettoPoint } from '../lib/esm/ed25519.js';
+import { readFileSync } from 'fs';
+import { default as zip215 } from './ed25519/zip215.json' assert { type: 'json' };
+import { hexToBytes, bytesToHex, randomBytes } from '@noble/hashes/utils';
+import { numberToBytesLE } from '../lib/esm/abstract/utils.js';
+import { sha512 } from '@noble/hashes/sha512';
+import { default as ed25519vectors } from './wycheproof/eddsa_test.json' assert { type: 'json' };
+import { default as x25519vectors } from './wycheproof/x25519_test.json' assert { type: 'json' };
+
+const ed = ed25519;
+const hex = bytesToHex;
+
+function to32Bytes(numOrStr) {
+  let hex = typeof numOrStr === 'string' ? numOrStr : numOrStr.toString(16);
+  return hexToBytes(hex.padStart(64, '0'));
+}
+
+function utf8ToBytes(str) {
+  if (typeof str !== 'string') {
+    throw new TypeError(`utf8ToBytes expected string, got ${typeof str}`);
+  }
+  return new TextEncoder().encode(str);
+}
+
+ed.utils.precompute(8);
+
+should('ed25519/should not accept >32byte private keys', () => {
+  const invalidPriv =
+    100000000000000000000000000000000000009000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000090000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000800073278156000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000n;
+  throws(() => ed.getPublicKey(invalidPriv));
+});
+should('ed25519/should verify recent signature', () => {
+  fc.assert(
+    fc.property(
+      fc.hexaString({ minLength: 2, maxLength: 32 }),
+      fc.bigInt(2n, ed.CURVE.n),
+      (message, privateKey) => {
+        const publicKey = ed.getPublicKey(to32Bytes(privateKey));
+        const signature = ed.sign(to32Bytes(message), to32Bytes(privateKey));
+        deepStrictEqual(publicKey.length, 32);
+        deepStrictEqual(signature.length, 64);
+        deepStrictEqual(ed.verify(signature, to32Bytes(message), publicKey), true);
+      }
+    ),
+    { numRuns: 5 }
+  );
+});
+should('ed25519/should not verify signature with wrong message', () => {
+  fc.assert(
+    fc.property(
+      fc.array(fc.integer({ min: 0x00, max: 0xff })),
+      fc.array(fc.integer({ min: 0x00, max: 0xff })),
+      fc.bigInt(1n, ed.CURVE.n),
+      (bytes, wrongBytes, privateKey) => {
+        const privKey = to32Bytes(privateKey);
+        const message = new Uint8Array(bytes);
+        const wrongMessage = new Uint8Array(wrongBytes);
+        const publicKey = ed.getPublicKey(privKey);
+        const signature = ed.sign(message, privKey);
+        deepStrictEqual(
+          ed.verify(signature, wrongMessage, publicKey),
+          bytes.toString() === wrongBytes.toString()
+        );
+      }
+    ),
+    { numRuns: 5 }
+  );
+});
+const privKey = to32Bytes('a665a45920422f9d417e4867ef');
+const msg = hexToBytes('874f9960c5d2b7a9b5fad383e1ba44719ebb743a');
+const wrongMsg = hexToBytes('589d8c7f1da0a24bc07b7381ad48b1cfc211af1c');
+should('ed25519/basic methods/should sign and verify', () => {
+  const publicKey = ed.getPublicKey(privKey);
+  const signature = ed.sign(msg, privKey);
+  deepStrictEqual(ed.verify(signature, msg, publicKey), true);
+});
+should('ed25519/basic methods/should not verify signature with wrong public key', () => {
+  const publicKey = ed.getPublicKey(12);
+  const signature = ed.sign(msg, privKey);
+  deepStrictEqual(ed.verify(signature, msg, publicKey), false);
+});
+should('ed25519/basic methods/should not verify signature with wrong hash', () => {
+  const publicKey = ed.getPublicKey(privKey);
+  const signature = ed.sign(msg, privKey);
+  deepStrictEqual(ed.verify(signature, wrongMsg, publicKey), false);
+});
+
+should('ed25519/sync methods/should sign and verify', () => {
+  const publicKey = ed.getPublicKey(privKey);
+  const signature = ed.sign(msg, privKey);
+  deepStrictEqual(ed.verify(signature, msg, publicKey), true);
+});
+should('ed25519/sync methods/should not verify signature with wrong public key', () => {
+  const publicKey = ed.getPublicKey(12);
+  const signature = ed.sign(msg, privKey);
+  deepStrictEqual(ed.verify(signature, msg, publicKey), false);
+});
+should('ed25519/sync methods/should not verify signature with wrong hash', () => {
+  const publicKey = ed.getPublicKey(privKey);
+  const signature = ed.sign(msg, privKey);
+  deepStrictEqual(ed.verify(signature, wrongMsg, publicKey), false);
+});
+
+// https://xmr.llcoins.net/addresstests.html
+should(
+  'ed25519/BASE_POINT.multiply()/should create right publicKey without SHA-512 hashing TEST 1',
+  () => {
+    const publicKey =
+      ed.Point.BASE.multiply(0x90af56259a4b6bfbc4337980d5d75fbe3c074630368ff3804d33028e5dbfa77n);
+    deepStrictEqual(
+      publicKey.toHex(),
+      '0f3b913371411b27e646b537e888f685bf929ea7aab93c950ed84433f064480d'
+    );
+  }
+);
+should(
+  'ed25519/BASE_POINT.multiply()/should create right publicKey without SHA-512 hashing TEST 2',
+  () => {
+    const publicKey =
+      ed.Point.BASE.multiply(0x364e8711a60780382a5d57b061c126f039940f28a9e91fe039d4d3094d8b88n);
+    deepStrictEqual(
+      publicKey.toHex(),
+      'ad545340b58610f0cd62f17d55af1ab11ecde9c084d5476865ddb4dbda015349'
+    );
+  }
+);
+should(
+  'ed25519/BASE_POINT.multiply()/should create right publicKey without SHA-512 hashing TEST 3',
+  () => {
+    const publicKey =
+      ed.Point.BASE.multiply(0xb9bf90ff3abec042752cac3a07a62f0c16cfb9d32a3fc2305d676ec2d86e941n);
+    deepStrictEqual(
+      publicKey.toHex(),
+      'e097c4415fe85724d522b2e449e8fd78dd40d20097bdc9ae36fe8ec6fe12cb8c'
+    );
+  }
+);
+should(
+  'ed25519/BASE_POINT.multiply()/should create right publicKey without SHA-512 hashing TEST 4',
+  () => {
+    const publicKey =
+      ed.Point.BASE.multiply(0x69d896f02d79524c9878e080308180e2859d07f9f54454e0800e8db0847a46en);
+    deepStrictEqual(
+      publicKey.toHex(),
+      'f12cb7c43b59971395926f278ce7c2eaded9444fbce62ca717564cb508a0db1d'
+    );
+  }
+);
+should('ed25519/BASE_POINT.multiply()/should throw Point#multiply on TEST 5', () => {
+  for (const num of [0n, 0, -1n, -1, 1.1]) {
+    throws(() => ed.Point.BASE.multiply(num));
+  }
+});
+
+// https://ed25519.cr.yp.to/python/sign.py
+// https://ed25519.cr.yp.to/python/sign.input
+const data = readFileSync('./test/ed25519/vectors.txt', 'utf-8');
+const vectors = data
+  .trim()
+  .split('\n')
+  .map((line) => line.split(':'));
+should('ed25519 official vectors/should match 1024 official vectors', () => {
+  for (let i = 0; i < vectors.length; i++) {
+    const vector = vectors[i];
+    // Extract.
+    const priv = vector[0].slice(0, 64);
+    const expectedPub = vector[1];
+    const msg = vector[2];
+    const expectedSignature = vector[3].slice(0, 128);
+
+    // Calculate
+    const pub = ed.getPublicKey(to32Bytes(priv));
+    deepStrictEqual(hex(pub), expectedPub);
+    deepStrictEqual(pub, ed.Point.fromHex(pub).toRawBytes());
+
+    const signature = hex(ed.sign(msg, priv));
+    // console.log('vector', i);
+    // expect(pub).toBe(expectedPub);
+    deepStrictEqual(signature, expectedSignature);
+  }
+});
+
+// https://tools.ietf.org/html/rfc8032#section-7
+should('rfc8032 vectors/should create right signature for 0x9d and empty string', () => {
+  const privateKey = '9d61b19deffd5a60ba844af492ec2cc44449c5697b326919703bac031cae7f60';
+  const publicKey = ed.getPublicKey(privateKey);
+  const message = '';
+  const signature = ed.sign(message, privateKey);
+  deepStrictEqual(
+    hex(publicKey),
+    'd75a980182b10ab7d54bfed3c964073a0ee172f3daa62325af021a68f707511a'
+  );
+  deepStrictEqual(
+    hex(signature),
+    'e5564300c360ac729086e2cc806e828a84877f1eb8e5d974d873e065224901555fb8821590a33bacc61e39701cf9b46bd25bf5f0595bbe24655141438e7a100b'
+  );
+});
+should('rfc8032 vectors/should create right signature for 0x4c and 72', () => {
+  const privateKey = '4ccd089b28ff96da9db6c346ec114e0f5b8a319f35aba624da8cf6ed4fb8a6fb';
+  const publicKey = ed.getPublicKey(privateKey);
+  const message = '72';
+  const signature = ed.sign(message, privateKey);
+  deepStrictEqual(
+    hex(publicKey),
+    '3d4017c3e843895a92b70aa74d1b7ebc9c982ccf2ec4968cc0cd55f12af4660c'
+  );
+  deepStrictEqual(
+    hex(signature),
+    '92a009a9f0d4cab8720e820b5f642540a2b27b5416503f8fb3762223ebdb69da085ac1e43e15996e458f3613d0f11d8c387b2eaeb4302aeeb00d291612bb0c00'
+  );
+});
+should('rfc8032 vectors/should create right signature for 0x00 and 5a', () => {
+  const privateKey = '002fdd1f7641793ab064bb7aa848f762e7ec6e332ffc26eeacda141ae33b1783';
+  const publicKey = ed.getPublicKey(privateKey);
+  const message =
+    '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';
+  const signature = ed.sign(message, privateKey);
+  deepStrictEqual(
+    hex(publicKey),
+    '77d1d8ebacd13f4e2f8a40e28c4a63bc9ce3bfb69716334bcb28a33eb134086c'
+  );
+  deepStrictEqual(
+    hex(signature),
+    '0df3aa0d0999ad3dc580378f52d152700d5b3b057f56a66f92112e441e1cb9123c66f18712c87efe22d2573777296241216904d7cdd7d5ea433928bd2872fa0c'
+  );
+});
+should('rfc8032 vectors/should create right signature for 0xf5 and long msg', () => {
+  const privateKey = 'f5e5767cf153319517630f226876b86c8160cc583bc013744c6bf255f5cc0ee5';
+  const publicKey = ed.getPublicKey(privateKey);
+  const message =
+    '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';
+  const signature = ed.sign(message, privateKey);
+  deepStrictEqual(
+    hex(publicKey),
+    '278117fc144c72340f67d0f2316e8386ceffbf2b2428c9c51fef7c597f1d426e'
+  );
+  deepStrictEqual(
+    hex(signature),
+    '0aab4c900501b3e24d7cdf4663326a3a87df5e4843b2cbdb67cbf6e460fec350aa5371b1508f9f4528ecea23c436d94b5e8fcd4f681e30a6ac00a9704a188a03'
+  );
+});
+
+// const PRIVATE_KEY = 0xa665a45920422f9d417e4867efn;
+// const MESSAGE = ripemd160(new Uint8Array([97, 98, 99, 100, 101, 102, 103]));
+// prettier-ignore
+// const MESSAGE = new Uint8Array([
+//   135, 79, 153, 96, 197, 210, 183, 169, 181, 250, 211, 131, 225, 186, 68, 113, 158, 187, 116, 58,
+// ]);
+// const WRONG_MESSAGE = ripemd160(new Uint8Array([98, 99, 100, 101, 102, 103]));
+// prettier-ignore
+// const WRONG_MESSAGE = new Uint8Array([
+//   88, 157, 140, 127, 29, 160, 162, 75, 192, 123, 115, 129, 173, 72, 177, 207, 194, 17, 175, 28,
+// ]);
+// // it("should verify just signed message", async () => {
+// //   await fc.assert(fc.asyncProperty(
+// //     fc.hexa(),
+// //     fc.bigInt(2n, ristretto25519.PRIME_ORDER),
+// //     async (message, privateKey) => {
+// //       const publicKey = await ristretto25519.getPublicKey(privateKey);
+// //       const signature = await ristretto25519.sign(message, privateKey);
+// //       expect(publicKey.length).toBe(32);
+// //       expect(signature.length).toBe(64);
+// //       expect(await ristretto25519.verify(signature, message, publicKey)).toBe(true);
+// //     }),
+// //    { numRuns: 1 }
+// //   );
+// // });
+// // it("should not verify sign with wrong message", async () => {
+// //   await fc.assert(fc.asyncProperty(
+// //     fc.array(fc.integer(0x00, 0xff)),
+// //     fc.array(fc.integer(0x00, 0xff)),
+// //     fc.bigInt(2n, ristretto25519.PRIME_ORDER),
+// //     async (bytes, wrongBytes, privateKey) => {
+// //       const message = new Uint8Array(bytes);
+// //       const wrongMessage = new Uint8Array(wrongBytes);
+// //       const publicKey = await ristretto25519.getPublicKey(privateKey);
+// //       const signature = await ristretto25519.sign(message, privateKey);
+// //       expect(await ristretto25519.verify(signature, wrongMessage, publicKey)).toBe(
+// //         bytes.toString() === wrongBytes.toString()
+// //       );
+// //     }),
+// //    { numRuns: 1 }
+// //   );
+// // });
+// // it("should sign and verify", async () => {
+// //   const publicKey = await ristretto25519.getPublicKey(PRIVATE_KEY);
+// //   const signature = await ristretto25519.sign(MESSAGE, PRIVATE_KEY);
+// //   expect(await ristretto25519.verify(signature, MESSAGE, publicKey)).toBe(true);
+// // });
+// // it("should not verify signature with wrong public key", async () => {
+// //   const publicKey = await ristretto25519.getPublicKey(12);
+// //   const signature = await ristretto25519.sign(MESSAGE, PRIVATE_KEY);
+// //   expect(await ristretto25519.verify(signature, MESSAGE, publicKey)).toBe(false);
+// // });
+// // it("should not verify signature with wrong hash", async () => {
+// //   const publicKey = await ristretto25519.getPublicKey(PRIVATE_KEY);
+// //   const signature = await ristretto25519.sign(MESSAGE, PRIVATE_KEY);
+// //   expect(await ristretto25519.verify(signature, WRONG_MESSAGE, publicKey)).toBe(false);
+// // });
+should('ristretto255/should follow the byte encodings of small multiples', () => {
+  const encodingsOfSmallMultiples = [
+    // This is the identity point
+    '0000000000000000000000000000000000000000000000000000000000000000',
+    // This is the basepoint
+    'e2f2ae0a6abc4e71a884a961c500515f58e30b6aa582dd8db6a65945e08d2d76',
+    // These are small multiples of the basepoint
+    '6a493210f7499cd17fecb510ae0cea23a110e8d5b901f8acadd3095c73a3b919',
+    '94741f5d5d52755ece4f23f044ee27d5d1ea1e2bd196b462166b16152a9d0259',
+    'da80862773358b466ffadfe0b3293ab3d9fd53c5ea6c955358f568322daf6a57',
+    'e882b131016b52c1d3337080187cf768423efccbb517bb495ab812c4160ff44e',
+    'f64746d3c92b13050ed8d80236a7f0007c3b3f962f5ba793d19a601ebb1df403',
+    '44f53520926ec81fbd5a387845beb7df85a96a24ece18738bdcfa6a7822a176d',
+    '903293d8f2287ebe10e2374dc1a53e0bc887e592699f02d077d5263cdd55601c',
+    '02622ace8f7303a31cafc63f8fc48fdc16e1c8c8d234b2f0d6685282a9076031',
+    '20706fd788b2720a1ed2a5dad4952b01f413bcf0e7564de8cdc816689e2db95f',
+    'bce83f8ba5dd2fa572864c24ba1810f9522bc6004afe95877ac73241cafdab42',
+    'e4549ee16b9aa03099ca208c67adafcafa4c3f3e4e5303de6026e3ca8ff84460',
+    'aa52e000df2e16f55fb1032fc33bc42742dad6bd5a8fc0be0167436c5948501f',
+    '46376b80f409b29dc2b5f6f0c52591990896e5716f41477cd30085ab7f10301e',
+    'e0c418f7c8d9c4cdd7395b93ea124f3ad99021bb681dfc3302a9d99a2e53e64e',
+  ];
+  let B = RistrettoPoint.BASE;
+  let P = RistrettoPoint.ZERO;
+  for (const encoded of encodingsOfSmallMultiples) {
+    deepStrictEqual(P.toHex(), encoded);
+    deepStrictEqual(RistrettoPoint.fromHex(encoded).toHex(), encoded);
+    P = P.add(B);
+  }
+});
+should('ristretto255/should not convert bad bytes encoding', () => {
+  const badEncodings = [
+    // These are all bad because they're non-canonical field encodings.
+    '00ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff',
+    'ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f',
+    'f3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f',
+    'edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f',
+    // These are all bad because they're negative field elements.
+    '0100000000000000000000000000000000000000000000000000000000000000',
+    '01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f',
+    'ed57ffd8c914fb201471d1c3d245ce3c746fcbe63a3679d51b6a516ebebe0e20',
+    'c34c4e1826e5d403b78e246e88aa051c36ccf0aafebffe137d148a2bf9104562',
+    'c940e5a4404157cfb1628b108db051a8d439e1a421394ec4ebccb9ec92a8ac78',
+    '47cfc5497c53dc8e61c91d17fd626ffb1c49e2bca94eed052281b510b1117a24',
+    'f1c6165d33367351b0da8f6e4511010c68174a03b6581212c71c0e1d026c3c72',
+    '87260f7a2f12495118360f02c26a470f450dadf34a413d21042b43b9d93e1309',
+    // These are all bad because they give a nonsquare x².
+    '26948d35ca62e643e26a83177332e6b6afeb9d08e4268b650f1f5bbd8d81d371',
+    '4eac077a713c57b4f4397629a4145982c661f48044dd3f96427d40b147d9742f',
+    'de6a7b00deadc788eb6b6c8d20c0ae96c2f2019078fa604fee5b87d6e989ad7b',
+    'bcab477be20861e01e4a0e295284146a510150d9817763caf1a6f4b422d67042',
+    '2a292df7e32cababbd9de088d1d1abec9fc0440f637ed2fba145094dc14bea08',
+    'f4a9e534fc0d216c44b218fa0c42d99635a0127ee2e53c712f70609649fdff22',
+    '8268436f8c4126196cf64b3c7ddbda90746a378625f9813dd9b8457077256731',
+    '2810e5cbc2cc4d4eece54f61c6f69758e289aa7ab440b3cbeaa21995c2f4232b',
+    // These are all bad because they give a negative xy value.
+    '3eb858e78f5a7254d8c9731174a94f76755fd3941c0ac93735c07ba14579630e',
+    'a45fdc55c76448c049a1ab33f17023edfb2be3581e9c7aade8a6125215e04220',
+    'd483fe813c6ba647ebbfd3ec41adca1c6130c2beeee9d9bf065c8d151c5f396e',
+    '8a2e1d30050198c65a54483123960ccc38aef6848e1ec8f5f780e8523769ba32',
+    '32888462f8b486c68ad7dd9610be5192bbeaf3b443951ac1a8118419d9fa097b',
+    '227142501b9d4355ccba290404bde41575b037693cef1f438c47f8fbf35d1165',
+    '5c37cc491da847cfeb9281d407efc41e15144c876e0170b499a96a22ed31e01e',
+    '445425117cb8c90edcbc7c1cc0e74f747f2c1efa5630a967c64f287792a48a4b',
+    // This is s = -1, which causes y = 0.
+    'ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f',
+  ];
+  for (const badBytes of badEncodings) {
+    const b = hexToBytes(badBytes);
+    throws(() => RistrettoPoint.fromHex(b), badBytes);
+  }
+});
+should('ristretto255/should create right points from uniform hash', async () => {
+  const labels = [
+    'Ristretto is traditionally a short shot of espresso coffee',
+    'made with the normal amount of ground coffee but extracted with',
+    'about half the amount of water in the same amount of time',
+    'by using a finer grind.',
+    'This produces a concentrated shot of coffee per volume.',
+    'Just pulling a normal shot short will produce a weaker shot',
+    'and is not a Ristretto as some believe.',
+  ];
+  const encodedHashToPoints = [
+    '3066f82a1a747d45120d1740f14358531a8f04bbffe6a819f86dfe50f44a0a46',
+    'f26e5b6f7d362d2d2a94c5d0e7602cb4773c95a2e5c31a64f133189fa76ed61b',
+    '006ccd2a9e6867e6a2c5cea83d3302cc9de128dd2a9a57dd8ee7b9d7ffe02826',
+    'f8f0c87cf237953c5890aec3998169005dae3eca1fbb04548c635953c817f92a',
+    'ae81e7dedf20a497e10c304a765c1767a42d6e06029758d2d7e8ef7cc4c41179',
+    'e2705652ff9f5e44d3e841bf1c251cf7dddb77d140870d1ab2ed64f1a9ce8628',
+    '80bd07262511cdde4863f8a7434cef696750681cb9510eea557088f76d9e5065',
+  ];
+
+  for (let i = 0; i < labels.length; i++) {
+    const hash = sha512(utf8ToBytes(labels[i]));
+    const point = RistrettoPoint.hashToCurve(hash);
+    deepStrictEqual(point.toHex(), encodedHashToPoints[i]);
+  }
+});
+
+should('input immutability: sign/verify are immutable', () => {
+  const privateKey = ed.utils.randomPrivateKey();
+  const publicKey = ed.getPublicKey(privateKey);
+
+  for (let i = 0; i < 100; i++) {
+    let payload = randomBytes(100);
+    let signature = ed.sign(payload, privateKey);
+    if (!ed.verify(signature, payload, publicKey)) {
+      throw new Error('Signature verification failed');
+    }
+    const signatureCopy = Buffer.alloc(signature.byteLength);
+    signatureCopy.set(signature, 0); // <-- breaks
+    payload = payload.slice();
+    signature = signature.slice();
+
+    if (!ed.verify(signatureCopy, payload, publicKey))
+      throw new Error('Copied signature verification failed');
+  }
+});
+
+// https://zips.z.cash/zip-0215
+// Vectors from https://gist.github.com/hdevalence/93ed42d17ecab8e42138b213812c8cc7
+should('ZIP-215 compliance tests/should pass all of them', () => {
+  const str = utf8ToBytes('Zcash');
+  for (let v of zip215) {
+    let noble = false;
+    try {
+      noble = ed.verify(v.sig_bytes, str, v.vk_bytes);
+    } catch (e) {
+      noble = false;
+    }
+    deepStrictEqual(noble, v.valid_zip215);
+  }
+});
+should('ZIP-215 compliance tests/disallows sig.s >= CURVE.n', () => {
+  const sig = new ed.Signature(ed.Point.BASE, 1n);
+  sig.s = ed.CURVE.n + 1n;
+  throws(() => ed.verify(sig, 'deadbeef', ed.Point.BASE));
+});
+
+const rfc7748Mul = [
+  {
+    scalar: 'a546e36bf0527c9d3b16154b82465edd62144c0ac1fc5a18506a2244ba449ac4',
+    u: 'e6db6867583030db3594c1a424b15f7c726624ec26b3353b10a903a6d0ab1c4c',
+    outputU: 'c3da55379de9c6908e94ea4df28d084f32eccf03491c71f754b4075577a28552',
+  },
+  {
+    scalar: '4b66e9d4d1b4673c5ad22691957d6af5c11b6421e0ea01d42ca4169e7918ba0d',
+    u: 'e5210f12786811d3f4b7959d0538ae2c31dbe7106fc03c3efc4cd549c715a493',
+    outputU: '95cbde9476e8907d7aade45cb4b873f88b595a68799fa152e6f8f7647aac7957',
+  },
+];
+for (let i = 0; i < rfc7748Mul.length; i++) {
+  const v = rfc7748Mul[i];
+  should(`RFC7748: scalarMult (${i})`, () => {
+    deepStrictEqual(hex(x25519.scalarMult(v.scalar, v.u)), v.outputU);
+  });
+}
+
+const rfc7748Iter = [
+  { scalar: '422c8e7a6227d7bca1350b3e2bb7279f7897b87bb6854b783c60e80311ae3079', iters: 1 },
+  { scalar: '684cf59ba83309552800ef566f2f4d3c1c3887c49360e3875f2eb94d99532c51', iters: 1000 },
+  // { scalar: '7c3911e0ab2586fd864497297e575e6f3bc601c0883c30df5f4dd2d24f665424', iters: 1000000 },
+];
+for (let i = 0; i < rfc7748Iter.length; i++) {
+  const { scalar, iters } = rfc7748Iter[i];
+  should(`RFC7748: scalarMult iteration (${i})`, () => {
+    let k = x25519.Gu;
+    for (let i = 0, u = k; i < iters; i++) [k, u] = [x25519.scalarMult(k, u), k];
+    deepStrictEqual(hex(k), scalar);
+  });
+}
+
+should('RFC7748 getSharedKey', () => {
+  const alicePrivate = '77076d0a7318a57d3c16c17251b26645df4c2f87ebc0992ab177fba51db92c2a';
+  const alicePublic = '8520f0098930a754748b7ddcb43ef75a0dbf3a0d26381af4eba4a98eaa9b4e6a';
+  const bobPrivate = '5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb';
+  const bobPublic = 'de9edb7d7b7dc1b4d35b61c2ece435373f8343c85b78674dadfc7e146f882b4f';
+  const shared = '4a5d9d5ba4ce2de1728e3bf480350f25e07e21c947d19e3376f09b3c1e161742';
+  deepStrictEqual(alicePublic, hex(x25519.getPublicKey(alicePrivate)));
+  deepStrictEqual(bobPublic, hex(x25519.getPublicKey(bobPrivate)));
+  deepStrictEqual(hex(x25519.scalarMult(alicePrivate, bobPublic)), shared);
+  deepStrictEqual(hex(x25519.scalarMult(bobPrivate, alicePublic)), shared);
+});
+
+// should('X25519/getSharedSecret() should be commutative', () => {
+//   for (let i = 0; i < 512; i++) {
+//     const asec = ed.utils.randomPrivateKey();
+//     const apub = ed.getPublicKey(asec);
+//     const bsec = ed.utils.randomPrivateKey();
+//     const bpub = ed.getPublicKey(bsec);
+//     try {
+//       deepStrictEqual(ed.getSharedSecret(asec, bpub), ed.getSharedSecret(bsec, apub));
+//     } catch (error) {
+//       console.error('not commutative', { asec, apub, bsec, bpub });
+//       throw error;
+//     }
+//   }
+// });
+
+// should('X25519: should convert base point to montgomery using fromPoint', () => {
+//   deepStrictEqual(
+//     hex(ed.montgomeryCurve.UfromPoint(ed.Point.BASE)),
+//     ed.montgomeryCurve.BASE_POINT_U
+//   );
+// });
+
+{
+  const group = x25519vectors.testGroups[0];
+  should(`Wycheproof/X25519`, () => {
+    for (let i = 0; i < group.tests.length; i++) {
+      const v = group.tests[i];
+      const comment = `(${i}, ${v.result}) ${v.comment}`;
+      if (v.result === 'valid' || v.result === 'acceptable') {
+        try {
+          const shared = hex(x25519.scalarMult(v.private, v.public));
+          deepStrictEqual(shared, v.shared, comment);
+        } catch (e) {
+          // We are more strict
+          if (e.message.includes('Expected valid scalar')) return;
+          if (e.message.includes('Invalid private or public key received')) return;
+          throw e;
+        }
+      } else if (v.result === 'invalid') {
+        let failed = false;
+        try {
+          x25519.scalarMult(v.private, v.public);
+        } catch (error) {
+          failed = true;
+        }
+        deepStrictEqual(failed, true, comment);
+      } else throw new Error('unknown test result');
+    }
+  });
+}
+
+should(`Wycheproof/ED25519`, () => {
+  for (let g = 0; g < ed25519vectors.testGroups.length; g++) {
+    const group = ed25519vectors.testGroups[g];
+    const key = group.key;
+    deepStrictEqual(hex(ed.getPublicKey(key.sk)), key.pk, `(${g}, public)`);
+    for (let i = 0; i < group.tests.length; i++) {
+      const v = group.tests[i];
+      const comment = `(${g}/${i}, ${v.result}): ${v.comment}`;
+      if (v.result === 'valid' || v.result === 'acceptable') {
+        deepStrictEqual(hex(ed.sign(v.msg, key.sk)), v.sig, comment);
+        deepStrictEqual(ed.verify(v.sig, v.msg, key.pk), true, comment);
+      } else if (v.result === 'invalid') {
+        let failed = false;
+        try {
+          failed = !ed.verify(v.sig, v.msg, key.pk);
+        } catch (error) {
+          failed = true;
+        }
+        deepStrictEqual(failed, true, comment);
+      } else throw new Error('unknown test result');
+    }
+  }
+});
+
+should('Property test issue #1', () => {
+  const message = new Uint8Array([12, 12, 12]);
+  const signature = ed.sign(message, to32Bytes(1n));
+  const publicKey = ed.getPublicKey(to32Bytes(1n)); // <- was 1n
+  deepStrictEqual(ed.verify(signature, message, publicKey), true);
+});
+
+const VECTORS_RFC8032_CTX = [
+  {
+    secretKey: '0305334e381af78f141cb666f6199f57bc3495335a256a95bd2a55bf546663f6',
+    publicKey: 'dfc9425e4f968f7f0c29f0259cf5f9aed6851c2bb4ad8bfb860cfee0ab248292',
+    message: 'f726936d19c800494e3fdaff20b276a8',
+    context: '666f6f',
+    signature:
+      '55a4cc2f70a54e04288c5f4cd1e45a7b' +
+      'b520b36292911876cada7323198dd87a' +
+      '8b36950b95130022907a7fb7c4e9b2d5' +
+      'f6cca685a587b4b21f4b888e4e7edb0d',
+  },
+  {
+    secretKey: '0305334e381af78f141cb666f6199f57bc3495335a256a95bd2a55bf546663f6',
+    publicKey: 'dfc9425e4f968f7f0c29f0259cf5f9aed6851c2bb4ad8bfb860cfee0ab248292',
+    message: 'f726936d19c800494e3fdaff20b276a8',
+    context: '626172',
+    signature:
+      'fc60d5872fc46b3aa69f8b5b4351d580' +
+      '8f92bcc044606db097abab6dbcb1aee3' +
+      '216c48e8b3b66431b5b186d1d28f8ee1' +
+      '5a5ca2df6668346291c2043d4eb3e90d',
+  },
+  {
+    secretKey: '0305334e381af78f141cb666f6199f57bc3495335a256a95bd2a55bf546663f6',
+    publicKey: 'dfc9425e4f968f7f0c29f0259cf5f9aed6851c2bb4ad8bfb860cfee0ab248292',
+    message: '508e9e6882b979fea900f62adceaca35',
+    context: '666f6f',
+    signature:
+      '8b70c1cc8310e1de20ac53ce28ae6e72' +
+      '07f33c3295e03bb5c0732a1d20dc6490' +
+      '8922a8b052cf99b7c4fe107a5abb5b2c' +
+      '4085ae75890d02df26269d8945f84b0b',
+  },
+  {
+    secretKey: 'ab9c2853ce297ddab85c993b3ae14bcad39b2c682beabc27d6d4eb20711d6560',
+    publicKey: '0f1d1274943b91415889152e893d80e93275a1fc0b65fd71b4b0dda10ad7d772',
+    message: 'f726936d19c800494e3fdaff20b276a8',
+    context: '666f6f',
+    signature:
+      '21655b5f1aa965996b3f97b3c849eafb' +
+      'a922a0a62992f73b3d1b73106a84ad85' +
+      'e9b86a7b6005ea868337ff2d20a7f5fb' +
+      'd4cd10b0be49a68da2b2e0dc0ad8960f',
+  },
+];
+
+for (let i = 0; i < VECTORS_RFC8032_CTX.length; i++) {
+  const v = VECTORS_RFC8032_CTX[i];
+  should(`RFC8032ctx/${i}`, () => {
+    deepStrictEqual(hex(ed25519ctx.getPublicKey(v.secretKey)), v.publicKey);
+    deepStrictEqual(hex(ed25519ctx.sign(v.message, v.secretKey, v.context)), v.signature);
+    deepStrictEqual(ed25519ctx.verify(v.signature, v.message, v.publicKey, v.context), true);
+  });
+}
+
+const VECTORS_RFC8032_PH = [
+  {
+    secretKey: '833fe62409237b9d62ec77587520911e9a759cec1d19755b7da901b96dca3d42',
+    publicKey: 'ec172b93ad5e563bf4932c70e1245034c35467ef2efd4d64ebf819683467e2bf',
+    message: '616263',
+    signature:
+      '98a70222f0b8121aa9d30f813d683f80' +
+      '9e462b469c7ff87639499bb94e6dae41' +
+      '31f85042463c2a355a2003d062adf5aa' +
+      'a10b8c61e636062aaad11c2a26083406',
+  },
+];
+
+for (let i = 0; i < VECTORS_RFC8032_PH.length; i++) {
+  const v = VECTORS_RFC8032_PH[i];
+  should(`RFC8032ph/${i}`, () => {
+    deepStrictEqual(hex(ed25519ph.getPublicKey(v.secretKey)), v.publicKey);
+    deepStrictEqual(hex(ed25519ph.sign(v.message, v.secretKey)), v.signature);
+    deepStrictEqual(ed25519ph.verify(v.signature, v.message, v.publicKey), true);
+  });
+}
+
+should('X25519 base point', () => {
+  const { y } = ed25519.Point.BASE;
+  const u = ed25519.utils.mod((y + 1n) * ed25519.utils.invert(1n - y, ed25519.CURVE.P));
+  deepStrictEqual(hex(numberToBytesLE(u, 32)), x25519.Gu);
+});
+
+// ESM is broken.
+import url from 'url';
+if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
+  should.run();
+}

test/ed448.test.js

@@ -0,0 +1,664 @@
+import { deepStrictEqual, throws } from 'assert';
+import { should } from 'micro-should';
+import * as fc from 'fast-check';
+import { ed448, ed448ph, x448 } from '../lib/esm/ed448.js';
+import { hexToBytes, bytesToHex, randomBytes } from '@noble/hashes/utils';
+import { numberToBytesLE } from '../lib/esm/abstract/utils.js';
+import { default as ed448vectors } from './wycheproof/ed448_test.json' assert { type: 'json' };
+import { default as x448vectors } from './wycheproof/x448_test.json' assert { type: 'json' };
+
+const ed = ed448;
+const hex = bytesToHex;
+ed.utils.precompute(4);
+
+should(`Basic`, () => {
+  const G1 = ed.Point.BASE;
+  deepStrictEqual(
+    G1.x,
+    224580040295924300187604334099896036246789641632564134246125461686950415467406032909029192869357953282578032075146446173674602635247710n
+  );
+  deepStrictEqual(
+    G1.y,
+    298819210078481492676017930443930673437544040154080242095928241372331506189835876003536878655418784733982303233503462500531545062832660n
+  );
+  const G2 = ed.Point.BASE.multiply(2n);
+  deepStrictEqual(
+    G2.x,
+    484559149530404593699549205258669689569094240458212040187660132787056912146709081364401144455726350866276831544947397859048262938744149n
+  );
+  deepStrictEqual(
+    G2.y,
+    494088759867433727674302672526735089350544552303727723746126484473087719117037293890093462157703888342865036477787453078312060500281069n
+  );
+  const G3 = ed.Point.BASE.multiply(3n);
+  deepStrictEqual(
+    G3.x,
+    23839778817283171003887799738662344287085130522697782688245073320169861206004018274567429238677677920280078599146891901463786155880335n
+  );
+  deepStrictEqual(
+    G3.y,
+    636046652612779686502873775776967954190574036985351036782021535703553242737829645273154208057988851307101009474686328623630835377952508n
+  );
+});
+
+should('Basic/decompress', () => {
+  const G1 = ed.Point.BASE;
+  const G2 = ed.Point.BASE.multiply(2n);
+  const G3 = ed.Point.BASE.multiply(3n);
+  const points = [G1, G2, G3];
+  const getXY = (p) => ({ x: p.x, y: p.y });
+  for (const p of points) deepStrictEqual(getXY(ed.Point.fromHex(p.toHex())), getXY(p));
+});
+
+const VECTORS_RFC8032 = [
+  {
+    secretKey:
+      '6c82a562cb808d10d632be89c8513ebf' +
+      '6c929f34ddfa8c9f63c9960ef6e348a3' +
+      '528c8a3fcc2f044e39a3fc5b94492f8f' +
+      '032e7549a20098f95b',
+    publicKey:
+      '5fd7449b59b461fd2ce787ec616ad46a' +
+      '1da1342485a70e1f8a0ea75d80e96778' +
+      'edf124769b46c7061bd6783df1e50f6c' +
+      'd1fa1abeafe8256180',
+    message: '',
+    signature:
+      '533a37f6bbe457251f023c0d88f976ae' +
+      '2dfb504a843e34d2074fd823d41a591f' +
+      '2b233f034f628281f2fd7a22ddd47d78' +
+      '28c59bd0a21bfd3980ff0d2028d4b18a' +
+      '9df63e006c5d1c2d345b925d8dc00b41' +
+      '04852db99ac5c7cdda8530a113a0f4db' +
+      'b61149f05a7363268c71d95808ff2e65' +
+      '2600',
+  },
+  {
+    secretKey:
+      'c4eab05d357007c632f3dbb48489924d' +
+      '552b08fe0c353a0d4a1f00acda2c463a' +
+      'fbea67c5e8d2877c5e3bc397a659949e' +
+      'f8021e954e0a12274e',
+    publicKey:
+      '43ba28f430cdff456ae531545f7ecd0a' +
+      'c834a55d9358c0372bfa0c6c6798c086' +
+      '6aea01eb00742802b8438ea4cb82169c' +
+      '235160627b4c3a9480',
+
+    message: '03',
+    signature:
+      '26b8f91727bd62897af15e41eb43c377' +
+      'efb9c610d48f2335cb0bd0087810f435' +
+      '2541b143c4b981b7e18f62de8ccdf633' +
+      'fc1bf037ab7cd779805e0dbcc0aae1cb' +
+      'cee1afb2e027df36bc04dcecbf154336' +
+      'c19f0af7e0a6472905e799f1953d2a0f' +
+      'f3348ab21aa4adafd1d234441cf807c0' +
+      '3a00',
+  },
+  {
+    secretKey:
+      'cd23d24f714274e744343237b93290f5' +
+      '11f6425f98e64459ff203e8985083ffd' +
+      'f60500553abc0e05cd02184bdb89c4cc' +
+      'd67e187951267eb328',
+    publicKey:
+      'dcea9e78f35a1bf3499a831b10b86c90' +
+      'aac01cd84b67a0109b55a36e9328b1e3' +
+      '65fce161d71ce7131a543ea4cb5f7e9f' +
+      '1d8b00696447001400',
+    message: '0c3e544074ec63b0265e0c',
+    signature:
+      '1f0a8888ce25e8d458a21130879b840a' +
+      '9089d999aaba039eaf3e3afa090a09d3' +
+      '89dba82c4ff2ae8ac5cdfb7c55e94d5d' +
+      '961a29fe0109941e00b8dbdeea6d3b05' +
+      '1068df7254c0cdc129cbe62db2dc957d' +
+      'bb47b51fd3f213fb8698f064774250a5' +
+      '028961c9bf8ffd973fe5d5c206492b14' +
+      '0e00',
+  },
+  {
+    secretKey:
+      '258cdd4ada32ed9c9ff54e63756ae582' +
+      'fb8fab2ac721f2c8e676a72768513d93' +
+      '9f63dddb55609133f29adf86ec9929dc' +
+      'cb52c1c5fd2ff7e21b',
+    publicKey:
+      '3ba16da0c6f2cc1f30187740756f5e79' +
+      '8d6bc5fc015d7c63cc9510ee3fd44adc' +
+      '24d8e968b6e46e6f94d19b945361726b' +
+      'd75e149ef09817f580',
+    message: '64a65f3cdedcdd66811e2915',
+    signature:
+      '7eeeab7c4e50fb799b418ee5e3197ff6' +
+      'bf15d43a14c34389b59dd1a7b1b85b4a' +
+      'e90438aca634bea45e3a2695f1270f07' +
+      'fdcdf7c62b8efeaf00b45c2c96ba457e' +
+      'b1a8bf075a3db28e5c24f6b923ed4ad7' +
+      '47c3c9e03c7079efb87cb110d3a99861' +
+      'e72003cbae6d6b8b827e4e6c143064ff' +
+      '3c00',
+  },
+  {
+    secretKey:
+      '7ef4e84544236752fbb56b8f31a23a10' +
+      'e42814f5f55ca037cdcc11c64c9a3b29' +
+      '49c1bb60700314611732a6c2fea98eeb' +
+      'c0266a11a93970100e',
+    publicKey:
+      'b3da079b0aa493a5772029f0467baebe' +
+      'e5a8112d9d3a22532361da294f7bb381' +
+      '5c5dc59e176b4d9f381ca0938e13c6c0' +
+      '7b174be65dfa578e80',
+    message: '64a65f3cdedcdd66811e2915e7',
+    signature:
+      '6a12066f55331b6c22acd5d5bfc5d712' +
+      '28fbda80ae8dec26bdd306743c5027cb' +
+      '4890810c162c027468675ecf645a8317' +
+      '6c0d7323a2ccde2d80efe5a1268e8aca' +
+      '1d6fbc194d3f77c44986eb4ab4177919' +
+      'ad8bec33eb47bbb5fc6e28196fd1caf5' +
+      '6b4e7e0ba5519234d047155ac727a105' +
+      '3100',
+  },
+  {
+    secretKey:
+      'd65df341ad13e008567688baedda8e9d' +
+      'cdc17dc024974ea5b4227b6530e339bf' +
+      'f21f99e68ca6968f3cca6dfe0fb9f4fa' +
+      'b4fa135d5542ea3f01',
+    publicKey:
+      'df9705f58edbab802c7f8363cfe5560a' +
+      'b1c6132c20a9f1dd163483a26f8ac53a' +
+      '39d6808bf4a1dfbd261b099bb03b3fb5' +
+      '0906cb28bd8a081f00',
+    message:
+      'bd0f6a3747cd561bdddf4640a332461a' +
+      '4a30a12a434cd0bf40d766d9c6d458e5' +
+      '512204a30c17d1f50b5079631f64eb31' +
+      '12182da3005835461113718d1a5ef944',
+    signature:
+      '554bc2480860b49eab8532d2a533b7d5' +
+      '78ef473eeb58c98bb2d0e1ce488a98b1' +
+      '8dfde9b9b90775e67f47d4a1c3482058' +
+      'efc9f40d2ca033a0801b63d45b3b722e' +
+      'f552bad3b4ccb667da350192b61c508c' +
+      'f7b6b5adadc2c8d9a446ef003fb05cba' +
+      '5f30e88e36ec2703b349ca229c267083' +
+      '3900',
+  },
+  {
+    secretKey:
+      '2ec5fe3c17045abdb136a5e6a913e32a' +
+      'b75ae68b53d2fc149b77e504132d3756' +
+      '9b7e766ba74a19bd6162343a21c8590a' +
+      'a9cebca9014c636df5',
+    publicKey:
+      '79756f014dcfe2079f5dd9e718be4171' +
+      'e2ef2486a08f25186f6bff43a9936b9b' +
+      'fe12402b08ae65798a3d81e22e9ec80e' +
+      '7690862ef3d4ed3a00',
+    message:
+      '15777532b0bdd0d1389f636c5f6b9ba7' +
+      '34c90af572877e2d272dd078aa1e567c' +
+      'fa80e12928bb542330e8409f31745041' +
+      '07ecd5efac61ae7504dabe2a602ede89' +
+      'e5cca6257a7c77e27a702b3ae39fc769' +
+      'fc54f2395ae6a1178cab4738e543072f' +
+      'c1c177fe71e92e25bf03e4ecb72f47b6' +
+      '4d0465aaea4c7fad372536c8ba516a60' +
+      '39c3c2a39f0e4d832be432dfa9a706a6' +
+      'e5c7e19f397964ca4258002f7c0541b5' +
+      '90316dbc5622b6b2a6fe7a4abffd9610' +
+      '5eca76ea7b98816af0748c10df048ce0' +
+      '12d901015a51f189f3888145c03650aa' +
+      '23ce894c3bd889e030d565071c59f409' +
+      'a9981b51878fd6fc110624dcbcde0bf7' +
+      'a69ccce38fabdf86f3bef6044819de11',
+    signature:
+      'c650ddbb0601c19ca11439e1640dd931' +
+      'f43c518ea5bea70d3dcde5f4191fe53f' +
+      '00cf966546b72bcc7d58be2b9badef28' +
+      '743954e3a44a23f880e8d4f1cfce2d7a' +
+      '61452d26da05896f0a50da66a239a8a1' +
+      '88b6d825b3305ad77b73fbac0836ecc6' +
+      '0987fd08527c1a8e80d5823e65cafe2a' +
+      '3d00',
+  },
+  {
+    secretKey:
+      '872d093780f5d3730df7c212664b37b8' +
+      'a0f24f56810daa8382cd4fa3f77634ec' +
+      '44dc54f1c2ed9bea86fafb7632d8be19' +
+      '9ea165f5ad55dd9ce8',
+    publicKey:
+      'a81b2e8a70a5ac94ffdbcc9badfc3feb' +
+      '0801f258578bb114ad44ece1ec0e799d' +
+      'a08effb81c5d685c0c56f64eecaef8cd' +
+      'f11cc38737838cf400',
+    message:
+      '6ddf802e1aae4986935f7f981ba3f035' +
+      '1d6273c0a0c22c9c0e8339168e675412' +
+      'a3debfaf435ed651558007db4384b650' +
+      'fcc07e3b586a27a4f7a00ac8a6fec2cd' +
+      '86ae4bf1570c41e6a40c931db27b2faa' +
+      '15a8cedd52cff7362c4e6e23daec0fbc' +
+      '3a79b6806e316efcc7b68119bf46bc76' +
+      'a26067a53f296dafdbdc11c77f7777e9' +
+      '72660cf4b6a9b369a6665f02e0cc9b6e' +
+      'dfad136b4fabe723d2813db3136cfde9' +
+      'b6d044322fee2947952e031b73ab5c60' +
+      '3349b307bdc27bc6cb8b8bbd7bd32321' +
+      '9b8033a581b59eadebb09b3c4f3d2277' +
+      'd4f0343624acc817804728b25ab79717' +
+      '2b4c5c21a22f9c7839d64300232eb66e' +
+      '53f31c723fa37fe387c7d3e50bdf9813' +
+      'a30e5bb12cf4cd930c40cfb4e1fc6225' +
+      '92a49588794494d56d24ea4b40c89fc0' +
+      '596cc9ebb961c8cb10adde976a5d602b' +
+      '1c3f85b9b9a001ed3c6a4d3b1437f520' +
+      '96cd1956d042a597d561a596ecd3d173' +
+      '5a8d570ea0ec27225a2c4aaff26306d1' +
+      '526c1af3ca6d9cf5a2c98f47e1c46db9' +
+      'a33234cfd4d81f2c98538a09ebe76998' +
+      'd0d8fd25997c7d255c6d66ece6fa56f1' +
+      '1144950f027795e653008f4bd7ca2dee' +
+      '85d8e90f3dc315130ce2a00375a318c7' +
+      'c3d97be2c8ce5b6db41a6254ff264fa6' +
+      '155baee3b0773c0f497c573f19bb4f42' +
+      '40281f0b1f4f7be857a4e59d416c06b4' +
+      'c50fa09e1810ddc6b1467baeac5a3668' +
+      'd11b6ecaa901440016f389f80acc4db9' +
+      '77025e7f5924388c7e340a732e554440' +
+      'e76570f8dd71b7d640b3450d1fd5f041' +
+      '0a18f9a3494f707c717b79b4bf75c984' +
+      '00b096b21653b5d217cf3565c9597456' +
+      'f70703497a078763829bc01bb1cbc8fa' +
+      '04eadc9a6e3f6699587a9e75c94e5bab' +
+      '0036e0b2e711392cff0047d0d6b05bd2' +
+      'a588bc109718954259f1d86678a579a3' +
+      '120f19cfb2963f177aeb70f2d4844826' +
+      '262e51b80271272068ef5b3856fa8535' +
+      'aa2a88b2d41f2a0e2fda7624c2850272' +
+      'ac4a2f561f8f2f7a318bfd5caf969614' +
+      '9e4ac824ad3460538fdc25421beec2cc' +
+      '6818162d06bbed0c40a387192349db67' +
+      'a118bada6cd5ab0140ee273204f628aa' +
+      'd1c135f770279a651e24d8c14d75a605' +
+      '9d76b96a6fd857def5e0b354b27ab937' +
+      'a5815d16b5fae407ff18222c6d1ed263' +
+      'be68c95f32d908bd895cd76207ae7264' +
+      '87567f9a67dad79abec316f683b17f2d' +
+      '02bf07e0ac8b5bc6162cf94697b3c27c' +
+      'd1fea49b27f23ba2901871962506520c' +
+      '392da8b6ad0d99f7013fbc06c2c17a56' +
+      '9500c8a7696481c1cd33e9b14e40b82e' +
+      '79a5f5db82571ba97bae3ad3e0479515' +
+      'bb0e2b0f3bfcd1fd33034efc6245eddd' +
+      '7ee2086ddae2600d8ca73e214e8c2b0b' +
+      'db2b047c6a464a562ed77b73d2d841c4' +
+      'b34973551257713b753632efba348169' +
+      'abc90a68f42611a40126d7cb21b58695' +
+      '568186f7e569d2ff0f9e745d0487dd2e' +
+      'b997cafc5abf9dd102e62ff66cba87',
+    signature:
+      'e301345a41a39a4d72fff8df69c98075' +
+      'a0cc082b802fc9b2b6bc503f926b65bd' +
+      'df7f4c8f1cb49f6396afc8a70abe6d8a' +
+      'ef0db478d4c6b2970076c6a0484fe76d' +
+      '76b3a97625d79f1ce240e7c576750d29' +
+      '5528286f719b413de9ada3e8eb78ed57' +
+      '3603ce30d8bb761785dc30dbc320869e' +
+      '1a00',
+  },
+];
+
+for (let i = 0; i < VECTORS_RFC8032.length; i++) {
+  const v = VECTORS_RFC8032[i];
+  should(`RFC8032/${i}`, () => {
+    deepStrictEqual(hex(ed.getPublicKey(v.secretKey)), v.publicKey);
+    deepStrictEqual(hex(ed.sign(v.message, v.secretKey)), v.signature);
+    deepStrictEqual(ed.verify(v.signature, v.message, v.publicKey), true);
+  });
+}
+
+should('ed448/should not accept >57byte private keys', async () => {
+  const invalidPriv =
+    100000000000000000000000000000000000009000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000090000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000800073278156000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000n;
+  throws(() => ed.getPublicKey(invalidPriv));
+});
+
+function to57Bytes(numOrStr) {
+  let hex = typeof numOrStr === 'string' ? numOrStr : numOrStr.toString(16);
+  return hexToBytes(hex.padStart(114, '0'));
+}
+
+should('ed448/should verify recent signature', () => {
+  fc.assert(
+    fc.property(
+      fc.hexaString({ minLength: 2, maxLength: 57 }),
+      fc.bigInt(2n, ed.CURVE.n),
+      (message, privateKey) => {
+        const publicKey = ed.getPublicKey(to57Bytes(privateKey));
+        const signature = ed.sign(to57Bytes(message), to57Bytes(privateKey));
+        deepStrictEqual(publicKey.length, 57);
+        deepStrictEqual(signature.length, 114);
+        deepStrictEqual(ed.verify(signature, to57Bytes(message), publicKey), true);
+      }
+    ),
+    { numRuns: 5 }
+  );
+});
+should('ed448/should not verify signature with wrong message', () => {
+  fc.assert(
+    fc.property(
+      fc.array(fc.integer({ min: 0x00, max: 0xff })),
+      fc.array(fc.integer({ min: 0x00, max: 0xff })),
+      fc.bigInt(1n, ed.CURVE.n),
+      (bytes, wrongBytes, privateKey) => {
+        const message = new Uint8Array(bytes);
+        const wrongMessage = new Uint8Array(wrongBytes);
+        const priv = to57Bytes(privateKey);
+        const publicKey = ed.getPublicKey(priv);
+        const signature = ed.sign(message, priv);
+        deepStrictEqual(
+          ed.verify(signature, wrongMessage, publicKey),
+          bytes.toString() === wrongBytes.toString()
+        );
+      }
+    ),
+    { numRuns: 5 }
+  );
+});
+const privKey = to57Bytes('a665a45920422f9d417e4867ef');
+const msg = hexToBytes('874f9960c5d2b7a9b5fad383e1ba44719ebb743a');
+const wrongMsg = hexToBytes('589d8c7f1da0a24bc07b7381ad48b1cfc211af1c');
+should('ed25519/basic methods/should sign and verify', () => {
+  const publicKey = ed.getPublicKey(privKey);
+  const signature = ed.sign(msg, privKey);
+  deepStrictEqual(ed.verify(signature, msg, publicKey), true);
+});
+should('ed25519/basic methods/should not verify signature with wrong public key', () => {
+  const publicKey = ed.getPublicKey(12);
+  const signature = ed.sign(msg, privKey);
+  deepStrictEqual(ed.verify(signature, msg, publicKey), false);
+});
+should('ed25519/basic methods/should not verify signature with wrong hash', () => {
+  const publicKey = ed.getPublicKey(privKey);
+  const signature = ed.sign(msg, privKey);
+  deepStrictEqual(ed.verify(signature, wrongMsg, publicKey), false);
+});
+
+should('ed25519/sync methods/should sign and verify', () => {
+  const publicKey = ed.getPublicKey(privKey);
+  const signature = ed.sign(msg, privKey);
+  deepStrictEqual(ed.verify(signature, msg, publicKey), true);
+});
+should('ed25519/sync methods/should not verify signature with wrong public key', async () => {
+  const publicKey = ed.getPublicKey(12);
+  const signature = ed.sign(msg, privKey);
+  deepStrictEqual(ed.verify(signature, msg, publicKey), false);
+});
+should('ed25519/sync methods/should not verify signature with wrong hash', async () => {
+  const publicKey = ed.getPublicKey(privKey);
+  const signature = ed.sign(msg, privKey);
+  deepStrictEqual(ed.verify(signature, wrongMsg, publicKey), false);
+});
+
+should('ed25519/BASE_POINT.multiply()/should throw Point#multiply on TEST 5', () => {
+  for (const num of [0n, 0, -1n, -1, 1.1]) {
+    throws(() => ed.Point.BASE.multiply(num));
+  }
+});
+
+should('input immutability: sign/verify are immutable', () => {
+  const privateKey = ed.utils.randomPrivateKey();
+  const publicKey = ed.getPublicKey(privateKey);
+
+  for (let i = 0; i < 100; i++) {
+    let payload = randomBytes(100);
+    let signature = ed.sign(payload, privateKey);
+    if (!ed.verify(signature, payload, publicKey)) {
+      throw new Error('Signature verification failed');
+    }
+    const signatureCopy = Buffer.alloc(signature.byteLength);
+    signatureCopy.set(signature, 0); // <-- breaks
+    payload = payload.slice();
+    signature = signature.slice();
+
+    if (!ed.verify(signatureCopy, payload, publicKey))
+      throw new Error('Copied signature verification failed');
+  }
+});
+
+{
+  for (let g = 0; g < ed448vectors.testGroups.length; g++) {
+    const group = ed448vectors.testGroups[g];
+    const key = group.key;
+    should(`Wycheproof/ED448(${g}, public)`, () => {
+      deepStrictEqual(hex(ed.getPublicKey(key.sk)), key.pk);
+    });
+    should(`Wycheproof/ED448`, () => {
+      for (let i = 0; i < group.tests.length; i++) {
+        const v = group.tests[i];
+        const index = `${g}/${i} ${v.comment}`;
+        if (v.result === 'valid' || v.result === 'acceptable') {
+          deepStrictEqual(hex(ed.sign(v.msg, key.sk)), v.sig, index);
+          deepStrictEqual(ed.verify(v.sig, v.msg, key.pk), true, index);
+        } else if (v.result === 'invalid') {
+          let failed = false;
+          try {
+            failed = !ed.verify(v.sig, v.msg, key.pk);
+          } catch (error) {
+            failed = true;
+          }
+          deepStrictEqual(failed, true, index);
+        } else throw new Error('unknown test result');
+      }
+    });
+  }
+}
+
+// ECDH
+const rfc7748Mul = [
+  {
+    scalar:
+      '3d262fddf9ec8e88495266fea19a34d28882acef045104d0d1aae121700a779c984c24f8cdd78fbff44943eba368f54b29259a4f1c600ad3',
+    u: '06fce640fa3487bfda5f6cf2d5263f8aad88334cbd07437f020f08f9814dc031ddbdc38c19c6da2583fa5429db94ada18aa7a7fb4ef8a086',
+    outputU:
+      'ce3e4ff95a60dc6697da1db1d85e6afbdf79b50a2412d7546d5f239fe14fbaadeb445fc66a01b0779d98223961111e21766282f73dd96b6f',
+  },
+  {
+    scalar:
+      '203d494428b8399352665ddca42f9de8fef600908e0d461cb021f8c538345dd77c3e4806e25f46d3315c44e0a5b4371282dd2c8d5be3095f',
+    u: '0fbcc2f993cd56d3305b0b7d9e55d4c1a8fb5dbb52f8e9a1e9b6201b165d015894e56c4d3570bee52fe205e28a78b91cdfbde71ce8d157db',
+    outputU:
+      '884a02576239ff7a2f2f63b2db6a9ff37047ac13568e1e30fe63c4a7ad1b3ee3a5700df34321d62077e63633c575c1c954514e99da7c179d',
+  },
+];
+for (let i = 0; i < rfc7748Mul.length; i++) {
+  const v = rfc7748Mul[i];
+  should(`RFC7748: scalarMult (${i})`, () => {
+    deepStrictEqual(hex(x448.scalarMult(v.scalar, v.u)), v.outputU);
+  });
+}
+
+const rfc7748Iter = [
+  {
+    scalar:
+      '3f482c8a9f19b01e6c46ee9711d9dc14fd4bf67af30765c2ae2b846a4d23a8cd0db897086239492caf350b51f833868b9bc2b3bca9cf4113',
+    iters: 1,
+  },
+  {
+    scalar:
+      'aa3b4749d55b9daf1e5b00288826c467274ce3ebbdd5c17b975e09d4af6c67cf10d087202db88286e2b79fceea3ec353ef54faa26e219f38',
+    iters: 1000,
+  },
+  // { scalar: '077f453681caca3693198420bbe515cae0002472519b3e67661a7e89cab94695c8f4bcd66e61b9b9c946da8d524de3d69bd9d9d66b997e37', iters: 1000000 },
+];
+for (let i = 0; i < rfc7748Iter.length; i++) {
+  const { scalar, iters } = rfc7748Iter[i];
+  should(`RFC7748: scalarMult iteration (${i})`, () => {
+    let k = x448.Gu;
+    for (let i = 0, u = k; i < iters; i++) [k, u] = [x448.scalarMult(k, u), k];
+    deepStrictEqual(hex(k), scalar);
+  });
+}
+
+should('RFC7748 getSharedKey', () => {
+  const alicePrivate =
+    '9a8f4925d1519f5775cf46b04b5800d4ee9ee8bae8bc5565d498c28dd9c9baf574a9419744897391006382a6f127ab1d9ac2d8c0a598726b';
+  const alicePublic =
+    '9b08f7cc31b7e3e67d22d5aea121074a273bd2b83de09c63faa73d2c22c5d9bbc836647241d953d40c5b12da88120d53177f80e532c41fa0';
+  const bobPrivate =
+    '1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d';
+  const bobPublic =
+    '3eb7a829b0cd20f5bcfc0b599b6feccf6da4627107bdb0d4f345b43027d8b972fc3e34fb4232a13ca706dcb57aec3dae07bdc1c67bf33609';
+  const shared =
+    '07fff4181ac6cc95ec1c16a94a0f74d12da232ce40a77552281d282bb60c0b56fd2464c335543936521c24403085d59a449a5037514a879d';
+  deepStrictEqual(alicePublic, hex(x448.getPublicKey(alicePrivate)));
+  deepStrictEqual(bobPublic, hex(x448.getPublicKey(bobPrivate)));
+  deepStrictEqual(hex(x448.scalarMult(alicePrivate, bobPublic)), shared);
+  deepStrictEqual(hex(x448.scalarMult(bobPrivate, alicePublic)), shared);
+});
+
+{
+  const group = x448vectors.testGroups[0];
+  should(`Wycheproof/X448`, () => {
+    for (let i = 0; i < group.tests.length; i++) {
+      const v = group.tests[i];
+      const index = `(${i}, ${v.result}) ${v.comment}`;
+      if (v.result === 'valid' || v.result === 'acceptable') {
+        try {
+          const shared = hex(x448.scalarMult(v.private, v.public));
+          deepStrictEqual(shared, v.shared, index);
+        } catch (e) {
+          // We are more strict
+          if (e.message.includes('Expected valid scalar')) return;
+          if (e.message.includes('Invalid private or public key received')) return;
+          if (e.message.includes('Expected 56 bytes')) return;
+          throw e;
+        }
+      } else if (v.result === 'invalid') {
+        let failed = false;
+        try {
+          x448.scalarMult(v.private, v.public);
+        } catch (error) {
+          failed = true;
+        }
+        deepStrictEqual(failed, true, index);
+      } else throw new Error('unknown test result');
+    }
+  });
+}
+
+// should('X448: should convert base point to montgomery using fromPoint', () => {
+//   deepStrictEqual(
+//     hex(ed.montgomeryCurve.UfromPoint(ed.Point.BASE)),
+//     ed.montgomeryCurve.BASE_POINT_U
+//   );
+// });
+
+// should('X448/getSharedSecret() should be commutative', async () => {
+//   for (let i = 0; i < 512; i++) {
+//     const asec = ed.utils.randomPrivateKey();
+//     const apub = ed.getPublicKey(asec);
+//     const bsec = ed.utils.randomPrivateKey();
+//     const bpub = ed.getPublicKey(bsec);
+//     try {
+//       deepStrictEqual(ed.getSharedSecret(asec, bpub), ed.getSharedSecret(bsec, apub));
+//     } catch (error) {
+//       console.error('not commutative', { asec, apub, bsec, bpub });
+//       throw error;
+//     }
+//   }
+// });
+
+const VECTORS_RFC8032_CTX = [
+  {
+    secretKey:
+      'c4eab05d357007c632f3dbb48489924d552b08fe0c353a0d4a1f00acda2c463afbea67c5e8d2877c5e3bc397a659949ef8021e954e0a12274e',
+    publicKey:
+      '43ba28f430cdff456ae531545f7ecd0ac834a55d9358c0372bfa0c6c6798c0866aea01eb00742802b8438ea4cb82169c235160627b4c3a9480',
+    message: '03',
+    context: '666f6f',
+    signature:
+      'd4f8f6131770dd46f40867d6fd5d5055' +
+      'de43541f8c5e35abbcd001b32a89f7d2' +
+      '151f7647f11d8ca2ae279fb842d60721' +
+      '7fce6e042f6815ea000c85741de5c8da' +
+      '1144a6a1aba7f96de42505d7a7298524' +
+      'fda538fccbbb754f578c1cad10d54d0d' +
+      '5428407e85dcbc98a49155c13764e66c' +
+      '3c00',
+  },
+];
+
+for (let i = 0; i < VECTORS_RFC8032_CTX.length; i++) {
+  const v = VECTORS_RFC8032_CTX[i];
+  should(`RFC8032ctx/${i}`, () => {
+    deepStrictEqual(hex(ed.getPublicKey(v.secretKey)), v.publicKey);
+    deepStrictEqual(hex(ed.sign(v.message, v.secretKey, v.context)), v.signature);
+    deepStrictEqual(ed.verify(v.signature, v.message, v.publicKey, v.context), true);
+  });
+}
+
+const VECTORS_RFC8032_PH = [
+  {
+    secretKey:
+      '833fe62409237b9d62ec77587520911e9a759cec1d19755b7da901b96dca3d42ef7822e0d5104127dc05d6dbefde69e3ab2cec7c867c6e2c49',
+    publicKey:
+      '259b71c19f83ef77a7abd26524cbdb3161b590a48f7d17de3ee0ba9c52beb743c09428a131d6b1b57303d90d8132c276d5ed3d5d01c0f53880',
+    message: '616263',
+    signature:
+      '822f6901f7480f3d5f562c592994d969' +
+      '3602875614483256505600bbc281ae38' +
+      '1f54d6bce2ea911574932f52a4e6cadd' +
+      '78769375ec3ffd1b801a0d9b3f4030cd' +
+      '433964b6457ea39476511214f97469b5' +
+      '7dd32dbc560a9a94d00bff07620464a3' +
+      'ad203df7dc7ce360c3cd3696d9d9fab9' +
+      '0f00',
+  },
+  {
+    secretKey:
+      '833fe62409237b9d62ec77587520911e9a759cec1d19755b7da901b96dca3d42ef7822e0d5104127dc05d6dbefde69e3ab2cec7c867c6e2c49',
+    publicKey:
+      '259b71c19f83ef77a7abd26524cbdb3161b590a48f7d17de3ee0ba9c52beb743c09428a131d6b1b57303d90d8132c276d5ed3d5d01c0f53880',
+    message: '616263',
+    context: '666f6f',
+    signature:
+      'c32299d46ec8ff02b54540982814dce9' +
+      'a05812f81962b649d528095916a2aa48' +
+      '1065b1580423ef927ecf0af5888f90da' +
+      '0f6a9a85ad5dc3f280d91224ba9911a3' +
+      '653d00e484e2ce232521481c8658df30' +
+      '4bb7745a73514cdb9bf3e15784ab7128' +
+      '4f8d0704a608c54a6b62d97beb511d13' +
+      '2100',
+  },
+];
+
+for (let i = 0; i < VECTORS_RFC8032_PH.length; i++) {
+  const v = VECTORS_RFC8032_PH[i];
+  should(`RFC8032ph/${i}`, () => {
+    deepStrictEqual(hex(ed448ph.getPublicKey(v.secretKey)), v.publicKey);
+    deepStrictEqual(hex(ed448ph.sign(v.message, v.secretKey, v.context)), v.signature);
+    deepStrictEqual(ed448ph.verify(v.signature, v.message, v.publicKey, v.context), true);
+  });
+}
+
+should('X448 base point', () => {
+  const { x, y } = ed448.Point.BASE;
+  const { P } = ed448.CURVE;
+  const invX = ed448.utils.invert(x * x, P); // x²
+  const u = ed448.utils.mod(y * y * invX, P); // (y²/x²)
+  deepStrictEqual(hex(numberToBytesLE(u, 56)), x448.Gu);
+});
+
+// ESM is broken.
+import url from 'url';
+if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
+  should.run();
+}

test/fixtures/rfc6979.json

@@ -28,16 +28,16 @@
         "Uy": "EEAB6F3DEBE455E3DBF85416F7030CBD94F34F2D6F232C69F3C1385A",
         "cases": [
             {
-                "k": "AD3029E0278F80643DE33917CE6908C70A8FF50A411F06E41DEDFCDC",
+                "k": "C1D1F2F10881088301880506805FEB4825FE09ACB6816C36991AA06D",
                 "message": "sample",
-                "r": "61AA3DA010E8E8406C656BC477A7A7189895E7E840CDFE8FF42307BA",
-                "s": "BC814050DAB5D23770879494F9E0A680DC1AF7161991BDE692B10101"
+                "r": "1CDFE6662DDE1E4A1EC4CDEDF6A1F5A2FB7FBD9145C12113E6ABFD3E",
+                "s": "A6694FD7718A21053F225D3F46197CA699D45006C06F871808F43EBC"
             },
             {
-                "k": "FF86F57924DA248D6E44E8154EB69F0AE2AEBAEE9931D0B5A969F904",
+                "k": "DF8B38D40DCA3E077D0AC520BF56B6D565134D9B5F2EAE0D34900524",
                 "message": "test",
-                "r": "AD04DDE87B84747A243A631EA47A1BA6D1FAA059149AD2440DE6FBA6",
-                "s": "178D49B1AE90E3D8B629BE3DB5683915F4E8C99FDF6E666CF37ADCFD"
+                "r": "C441CE8E261DED634E4CF84910E4C5D1D22C5CF3B732BB204DBEF019",
+                "s": "902F42847A63BDC5F6046ADA114953120F99442D76510150F372A3F4"
             }
         ]
     },

test/hash-to-curve.test.js

@@ -0,0 +1,107 @@
+import { deepStrictEqual } from 'assert';
+import { should } from 'micro-should';
+import { bytesToHex } from '@noble/hashes/utils';
+// Generic tests for all curves in package
+import { sha256 } from '@noble/hashes/sha256';
+import { sha512 } from '@noble/hashes/sha512';
+import { secp256r1 } from '../lib/esm/p256.js';
+import { secp384r1 } from '../lib/esm/p384.js';
+import { secp521r1 } from '../lib/esm/p521.js';
+import { secp256k1 } from '../lib/esm/secp256k1.js';
+import { bls12_381 } from '../lib/esm/bls12-381.js';
+import { stringToBytes, expand_message_xmd } from '../lib/esm/abstract/hash-to-curve.js';
+
+import { default as xmd_sha256_38 } from './hash-to-curve/expand_message_xmd_SHA256_38.json' assert { type: 'json' };
+import { default as xmd_sha256_256 } from './hash-to-curve/expand_message_xmd_SHA256_256.json' assert { type: 'json' };
+import { default as xmd_sha512_38 } from './hash-to-curve/expand_message_xmd_SHA512_38.json' assert { type: 'json' };
+// P256
+import { default as p256_ro } from './hash-to-curve/P256_XMD:SHA-256_SSWU_RO_.json' assert { type: 'json' };
+import { default as p256_nu } from './hash-to-curve/P256_XMD:SHA-256_SSWU_NU_.json' assert { type: 'json' };
+// P384
+import { default as p384_ro } from './hash-to-curve/P384_XMD:SHA-384_SSWU_RO_.json' assert { type: 'json' };
+import { default as p384_nu } from './hash-to-curve/P384_XMD:SHA-384_SSWU_NU_.json' assert { type: 'json' };
+// P521
+import { default as p521_ro } from './hash-to-curve/P521_XMD:SHA-512_SSWU_RO_.json' assert { type: 'json' };
+import { default as p521_nu } from './hash-to-curve/P521_XMD:SHA-512_SSWU_NU_.json' assert { type: 'json' };
+// secp256k1
+import { default as secp256k1_ro } from './hash-to-curve/secp256k1_XMD:SHA-256_SSWU_RO_.json' assert { type: 'json' };
+import { default as secp256k1_nu } from './hash-to-curve/secp256k1_XMD:SHA-256_SSWU_NU_.json' assert { type: 'json' };
+// bls-G1
+import { default as g1_ro } from './hash-to-curve/BLS12381G1_XMD:SHA-256_SSWU_RO_.json' assert { type: 'json' };
+import { default as g1_nu } from './hash-to-curve/BLS12381G1_XMD:SHA-256_SSWU_NU_.json' assert { type: 'json' };
+// bls-G2
+import { default as g2_ro } from './hash-to-curve/BLS12381G2_XMD:SHA-256_SSWU_RO_.json' assert { type: 'json' };
+import { default as g2_nu } from './hash-to-curve/BLS12381G2_XMD:SHA-256_SSWU_NU_.json' assert { type: 'json' };
+// ed25519
+import { default as ed25519_ro } from './hash-to-curve/edwards25519_XMD:SHA-512_ELL2_RO_.json' assert { type: 'json' };
+import { default as ed25519_nu } from './hash-to-curve/edwards25519_XMD:SHA-512_ELL2_NU_.json' assert { type: 'json' };
+// ed448
+import { default as ed448_ro } from './hash-to-curve/edwards448_XOF:SHAKE256_ELL2_RO_.json' assert { type: 'json' };
+import { default as ed448_nu } from './hash-to-curve/edwards448_XOF:SHAKE256_ELL2_NU_.json' assert { type: 'json' };
+
+function testExpandXMD(hash, vectors) {
+  for (let i = 0; i < vectors.tests.length; i++) {
+    const t = vectors.tests[i];
+    should(`expand_message_xmd/${vectors.hash}/${vectors.DST.length}/${i}`, () => {
+      const p = expand_message_xmd(
+        stringToBytes(t.msg),
+        stringToBytes(vectors.DST),
+        t.len_in_bytes,
+        hash
+      );
+      deepStrictEqual(bytesToHex(p), t.uniform_bytes);
+    });
+  }
+}
+
+testExpandXMD(sha256, xmd_sha256_38);
+testExpandXMD(sha256, xmd_sha256_256);
+testExpandXMD(sha512, xmd_sha512_38);
+
+function stringToFp(s) {
+  // bls-G2 support
+  if (s.includes(',')) {
+    const [c0, c1] = s.split(',').map(BigInt);
+    return { c0, c1 };
+  }
+  return BigInt(s);
+}
+
+function testCurve(curve, ro, nu) {
+  for (let i = 0; i < ro.vectors.length; i++) {
+    const t = ro.vectors[i];
+    should(`${ro.curve}/${ro.ciphersuite}(${i})`, () => {
+      const p = curve.Point.hashToCurve(stringToBytes(t.msg), {
+        DST: ro.dst,
+      });
+      deepStrictEqual(p.x, stringToFp(t.P.x), 'Px');
+      deepStrictEqual(p.y, stringToFp(t.P.y), 'Py');
+    });
+  }
+  for (let i = 0; i < nu.vectors.length; i++) {
+    const t = nu.vectors[i];
+    should(`${nu.curve}/${nu.ciphersuite}(${i})`, () => {
+      const p = curve.Point.encodeToCurve(stringToBytes(t.msg), {
+        DST: nu.dst,
+      });
+      deepStrictEqual(p.x, stringToFp(t.P.x), 'Px');
+      deepStrictEqual(p.y, stringToFp(t.P.y), 'Py');
+    });
+  }
+}
+
+testCurve(secp256r1, p256_ro, p256_nu);
+testCurve(secp384r1, p384_ro, p384_nu);
+testCurve(secp521r1, p521_ro, p521_nu);
+// TODO: remove same tests from bls12
+testCurve(bls12_381.G1, g1_ro, g1_nu);
+testCurve(bls12_381.G2, g2_ro, g2_nu);
+testCurve(secp256k1, secp256k1_ro, secp256k1_nu);
+//testCurve(ed25519, ed25519_ro, ed25519_nu);
+//testCurve(ed448, ed448_ro, ed448_nu);
+
+// ESM is broken.
+import url from 'url';
+if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
+  should.run();
+}

test/hash-to-curve/BLS12381G1_XMD:SHA-256_SSWU_NU_.json

@@ -0,0 +1,90 @@
+{
+  "L": "0x40",
+  "Z": "0xb",
+  "ciphersuite": "BLS12381G1_XMD:SHA-256_SSWU_NU_",
+  "curve": "BLS12-381 G1",
+  "dst": "QUUX-V01-CS02-with-BLS12381G1_XMD:SHA-256_SSWU_NU_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x1",
+    "p": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab"
+  },
+  "hash": "sha256",
+  "k": "0x80",
+  "map": {
+    "name": "SSWU"
+  },
+  "randomOracle": false,
+  "vectors": [
+    {
+      "P": {
+        "x": "0x184bb665c37ff561a89ec2122dd343f20e0f4cbcaec84e3c3052ea81d1834e192c426074b02ed3dca4e7676ce4ce48ba",
+        "y": "0x04407b8d35af4dacc809927071fc0405218f1401a6d15af775810e4e460064bcc9468beeba82fdc751be70476c888bf3"
+      },
+      "Q": {
+        "x": "0x11398d3b324810a1b093f8e35aa8571cced95858207e7f49c4fd74656096d61d8a2f9a23cdb18a4dd11cd1d66f41f709",
+        "y": "0x19316b6fb2ba7717355d5d66a361899057e1e84a6823039efc7beccefe09d023fb2713b1c415fcf278eb0c39a89b4f72"
+      },
+      "msg": "",
+      "u": [
+        "0x156c8a6a2c184569d69a76be144b5cdc5141d2d2ca4fe341f011e25e3969c55ad9e9b9ce2eb833c81a908e5fa4ac5f03"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x009769f3ab59bfd551d53a5f846b9984c59b97d6842b20a2c565baa167945e3d026a3755b6345df8ec7e6acb6868ae6d",
+        "y": "0x1532c00cf61aa3d0ce3e5aa20c3b531a2abd2c770a790a2613818303c6b830ffc0ecf6c357af3317b9575c567f11cd2c"
+      },
+      "Q": {
+        "x": "0x1998321bc27ff6d71df3051b5aec12ff47363d81a5e9d2dff55f444f6ca7e7d6af45c56fd029c58237c266ef5cda5254",
+        "y": "0x034d274476c6307ae584f951c82e7ea85b84f72d28f4d6471732356121af8d62a49bc263e8eb913a6cf6f125995514ee"
+      },
+      "msg": "abc",
+      "u": [
+        "0x147e1ed29f06e4c5079b9d14fc89d2820d32419b990c1c7bb7dbea2a36a045124b31ffbde7c99329c05c559af1c6cc82"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x1974dbb8e6b5d20b84df7e625e2fbfecb2cdb5f77d5eae5fb2955e5ce7313cae8364bc2fff520a6c25619739c6bdcb6a",
+        "y": "0x15f9897e11c6441eaa676de141c8d83c37aab8667173cbe1dfd6de74d11861b961dccebcd9d289ac633455dfcc7013a3"
+      },
+      "Q": {
+        "x": "0x17d502fa43bd6a4cad2859049a0c3ecefd60240d129be65da271a4c03a9c38fa78163b9d2a919d2beb57df7d609b4919",
+        "y": "0x109019902ae93a8732abecf2ff7fecd2e4e305eb91f41c9c3267f16b6c19de138c7272947f25512745da6c466cdfd1ac"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x04090815ad598a06897dd89bcda860f25837d54e897298ce31e6947378134d3761dc59a572154963e8c954919ecfa82d"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x0a7a047c4a8397b3446450642c2ac64d7239b61872c9ae7a59707a8f4f950f101e766afe58223b3bff3a19a7f754027c",
+        "y": "0x1383aebba1e4327ccff7cf9912bda0dbc77de048b71ef8c8a81111d71dc33c5e3aa6edee9cf6f5fe525d50cc50b77cc9"
+      },
+      "Q": {
+        "x": "0x112eb92dd2b3aa9cd38b08de4bef603f2f9fb0ca226030626a9a2e47ad1e9847fe0a5ed13766c339e38f514bba143b21",
+        "y": "0x17542ce2f8d0a54f2c5ba8c4b14e10b22d5bcd7bae2af3c965c8c872b571058c720eac448276c99967ded2bf124490e1"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x08dccd088ca55b8bfbc96fb50bb25c592faa867a8bb78d4e94a8cc2c92306190244532e91feba2b7fed977e3c3bb5a1f"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x0e7a16a975904f131682edbb03d9560d3e48214c9986bd50417a77108d13dc957500edf96462a3d01e62dc6cd468ef11",
+        "y": "0x0ae89e677711d05c30a48d6d75e76ca9fb70fe06c6dd6ff988683d89ccde29ac7d46c53bb97a59b1901abf1db66052db"
+      },
+      "Q": {
+        "x": "0x1775d400a1bacc1c39c355da7e96d2d1c97baa9430c4a3476881f8521c09a01f921f592607961efc99c4cd46bd78ca19",
+        "y": "0x1109b5d59f65964315de65a7a143e86eabc053104ed289cf480949317a5685fad7254ff8e7fe6d24d3104e5d55ad6370"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x0dd824886d2123a96447f6c56e3a3fa992fbfefdba17b6673f9f630ff19e4d326529db37e1c1be43f905bf9202e0278d"
+      ]
+    }
+  ]
+}

test/hash-to-curve/BLS12381G1_XMD:SHA-256_SSWU_RO_.json

@@ -0,0 +1,115 @@
+{
+  "L": "0x40",
+  "Z": "0xb",
+  "ciphersuite": "BLS12381G1_XMD:SHA-256_SSWU_RO_",
+  "curve": "BLS12-381 G1",
+  "dst": "QUUX-V01-CS02-with-BLS12381G1_XMD:SHA-256_SSWU_RO_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x1",
+    "p": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab"
+  },
+  "hash": "sha256",
+  "k": "0x80",
+  "map": {
+    "name": "SSWU"
+  },
+  "randomOracle": true,
+  "vectors": [
+    {
+      "P": {
+        "x": "0x052926add2207b76ca4fa57a8734416c8dc95e24501772c814278700eed6d1e4e8cf62d9c09db0fac349612b759e79a1",
+        "y": "0x08ba738453bfed09cb546dbb0783dbb3a5f1f566ed67bb6be0e8c67e2e81a4cc68ee29813bb7994998f3eae0c9c6a265"
+      },
+      "Q0": {
+        "x": "0x11a3cce7e1d90975990066b2f2643b9540fa40d6137780df4e753a8054d07580db3b7f1f03396333d4a359d1fe3766fe",
+        "y": "0x0eeaf6d794e479e270da10fdaf768db4c96b650a74518fc67b04b03927754bac66f3ac720404f339ecdcc028afa091b7"
+      },
+      "Q1": {
+        "x": "0x160003aaf1632b13396dbad518effa00fff532f604de1a7fc2082ff4cb0afa2d63b2c32da1bef2bf6c5ca62dc6b72f9c",
+        "y": "0x0d8bb2d14e20cf9f6036152ed386d79189415b6d015a20133acb4e019139b94e9c146aaad5817f866c95d609a361735e"
+      },
+      "msg": "",
+      "u": [
+        "0x0ba14bd907ad64a016293ee7c2d276b8eae71f25a4b941eece7b0d89f17f75cb3ae5438a614fb61d6835ad59f29c564f",
+        "0x019b9bd7979f12657976de2884c7cce192b82c177c80e0ec604436a7f538d231552f0d96d9f7babe5fa3b19b3ff25ac9"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x03567bc5ef9c690c2ab2ecdf6a96ef1c139cc0b2f284dca0a9a7943388a49a3aee664ba5379a7655d3c68900be2f6903",
+        "y": "0x0b9c15f3fe6e5cf4211f346271d7b01c8f3b28be689c8429c85b67af215533311f0b8dfaaa154fa6b88176c229f2885d"
+      },
+      "Q0": {
+        "x": "0x125435adce8e1cbd1c803e7123f45392dc6e326d292499c2c45c5865985fd74fe8f042ecdeeec5ecac80680d04317d80",
+        "y": "0x0e8828948c989126595ee30e4f7c931cbd6f4570735624fd25aef2fa41d3f79cfb4b4ee7b7e55a8ce013af2a5ba20bf2"
+      },
+      "Q1": {
+        "x": "0x11def93719829ecda3b46aa8c31fc3ac9c34b428982b898369608e4f042babee6c77ab9218aad5c87ba785481eff8ae4",
+        "y": "0x0007c9cef122ccf2efd233d6eb9bfc680aa276652b0661f4f820a653cec1db7ff69899f8e52b8e92b025a12c822a6ce6"
+      },
+      "msg": "abc",
+      "u": [
+        "0x0d921c33f2bad966478a03ca35d05719bdf92d347557ea166e5bba579eea9b83e9afa5c088573c2281410369fbd32951",
+        "0x003574a00b109ada2f26a37a91f9d1e740dffd8d69ec0c35e1e9f4652c7dba61123e9dd2e76c655d956e2b3462611139"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x11e0b079dea29a68f0383ee94fed1b940995272407e3bb916bbf268c263ddd57a6a27200a784cbc248e84f357ce82d98",
+        "y": "0x03a87ae2caf14e8ee52e51fa2ed8eefe80f02457004ba4d486d6aa1f517c0889501dc7413753f9599b099ebcbbd2d709"
+      },
+      "Q0": {
+        "x": "0x08834484878c217682f6d09a4b51444802fdba3d7f2df9903a0ddadb92130ebbfa807fffa0eabf257d7b48272410afff",
+        "y": "0x0b318f7ecf77f45a0f038e62d7098221d2dbbca2a394164e2e3fe953dc714ac2cde412d8f2d7f0c03b259e6795a2508e"
+      },
+      "Q1": {
+        "x": "0x158418ed6b27e2549f05531a8281b5822b31c3bf3144277fbb977f8d6e2694fedceb7011b3c2b192f23e2a44b2bd106e",
+        "y": "0x1879074f344471fac5f839e2b4920789643c075792bec5af4282c73f7941cda5aa77b00085eb10e206171b9787c4169f"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x062d1865eb80ebfa73dcfc45db1ad4266b9f3a93219976a3790ab8d52d3e5f1e62f3b01795e36834b17b70e7b76246d4",
+        "0x0cdc3e2f271f29c4ff75020857ce6c5d36008c9b48385ea2f2bf6f96f428a3deb798aa033cd482d1cdc8b30178b08e3a"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x15f68eaa693b95ccb85215dc65fa81038d69629f70aeee0d0f677cf22285e7bf58d7cb86eefe8f2e9bc3f8cb84fac488",
+        "y": "0x1807a1d50c29f430b8cafc4f8638dfeeadf51211e1602a5f184443076715f91bb90a48ba1e370edce6ae1062f5e6dd38"
+      },
+      "Q0": {
+        "x": "0x0cbd7f84ad2c99643fea7a7ac8f52d63d66cefa06d9a56148e58b984b3dd25e1f41ff47154543343949c64f88d48a710",
+        "y": "0x052c00e4ed52d000d94881a5638ae9274d3efc8bc77bc0e5c650de04a000b2c334a9e80b85282a00f3148dfdface0865"
+      },
+      "Q1": {
+        "x": "0x06493fb68f0d513af08be0372f849436a787e7b701ae31cb964d968021d6ba6bd7d26a38aaa5a68e8c21a6b17dc8b579",
+        "y": "0x02e98f2ccf5802b05ffaac7c20018bc0c0b2fd580216c4aa2275d2909dc0c92d0d0bdc979226adeb57a29933536b6bb4"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x010476f6a060453c0b1ad0b628f3e57c23039ee16eea5e71bb87c3b5419b1255dc0e5883322e563b84a29543823c0e86",
+        "0x0b1a912064fb0554b180e07af7e787f1f883a0470759c03c1b6509eb8ce980d1670305ae7b928226bb58fdc0a419f46e"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x082aabae8b7dedb0e78aeb619ad3bfd9277a2f77ba7fad20ef6aabdc6c31d19ba5a6d12283553294c1825c4b3ca2dcfe",
+        "y": "0x05b84ae5a942248eea39e1d91030458c40153f3b654ab7872d779ad1e942856a20c438e8d99bc8abfbf74729ce1f7ac8"
+      },
+      "Q0": {
+        "x": "0x0cf97e6dbd0947857f3e578231d07b309c622ade08f2c08b32ff372bd90db19467b2563cc997d4407968d4ac80e154f8",
+        "y": "0x127f0cddf2613058101a5701f4cb9d0861fd6c2a1b8e0afe194fccf586a3201a53874a2761a9ab6d7220c68661a35ab3"
+      },
+      "Q1": {
+        "x": "0x092f1acfa62b05f95884c6791fba989bbe58044ee6355d100973bf9553ade52b47929264e6ae770fb264582d8dce512a",
+        "y": "0x028e6d0169a72cfedb737be45db6c401d3adfb12c58c619c82b93a5dfcccef12290de530b0480575ddc8397cda0bbebf"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x0a8ffa7447f6be1c5a2ea4b959c9454b431e29ccc0802bc052413a9c5b4f9aac67a93431bd480d15be1e057c8a08e8c6",
+        "0x05d487032f602c90fa7625dbafe0f4a49ef4a6b0b33d7bb349ff4cf5410d297fd6241876e3e77b651cfc8191e40a68b7"
+      ]
+    }
+  ]
+}

test/hash-to-curve/BLS12381G2_XMD:SHA-256_SSWU_NU_.json

@@ -0,0 +1,90 @@
+{
+  "L": "0x40",
+  "Z": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaa9,0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa",
+  "ciphersuite": "BLS12381G2_XMD:SHA-256_SSWU_NU_",
+  "curve": "BLS12-381 G2",
+  "dst": "QUUX-V01-CS02-with-BLS12381G2_XMD:SHA-256_SSWU_NU_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x2",
+    "p": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab"
+  },
+  "hash": "sha256",
+  "k": "0x80",
+  "map": {
+    "name": "SSWU"
+  },
+  "randomOracle": false,
+  "vectors": [
+    {
+      "P": {
+        "x": "0x00e7f4568a82b4b7dc1f14c6aaa055edf51502319c723c4dc2688c7fe5944c213f510328082396515734b6612c4e7bb7,0x126b855e9e69b1f691f816e48ac6977664d24d99f8724868a184186469ddfd4617367e94527d4b74fc86413483afb35b",
+        "y": "0x0caead0fd7b6176c01436833c79d305c78be307da5f6af6c133c47311def6ff1e0babf57a0fb5539fce7ee12407b0a42,0x1498aadcf7ae2b345243e281ae076df6de84455d766ab6fcdaad71fab60abb2e8b980a440043cd305db09d283c895e3d"
+      },
+      "Q": {
+        "x": "0x18ed3794ad43c781816c523776188deafba67ab773189b8f18c49bc7aa841cd81525171f7a5203b2a340579192403bef,0x0727d90785d179e7b5732c8a34b660335fed03b913710b60903cf4954b651ed3466dc3728e21855ae822d4a0f1d06587",
+        "y": "0x00764a5cf6c5f61c52c838523460eb2168b5a5b43705e19cb612e006f29b717897facfd15dd1c8874c915f6d53d0342d,0x19290bb9797c12c1d275817aa2605ebe42275b66860f0e4d04487ebc2e47c50b36edd86c685a60c20a2bd584a82b011a"
+      },
+      "msg": "",
+      "u": [
+        "0x07355d25caf6e7f2f0cb2812ca0e513bd026ed09dda65b177500fa31714e09ea0ded3a078b526bed3307f804d4b93b04,0x02829ce3c021339ccb5caf3e187f6370e1e2a311dec9b75363117063ab2015603ff52c3d3b98f19c2f65575e99e8b78c"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x108ed59fd9fae381abfd1d6bce2fd2fa220990f0f837fa30e0f27914ed6e1454db0d1ee957b219f61da6ff8be0d6441f,0x0296238ea82c6d4adb3c838ee3cb2346049c90b96d602d7bb1b469b905c9228be25c627bffee872def773d5b2a2eb57d",
+        "y": "0x033f90f6057aadacae7963b0a0b379dd46750c1c94a6357c99b65f63b79e321ff50fe3053330911c56b6ceea08fee656,0x153606c417e59fb331b7ae6bce4fbf7c5190c33ce9402b5ebe2b70e44fca614f3f1382a3625ed5493843d0b0a652fc3f"
+      },
+      "Q": {
+        "x": "0x0f40e1d5025ecef0d850aa0bb7bbeceab21a3d4e85e6bee857805b09693051f5b25428c6be343edba5f14317fcc30143,0x02e0d261f2b9fee88b82804ec83db330caa75fbb12719cfa71ccce1c532dc4e1e79b0a6a281ed8d3817524286c8bc04c",
+        "y": "0x0cf4a4adc5c66da0bca4caddc6a57ecd97c8252d7526a8ff478e0dfed816c4d321b5c3039c6683ae9b1e6a3a38c9c0ae,0x11cad1646bb3768c04be2ab2bbe1f80263b7ff6f8f9488f5bc3b6850e5a3e97e20acc583613c69cf3d2bfe8489744ebb"
+      },
+      "msg": "abc",
+      "u": [
+        "0x138879a9559e24cecee8697b8b4ad32cced053138ab913b99872772dc753a2967ed50aabc907937aefb2439ba06cc50c,0x0a1ae7999ea9bab1dcc9ef8887a6cb6e8f1e22566015428d220b7eec90ffa70ad1f624018a9ad11e78d588bd3617f9f2"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x038af300ef34c7759a6caaa4e69363cafeed218a1f207e93b2c70d91a1263d375d6730bd6b6509dcac3ba5b567e85bf3,0x0da75be60fb6aa0e9e3143e40c42796edf15685cafe0279afd2a67c3dff1c82341f17effd402e4f1af240ea90f4b659b",
+        "y": "0x19b148cbdf163cf0894f29660d2e7bfb2b68e37d54cc83fd4e6e62c020eaa48709302ef8e746736c0e19342cc1ce3df4,0x0492f4fed741b073e5a82580f7c663f9b79e036b70ab3e51162359cec4e77c78086fe879b65ca7a47d34374c8315ac5e"
+      },
+      "Q": {
+        "x": "0x13a9d4a738a85c9f917c7be36b240915434b58679980010499b9ae8d7a1bf7fbe617a15b3cd6060093f40d18e0f19456,0x16fa88754e7670366a859d6f6899ad765bf5a177abedb2740aacc9252c43f90cd0421373fbd5b2b76bb8f5c4886b5d37",
+        "y": "0x0a7fa7d82c46797039398253e8765a4194100b330dfed6d7fbb46d6fbf01e222088779ac336e3675c7a7a0ee05bbb6e3,0x0c6ee170ab766d11fa9457cef53253f2628010b2cffc102b3b28351eb9df6c281d3cfc78e9934769d661b72a5265338d"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x18c16fe362b7dbdfa102e42bdfd3e2f4e6191d479437a59db4eb716986bf08ee1f42634db66bde97d6c16bbfd342b3b8,0x0e37812ce1b146d998d5f92bdd5ada2a31bfd63dfe18311aa91637b5f279dd045763166aa1615e46a50d8d8f475f184e"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x0c5ae723be00e6c3f0efe184fdc0702b64588fe77dda152ab13099a3bacd3876767fa7bbad6d6fd90b3642e902b208f9,0x12c8c05c1d5fc7bfa847f4d7d81e294e66b9a78bc9953990c358945e1f042eedafce608b67fdd3ab0cb2e6e263b9b1ad",
+        "y": "0x04e77ddb3ede41b5ec4396b7421dd916efc68a358a0d7425bddd253547f2fb4830522358491827265dfc5bcc1928a569,0x11c624c56dbe154d759d021eec60fab3d8b852395a89de497e48504366feedd4662d023af447d66926a28076813dd646"
+      },
+      "Q": {
+        "x": "0x0a08b2f639855dfdeaaed972702b109e2241a54de198b2b4cd12ad9f88fa419a6086a58d91fc805de812ea29bee427c2,0x04a7442e4cb8b42ef0f41dac9ee74e65ecad3ce0851f0746dc47568b0e7a8134121ed09ba054509232c49148aef62cda",
+        "y": "0x05d60b1f04212b2c87607458f71d770f43973511c260f0540eef3a565f42c7ce59aa1cea684bb2a7bcab84acd2f36c8c,0x1017aa5747ba15505ece266a86b0ca9c712f41a254b76ca04094ca442ce45ecd224bd5544cd16685d0d1b9d156dd0531"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x08d4a0997b9d52fecf99427abb721f0fa779479963315fe21c6445250de7183e3f63bfdf86570da8929489e421d4ee95,0x16cb4ccad91ec95aab070f22043916cd6a59c4ca94097f7f510043d48515526dc8eaaea27e586f09151ae613688d5a89"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x0ea4e7c33d43e17cc516a72f76437c4bf81d8f4eac69ac355d3bf9b71b8138d55dc10fd458be115afa798b55dac34be1,0x1565c2f625032d232f13121d3cfb476f45275c303a037faa255f9da62000c2c864ea881e2bcddd111edc4a3c0da3e88d",
+        "y": "0x043b6f5fe4e52c839148dc66f2b3751e69a0f6ebb3d056d6465d50d4108543ecd956e10fa1640dfd9bc0030cc2558d28,0x0f8991d2a1ad662e7b6f58ab787947f1fa607fce12dde171bc17903b012091b657e15333e11701edcf5b63ba2a561247"
+      },
+      "Q": {
+        "x": "0x19592c812d5a50c5601062faba14c7d670711745311c879de1235a0a11c75aab61327bf2d1725db07ec4d6996a682886,0x0eef4fa41ddc17ed47baf447a2c498548f3c72a02381313d13bef916e240b61ce125539090d62d9fbb14a900bf1b8e90",
+        "y": "0x1260d6e0987eae96af9ebe551e08de22b37791d53f4db9e0d59da736e66699735793e853e26362531fe4adf99c1883e3,0x0dbace5df0a4ac4ac2f45d8fdf8aee45484576fdd6efc4f98ab9b9f4112309e628255e183022d98ea5ed6e47ca00306c"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x03f80ce4ff0ca2f576d797a3660e3f65b274285c054feccc3215c879e2c0589d376e83ede13f93c32f05da0f68fd6a10,0x006488a837c5413746d868d1efb7232724da10eca410b07d8b505b9363bdccf0a1fc0029bad07d65b15ccfe6dd25e20d"
+      ]
+    }
+  ]
+}

test/hash-to-curve/BLS12381G2_XMD:SHA-256_SSWU_RO_.json

@@ -0,0 +1,115 @@
+{
+  "L": "0x40",
+  "Z": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaa9,0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa",
+  "ciphersuite": "BLS12381G2_XMD:SHA-256_SSWU_RO_",
+  "curve": "BLS12-381 G2",
+  "dst": "QUUX-V01-CS02-with-BLS12381G2_XMD:SHA-256_SSWU_RO_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x2",
+    "p": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab"
+  },
+  "hash": "sha256",
+  "k": "0x80",
+  "map": {
+    "name": "SSWU"
+  },
+  "randomOracle": true,
+  "vectors": [
+    {
+      "P": {
+        "x": "0x0141ebfbdca40eb85b87142e130ab689c673cf60f1a3e98d69335266f30d9b8d4ac44c1038e9dcdd5393faf5c41fb78a,0x05cb8437535e20ecffaef7752baddf98034139c38452458baeefab379ba13dff5bf5dd71b72418717047f5b0f37da03d",
+        "y": "0x0503921d7f6a12805e72940b963c0cf3471c7b2a524950ca195d11062ee75ec076daf2d4bc358c4b190c0c98064fdd92,0x12424ac32561493f3fe3c260708a12b7c620e7be00099a974e259ddc7d1f6395c3c811cdd19f1e8dbf3e9ecfdcbab8d6"
+      },
+      "Q0": {
+        "x": "0x019ad3fc9c72425a998d7ab1ea0e646a1f6093444fc6965f1cad5a3195a7b1e099c050d57f45e3fa191cc6d75ed7458c,0x171c88b0b0efb5eb2b88913a9e74fe111a4f68867b59db252ce5868af4d1254bfab77ebde5d61cd1a86fb2fe4a5a1c1d",
+        "y": "0x0ba10604e62bdd9eeeb4156652066167b72c8d743b050fb4c1016c31b505129374f76e03fa127d6a156213576910fef3,0x0eb22c7a543d3d376e9716a49b72e79a89c9bfe9feee8533ed931cbb5373dde1fbcd7411d8052e02693654f71e15410a"
+      },
+      "Q1": {
+        "x": "0x113d2b9cd4bd98aee53470b27abc658d91b47a78a51584f3d4b950677cfb8a3e99c24222c406128c91296ef6b45608be,0x13855912321c5cb793e9d1e88f6f8d342d49c0b0dbac613ee9e17e3c0b3c97dfbb5a49cc3fb45102fdbaf65e0efe2632",
+        "y": "0x0fd3def0b7574a1d801be44fde617162aa2e89da47f464317d9bb5abc3a7071763ce74180883ad7ad9a723a9afafcdca,0x056f617902b3c0d0f78a9a8cbda43a26b65f602f8786540b9469b060db7b38417915b413ca65f875c130bebfaa59790c"
+      },
+      "msg": "",
+      "u": [
+        "0x03dbc2cce174e91ba93cbb08f26b917f98194a2ea08d1cce75b2b9cc9f21689d80bd79b594a613d0a68eb807dfdc1cf8,0x05a2acec64114845711a54199ea339abd125ba38253b70a92c876df10598bd1986b739cad67961eb94f7076511b3b39a",
+        "0x02f99798e8a5acdeed60d7e18e9120521ba1f47ec090984662846bc825de191b5b7641148c0dbc237726a334473eee94,0x145a81e418d4010cc027a68f14391b30074e89e60ee7a22f87217b2f6eb0c4b94c9115b436e6fa4607e95a98de30a435"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x02c2d18e033b960562aae3cab37a27ce00d80ccd5ba4b7fe0e7a210245129dbec7780ccc7954725f4168aff2787776e6,0x139cddbccdc5e91b9623efd38c49f81a6f83f175e80b06fc374de9eb4b41dfe4ca3a230ed250fbe3a2acf73a41177fd8",
+        "y": "0x1787327b68159716a37440985269cf584bcb1e621d3a7202be6ea05c4cfe244aeb197642555a0645fb87bf7466b2ba48,0x00aa65dae3c8d732d10ecd2c50f8a1baf3001578f71c694e03866e9f3d49ac1e1ce70dd94a733534f106d4cec0eddd16"
+      },
+      "Q0": {
+        "x": "0x12b2e525281b5f4d2276954e84ac4f42cf4e13b6ac4228624e17760faf94ce5706d53f0ca1952f1c5ef75239aeed55ad,0x05d8a724db78e570e34100c0bc4a5fa84ad5839359b40398151f37cff5a51de945c563463c9efbdda569850ee5a53e77",
+        "y": "0x02eacdc556d0bdb5d18d22f23dcb086dd106cad713777c7e6407943edbe0b3d1efe391eedf11e977fac55f9b94f2489c,0x04bbe48bfd5814648d0b9e30f0717b34015d45a861425fabc1ee06fdfce36384ae2c808185e693ae97dcde118f34de41"
+      },
+      "Q1": {
+        "x": "0x19f18cc5ec0c2f055e47c802acc3b0e40c337256a208001dde14b25afced146f37ea3d3ce16834c78175b3ed61f3c537,0x15b0dadc256a258b4c68ea43605dffa6d312eef215c19e6474b3e101d33b661dfee43b51abbf96fee68fc6043ac56a58",
+        "y": "0x05e47c1781286e61c7ade887512bd9c2cb9f640d3be9cf87ea0bad24bd0ebfe946497b48a581ab6c7d4ca74b5147287f,0x19f98db2f4a1fcdf56a9ced7b320ea9deecf57c8e59236b0dc21f6ee7229aa9705ce9ac7fe7a31c72edca0d92370c096"
+      },
+      "msg": "abc",
+      "u": [
+        "0x15f7c0aa8f6b296ab5ff9c2c7581ade64f4ee6f1bf18f55179ff44a2cf355fa53dd2a2158c5ecb17d7c52f63e7195771,0x01c8067bf4c0ba709aa8b9abc3d1cef589a4758e09ef53732d670fd8739a7274e111ba2fcaa71b3d33df2a3a0c8529dd",
+        "0x187111d5e088b6b9acfdfad078c4dacf72dcd17ca17c82be35e79f8c372a693f60a033b461d81b025864a0ad051a06e4,0x08b852331c96ed983e497ebc6dee9b75e373d923b729194af8e72a051ea586f3538a6ebb1e80881a082fa2b24df9f566"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x121982811d2491fde9ba7ed31ef9ca474f0e1501297f68c298e9f4c0028add35aea8bb83d53c08cfc007c1e005723cd0,0x190d119345b94fbd15497bcba94ecf7db2cbfd1e1fe7da034d26cbba169fb3968288b3fafb265f9ebd380512a71c3f2c",
+        "y": "0x05571a0f8d3c08d094576981f4a3b8eda0a8e771fcdcc8ecceaf1356a6acf17574518acb506e435b639353c2e14827c8,0x0bb5e7572275c567462d91807de765611490205a941a5a6af3b1691bfe596c31225d3aabdf15faff860cb4ef17c7c3be"
+      },
+      "Q0": {
+        "x": "0x0f48f1ea1318ddb713697708f7327781fb39718971d72a9245b9731faaca4dbaa7cca433d6c434a820c28b18e20ea208,0x06051467c8f85da5ba2540974758f7a1e0239a5981de441fdd87680a995649c211054869c50edbac1f3a86c561ba3162",
+        "y": "0x168b3d6df80069dbbedb714d41b32961ad064c227355e1ce5fac8e105de5e49d77f0c64867f3834848f152497eb76333,0x134e0e8331cee8cb12f9c2d0742714ed9eee78a84d634c9a95f6a7391b37125ed48bfc6e90bf3546e99930ff67cc97bc"
+      },
+      "Q1": {
+        "x": "0x004fd03968cd1c99a0dd84551f44c206c84dcbdb78076c5bfee24e89a92c8508b52b88b68a92258403cbe1ea2da3495f,0x1674338ea298281b636b2eb0fe593008d03171195fd6dcd4531e8a1ed1f02a72da238a17a635de307d7d24aa2d969a47",
+        "y": "0x0dc7fa13fff6b12558419e0a1e94bfc3cfaf67238009991c5f24ee94b632c3d09e27eca329989aee348a67b50d5e236c,0x169585e164c131103d85324f2d7747b23b91d66ae5d947c449c8194a347969fc6bbd967729768da485ba71868df8aed2"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x0313d9325081b415bfd4e5364efaef392ecf69b087496973b229303e1816d2080971470f7da112c4eb43053130b785e1,0x062f84cb21ed89406890c051a0e8b9cf6c575cf6e8e18ecf63ba86826b0ae02548d83b483b79e48512b82a6c0686df8f",
+        "0x1739123845406baa7be5c5dc74492051b6d42504de008c635f3535bb831d478a341420e67dcc7b46b2e8cba5379cca97,0x01897665d9cb5db16a27657760bbea7951f67ad68f8d55f7113f24ba6ddd82caef240a9bfa627972279974894701d975"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x19a84dd7248a1066f737cc34502ee5555bd3c19f2ecdb3c7d9e24dc65d4e25e50d83f0f77105e955d78f4762d33c17da,0x0934aba516a52d8ae479939a91998299c76d39cc0c035cd18813bec433f587e2d7a4fef038260eef0cef4d02aae3eb91",
+        "y": "0x14f81cd421617428bc3b9fe25afbb751d934a00493524bc4e065635b0555084dd54679df1536101b2c979c0152d09192,0x09bcccfa036b4847c9950780733633f13619994394c23ff0b32fa6b795844f4a0673e20282d07bc69641cee04f5e5662"
+      },
+      "Q0": {
+        "x": "0x09eccbc53df677f0e5814e3f86e41e146422834854a224bf5a83a50e4cc0a77bfc56718e8166ad180f53526ea9194b57,0x0c3633943f91daee715277bd644fba585168a72f96ded64fc5a384cce4ec884a4c3c30f08e09cd2129335dc8f67840ec",
+        "y": "0x0eb6186a0457d5b12d132902d4468bfeb7315d83320b6c32f1c875f344efcba979952b4aa418589cb01af712f98cc555,0x119e3cf167e69eb16c1c7830e8df88856d48be12e3ff0a40791a5cd2f7221311d4bf13b1847f371f467357b3f3c0b4c7"
+      },
+      "Q1": {
+        "x": "0x0eb3aabc1ddfce17ff18455fcc7167d15ce6b60ddc9eb9b59f8d40ab49420d35558686293d046fc1e42f864b7f60e381,0x198bdfb19d7441ebcca61e8ff774b29d17da16547d2c10c273227a635cacea3f16826322ae85717630f0867539b5ed8b",
+        "y": "0x0aaf1dee3adf3ed4c80e481c09b57ea4c705e1b8d25b897f0ceeec3990748716575f92abff22a1c8f4582aff7b872d52,0x0d058d9061ed27d4259848a06c96c5ca68921a5d269b078650c882cb3c2bd424a8702b7a6ee4e0ead9982baf6843e924"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x025820cefc7d06fd38de7d8e370e0da8a52498be9b53cba9927b2ef5c6de1e12e12f188bbc7bc923864883c57e49e253,0x034147b77ce337a52e5948f66db0bab47a8d038e712123bb381899b6ab5ad20f02805601e6104c29df18c254b8618c7b",
+        "0x0930315cae1f9a6017c3f0c8f2314baa130e1cf13f6532bff0a8a1790cd70af918088c3db94bda214e896e1543629795,0x10c4df2cacf67ea3cb3108b00d4cbd0b3968031ebc8eac4b1ebcefe84d6b715fde66bef0219951ece29d1facc8a520ef"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x01a6ba2f9a11fa5598b2d8ace0fbe0a0eacb65deceb476fbbcb64fd24557c2f4b18ecfc5663e54ae16a84f5ab7f62534,0x11fca2ff525572795a801eed17eb12785887c7b63fb77a42be46ce4a34131d71f7a73e95fee3f812aea3de78b4d01569",
+        "y": "0x0b6798718c8aed24bc19cb27f866f1c9effcdbf92397ad6448b5c9db90d2b9da6cbabf48adc1adf59a1a28344e79d57e,0x03a47f8e6d1763ba0cad63d6114c0accbef65707825a511b251a660a9b3994249ae4e63fac38b23da0c398689ee2ab52"
+      },
+      "Q0": {
+        "x": "0x17cadf8d04a1a170f8347d42856526a24cc466cb2ddfd506cff01191666b7f944e31244d662c904de5440516a2b09004,0x0d13ba91f2a8b0051cf3279ea0ee63a9f19bc9cb8bfcc7d78b3cbd8cc4fc43ba726774b28038213acf2b0095391c523e",
+        "y": "0x17ef19497d6d9246fa94d35575c0f8d06ee02f21a284dbeaa78768cb1e25abd564e3381de87bda26acd04f41181610c5,0x12c3c913ba4ed03c24f0721a81a6be7430f2971ffca8fd1729aafe496bb725807531b44b34b59b3ae5495e5a2dcbd5c8"
+      },
+      "Q1": {
+        "x": "0x16ec57b7fe04c71dfe34fb5ad84dbce5a2dbbd6ee085f1d8cd17f45e8868976fc3c51ad9eeda682c7869024d24579bfd,0x13103f7aace1ae1420d208a537f7d3a9679c287208026e4e3439ab8cd534c12856284d95e27f5e1f33eec2ce656533b0",
+        "y": "0x0958b2c4c2c10fcef5a6c59b9e92c4a67b0fae3e2e0f1b6b5edad9c940b8f3524ba9ebbc3f2ceb3cfe377655b3163bd7,0x0ccb594ed8bd14ca64ed9cb4e0aba221be540f25dd0d6ba15a4a4be5d67bcf35df7853b2d8dad3ba245f1ea3697f66aa"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x190b513da3e66fc9a3587b78c76d1d132b1152174d0b83e3c1114066392579a45824c5fa17649ab89299ddd4bda54935,0x12ab625b0fe0ebd1367fe9fac57bb1168891846039b4216b9d94007b674de2d79126870e88aeef54b2ec717a887dcf39",
+        "0x0e6a42010cf435fb5bacc156a585e1ea3294cc81d0ceb81924d95040298380b164f702275892cedd81b62de3aba3f6b5,0x117d9a0defc57a33ed208428cb84e54c85a6840e7648480ae428838989d25d97a0af8e3255be62b25c2a85630d2dddd8"
+      ]
+    }
+  ]
+}

test/hash-to-curve/P256_XMD:SHA-256_SSWU_NU_.json

@@ -0,0 +1,90 @@
+{
+  "L": "0x30",
+  "Z": "0xffffffff00000001000000000000000000000000fffffffffffffffffffffff5",
+  "ciphersuite": "P256_XMD:SHA-256_SSWU_NU_",
+  "curve": "NIST P-256",
+  "dst": "QUUX-V01-CS02-with-P256_XMD:SHA-256_SSWU_NU_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x1",
+    "p": "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff"
+  },
+  "hash": "sha256",
+  "k": "0x80",
+  "map": {
+    "name": "SSWU"
+  },
+  "randomOracle": false,
+  "vectors": [
+    {
+      "P": {
+        "x": "0xf871caad25ea3b59c16cf87c1894902f7e7b2c822c3d3f73596c5ace8ddd14d1",
+        "y": "0x87b9ae23335bee057b99bac1e68588b18b5691af476234b8971bc4f011ddc99b"
+      },
+      "Q": {
+        "x": "0xf871caad25ea3b59c16cf87c1894902f7e7b2c822c3d3f73596c5ace8ddd14d1",
+        "y": "0x87b9ae23335bee057b99bac1e68588b18b5691af476234b8971bc4f011ddc99b"
+      },
+      "msg": "",
+      "u": [
+        "0xb22d487045f80e9edcb0ecc8d4bf77833e2bf1f3a54004d7df1d57f4802d311f"
+      ]
+    },
+    {
+      "P": {
+        "x": "0xfc3f5d734e8dce41ddac49f47dd2b8a57257522a865c124ed02b92b5237befa4",
+        "y": "0xfe4d197ecf5a62645b9690599e1d80e82c500b22ac705a0b421fac7b47157866"
+      },
+      "Q": {
+        "x": "0xfc3f5d734e8dce41ddac49f47dd2b8a57257522a865c124ed02b92b5237befa4",
+        "y": "0xfe4d197ecf5a62645b9690599e1d80e82c500b22ac705a0b421fac7b47157866"
+      },
+      "msg": "abc",
+      "u": [
+        "0xc7f96eadac763e176629b09ed0c11992225b3a5ae99479760601cbd69c221e58"
+      ]
+    },
+    {
+      "P": {
+        "x": "0xf164c6674a02207e414c257ce759d35eddc7f55be6d7f415e2cc177e5d8faa84",
+        "y": "0x3aa274881d30db70485368c0467e97da0e73c18c1d00f34775d012b6fcee7f97"
+      },
+      "Q": {
+        "x": "0xf164c6674a02207e414c257ce759d35eddc7f55be6d7f415e2cc177e5d8faa84",
+        "y": "0x3aa274881d30db70485368c0467e97da0e73c18c1d00f34775d012b6fcee7f97"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x314e8585fa92068b3ea2c3bab452d4257b38be1c097d58a21890456c2929614d"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x324532006312be4f162614076460315f7a54a6f85544da773dc659aca0311853",
+        "y": "0x8d8197374bcd52de2acfefc8a54fe2c8d8bebd2a39f16be9b710e4b1af6ef883"
+      },
+      "Q": {
+        "x": "0x324532006312be4f162614076460315f7a54a6f85544da773dc659aca0311853",
+        "y": "0x8d8197374bcd52de2acfefc8a54fe2c8d8bebd2a39f16be9b710e4b1af6ef883"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x752d8eaa38cd785a799a31d63d99c2ae4261823b4a367b133b2c6627f48858ab"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x5c4bad52f81f39c8e8de1260e9a06d72b8b00a0829a8ea004a610b0691bea5d9",
+        "y": "0xc801e7c0782af1f74f24fc385a8555da0582032a3ce038de637ccdcb16f7ef7b"
+      },
+      "Q": {
+        "x": "0x5c4bad52f81f39c8e8de1260e9a06d72b8b00a0829a8ea004a610b0691bea5d9",
+        "y": "0xc801e7c0782af1f74f24fc385a8555da0582032a3ce038de637ccdcb16f7ef7b"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x0e1527840b9df2dfbef966678ff167140f2b27c4dccd884c25014dce0e41dfa3"
+      ]
+    }
+  ]
+}

test/hash-to-curve/P256_XMD:SHA-256_SSWU_RO_.json

@@ -0,0 +1,115 @@
+{
+  "L": "0x30",
+  "Z": "0xffffffff00000001000000000000000000000000fffffffffffffffffffffff5",
+  "ciphersuite": "P256_XMD:SHA-256_SSWU_RO_",
+  "curve": "NIST P-256",
+  "dst": "QUUX-V01-CS02-with-P256_XMD:SHA-256_SSWU_RO_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x1",
+    "p": "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff"
+  },
+  "hash": "sha256",
+  "k": "0x80",
+  "map": {
+    "name": "SSWU"
+  },
+  "randomOracle": true,
+  "vectors": [
+    {
+      "P": {
+        "x": "0x2c15230b26dbc6fc9a37051158c95b79656e17a1a920b11394ca91c44247d3e4",
+        "y": "0x8a7a74985cc5c776cdfe4b1f19884970453912e9d31528c060be9ab5c43e8415"
+      },
+      "Q0": {
+        "x": "0xab640a12220d3ff283510ff3f4b1953d09fad35795140b1c5d64f313967934d5",
+        "y": "0xdccb558863804a881d4fff3455716c836cef230e5209594ddd33d85c565b19b1"
+      },
+      "Q1": {
+        "x": "0x51cce63c50d972a6e51c61334f0f4875c9ac1cd2d3238412f84e31da7d980ef5",
+        "y": "0xb45d1a36d00ad90e5ec7840a60a4de411917fbe7c82c3949a6e699e5a1b66aac"
+      },
+      "msg": "",
+      "u": [
+        "0xad5342c66a6dd0ff080df1da0ea1c04b96e0330dd89406465eeba11582515009",
+        "0x8c0f1d43204bd6f6ea70ae8013070a1518b43873bcd850aafa0a9e220e2eea5a"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x0bb8b87485551aa43ed54f009230450b492fead5f1cc91658775dac4a3388a0f",
+        "y": "0x5c41b3d0731a27a7b14bc0bf0ccded2d8751f83493404c84a88e71ffd424212e"
+      },
+      "Q0": {
+        "x": "0x5219ad0ddef3cc49b714145e91b2f7de6ce0a7a7dc7406c7726c7e373c58cb48",
+        "y": "0x7950144e52d30acbec7b624c203b1996c99617d0b61c2442354301b191d93ecf"
+      },
+      "Q1": {
+        "x": "0x019b7cb4efcfeaf39f738fe638e31d375ad6837f58a852d032ff60c69ee3875f",
+        "y": "0x589a62d2b22357fed5449bc38065b760095ebe6aeac84b01156ee4252715446e"
+      },
+      "msg": "abc",
+      "u": [
+        "0xafe47f2ea2b10465cc26ac403194dfb68b7f5ee865cda61e9f3e07a537220af1",
+        "0x379a27833b0bfe6f7bdca08e1e83c760bf9a338ab335542704edcd69ce9e46e0"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x65038ac8f2b1def042a5df0b33b1f4eca6bff7cb0f9c6c1526811864e544ed80",
+        "y": "0xcad44d40a656e7aff4002a8de287abc8ae0482b5ae825822bb870d6df9b56ca3"
+      },
+      "Q0": {
+        "x": "0xa17bdf2965eb88074bc01157e644ed409dac97cfcf0c61c998ed0fa45e79e4a2",
+        "y": "0x4f1bc80c70d411a3cc1d67aeae6e726f0f311639fee560c7f5a664554e3c9c2e"
+      },
+      "Q1": {
+        "x": "0x7da48bb67225c1a17d452c983798113f47e438e4202219dd0715f8419b274d66",
+        "y": "0xb765696b2913e36db3016c47edb99e24b1da30e761a8a3215dc0ec4d8f96e6f9"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x0fad9d125a9477d55cf9357105b0eb3a5c4259809bf87180aa01d651f53d312c",
+        "0xb68597377392cd3419d8fcc7d7660948c8403b19ea78bbca4b133c9d2196c0fb"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x4be61ee205094282ba8a2042bcb48d88dfbb609301c49aa8b078533dc65a0b5d",
+        "y": "0x98f8df449a072c4721d241a3b1236d3caccba603f916ca680f4539d2bfb3c29e"
+      },
+      "Q0": {
+        "x": "0xc76aaa823aeadeb3f356909cb08f97eee46ecb157c1f56699b5efebddf0e6398",
+        "y": "0x776a6f45f528a0e8d289a4be12c4fab80762386ec644abf2bffb9b627e4352b1"
+      },
+      "Q1": {
+        "x": "0x418ac3d85a5ccc4ea8dec14f750a3a9ec8b85176c95a7022f391826794eb5a75",
+        "y": "0xfd6604f69e9d9d2b74b072d14ea13050db72c932815523305cb9e807cc900aff"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x3bbc30446f39a7befad080f4d5f32ed116b9534626993d2cc5033f6f8d805919",
+        "0x76bb02db019ca9d3c1e02f0c17f8baf617bbdae5c393a81d9ce11e3be1bf1d33"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x457ae2981f70ca85d8e24c308b14db22f3e3862c5ea0f652ca38b5e49cd64bc5",
+        "y": "0xecb9f0eadc9aeed232dabc53235368c1394c78de05dd96893eefa62b0f4757dc"
+      },
+      "Q0": {
+        "x": "0xd88b989ee9d1295df413d4456c5c850b8b2fb0f5402cc5c4c7e815412e926db8",
+        "y": "0xbb4a1edeff506cf16def96afff41b16fc74f6dbd55c2210e5b8f011ba32f4f40"
+      },
+      "Q1": {
+        "x": "0xa281e34e628f3a4d2a53fa87ff973537d68ad4fbc28d3be5e8d9f6a2571c5a4b",
+        "y": "0xf6ed88a7aab56a488100e6f1174fa9810b47db13e86be999644922961206e184"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x4ebc95a6e839b1ae3c63b847798e85cb3c12d3817ec6ebc10af6ee51adb29fec",
+        "0x4e21af88e22ea80156aff790750121035b3eefaa96b425a8716e0d20b4e269ee"
+      ]
+    }
+  ]
+}

test/hash-to-curve/P384_XMD:SHA-384_SSWU_NU_.json

@@ -0,0 +1,90 @@
+{
+  "L": "0x48",
+  "Z": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffff3",
+  "ciphersuite": "P384_XMD:SHA-384_SSWU_NU_",
+  "curve": "NIST P-384",
+  "dst": "QUUX-V01-CS02-with-P384_XMD:SHA-384_SSWU_NU_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x1",
+    "p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff"
+  },
+  "hash": "sha384",
+  "k": "0xc0",
+  "map": {
+    "name": "SSWU"
+  },
+  "randomOracle": false,
+  "vectors": [
+    {
+      "P": {
+        "x": "0xde5a893c83061b2d7ce6a0d8b049f0326f2ada4b966dc7e72927256b033ef61058029a3bfb13c1c7ececd6641881ae20",
+        "y": "0x63f46da6139785674da315c1947e06e9a0867f5608cf24724eb3793a1f5b3809ee28eb21a0c64be3be169afc6cdb38ca"
+      },
+      "Q": {
+        "x": "0xde5a893c83061b2d7ce6a0d8b049f0326f2ada4b966dc7e72927256b033ef61058029a3bfb13c1c7ececd6641881ae20",
+        "y": "0x63f46da6139785674da315c1947e06e9a0867f5608cf24724eb3793a1f5b3809ee28eb21a0c64be3be169afc6cdb38ca"
+      },
+      "msg": "",
+      "u": [
+        "0xbc7dc1b2cdc5d588a66de3276b0f24310d4aca4977efda7d6272e1be25187b001493d267dc53b56183c9e28282368e60"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x1f08108b87e703c86c872ab3eb198a19f2b708237ac4be53d7929fb4bd5194583f40d052f32df66afe5249c9915d139b",
+        "y": "0x1369dc8d5bf038032336b989994874a2270adadb67a7fcc32f0f8824bc5118613f0ac8de04a1041d90ff8a5ad555f96c"
+      },
+      "Q": {
+        "x": "0x1f08108b87e703c86c872ab3eb198a19f2b708237ac4be53d7929fb4bd5194583f40d052f32df66afe5249c9915d139b",
+        "y": "0x1369dc8d5bf038032336b989994874a2270adadb67a7fcc32f0f8824bc5118613f0ac8de04a1041d90ff8a5ad555f96c"
+      },
+      "msg": "abc",
+      "u": [
+        "0x9de6cf41e6e41c03e4a7784ac5c885b4d1e49d6de390b3cdd5a1ac5dd8c40afb3dfd7bb2686923bab644134483fc1926"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x4dac31ec8a82ee3c02ba2d7c9fa431f1e59ffe65bf977b948c59e1d813c2d7963c7be81aa6db39e78ff315a10115c0d0",
+        "y": "0x845333cdb5702ad5c525e603f302904d6fc84879f0ef2ee2014a6b13edd39131bfd66f7bd7cdc2d9ccf778f0c8892c3f"
+      },
+      "Q": {
+        "x": "0x4dac31ec8a82ee3c02ba2d7c9fa431f1e59ffe65bf977b948c59e1d813c2d7963c7be81aa6db39e78ff315a10115c0d0",
+        "y": "0x845333cdb5702ad5c525e603f302904d6fc84879f0ef2ee2014a6b13edd39131bfd66f7bd7cdc2d9ccf778f0c8892c3f"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x84e2d430a5e2543573e58e368af41821ca3ccc97baba7e9aab51a84543d5a0298638a22ceee6090d9d642921112af5b7"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x13c1f8c52a492183f7c28e379b0475486718a7e3ac1dfef39283b9ce5fb02b73f70c6c1f3dfe0c286b03e2af1af12d1d",
+        "y": "0x57e101887e73e40eab8963324ed16c177d55eb89f804ec9df06801579820420b5546b579008df2145fd770f584a1a54c"
+      },
+      "Q": {
+        "x": "0x13c1f8c52a492183f7c28e379b0475486718a7e3ac1dfef39283b9ce5fb02b73f70c6c1f3dfe0c286b03e2af1af12d1d",
+        "y": "0x57e101887e73e40eab8963324ed16c177d55eb89f804ec9df06801579820420b5546b579008df2145fd770f584a1a54c"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x504e4d5a529333b9205acaa283107bd1bffde753898f7744161f7dd19ba57fbb6a64214a2e00ddd2613d76cd508ddb30"
+      ]
+    },
+    {
+      "P": {
+        "x": "0xaf129727a4207a8cb9e9dce656d88f79fce25edbcea350499d65e9bf1204537bdde73c7cefb752a6ed5ebcd44e183302",
+        "y": "0xce68a3d5e161b2e6a968e4ddaa9e51504ad1516ec170c7eef3ca6b5327943eca95d90b23b009ba45f58b72906f2a99e2"
+      },
+      "Q": {
+        "x": "0xaf129727a4207a8cb9e9dce656d88f79fce25edbcea350499d65e9bf1204537bdde73c7cefb752a6ed5ebcd44e183302",
+        "y": "0xce68a3d5e161b2e6a968e4ddaa9e51504ad1516ec170c7eef3ca6b5327943eca95d90b23b009ba45f58b72906f2a99e2"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x7b01ce9b8c5a60d9fbc202d6dde92822e46915d8c17e03fcb92ece1ed6074d01e149fc9236def40d673de903c1d4c166"
+      ]
+    }
+  ]
+}

test/hash-to-curve/P384_XMD:SHA-384_SSWU_RO_.json

@@ -0,0 +1,115 @@
+{
+  "L": "0x48",
+  "Z": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffff3",
+  "ciphersuite": "P384_XMD:SHA-384_SSWU_RO_",
+  "curve": "NIST P-384",
+  "dst": "QUUX-V01-CS02-with-P384_XMD:SHA-384_SSWU_RO_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x1",
+    "p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff"
+  },
+  "hash": "sha384",
+  "k": "0xc0",
+  "map": {
+    "name": "SSWU"
+  },
+  "randomOracle": true,
+  "vectors": [
+    {
+      "P": {
+        "x": "0xeb9fe1b4f4e14e7140803c1d99d0a93cd823d2b024040f9c067a8eca1f5a2eeac9ad604973527a356f3fa3aeff0e4d83",
+        "y": "0x0c21708cff382b7f4643c07b105c2eaec2cead93a917d825601e63c8f21f6abd9abc22c93c2bed6f235954b25048bb1a"
+      },
+      "Q0": {
+        "x": "0xe4717e29eef38d862bee4902a7d21b44efb58c464e3e1f0d03894d94de310f8ffc6de86786dd3e15a1541b18d4eb2846",
+        "y": "0x6b95a6e639822312298a47526bb77d9cd7bcf76244c991c8cd70075e2ee6e8b9a135c4a37e3c0768c7ca871c0ceb53d4"
+      },
+      "Q1": {
+        "x": "0x509527cfc0750eedc53147e6d5f78596c8a3b7360e0608e2fab0563a1670d58d8ae107c9f04bcf90e89489ace5650efd",
+        "y": "0x33337b13cb35e173fdea4cb9e8cce915d836ff57803dbbeb7998aa49d17df2ff09b67031773039d09fbd9305a1566bc4"
+      },
+      "msg": "",
+      "u": [
+        "0x25c8d7dc1acd4ee617766693f7f8829396065d1b447eedb155871feffd9c6653279ac7e5c46edb7010a0e4ff64c9f3b4",
+        "0x59428be4ed69131df59a0c6a8e188d2d4ece3f1b2a3a02602962b47efa4d7905945b1e2cc80b36aa35c99451073521ac"
+      ]
+    },
+    {
+      "P": {
+        "x": "0xe02fc1a5f44a7519419dd314e29863f30df55a514da2d655775a81d413003c4d4e7fd59af0826dfaad4200ac6f60abe1",
+        "y": "0x01f638d04d98677d65bef99aef1a12a70a4cbb9270ec55248c04530d8bc1f8f90f8a6a859a7c1f1ddccedf8f96d675f6"
+      },
+      "Q0": {
+        "x": "0xfc853b69437aee9a19d5acf96a4ee4c5e04cf7b53406dfaa2afbdd7ad2351b7f554e4bbc6f5db4177d4d44f933a8f6ee",
+        "y": "0x7e042547e01834c9043b10f3a8221c4a879cb156f04f72bfccab0c047a304e30f2aa8b2e260d34c4592c0c33dd0c6482"
+      },
+      "Q1": {
+        "x": "0x57912293709b3556b43a2dfb137a315d256d573b82ded120ef8c782d607c05d930d958e50cb6dc1cc480b9afc38c45f1",
+        "y": "0xde9387dab0eef0bda219c6f168a92645a84665c4f2137c14270fb424b7532ff84843c3da383ceea24c47fa343c227bb8"
+      },
+      "msg": "abc",
+      "u": [
+        "0x53350214cb6bef0b51abb791b1c4209a2b4c16a0c67e1ab1401017fad774cd3b3f9a8bcdf7f6229dd8dd5a075cb149a0",
+        "0xc0473083898f63e03f26f14877a2407bd60c75ad491e7d26cbc6cc5ce815654075ec6b6898c7a41d74ceaf720a10c02e"
+      ]
+    },
+    {
+      "P": {
+        "x": "0xbdecc1c1d870624965f19505be50459d363c71a699a496ab672f9a5d6b78676400926fbceee6fcd1780fe86e62b2aa89",
+        "y": "0x57cf1f99b5ee00f3c201139b3bfe4dd30a653193778d89a0accc5e0f47e46e4e4b85a0595da29c9494c1814acafe183c"
+      },
+      "Q0": {
+        "x": "0x0ceece45b73f89844671df962ad2932122e878ad2259e650626924e4e7f132589341dec1480ebcbbbe3509d11fb570b7",
+        "y": "0xfafd71a3115298f6be4ae5c6dfc96c400cfb55760f185b7b03f3fa45f3f91eb65d27628b3c705cafd0466fafa54883ce"
+      },
+      "Q1": {
+        "x": "0xdea1be8d3f9be4cbf4fab9d71d549dde76875b5d9b876832313a083ec81e528cbc2a0a1d0596b3bcb0ba77866b129776",
+        "y": "0xeb15fe71662214fb03b65541f40d3eb0f4cf5c3b559f647da138c9f9b7484c48a08760e02c16f1992762cb7298fa52cf"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0xaab7fb87238cf6b2ab56cdcca7e028959bb2ea599d34f68484139dde85ec6548a6e48771d17956421bdb7790598ea52e",
+        "0x26e8d833552d7844d167833ca5a87c35bcfaa5a0d86023479fb28e5cd6075c18b168bf1f5d2a0ea146d057971336d8d1"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x03c3a9f401b78c6c36a52f07eeee0ec1289f178adf78448f43a3850e0456f5dd7f7633dd31676d990eda32882ab486c0",
+        "y": "0xcc183d0d7bdfd0a3af05f50e16a3f2de4abbc523215bf57c848d5ea662482b8c1f43dc453a93b94a8026db58f3f5d878"
+      },
+      "Q0": {
+        "x": "0x051a22105e0817a35d66196338c8d85bd52690d79bba373ead8a86dd9899411513bb9f75273f6483395a7847fb21edb4",
+        "y": "0xf168295c1bbcff5f8b01248e9dbc885335d6d6a04aea960f7384f746ba6502ce477e624151cc1d1392b00df0f5400c06"
+      },
+      "Q1": {
+        "x": "0x6ad7bc8ed8b841efd8ad0765c8a23d0b968ec9aa360a558ff33500f164faa02bee6c704f5f91507c4c5aad2b0dc5b943",
+        "y": "0x47313cc0a873ade774048338fc34ca5313f96bbf6ae22ac6ef475d85f03d24792dc6afba8d0b4a70170c1b4f0f716629"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x04c00051b0de6e726d228c85bf243bf5f4789efb512b22b498cde3821db9da667199b74bd5a09a79583c6d353a3bb41c",
+        "0x97580f218255f899f9204db64cd15e6a312cb4d8182375d1e5157c8f80f41d6a1a4b77fb1ded9dce56c32058b8d5202b"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x7b18d210b1f090ac701f65f606f6ca18fb8d081e3bc6cbd937c5604325f1cdea4c15c10a54ef303aabf2ea58bd9947a4",
+        "y": "0xea857285a33abb516732915c353c75c576bf82ccc96adb63c094dde580021eddeafd91f8c0bfee6f636528f3d0c47fd2"
+      },
+      "Q0": {
+        "x": "0x42e6666f505e854187186bad3011598d9278b9d6e3e4d2503c3d236381a56748dec5d139c223129b324df53fa147c4df",
+        "y": "0x8ee51dbda46413bf621838cc935d18d617881c6f33f3838a79c767a1e5618e34b22f79142df708d2432f75c7366c8512"
+      },
+      "Q1": {
+        "x": "0x4ff01ceeba60484fa1bc0d825fe1e5e383d8f79f1e5bb78e5fb26b7a7ef758153e31e78b9d60ce75c5e32e43869d4e12",
+        "y": "0x0f84b978fac8ceda7304b47e229d6037d32062e597dc7a9b95bcd9af441f3c56c619a901d21635f9ec6ab4710b9fcd0e"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x480cb3ac2c389db7f9dac9c396d2647ae946db844598971c26d1afd53912a1491199c0a5902811e4b809c26fcd37a014",
+        "0xd28435eb34680e148bf3908536e42231cba9e1f73ae2c6902a222a89db5c49c97db2f8fa4d4cd6e424b17ac60bdb9bb6"
+      ]
+    }
+  ]
+}

test/hash-to-curve/P521_XMD:SHA-512_SSWU_NU_.json

@@ -0,0 +1,90 @@
+{
+  "L": "0x62",
+  "Z": "0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffb",
+  "ciphersuite": "P521_XMD:SHA-512_SSWU_NU_",
+  "curve": "NIST P-521",
+  "dst": "QUUX-V01-CS02-with-P521_XMD:SHA-512_SSWU_NU_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x1",
+    "p": "0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
+  },
+  "hash": "sha512",
+  "k": "0x100",
+  "map": {
+    "name": "SSWU"
+  },
+  "randomOracle": false,
+  "vectors": [
+    {
+      "P": {
+        "x": "0x01ec604b4e1e3e4c7449b7a41e366e876655538acf51fd40d08b97be066f7d020634e906b1b6942f9174b417027c953d75fb6ec64b8cee2a3672d4f1987d13974705",
+        "y": "0x00944fc439b4aad2463e5c9cfa0b0707af3c9a42e37c5a57bb4ecd12fef9fb21508568aedcdd8d2490472df4bbafd79081c81e99f4da3286eddf19be47e9c4cf0e91"
+      },
+      "Q": {
+        "x": "0x01ec604b4e1e3e4c7449b7a41e366e876655538acf51fd40d08b97be066f7d020634e906b1b6942f9174b417027c953d75fb6ec64b8cee2a3672d4f1987d13974705",
+        "y": "0x00944fc439b4aad2463e5c9cfa0b0707af3c9a42e37c5a57bb4ecd12fef9fb21508568aedcdd8d2490472df4bbafd79081c81e99f4da3286eddf19be47e9c4cf0e91"
+      },
+      "msg": "",
+      "u": [
+        "0x01e4947fe62a4e47792cee2798912f672fff820b2556282d9843b4b465940d7683a986f93ccb0e9a191fbc09a6e770a564490d2a4ae51b287ca39f69c3d910ba6a4f"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x00c720ab56aa5a7a4c07a7732a0a4e1b909e32d063ae1b58db5f0eb5e09f08a9884bff55a2bef4668f715788e692c18c1915cd034a6b998311fcf46924ce66a2be9a",
+        "y": "0x003570e87f91a4f3c7a56be2cb2a078ffc153862a53d5e03e5dad5bccc6c529b8bab0b7dbb157499e1949e4edab21cf5d10b782bc1e945e13d7421ad8121dbc72b1d"
+      },
+      "Q": {
+        "x": "0x00c720ab56aa5a7a4c07a7732a0a4e1b909e32d063ae1b58db5f0eb5e09f08a9884bff55a2bef4668f715788e692c18c1915cd034a6b998311fcf46924ce66a2be9a",
+        "y": "0x003570e87f91a4f3c7a56be2cb2a078ffc153862a53d5e03e5dad5bccc6c529b8bab0b7dbb157499e1949e4edab21cf5d10b782bc1e945e13d7421ad8121dbc72b1d"
+      },
+      "msg": "abc",
+      "u": [
+        "0x0019b85ef78596efc84783d42799e80d787591fe7432dee1d9fa2b7651891321be732ddf653fa8fefa34d86fb728db569d36b5b6ed3983945854b2fc2dc6a75aa25b"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x00bcaf32a968ff7971b3bbd9ce8edfbee1309e2019d7ff373c38387a782b005dce6ceffccfeda5c6511c8f7f312f343f3a891029c5858f45ee0bf370aba25fc990cc",
+        "y": "0x00923517e767532d82cb8a0b59705eec2b7779ce05f9181c7d5d5e25694ef8ebd4696343f0bc27006834d2517215ecf79482a84111f50c1bae25044fe1dd77744bbd"
+      },
+      "Q": {
+        "x": "0x00bcaf32a968ff7971b3bbd9ce8edfbee1309e2019d7ff373c38387a782b005dce6ceffccfeda5c6511c8f7f312f343f3a891029c5858f45ee0bf370aba25fc990cc",
+        "y": "0x00923517e767532d82cb8a0b59705eec2b7779ce05f9181c7d5d5e25694ef8ebd4696343f0bc27006834d2517215ecf79482a84111f50c1bae25044fe1dd77744bbd"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x01dba0d7fa26a562ee8a9014ebc2cca4d66fd9de036176aca8fc11ef254cd1bc208847ab7701dbca7af328b3f601b11a1737a899575a5c14f4dca5aaca45e9935e07"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x001ac69014869b6c4ad7aa8c443c255439d36b0e48a0f57b03d6fe9c40a66b4e2eaed2a93390679a5cc44b3a91862b34b673f0e92c83187da02bf3db967d867ce748",
+        "y": "0x00d5603d530e4d62b30fccfa1d90c2206654d74291c1db1c25b86a051ee3fffc294e5d56f2e776853406bd09206c63d40f37ad8829524cf89ad70b5d6e0b4a3b7341"
+      },
+      "Q": {
+        "x": "0x001ac69014869b6c4ad7aa8c443c255439d36b0e48a0f57b03d6fe9c40a66b4e2eaed2a93390679a5cc44b3a91862b34b673f0e92c83187da02bf3db967d867ce748",
+        "y": "0x00d5603d530e4d62b30fccfa1d90c2206654d74291c1db1c25b86a051ee3fffc294e5d56f2e776853406bd09206c63d40f37ad8829524cf89ad70b5d6e0b4a3b7341"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x00844da980675e1244cb209dcf3ea0aabec23bd54b2cda69fff86eb3acc318bf3d01bae96e9cd6f4c5ceb5539df9a7ad7fcc5e9d54696081ba9782f3a0f6d14987e3"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x01801de044c517a80443d2bd4f503a9e6866750d2f94a22970f62d721f96e4310e4a828206d9cdeaa8f2d476705cc3bbc490a6165c687668f15ec178a17e3d27349b",
+        "y": "0x0068889ea2e1442245fe42bfda9e58266828c0263119f35a61631a3358330f3bb84443fcb54fcd53a1d097fccbe310489b74ee143fc2938959a83a1f7dd4a6fd395b"
+      },
+      "Q": {
+        "x": "0x01801de044c517a80443d2bd4f503a9e6866750d2f94a22970f62d721f96e4310e4a828206d9cdeaa8f2d476705cc3bbc490a6165c687668f15ec178a17e3d27349b",
+        "y": "0x0068889ea2e1442245fe42bfda9e58266828c0263119f35a61631a3358330f3bb84443fcb54fcd53a1d097fccbe310489b74ee143fc2938959a83a1f7dd4a6fd395b"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x01aab1fb7e5cd44ba4d9f32353a383cb1bb9eb763ed40b32bdd5f666988970205998c0e44af6e2b5f6f8e48e969b3f649cae3c6ab463e1b274d968d91c02f00cce91"
+      ]
+    }
+  ]
+}

test/hash-to-curve/P521_XMD:SHA-512_SSWU_RO_.json

@@ -0,0 +1,115 @@
+{
+  "L": "0x62",
+  "Z": "0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffb",
+  "ciphersuite": "P521_XMD:SHA-512_SSWU_RO_",
+  "curve": "NIST P-521",
+  "dst": "QUUX-V01-CS02-with-P521_XMD:SHA-512_SSWU_RO_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x1",
+    "p": "0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
+  },
+  "hash": "sha512",
+  "k": "0x100",
+  "map": {
+    "name": "SSWU"
+  },
+  "randomOracle": true,
+  "vectors": [
+    {
+      "P": {
+        "x": "0x00fd767cebb2452030358d0e9cf907f525f50920c8f607889a6a35680727f64f4d66b161fafeb2654bea0d35086bec0a10b30b14adef3556ed9f7f1bc23cecc9c088",
+        "y": "0x0169ba78d8d851e930680322596e39c78f4fe31b97e57629ef6460ddd68f8763fd7bd767a4e94a80d3d21a3c2ee98347e024fc73ee1c27166dc3fe5eeef782be411d"
+      },
+      "Q0": {
+        "x": "0x00b70ae99b6339fffac19cb9bfde2098b84f75e50ac1e80d6acb954e4534af5f0e9c4a5b8a9c10317b8e6421574bae2b133b4f2b8c6ce4b3063da1d91d34fa2b3a3c",
+        "y": "0x007f368d98a4ddbf381fb354de40e44b19e43bb11a1278759f4ea7b485e1b6db33e750507c071250e3e443c1aaed61f2c28541bb54b1b456843eda1eb15ec2a9b36e"
+      },
+      "Q1": {
+        "x": "0x01143d0e9cddcdacd6a9aafe1bcf8d218c0afc45d4451239e821f5d2a56df92be942660b532b2aa59a9c635ae6b30e803c45a6ac871432452e685d661cd41cf67214",
+        "y": "0x00ff75515df265e996d702a5380defffab1a6d2bc232234c7bcffa433cd8aa791fbc8dcf667f08818bffa739ae25773b32073213cae9a0f2a917a0b1301a242dda0c"
+      },
+      "msg": "",
+      "u": [
+        "0x01e5f09974e5724f25286763f00ce76238c7a6e03dc396600350ee2c4135fb17dc555be99a4a4bae0fd303d4f66d984ed7b6a3ba386093752a855d26d559d69e7e9e",
+        "0x00ae593b42ca2ef93ac488e9e09a5fe5a2f6fb330d18913734ff602f2a761fcaaf5f596e790bcc572c9140ec03f6cccc38f767f1c1975a0b4d70b392d95a0c7278aa"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x002f89a1677b28054b50d15e1f81ed6669b5a2158211118ebdef8a6efc77f8ccaa528f698214e4340155abc1fa08f8f613ef14a043717503d57e267d57155cf784a4",
+        "y": "0x010e0be5dc8e753da8ce51091908b72396d3deed14ae166f66d8ebf0a4e7059ead169ea4bead0232e9b700dd380b316e9361cfdba55a08c73545563a80966ecbb86d"
+      },
+      "Q0": {
+        "x": "0x01b254e1c99c835836f0aceebba7d77750c48366ecb07fb658e4f5b76e229ae6ca5d271bb0006ffcc42324e15a6d3daae587f9049de2dbb0494378ffb60279406f56",
+        "y": "0x01845f4af72fc2b1a5a2fe966f6a97298614288b456cfc385a425b686048b25c952fbb5674057e1eb055d04568c0679a8e2dda3158dc16ac598dbb1d006f5ad915b0"
+      },
+      "Q1": {
+        "x": "0x007f08e813c620e527c961b717ffc74aac7afccb9158cebc347d5715d5c2214f952c97e194f11d114d80d3481ed766ac0a3dba3eb73f6ff9ccb9304ad10bbd7b4a36",
+        "y": "0x0022468f92041f9970a7cc025d71d5b647f822784d29ca7b3bc3b0829d6bb8581e745f8d0cc9dc6279d0450e779ac2275c4c3608064ad6779108a7828ebd9954caeb"
+      },
+      "msg": "abc",
+      "u": [
+        "0x003d00c37e95f19f358adeeaa47288ec39998039c3256e13c2a4c00a7cb61a34c8969472960150a27276f2390eb5e53e47ab193351c2d2d9f164a85c6a5696d94fe8",
+        "0x01f3cbd3df3893a45a2f1fecdac4d525eb16f345b03e2820d69bc580f5cbe9cb89196fdf720ef933c4c0361fcfe29940fd0db0a5da6bafb0bee8876b589c41365f15"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x006e200e276a4a81760099677814d7f8794a4a5f3658442de63c18d2244dcc957c645e94cb0754f95fcf103b2aeaf94411847c24187b89fb7462ad3679066337cbc4",
+        "y": "0x001dd8dfa9775b60b1614f6f169089d8140d4b3e4012949b52f98db2deff3e1d97bf73a1fa4d437d1dcdf39b6360cc518d8ebcc0f899018206fded7617b654f6b168"
+      },
+      "Q0": {
+        "x": "0x0021482e8622aac14da60e656043f79a6a110cbae5012268a62dd6a152c41594549f373910ebed170ade892dd5a19f5d687fae7095a461d583f8c4295f7aaf8cd7da",
+        "y": "0x0177e2d8c6356b7de06e0b5712d8387d529b848748e54a8bc0ef5f1475aa569f8f492fa85c3ad1c5edc51faf7911f11359bfa2a12d2ef0bd73df9cb5abd1b101c8b1"
+      },
+      "Q1": {
+        "x": "0x00abeafb16fdbb5eb95095678d5a65c1f293291dfd20a3751dbe05d0a9bfe2d2eef19449fe59ec32cdd4a4adc3411177c0f2dffd0159438706159a1bbd0567d9b3d0",
+        "y": "0x007cc657f847db9db651d91c801741060d63dab4056d0a1d3524e2eb0e819954d8f677aa353bd056244a88f00017e00c3ce8beeedb4382d83d74418bd48930c6c182"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x00183ee1a9bbdc37181b09ec336bcaa34095f91ef14b66b1485c166720523dfb81d5c470d44afcb52a87b704dbc5c9bc9d0ef524dec29884a4795f55c1359945baf3",
+        "0x00504064fd137f06c81a7cf0f84aa7e92b6b3d56c2368f0a08f44776aa8930480da1582d01d7f52df31dca35ee0a7876500ece3d8fe0293cd285f790c9881c998d5e"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x01b264a630bd6555be537b000b99a06761a9325c53322b65bdc41bf196711f9708d58d34b3b90faf12640c27b91c70a507998e55940648caa8e71098bf2bc8d24664",
+        "y": "0x01ea9f445bee198b3ee4c812dcf7b0f91e0881f0251aab272a12201fd89b1a95733fd2a699c162b639e9acdcc54fdc2f6536129b6beb0432be01aa8da02df5e59aaa"
+      },
+      "Q0": {
+        "x": "0x0005eac7b0b81e38727efcab1e375f6779aea949c3e409b53a1d37aa2acbac87a7e6ad24aafbf3c52f82f7f0e21b872e88c55e17b7fa21ce08a94ea2121c42c2eb73",
+        "y": "0x00a173b6a53a7420dbd61d4a21a7c0a52de7a5c6ce05f31403bef747d16cc8604a039a73bdd6e114340e55dacd6bea8e217ffbadfb8c292afa3e1b2afc839a6ce7bb"
+      },
+      "Q1": {
+        "x": "0x01881e3c193a69e4d88d8180a6879b74782a0bc7e529233e9f84bf7f17d2f319c36920ffba26f9e57a1e045cc7822c834c239593b6e142a694aa00c757b0db79e5e8",
+        "y": "0x01558b16d396d866e476e001f2dd0758927655450b84e12f154032c7c2a6db837942cd9f44b814f79b4d729996ced61eec61d85c675139cbffe3fbf071d2c21cfecb"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x0159871e222689aad7694dc4c3480a49807b1eedd9c8cb4ae1b219d5ba51655ea5b38e2e4f56b36bf3e3da44a7b139849d28f598c816fe1bc7ed15893b22f63363c3",
+        "0x004ef0cffd475152f3858c0a8ccbdf7902d8261da92744e98df9b7fadb0a5502f29c5086e76e2cf498f47321434a40b1504911552ce44ad7356a04e08729ad9411f5"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x00c12bc3e28db07b6b4d2a2b1167ab9e26fc2fa85c7b0498a17b0347edf52392856d7e28b8fa7a2dd004611159505835b687ecf1a764857e27e9745848c436ef3925",
+        "y": "0x01cd287df9a50c22a9231beb452346720bb163344a41c5f5a24e8335b6ccc595fd436aea89737b1281aecb411eb835f0b939073fdd1dd4d5a2492e91ef4a3c55bcbd"
+      },
+      "Q0": {
+        "x": "0x00041f6eb92af8777260718e4c22328a7d74203350c6c8f5794d99d5789766698f459b83d5068276716f01429934e40af3d1111a22780b1e07e72238d2207e5386be",
+        "y": "0x001c712f0182813942b87cab8e72337db017126f52ed797dd234584ac9ae7e80dfe7abea11db02cf1855312eae1447dbaecc9d7e8c880a5e76a39f6258074e1bc2e0"
+      },
+      "Q1": {
+        "x": "0x0125c0b69bcf55eab49280b14f707883405028e05c927cd7625d4e04115bd0e0e6323b12f5d43d0d6d2eff16dbcf244542f84ec058911260dc3bb6512ab5db285fbd",
+        "y": "0x008bddfb803b3f4c761458eb5f8a0aee3e1f7f68e9d7424405fa69172919899317fb6ac1d6903a432d967d14e0f80af63e7035aaae0c123e56862ce969456f99f102"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x0033d06d17bc3b9a3efc081a05d65805a14a3050a0dd4dfb4884618eb5c73980a59c5a246b18f58ad022dd3630faa22889fbb8ba1593466515e6ab4aeb7381c26334",
+        "0x0092290ab99c3fea1a5b8fb2ca49f859994a04faee3301cefab312d34227f6a2d0c3322cf76861c6a3683bdaa2dd2a6daa5d6906c663e065338b2344d20e313f1114"
+      ]
+    }
+  ]
+}

test/hash-to-curve/curve25519_XMD:SHA-512_ELL2_NU_.json

@@ -0,0 +1,90 @@
+{
+  "L": "0x30",
+  "Z": "0x2",
+  "ciphersuite": "curve25519_XMD:SHA-512_ELL2_NU_",
+  "curve": "curve25519",
+  "dst": "QUUX-V01-CS02-with-curve25519_XMD:SHA-512_ELL2_NU_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x1",
+    "p": "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed"
+  },
+  "hash": "sha512",
+  "k": "0x80",
+  "map": {
+    "name": "ELL2"
+  },
+  "randomOracle": false,
+  "vectors": [
+    {
+      "P": {
+        "x": "0x1bb913f0c9daefa0b3375378ffa534bda5526c97391952a7789eb976edfe4d08",
+        "y": "0x4548368f4f983243e747b62a600840ae7c1dab5c723991f85d3a9768479f3ec4"
+      },
+      "Q": {
+        "x": "0x51125222da5e763d97f3c10fcc92ea6860b9ccbbd2eb1285728f566721c1e65b",
+        "y": "0x343d2204f812d3dfc5304a5808c6c0d81a903a5d228b342442aa3c9ba5520a3d"
+      },
+      "msg": "",
+      "u": [
+        "0x608d892b641f0328523802a6603427c26e55e6f27e71a91a478148d45b5093cd"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x7c22950b7d900fa866334262fcaea47a441a578df43b894b4625c9b450f9a026",
+        "y": "0x5547bc00e4c09685dcbc6cb6765288b386d8bdcb595fa5a6e3969e08097f0541"
+      },
+      "Q": {
+        "x": "0x7d56d1e08cb0ccb92baf069c18c49bb5a0dcd927eff8dcf75ca921ef7f3e6eeb",
+        "y": "0x404d9a7dc25c9c05c44ab9a94590e7c3fe2dcec74533a0b24b188a5d5dacf429"
+      },
+      "msg": "abc",
+      "u": [
+        "0x46f5b22494bfeaa7f232cc8d054be68561af50230234d7d1d63d1d9abeca8da5"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x31ad08a8b0deeb2a4d8b0206ca25f567ab4e042746f792f4b7973f3ae2096c52",
+        "y": "0x405070c28e78b4fa269427c82827261991b9718bd6c6e95d627d701a53c30db1"
+      },
+      "Q": {
+        "x": "0x3fbe66b9c9883d79e8407150e7c2a1c8680bee496c62fabe4619a72b3cabe90f",
+        "y": "0x08ec476147c9a0a3ff312d303dbbd076abb7551e5fce82b48ab14b433f8d0a7b"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x235fe40c443766ce7e18111c33862d66c3b33267efa50d50f9e8e5d252a40aaa"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x027877759d155b1997d0d84683a313eb78bdb493271d935b622900459d52ceaa",
+        "y": "0x54d691731a53baa30707f4a87121d5169fb5d587d70fb0292b5830dedbec4c18"
+      },
+      "Q": {
+        "x": "0x227e0bb89de700385d19ec40e857db6e6a3e634b1c32962f370d26f84ff19683",
+        "y": "0x5f86ff3851d262727326a32c1bf7655a03665830fa7f1b8b1e5a09d85bc66e4a"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x001e92a544463bda9bd04ddbe3d6eed248f82de32f522669efc5ddce95f46f5b"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x5fd892c0958d1a75f54c3182a18d286efab784e774d1e017ba2fb252998b5dc1",
+        "y": "0x750af3c66101737423a4519ac792fb93337bd74ee751f19da4cf1e94f4d6d0b8"
+      },
+      "Q": {
+        "x": "0x3bcd651ee54d5f7b6013898aab251ee8ecc0688166fce6e9548d38472f6bd196",
+        "y": "0x1bb36ad9197299f111b4ef21271c41f4b7ecf5543db8bb5931307ebdb2eaa465"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x1a68a1af9f663592291af987203393f707305c7bac9c8d63d6a729bdc553dc19"
+      ]
+    }
+  ]
+}

test/hash-to-curve/curve25519_XMD:SHA-512_ELL2_RO_.json

@@ -0,0 +1,115 @@
+{
+  "L": "0x30",
+  "Z": "0x2",
+  "ciphersuite": "curve25519_XMD:SHA-512_ELL2_RO_",
+  "curve": "curve25519",
+  "dst": "QUUX-V01-CS02-with-curve25519_XMD:SHA-512_ELL2_RO_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x1",
+    "p": "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed"
+  },
+  "hash": "sha512",
+  "k": "0x80",
+  "map": {
+    "name": "ELL2"
+  },
+  "randomOracle": true,
+  "vectors": [
+    {
+      "P": {
+        "x": "0x2de3780abb67e861289f5749d16d3e217ffa722192d16bbd9d1bfb9d112b98c0",
+        "y": "0x3b5dc2a498941a1033d176567d457845637554a2fe7a3507d21abd1c1bd6e878"
+      },
+      "Q0": {
+        "x": "0x36b4df0c864c64707cbf6cf36e9ee2c09a6cb93b28313c169be29561bb904f98",
+        "y": "0x6cd59d664fb58c66c892883cd0eb792e52055284dac3907dd756b45d15c3983d"
+      },
+      "Q1": {
+        "x": "0x3fa114783a505c0b2b2fbeef0102853c0b494e7757f2a089d0daae7ed9a0db2b",
+        "y": "0x76c0fe7fec932aaafb8eefb42d9cbb32eb931158f469ff3050af15cfdbbeff94"
+      },
+      "msg": "",
+      "u": [
+        "0x005fe8a7b8fef0a16c105e6cadf5a6740b3365e18692a9c05bfbb4d97f645a6a",
+        "0x1347edbec6a2b5d8c02e058819819bee177077c9d10a4ce165aab0fd0252261a"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x2b4419f1f2d48f5872de692b0aca72cc7b0a60915dd70bde432e826b6abc526d",
+        "y": "0x1b8235f255a268f0a6fa8763e97eb3d22d149343d495da1160eff9703f2d07dd"
+      },
+      "Q0": {
+        "x": "0x16b3d86e056b7970fa00165f6f48d90b619ad618791661b7b5e1ec78be10eac1",
+        "y": "0x4ab256422d84c5120b278cbdfc4e1facc5baadffeccecf8ee9bf3946106d50ca"
+      },
+      "Q1": {
+        "x": "0x7ec29ddbf34539c40adfa98fcb39ec36368f47f30e8f888cc7e86f4d46e0c264",
+        "y": "0x10d1abc1cae2d34c06e247f2141ba897657fb39f1080d54f09ce0af128067c74"
+      },
+      "msg": "abc",
+      "u": [
+        "0x49bed021c7a3748f09fa8cdfcac044089f7829d3531066ac9e74e0994e05bc7d",
+        "0x5c36525b663e63389d886105cee7ed712325d5a97e60e140aba7e2ce5ae851b6"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x68ca1ea5a6acf4e9956daa101709b1eee6c1bb0df1de3b90d4602382a104c036",
+        "y": "0x2a375b656207123d10766e68b938b1812a4a6625ff83cb8d5e86f58a4be08353"
+      },
+      "Q0": {
+        "x": "0x71de3dadfe268872326c35ac512164850860567aea0e7325e6b91a98f86533ad",
+        "y": "0x26a08b6e9a18084c56f2147bf515414b9b63f1522e1b6c5649f7d4b0324296ec"
+      },
+      "Q1": {
+        "x": "0x5704069021f61e41779e2ba6b932268316d6d2a6f064f997a22fef16d1eaeaca",
+        "y": "0x50483c7540f64fb4497619c050f2c7fe55454ec0f0e79870bb44302e34232210"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x6412b7485ba26d3d1b6c290a8e1435b2959f03721874939b21782df17323d160",
+        "0x24c7b46c1c6d9a21d32f5707be1380ab82db1054fde82865d5c9e3d968f287b2"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x096e9c8bae6c06b554c1ee69383bb0e82267e064236b3a30608d4ed20b73ac5a",
+        "y": "0x1eb5a62612cafb32b16c3329794645b5b948d9f8ffe501d4e26b073fef6de355"
+      },
+      "Q0": {
+        "x": "0x7a94d45a198fb5daa381f45f2619ab279744efdd8bd8ed587fc5b65d6cea1df0",
+        "y": "0x67d44f85d376e64bb7d713585230cdbfafc8e2676f7568e0b6ee59361116a6e1"
+      },
+      "Q1": {
+        "x": "0x30506fb7a32136694abd61b6113770270debe593027a968a01f271e146e60c18",
+        "y": "0x7eeee0e706b40c6b5174e551426a67f975ad5a977ee2f01e8e20a6d612458c3b"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x5e123990f11bbb5586613ffabdb58d47f64bb5f2fa115f8ea8df0188e0c9e1b5",
+        "0x5e8553eb00438a0bb1e7faa59dec6d8087f9c8011e5fb8ed9df31cb6c0d4ac19"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x1bc61845a138e912f047b5e70ba9606ba2a447a4dade024c8ef3dd42b7bbc5fe",
+        "y": "0x623d05e47b70e25f7f1d51dda6d7c23c9a18ce015fe3548df596ea9e38c69bf1"
+      },
+      "Q0": {
+        "x": "0x02d606e2699b918ee36f2818f2bc5013e437e673c9f9b9cdc15fd0c5ee913970",
+        "y": "0x29e9dc92297231ef211245db9e31767996c5625dfbf92e1c8107ef887365de1e"
+      },
+      "Q1": {
+        "x": "0x38920e9b988d1ab7449c0fa9a6058192c0c797bb3d42ac345724341a1aa98745",
+        "y": "0x24dcc1be7c4d591d307e89049fd2ed30aae8911245a9d8554bf6032e5aa40d3d"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x20f481e85da7a3bf60ac0fb11ed1d0558fc6f941b3ac5469aa8b56ec883d6d7d",
+        "0x017d57fd257e9a78913999a23b52ca988157a81b09c5442501d07fed20869465"
+      ]
+    }
+  ]
+}

test/hash-to-curve/curve448_XOF:SHAKE256_ELL2_NU_.json

@@ -0,0 +1,90 @@
+{
+  "L": "0x54",
+  "Z": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffffffffffffffffffffffffffffffffffffffffffffffffffffe",
+  "ciphersuite": "curve448_XOF:SHAKE256_ELL2_NU_",
+  "curve": "curve448",
+  "dst": "QUUX-V01-CS02-with-curve448_XOF:SHAKE256_ELL2_NU_",
+  "expand": "XOF",
+  "field": {
+    "m": "0x1",
+    "p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
+  },
+  "hash": "shake_256",
+  "k": "0xe0",
+  "map": {
+    "name": "ELL2"
+  },
+  "randomOracle": false,
+  "vectors": [
+    {
+      "P": {
+        "x": "0xb65e8dbb279fd656f926f68d463b13ca7a982b32f5da9c7cc58afcf6199e4729863fb75ca9ae3c95c6887d95a5102637a1c5c40ff0aafadc",
+        "y": "0xea1ea211cf29eca11c057fe8248181591a19f6ac51d45843a65d4bb8b71bc83a64c771ed7686218a278ef1c5d620f3d26b53162188645453"
+      },
+      "Q": {
+        "x": "0xe6304424de5af3f556d3e645600530c53ad949891c3e60ba041dd5f68a93901beff8440164477d348c13d28e27bfcd360c44c80b4c7d4cea",
+        "y": "0x4160a8f2043a347185406a6a7e50973b98b82edbdfa3209b0e1c90118e10eeb45045b0990d4b2b0708a30eca17df40ad53c9100f20c10b44"
+      },
+      "msg": "",
+      "u": [
+        "0x242c70f74eac8184116c71630d284cf8a742fc463e710545847ff64d8e9161cb9f599728a18a32dbd8b67c3bec5d64c9b1d2f2cde7b5888d"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x51aceca4fa95854bbaba58d8a5e17a86c07acadef32e1188cafda26232131800002cc2f27c7aec454e5e0c615bddffb7df6a5f7f0f14793f",
+        "y": "0xc590c9246eb28b08dee816d608ef233ea5d76e305dc458774a1e1bd880387e6734219e2018e4aa50a49486dce0ba8740065da37e6cf5212c"
+      },
+      "Q": {
+        "x": "0xde0dc93df9ce7953452f20e270699c1e7dacd5d571c226d77f53b7e3053d16f8a81b1601efb362054e973c8e733b663af93f00cb81baf130",
+        "y": "0x8c5bdec6fa6690905f6eff966b0f98f5a8161493bd04976684d4ec1f4512fa8743d86860b2ff2c5d67e9c145fd906f2cb89ff812c6b9883f"
+      },
+      "msg": "abc",
+      "u": [
+        "0xef6dcb75b696d325fb36d66b104700df1480c4c17ea9190d447eee1e7e4c9b7f36bbfb8ba7ba7c4cb6b07fed16531c1ac7a26a3618b40b34"
+      ]
+    },
+    {
+      "P": {
+        "x": "0xc6d65987f146b8d0cb5d2c44e1872ac3af1f458f6a8bd8c232ffe8b9d09496229a5a27f350eb7d97305bcc4e0f38328718352e8e3129ed71",
+        "y": "0x4d2f901bf333fdc4135b954f20d59207e9f6a4ecf88ce5af11c892b44f79766ec4ecc9f60d669b95ca8940f39b1b7044140ac2040c1bf659"
+      },
+      "Q": {
+        "x": "0xdc29532761f03c24d57f530da4c24acc4c676d185becaa89fcc083266541fb7f10ecec91dac64a34cd988274633ae25c4d784aee52de47a8",
+        "y": "0xa5f6da11259c69f2e07fce6a7b6afec4c25bd2df83426765f9c0704111da24c6a0550d5c7aac7d648d55f7640d50be99c926195e852adaac"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x3012ba5d9b3bb648e4613833a26ecaeadb3e8c8bba07fc90ac3da0375769289c44d3dc87474b23df7f45f9a4030892cda689e343aeeea6ad"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x9b8d008863beb4a02fb9e4efefd2eba867307fb1c7ce01746115d32e1db551bb254e8e3e4532d5c74a83949a69a60519ecc9178083cbe943",
+        "y": "0x346a1fca454d1e67c628437c270ec0f0c4256bb774fe6c0e49de7004ff6d9199e2cd99d8f7575a96aafc4dc8db1811ba0a44317581f41371"
+      },
+      "Q": {
+        "x": "0x512803d89f59c57376e6570cd54c4e901643e089cd9456f549daa4372b8b52679860b68aa8bedfaa88970f15ab6098d5f252083ac98a58c9",
+        "y": "0x3d9b6593c7941a20d76161c9a171f1e507495a08f03dfcae33a2ac3602698e46a74d1039b583c984036f590eaa43d20ba5aada3ffb552f77"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0xfe952ac0149f92436bba12ea2e542aa226f4fc074d79ff462c41b327968a649a495a8a93b6c3044af2273456abb5e166ce4fb8c9b10c8c2e"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x8746dc34799112d1f20acda9d7f722c9abb29b1fb6b7e9e566983843c20bd7c9bfad21b45c5166b808d2f5d44e188f1fdaf29cdee8a72e4c",
+        "y": "0x7c1293484c9287c298a1a0600c64347eee8530acf563cd8705e05728274d8cd8101835f8003b6f3b78b5beb28f5be188a3d7bce1ec5a36b1"
+      },
+      "Q": {
+        "x": "0x08aed6480793218034fd3b3b0867943d7e0bd1b6f76b4929e0885bd082b84d4449341da6038bb08229ad9eb7d518dff2c7ea50148e70a4db",
+        "y": "0xe00d32244561ebd4b5f4ef70fcac75a06416be0a1c1b304e7bd361a6a6586915bb902a323eaf73cf7738e70d34282f61485395ab2833d2c1"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0xafd3d7ad9d819be7561706e050d4f30b634b203387ab682739365f62cd7393ca2cf18cd07a3d3af8dd163f043ac7457c2eb145b4a56170a9"
+      ]
+    }
+  ]
+}

test/hash-to-curve/curve448_XOF:SHAKE256_ELL2_RO_.json

@@ -0,0 +1,115 @@
+{
+  "L": "0x54",
+  "Z": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffffffffffffffffffffffffffffffffffffffffffffffffffffe",
+  "ciphersuite": "curve448_XOF:SHAKE256_ELL2_RO_",
+  "curve": "curve448",
+  "dst": "QUUX-V01-CS02-with-curve448_XOF:SHAKE256_ELL2_RO_",
+  "expand": "XOF",
+  "field": {
+    "m": "0x1",
+    "p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
+  },
+  "hash": "shake_256",
+  "k": "0xe0",
+  "map": {
+    "name": "ELL2"
+  },
+  "randomOracle": true,
+  "vectors": [
+    {
+      "P": {
+        "x": "0x5ea5ff623d27c75e73717514134e73e419f831a875ca9e82915fdfc7069d0a9f8b532cfb32b1d8dd04ddeedbe3fa1d0d681c01e825d6a9ea",
+        "y": "0xafadd8de789f8f8e3516efbbe313a7eba364c939ecba00dabf4ced5c563b18e70a284c17d8f46b564c4e6ce11784a3825d941116622128c1"
+      },
+      "Q0": {
+        "x": "0x3ba318806f89c19cc019f51e33eb6b8c038dab892e858ce7c7f2c2ac58618d06146a5fef31e49af49588d4d3db1bcf02bd4e4a733e37065d",
+        "y": "0xb30b4cfc2fd14d9d4b70456c0f5c6f6070be551788893d570e7955675a20f6c286d01d6e90d2fb500d2efb8f4e18db7f8268bb9b7fbc5975"
+      },
+      "Q1": {
+        "x": "0xf03a48cf003f63be61ca055fec87c750434da07a15f8aa6210389ff85943b5166484339c8bea1af9fc571313d35ed2fbb779408b760c4cbd",
+        "y": "0x23943a33b2954dc54b76a8222faf5b7e18405a41f5ecc61bf1b8df1f9cbfad057307ed0c7b721f19c0390b8ee3a2dec223671f9ff905fda7"
+      },
+      "msg": "",
+      "u": [
+        "0xc704c7b3d3b36614cf3eedd0324fe6fe7d1402c50efd16cff89ff63f50938506280d3843478c08e24f7842f4e3ef45f6e3c4897f9d976148",
+        "0xc25427dc97fff7a5ad0a78654e2c6c27b1c1127b5b53c7950cd1fd6edd2703646b25f341e73deedfebf022d1d3cecd02b93b4d585ead3ed7"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x9b2f7ce34878d7cebf34c582db14958308ea09366d1ec71f646411d3de0ae564d082b06f40cd30dfc08d9fb7cb21df390cf207806ad9d0e4",
+        "y": "0x138a0eef0a4993ea696152ed7db61f7ddb4e8100573591e7466d61c0c568ecaec939e36a84d276f34c402526d8989a96e99760c4869ed633"
+      },
+      "Q0": {
+        "x": "0x26714783887ec444fbade9ae350dc13e8d5a64150679232560726a73d36e28bd56766d7d0b0899d79c8d1c889ae333f601c57532ff3c4f09",
+        "y": "0x080e486f8f5740dbbe82305160cab9fac247b0b22a54d961de675037c3036fa68464c8756478c322ae0aeb9ba386fe626cebb0bcca46840c"
+      },
+      "Q1": {
+        "x": "0x0d9741d10421691a8ebc7778b5f623260fdf8b28ae28d776efcb8e0d5fbb65139a2f828617835f527cb2ca24a8f5fc8e84378343c43d096d",
+        "y": "0x54f4c499bf3d5b154511913f9615bd914969b65cfb74508d7ae5a169e9595b7cbcab9a1485e07b2ce426e4fbed052f03842c4313b7dbe39a"
+      },
+      "msg": "abc",
+      "u": [
+        "0x2dd95593dfee26fe0d218d3d9a0a23d9e1a262fd1d0b602483d08415213e75e2db3c69b0a5bc89e71bcefc8c723d2b6a0cf263f02ad2aa70",
+        "0x272e4c79a1290cc6d2bc4f4f9d31bf7fbe956ca303c04518f117d77c0e9d850796fc3e1e2bcb9c75e8eaaded5e150333cae9931868047c9d"
+      ]
+    },
+    {
+      "P": {
+        "x": "0xf54ecd14b85a50eeeee0618452df3a75be7bfba11da5118774ae4ea55ac204e153f77285d780c4acee6c96abe3577a0c0b00be6e790cf194",
+        "y": "0x935247a64bf78c107069943c7e3ecc52acb27ce4a3230407c8357341685ea2152e8c3da93f8cd77da1bddb5bb759c6e7ae7d516dced42850"
+      },
+      "Q0": {
+        "x": "0x946d91bd50c90ef70743e0dd194bddd68bb630f4e67e5b93e15a9b94e62cb85134467993501759525c1f4fdbf06f10ddaf817847d735e062",
+        "y": "0x185cf511262ec1e9b3c3cbdc015ab93df4e71cbe87766917d81c9f3419d480407c1462385122c84982d4dae60c3ae4acce0089e37ad65934"
+      },
+      "Q1": {
+        "x": "0x01778f4797b717cd6f83c193b2dfb92a1606a36ede941b0f6ab0ac71ad0eac756d17604bf054398887da907e41065d3595f178ae802f2087",
+        "y": "0xb4ca727d0bda895e0eee7eb3cbc28710fa2e90a73b568cae26bd7c2e73b70a9fa0affe1096f0810198890ed65d8935886b6e60dc4c569dc6"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x6aab71a38391639f27e49eae8b1cb6b7172a1f478190ece293957e7cdb2391e7cc1c4261970d9c1bbf9c3915438f74fbd7eb5cd4d4d17ace",
+        "0xc80b8380ca47a3bcbf76caa75cef0e09f3d270d5ee8f676cde11aedf41aaca6741bd81a86232bd336ccb42efad39f06542bc06a67b65909e"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x5bd67c4f88adf6beb10f7e0d0054659776a55c97b809ec8b3101729e104fd0f684e103792f267fd87cc4afc25a073956ef4f268fb02824d5",
+        "y": "0xda1f5cb16a352719e4cb064cf47ba72aeba7752d03e8ca2c56229f419b4ef378785a5af1a53dd7ab4d467c1f92f7b139b3752faf29c96432"
+      },
+      "Q0": {
+        "x": "0xc2d275826d6ad55e41a22318f6b6240f1f862a2e231120ff41eadbec319756032e8cef2a7ac6c10214fa0608c17fcaf61ec2694a8a2b358b",
+        "y": "0x93d2e092762b135509840e609d413200df800d99da91d8b82840666cac30e7a3520adbaa4b089bfdc86132e42729f651d022f4782502f12c"
+      },
+      "Q1": {
+        "x": "0x3c0880ece7244036e9a45944a85599f9809d772f770cc237ac41b21aa71615e4f3bb08f64fca618896e4f6cf5bd92e16b89d2cf6e1956bfb",
+        "y": "0x45cce4beb96505cac5976b3d2673641e9bcd18d3462bbb453d293e5282740a6389cfeae610adc7bd425c728541ceec83fcc999164af43fb5"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0xcb5c27e51f9c18ee8ffdb6be230f4eb4f2c2481963b2293484f08da2241c1ff59f80978e6defe9d70e34abba2fcbe12dc3a1eb2c5d3d2e4a",
+        "0xc895e8afecec5466e126fa70fc4aa784b8009063afb10e3ee06a9b22318256aa8693b0c85b955cf2d6540b8ed71e729af1b8d5ca3b116cd7"
+      ]
+    },
+    {
+      "P": {
+        "x": "0xea441c10b3636ecedd5c0dfcae96384cc40de8390a0ab648765b4508da12c586d55dc981275776507ebca0e4d1bcaa302bb69dcfa31b3451",
+        "y": "0xfee0192d49bcc0c28d954763c2cbe739b9265c4bebe3883803c64971220cfda60b9ac99ad986cd908c0534b260b5cfca46f6c2b0f3f21bda"
+      },
+      "Q0": {
+        "x": "0x4321ab02a9849128691e9b80a5c5576793a218de14885fddccb91f17ceb1646ea00a28b69ad211e1f14f17739612dbde3782319bdf009689",
+        "y": "0x1b8a7b539519eec0ea9f7a46a43822e16cba39a439733d6847ac44a806b8adb3e1a75ea48a1228b8937ba85c6cb6ee01046e10cad8953b1e"
+      },
+      "Q1": {
+        "x": "0x126d744da6a14fddec0f78a9cee4571c1320ac7645b600187812e4d7021f98fc4703732c54daec787206e1f34d9dbbf4b292c68160b8bfbd",
+        "y": "0x136eebe6020f2389d448923899a1a38a4c8ad74254e0686e91c4f93c1f8f8e1bd619ffb7c1281467882a9c957d22d50f65c5b72b2aee11af"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x8cba93a007bb2c801b1769e026b1fa1640b14a34cf3029db3c7fd6392745d6fec0f7870b5071d6da4402cedbbde28ae4e50ab30e1049a238",
+        "0x4223746145069e4b8a981acc3404259d1a2c3ecfed5d864798a89d45f81a2c59e2d40eb1d5f0fe11478cbb2bb30246dd388cb932ad7bb330"
+      ]
+    }
+  ]
+}

test/hash-to-curve/edwards25519_XMD:SHA-512_ELL2_NU_.json

@@ -0,0 +1,90 @@
+{
+  "L": "0x30",
+  "Z": "0x2",
+  "ciphersuite": "edwards25519_XMD:SHA-512_ELL2_NU_",
+  "curve": "edwards25519",
+  "dst": "QUUX-V01-CS02-with-edwards25519_XMD:SHA-512_ELL2_NU_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x1",
+    "p": "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed"
+  },
+  "hash": "sha512",
+  "k": "0x80",
+  "map": {
+    "name": "ELL2"
+  },
+  "randomOracle": false,
+  "vectors": [
+    {
+      "P": {
+        "x": "0x1ff2b70ecf862799e11b7ae744e3489aa058ce805dd323a936375a84695e76da",
+        "y": "0x222e314d04a4d5725e9f2aff9fb2a6b69ef375a1214eb19021ceab2d687f0f9b"
+      },
+      "Q": {
+        "x": "0x42836f691d05211ebc65ef8fcf01e0fb6328ec9c4737c26050471e50803022eb",
+        "y": "0x22cb4aaa555e23bd460262d2130d6a3c9207aa8bbb85060928beb263d6d42a95"
+      },
+      "msg": "",
+      "u": [
+        "0x7f3e7fb9428103ad7f52db32f9df32505d7b427d894c5093f7a0f0374a30641d"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x5f13cc69c891d86927eb37bd4afc6672360007c63f68a33ab423a3aa040fd2a8",
+        "y": "0x67732d50f9a26f73111dd1ed5dba225614e538599db58ba30aaea1f5c827fa42"
+      },
+      "Q": {
+        "x": "0x333e41b61c6dd43af220c1ac34a3663e1cf537f996bab50ab66e33c4bd8e4e19",
+        "y": "0x51b6f178eb08c4a782c820e306b82c6e273ab22e258d972cd0c511787b2a3443"
+      },
+      "msg": "abc",
+      "u": [
+        "0x09cfa30ad79bd59456594a0f5d3a76f6b71c6787b04de98be5cd201a556e253b"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x1dd2fefce934ecfd7aae6ec998de088d7dd03316aa1847198aecf699ba6613f1",
+        "y": "0x2f8a6c24dd1adde73909cada6a4a137577b0f179d336685c4a955a0a8e1a86fb"
+      },
+      "Q": {
+        "x": "0x55186c242c78e7d0ec5b6c9553f04c6aeef64e69ec2e824472394da32647cfc6",
+        "y": "0x5b9ea3c265ee42256a8f724f616307ef38496ef7eba391c08f99f3bea6fa88f0"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x475ccff99225ef90d78cc9338e9f6a6bb7b17607c0c4428937de75d33edba941"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x35fbdc5143e8a97afd3096f2b843e07df72e15bfca2eaf6879bf97c5d3362f73",
+        "y": "0x2af6ff6ef5ebba128b0774f4296cb4c2279a074658b083b8dcca91f57a603450"
+      },
+      "Q": {
+        "x": "0x024b6e1621606dca8071aa97b43dce4040ca78284f2a527dcf5d0fbfac2b07e7",
+        "y": "0x5102353883d739bdc9f8a3af650342b171217167dcce34f8db57208ec1dfdbf2"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x049a1c8bd51bcb2aec339f387d1ff51428b88d0763a91bcdf6929814ac95d03d"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x6e5e1f37e99345887fc12111575fc1c3e36df4b289b8759d23af14d774b66bff",
+        "y": "0x2c90c3d39eb18ff291d33441b35f3262cdd307162cc97c31bfcc7a4245891a37"
+      },
+      "Q": {
+        "x": "0x3e6368cff6e88a58e250c54bd27d2c989ae9b3acb6067f2651ad282ab8c21cd9",
+        "y": "0x38fb39f1566ca118ae6c7af42810c0bb9767ae5960abb5a8ca792530bfb9447d"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x3cb0178a8137cefa5b79a3a57c858d7eeeaa787b2781be4a362a2f0750d24fa0"
+      ]
+    }
+  ]
+}

test/hash-to-curve/edwards25519_XMD:SHA-512_ELL2_RO_.json

@@ -0,0 +1,115 @@
+{
+  "L": "0x30",
+  "Z": "0x2",
+  "ciphersuite": "edwards25519_XMD:SHA-512_ELL2_RO_",
+  "curve": "edwards25519",
+  "dst": "QUUX-V01-CS02-with-edwards25519_XMD:SHA-512_ELL2_RO_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x1",
+    "p": "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed"
+  },
+  "hash": "sha512",
+  "k": "0x80",
+  "map": {
+    "name": "ELL2"
+  },
+  "randomOracle": true,
+  "vectors": [
+    {
+      "P": {
+        "x": "0x3c3da6925a3c3c268448dcabb47ccde5439559d9599646a8260e47b1e4822fc6",
+        "y": "0x09a6c8561a0b22bef63124c588ce4c62ea83a3c899763af26d795302e115dc21"
+      },
+      "Q0": {
+        "x": "0x6549118f65bb617b9e8b438decedc73c496eaed496806d3b2eb9ee60b88e09a7",
+        "y": "0x7315bcc8cf47ed68048d22bad602c6680b3382a08c7c5d3f439a973fb4cf9feb"
+      },
+      "Q1": {
+        "x": "0x31dcfc5c58aa1bee6e760bf78cbe71c2bead8cebb2e397ece0f37a3da19c9ed2",
+        "y": "0x7876d81474828d8a5928b50c82420b2bd0898d819e9550c5c82c39fc9bafa196"
+      },
+      "msg": "",
+      "u": [
+        "0x03fef4813c8cb5f98c6eef88fae174e6e7d5380de2b007799ac7ee712d203f3a",
+        "0x780bdddd137290c8f589dc687795aafae35f6b674668d92bf92ae793e6a60c75"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x608040b42285cc0d72cbb3985c6b04c935370c7361f4b7fbdb1ae7f8c1a8ecad",
+        "y": "0x1a8395b88338f22e435bbd301183e7f20a5f9de643f11882fb237f88268a5531"
+      },
+      "Q0": {
+        "x": "0x5c1525bd5d4b4e034512949d187c39d48e8cd84242aa4758956e4adc7d445573",
+        "y": "0x2bf426cf7122d1a90abc7f2d108befc2ef415ce8c2d09695a7407240faa01f29"
+      },
+      "Q1": {
+        "x": "0x37b03bba828860c6b459ddad476c83e0f9285787a269df2156219b7e5c86210c",
+        "y": "0x285ebf5412f84d0ad7bb4e136729a9ffd2195d5b8e73c0dc85110ce06958f432"
+      },
+      "msg": "abc",
+      "u": [
+        "0x5081955c4141e4e7d02ec0e36becffaa1934df4d7a270f70679c78f9bd57c227",
+        "0x005bdc17a9b378b6272573a31b04361f21c371b256252ae5463119aa0b925b76"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x6d7fabf47a2dc03fe7d47f7dddd21082c5fb8f86743cd020f3fb147d57161472",
+        "y": "0x53060a3d140e7fbcda641ed3cf42c88a75411e648a1add71217f70ea8ec561a6"
+      },
+      "Q0": {
+        "x": "0x3ac463dd7fddb773b069c5b2b01c0f6b340638f54ee3bd92d452fcec3015b52d",
+        "y": "0x7b03ba1e8db9ec0b390d5c90168a6a0b7107156c994c674b61fe696cbeb46baf"
+      },
+      "Q1": {
+        "x": "0x0757e7e904f5e86d2d2f4acf7e01c63827fde2d363985aa7432106f1b3a444ec",
+        "y": "0x50026c96930a24961e9d86aa91ea1465398ff8e42015e2ec1fa397d416f6a1c0"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x285ebaa3be701b79871bcb6e225ecc9b0b32dff2d60424b4c50642636a78d5b3",
+        "0x2e253e6a0ef658fedb8e4bd6a62d1544fd6547922acb3598ec6b369760b81b31"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x5fb0b92acedd16f3bcb0ef83f5c7b7a9466b5f1e0d8d217421878ea3686f8524",
+        "y": "0x2eca15e355fcfa39d2982f67ddb0eea138e2994f5956ed37b7f72eea5e89d2f7"
+      },
+      "Q0": {
+        "x": "0x703e69787ea7524541933edf41f94010a201cc841c1cce60205ec38513458872",
+        "y": "0x32bb192c4f89106466f0874f5fd56a0d6b6f101cb714777983336c159a9bec75"
+      },
+      "Q1": {
+        "x": "0x0c9077c5c31720ed9413abe59bf49ce768506128d810cb882435aa90f713ef6b",
+        "y": "0x7d5aec5210db638c53f050597964b74d6dda4be5b54fa73041bf909ccb3826cb"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x4fedd25431c41f2a606952e2945ef5e3ac905a42cf64b8b4d4a83c533bf321af",
+        "0x02f20716a5801b843987097a8276b6d869295b2e11253751ca72c109d37485a9"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x0efcfde5898a839b00997fbe40d2ebe950bc81181afbd5cd6b9618aa336c1e8c",
+        "y": "0x6dc2fc04f266c5c27f236a80b14f92ccd051ef1ff027f26a07f8c0f327d8f995"
+      },
+      "Q0": {
+        "x": "0x21091b2e3f9258c7dfa075e7ae513325a94a3d8a28e1b1cb3b5b6f5d65675592",
+        "y": "0x41a33d324c89f570e0682cdf7bdb78852295daf8084c669f2cc9692896ab5026"
+      },
+      "Q1": {
+        "x": "0x4c07ec48c373e39a23bd7954f9e9b66eeab9e5ee1279b867b3d5315aa815454f",
+        "y": "0x67ccac7c3cb8d1381242d8d6585c57eabaddbb5dca5243a68a8aeb5477d94b3a"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x6e34e04a5106e9bd59f64aba49601bf09d23b27f7b594e56d5de06df4a4ea33b",
+        "0x1c1c2cb59fc053f44b86c5d5eb8c1954b64976d0302d3729ff66e84068f5fd96"
+      ]
+    }
+  ]
+}

test/hash-to-curve/edwards448_XOF:SHAKE256_ELL2_NU_.json

@@ -0,0 +1,90 @@
+{
+  "L": "0x54",
+  "Z": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffffffffffffffffffffffffffffffffffffffffffffffffffffe",
+  "ciphersuite": "edwards448_XOF:SHAKE256_ELL2_NU_",
+  "curve": "edwards448",
+  "dst": "QUUX-V01-CS02-with-edwards448_XOF:SHAKE256_ELL2_NU_",
+  "expand": "XOF",
+  "field": {
+    "m": "0x1",
+    "p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
+  },
+  "hash": "shake_256",
+  "k": "0xe0",
+  "map": {
+    "name": "ELL2"
+  },
+  "randomOracle": false,
+  "vectors": [
+    {
+      "P": {
+        "x": "0xeb5a1fc376fd73230af2de0f3374087cc7f279f0460114cf0a6c12d6d044c16de34ec2350c34b26bf110377655ab77936869d085406af71e",
+        "y": "0xdf5dcea6d42e8f494b279a500d09e895d26ac703d75ca6d118e8ca58bf6f608a2a383f292fce1563ff995dce75aede1fdc8e7c0c737ae9ad"
+      },
+      "Q": {
+        "x": "0x4b2abf8c0fca49d027c2a81bf73bb5990e05f3e76c7ba137cc0b89415ccd55ce7f191cc0c11b0560c1cdc2a8085dd56996079e05a3cd8dde",
+        "y": "0x82532f5b0cb3bfb8542d3228d055bfe61129dbeae8bace80cf61f17725e8ec8226a24f0e687f78f01da88e3b2715194a03dca7c0a96bbf04"
+      },
+      "msg": "",
+      "u": [
+        "0x1368aefc0416867ea2cfc515416bcbeecc9ec81c4ecbd52ccdb91e06996b3f359bc930eef6743c7a2dd7adb785bc7093ed044efed95086d7"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x4623a64bceaba3202df76cd8b6e3daf70164f3fcbda6d6e340f7fab5cdf89140d955f722524f5fe4d968fef6ba2853ff4ea086c2f67d8110",
+        "y": "0xabaac321a169761a8802ab5b5d10061fec1a83c670ac6bc95954700317ee5f82870120e0e2c5a21b12a0c7ad17ebd343363604c4bcecafd1"
+      },
+      "Q": {
+        "x": "0xb1ca5bef2f157673a210f56c9b0039db8399e4749585abac64f831f74ed1ec5f591928976c687c06d57686bacb98440e77af878349cdf2d2",
+        "y": "0x5bbfd6a3730d517b03c3cd9e2eed94af12891334ec090e0495c2edc588e9e10b6f63b03a62076808cbcd6da95adfb5af76c136b2d42e0dac"
+      },
+      "msg": "abc",
+      "u": [
+        "0xcda3b0ecfe054c4077007d7300969ec24f4c741300b630ec9188ebab31a5ae0065612ee22d9f793733179ffc2e10c53ca5b539057aafdc2f"
+      ]
+    },
+    {
+      "P": {
+        "x": "0xe9eb562e76db093baa43a31b7edd04ec4aadcef3389a7b9c58a19cf87f8ae3d154e134b6b3ed45847a741e33df51903da681629a4b8bcc2e",
+        "y": "0x0cf6606927ad7eb15dbc193993bc7e4dda744b311a8ec4274c8f738f74f605934582474c79260f60280fe35bd37d4347e59184cbfa12cbc4"
+      },
+      "Q": {
+        "x": "0x958a51e2f02e0dfd3930709010d5d16f869adb9d8a8f7c01139911d206c20cdb7bfb40ee33ba30536a99f49362fa7633d0f417fc3914fe21",
+        "y": "0xf4307a36ab6612fa97501497f01afa109733ce85875935551c3ca90f0fa7e0097a8640bb7e5dbcc38ab32b23b748790f2261f2c44c3bf3ba"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0xd36bae98351512c382c7a3e1eba22497574f11fef9867901b1a2700b39fa2cd0d38ed4380387a99162b7ba0240c743f0532ef60d577c413d"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x122a3234d34b26c69749f23356452bf9501efa2d94859d5ef741fef024156d9d191a03a2ad24c38186f93e02d05572575968b083d8a39738",
+        "y": "0xddf55e74eb4414c2c1fa4aa6bc37c4ab470a3fed6bb5af1e43570309b162fb61879bb15f9ea49c712efd42d0a71666430f9f0d4a20505050"
+      },
+      "Q": {
+        "x": "0xe7e1f2d13548ac2c8fcd346e4c63606545bf93652011721e83ac3b64226f77a8823d3881e164bc6ca45505b236e8e3721c028052fcc9ade5",
+        "y": "0x7e0f340501bf25f018b9d374c2acbdd43c07261d85a6ef3c855113d4e023634db59a87b8fab9efe04ed1fee302c8a4994e83bdda32bd9c0b"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x5945744d27122f89da3daf76ab4db9616053df64e25d30ec9a00667ee6710240579c1db8f8ef3386f3f4f413cfb325ac14094d582026a971"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x221704949b1ce1ab8dd174dc9b8c56fcffa27179569ce9219c0c2fe183d3d23343a4c42a0e2e9d6b9d0feb1df3883ec489b6671d1fa64089",
+        "y": "0xebdecfdc87142d1a919034bf22ecfad934c9a85effff14b594ae2c00943ca62a39d6ee3be9df0bb504ce8a9e1669bc6959c42ad6a1d3b686"
+      },
+      "Q": {
+        "x": "0x0fd3bb833c1d7a5b319d1d4117406a23b9aece976186ecb18a11a635e6fbdb920d47e04762b1f2a8c59d2f8435d0fdefe501f544cda23dbf",
+        "y": "0xf13b0dad4d5eeb120f2443ac4392f8096a1396f5014ec2a3506a347fef8076a7282035cf619599b1919cf29df5ce87711c11688aab7700a6"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x1192e378043f01cedc7ea0209321519213b0184ea0d8575816bcd9182a367823e1eecc2faf1df8f79b24027a4b9bfa208cd320e79bef06ea"
+      ]
+    }
+  ]
+}

test/hash-to-curve/edwards448_XOF:SHAKE256_ELL2_RO_.json

@@ -0,0 +1,115 @@
+{
+  "L": "0x54",
+  "Z": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffffffffffffffffffffffffffffffffffffffffffffffffffffe",
+  "ciphersuite": "edwards448_XOF:SHAKE256_ELL2_RO_",
+  "curve": "edwards448",
+  "dst": "QUUX-V01-CS02-with-edwards448_XOF:SHAKE256_ELL2_RO_",
+  "expand": "XOF",
+  "field": {
+    "m": "0x1",
+    "p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
+  },
+  "hash": "shake_256",
+  "k": "0xe0",
+  "map": {
+    "name": "ELL2"
+  },
+  "randomOracle": true,
+  "vectors": [
+    {
+      "P": {
+        "x": "0x73036d4a88949c032f01507005c133884e2f0d81f9a950826245dda9e844fc78186c39daaa7147ead3e462cff60e9c6340b58134480b4d17",
+        "y": "0x94c1d61b43728e5d784ef4fcb1f38e1075f3aef5e99866911de5a234f1aafdc26b554344742e6ba0420b71b298671bbeb2b7736618634610"
+      },
+      "Q0": {
+        "x": "0xc08177330869db17fb81a5e6e53b36d29086d806269760f2e4cabaa4015f5dbadb7ca2ba594d96a89d0ca4f0944489e1ef393d53db85096f",
+        "y": "0x02e894598c050eeb7195f5791f1a5f65da3776b7534be37640bcbf95d4b915bd22333c50387583507169708fbd7bea0d7aa385dcc614be9c"
+      },
+      "Q1": {
+        "x": "0x770877fd3b6c5503398157b68a9d3609f585f40e1ebebdd69bb0e4d3d9aa811995ce75333fdadfa50db886a35959cc59cffd5c9710daca25",
+        "y": "0xb27fef77aa6231fbbc27538fa90eaca8abd03eb1e62fdae4ec5e828117c3b8b3ff8c34d0a6e6d79fff16d339b94ae8ede33331d5b464c792"
+      },
+      "msg": "",
+      "u": [
+        "0x0847c5ebf957d3370b1f98fde499fb3e659996d9fc9b5707176ade785ba72cd84b8a5597c12b1024be5f510fa5ba99642c4cec7f3f69d3e7",
+        "0xf8cbd8a7ae8c8deed071f3ac4b93e7cfcb8f1eac1645d699fd6d3881cb295a5d3006d9449ed7cad412a77a1fe61e84a9e41d59ef384d6f9a"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x4e0158acacffa545adb818a6ed8e0b870e6abc24dfc1dc45cf9a052e98469275d9ff0c168d6a5ac7ec05b742412ee090581f12aa398f9f8c",
+        "y": "0x894d3fa437b2d2e28cdc3bfaade035430f350ec5239b6b406b5501da6f6d6210ff26719cad83b63e97ab26a12df6dec851d6bf38e294af9a"
+      },
+      "Q0": {
+        "x": "0x7544612a97f4419c94ab0f621a1ee8ccf46c6657b8e0778ec9718bf4b41bc774487ad87d9b1e617aa49d3a4dd35a3cf57cd390ebf0429952",
+        "y": "0xd3ab703e60267d796b485bb58a28f934bd0133a6d1bbdfeda5277fa293310be262d7f653a5adffa608c37ed45c0e6008e54a16e1a342e4df"
+      },
+      "Q1": {
+        "x": "0x6262f18d064bc131ade1b8bbcf1cbdf984f4f88153fcc9f94c888af35d5e41aae84c12f169a55d8abf06e6de6c5b23079e587a58cf73303e",
+        "y": "0x6d57589e901abe7d947c93ab02c307ad9093ed9a83eb0b6e829fb7318d590381ca25f3cc628a36a924a9ddfcf3cbedf94edf3b338ea77403"
+      },
+      "msg": "abc",
+      "u": [
+        "0x04d975cd938ab49be3e81703d6a57cca84ed80d2ff6d4756d3f22947fb5b70ab0231f0087cbfb4b7cae73b41b0c9396b356a4831d9a14322",
+        "0x2547ca887ac3db7b5fad3a098aa476e90078afe1358af6c63d677d6edfd2100bc004e0f5db94dd2560fc5b308e223241d00488c9ca6b0ef2"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x2c25b4503fadc94b27391933b557abdecc601c13ed51c5de68389484f93dbd6c22e5f962d9babf7a39f39f994312f8ca23344847e1fbf176",
+        "y": "0xd5e6f5350f430e53a110f5ac7fcc82a96cb865aeca982029522d32601e41c042a9dfbdfbefa2b0bdcdc3bc58cca8a7cd546803083d3a8548"
+      },
+      "Q0": {
+        "x": "0x1457b60c12e00e47ceb3ce64b57e7c3c61636475443d704a8e2b2ab0a5ac7e4b3909435416784e16e19929c653b1bdcd9478a8e5331ca9ae",
+        "y": "0x935d9f75f7a0babbc39c0a1c3b412518ed8a24bc2c4886722fb4b7d4a747af98e4e2528c75221e2dffd3424abb436e10539a74caaafa3ea3"
+      },
+      "Q1": {
+        "x": "0xb44d9e34211b4028f24117e856585ed81448f3c8b934987a1c5939c86048737a08d85934fec6b3c2ef9f09cbd365cf22744f2e4ce69762a4",
+        "y": "0xdc996c1736f4319868f897d9a27c45b02dd3bc6b7ca356a039606e5406e131a0bbe8238208b327b00853e8af84b58b13443e705425563323"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x10659ce25588db4e4be6f7c791a79eb21a7f24aaaca76a6ca3b83b80aaf95aa328fe7d569a1ac99f9cd216edf3915d72632f1a8b990e250c",
+        "0x9243e5b6c480683fd533e81f4a778349a309ce00bd163a29eb9fa8dbc8f549242bef33e030db21cffacd408d2c4264b93e476c6a8590e7aa"
+      ]
+    },
+    {
+      "P": {
+        "x": "0xa1861a9464ae31249a0e60bf38791f3663049a3f5378998499a83292e159a2fecff838eb9bc6939e5c6ae76eb074ad4aae39b55b72ca0b9a",
+        "y": "0x580a2798c5b904f8adfec5bd29fb49b4633cd9f8c2935eb4a0f12e5dfa0285680880296bb729c6405337525fb5ed3dff930c137314f60401"
+      },
+      "Q0": {
+        "x": "0x9d355251e245e4b13ed4ea3e5a3c55bf9b7211f1704771f2e1d8f1a65610c468b1cf70c6c2ce30dcaad54ad9e5439471ec554b862ec8875a",
+        "y": "0x6689ba36a242af69ac2aadb955d15e982d9b04f5d77f7609ebf7429587feb7e5ce27490b9c72114509f89565122074e46a614d7fd7c800bd"
+      },
+      "Q1": {
+        "x": "0xc4b3d3ad4d2d62739a62989532992c1081e9474a201085b4616da5706cab824693b9fb428a201bcd1639a4588cc43b9eb841dbca74219b1f",
+        "y": "0x265286f5dee8f3d894b5649da8565b58e96b4cfd44b462a2883ea64dbcda21a00706ea3fea53fc2d769084b0b74589e91d0384d7118909fb"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0xc80390020e578f009ead417029eff6cd0926110922db63ab98395e3bdfdd5d8a65b1a2b8d495dc8c5e59b7f3518731f7dfc0f93ace5dee4b",
+        "0x1c4dc6653a445bbef2add81d8e90a6c8591a788deb91d0d3f1519a2e4a460313041b77c1b0817f2e80b388e5c3e49f37d787dc1f85e4324a"
+      ]
+    },
+    {
+      "P": {
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+        "y": "0x5e273fcfff6b007bb6771e90509275a71ff1480c459ded26fc7b10664db0a68aaa98bc7ecb07e49cf05b80ae5ac653fbdd14276bbd35ccbc"
+      },
+      "Q0": {
+        "x": "0xd1a5eba4a332514b69760948af09ceaeddbbb9fd4cb1f19b78349c2ee4cf9ee86dbcf9064659a4a0566fe9c34d90aec86f0801edc131ad9b",
+        "y": "0x5d0a75a3014c3269c33b1b5da80706a4f097893461df286353484d8031cd607c98edc2a846c77a841f057c7251eb45077853c7b205957e52"
+      },
+      "Q1": {
+        "x": "0x69583b00dc6b2aced6ffa44630cc8c8cd0dd0649f57588dd0fb1daad2ce132e281d01e3f25ccd3f405be759975c6484268bfe8f5e5f23c30",
+        "y": "0x8418484035f60bdccf48cb488634c2dfb40272123435f7e654fb6f254c6c42e7e38f1fa79a637a168a28de6c275232b704f9ded0ff76dd94"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x163c79ab0210a4b5e4f44fb19437ea965bf5431ab233ef16606f0b03c5f16a3feb7d46a5a675ce8f606e9c2bf74ee5336c54a1e54919f13f",
+        "0xf99666bde4995c4088333d6c2734687e815f80a99c6da02c47df4b51f6c9d9ed466b4fecf7d9884990a8e0d0be6907fa437e0b1a27f49265"
+      ]
+    }
+  ]
+}

test/hash-to-curve/expand_message_xmd_SHA256_256.json

@@ -0,0 +1,78 @@
+{
+  "DST": "QUUX-V01-CS02-with-expander-SHA256-128-long-DST-1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111",
+  "hash": "SHA256",
+  "k": 128,
+  "name": "expand_message_xmd",
+  "tests": [
+    {
+      "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "len_in_bytes": "0x20",
+      "msg": "",
+      "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "uniform_bytes": "e8dc0c8b686b7ef2074086fbdd2f30e3f8bfbd3bdf177f73f04b97ce618a3ed3"
+    },
+    {
+      "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "len_in_bytes": "0x20",
+      "msg": "abc",
+      "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000616263002000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "uniform_bytes": "52dbf4f36cf560fca57dedec2ad924ee9c266341d8f3d6afe5171733b16bbb12"
+    },
+    {
+      "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "len_in_bytes": "0x20",
+      "msg": "abcdef0123456789",
+      "msg_prime": "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000061626364656630313233343536373839002000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "uniform_bytes": "35387dcf22618f3728e6c686490f8b431f76550b0b2c61cbc1ce7001536f4521"
+    },
+    {
+      "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "len_in_bytes": "0x20",
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000713132385f7171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171002000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "uniform_bytes": "01b637612bb18e840028be900a833a74414140dde0c4754c198532c3a0ba42bc"
+    },
+    {
+      "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "len_in_bytes": "0x20",
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000613531325f6161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161002000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "uniform_bytes": "20cce7033cabc5460743180be6fa8aac5a103f56d481cf369a8accc0c374431b"
+    },
+    {
+      "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "len_in_bytes": "0x80",
+      "msg": "",
+      "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000008000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "uniform_bytes": "14604d85432c68b757e485c8894db3117992fc57e0e136f71ad987f789a0abc287c47876978e2388a02af86b1e8d1342e5ce4f7aaa07a87321e691f6fba7e0072eecc1218aebb89fb14a0662322d5edbd873f0eb35260145cd4e64f748c5dfe60567e126604bcab1a3ee2dc0778102ae8a5cfd1429ebc0fa6bf1a53c36f55dfc"
+    },
+    {
+      "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "len_in_bytes": "0x80",
+      "msg": "abc",
+      "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000616263008000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "uniform_bytes": "1a30a5e36fbdb87077552b9d18b9f0aee16e80181d5b951d0471d55b66684914aef87dbb3626eaabf5ded8cd0686567e503853e5c84c259ba0efc37f71c839da2129fe81afdaec7fbdc0ccd4c794727a17c0d20ff0ea55e1389d6982d1241cb8d165762dbc39fb0cee4474d2cbbd468a835ae5b2f20e4f959f56ab24cd6fe267"
+    },
+    {
+      "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "len_in_bytes": "0x80",
+      "msg": "abcdef0123456789",
+      "msg_prime": "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000061626364656630313233343536373839008000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "uniform_bytes": "d2ecef3635d2397f34a9f86438d772db19ffe9924e28a1caf6f1c8f15603d4028f40891044e5c7e39ebb9b31339979ff33a4249206f67d4a1e7c765410bcd249ad78d407e303675918f20f26ce6d7027ed3774512ef5b00d816e51bfcc96c3539601fa48ef1c07e494bdc37054ba96ecb9dbd666417e3de289d4f424f502a982"
+    },
+    {
+      "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "len_in_bytes": "0x80",
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000713132385f7171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171008000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "uniform_bytes": "ed6e8c036df90111410431431a232d41a32c86e296c05d426e5f44e75b9a50d335b2412bc6c91e0a6dc131de09c43110d9180d0a70f0d6289cb4e43b05f7ee5e9b3f42a1fad0f31bac6a625b3b5c50e3a83316783b649e5ecc9d3b1d9471cb5024b7ccf40d41d1751a04ca0356548bc6e703fca02ab521b505e8e45600508d32"
+    },
+    {
+      "DST_prime": "412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "len_in_bytes": "0x80",
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000613531325f6161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161008000412717974da474d0f8c420f320ff81e8432adb7c927d9bd082b4fb4d16c0a23620",
+      "uniform_bytes": "78b53f2413f3c688f07732c10e5ced29a17c6a16f717179ffbe38d92d6c9ec296502eb9889af83a1928cd162e845b0d3c5424e83280fed3d10cffb2f8431f14e7a23f4c68819d40617589e4c41169d0b56e0e3535be1fd71fbb08bb70c5b5ffed953d6c14bf7618b35fc1f4c4b30538236b4b08c9fbf90462447a8ada60be495"
+    }
+  ]
+}

test/hash-to-curve/expand_message_xmd_SHA256_38.json

@@ -0,0 +1,78 @@
+{
+  "DST": "QUUX-V01-CS02-with-expander-SHA256-128",
+  "hash": "SHA256",
+  "k": 128,
+  "name": "expand_message_xmd",
+  "tests": [
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "len_in_bytes": "0x20",
+      "msg": "",
+      "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002000515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "uniform_bytes": "68a985b87eb6b46952128911f2a4412bbc302a9d759667f87f7a21d803f07235"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "len_in_bytes": "0x20",
+      "msg": "abc",
+      "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000616263002000515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "uniform_bytes": "d8ccab23b5985ccea865c6c97b6e5b8350e794e603b4b97902f53a8a0d605615"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "len_in_bytes": "0x20",
+      "msg": "abcdef0123456789",
+      "msg_prime": "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000061626364656630313233343536373839002000515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "uniform_bytes": "eff31487c770a893cfb36f912fbfcbff40d5661771ca4b2cb4eafe524333f5c1"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "len_in_bytes": "0x20",
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000713132385f7171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171002000515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "uniform_bytes": "b23a1d2b4d97b2ef7785562a7e8bac7eed54ed6e97e29aa51bfe3f12ddad1ff9"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "len_in_bytes": "0x20",
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000613531325f6161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161002000515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "uniform_bytes": "4623227bcc01293b8c130bf771da8c298dede7383243dc0993d2d94823958c4c"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "len_in_bytes": "0x80",
+      "msg": "",
+      "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000008000515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "uniform_bytes": "af84c27ccfd45d41914fdff5df25293e221afc53d8ad2ac06d5e3e29485dadbee0d121587713a3e0dd4d5e69e93eb7cd4f5df4cd103e188cf60cb02edc3edf18eda8576c412b18ffb658e3dd6ec849469b979d444cf7b26911a08e63cf31f9dcc541708d3491184472c2c29bb749d4286b004ceb5ee6b9a7fa5b646c993f0ced"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "len_in_bytes": "0x80",
+      "msg": "abc",
+      "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000616263008000515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "uniform_bytes": "abba86a6129e366fc877aab32fc4ffc70120d8996c88aee2fe4b32d6c7b6437a647e6c3163d40b76a73cf6a5674ef1d890f95b664ee0afa5359a5c4e07985635bbecbac65d747d3d2da7ec2b8221b17b0ca9dc8a1ac1c07ea6a1e60583e2cb00058e77b7b72a298425cd1b941ad4ec65e8afc50303a22c0f99b0509b4c895f40"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "len_in_bytes": "0x80",
+      "msg": "abcdef0123456789",
+      "msg_prime": "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000061626364656630313233343536373839008000515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "uniform_bytes": "ef904a29bffc4cf9ee82832451c946ac3c8f8058ae97d8d629831a74c6572bd9ebd0df635cd1f208e2038e760c4994984ce73f0d55ea9f22af83ba4734569d4bc95e18350f740c07eef653cbb9f87910d833751825f0ebefa1abe5420bb52be14cf489b37fe1a72f7de2d10be453b2c9d9eb20c7e3f6edc5a60629178d9478df"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "len_in_bytes": "0x80",
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000713132385f7171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171008000515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "uniform_bytes": "80be107d0884f0d881bb460322f0443d38bd222db8bd0b0a5312a6fedb49c1bbd88fd75d8b9a09486c60123dfa1d73c1cc3169761b17476d3c6b7cbbd727acd0e2c942f4dd96ae3da5de368d26b32286e32de7e5a8cb2949f866a0b80c58116b29fa7fabb3ea7d520ee603e0c25bcaf0b9a5e92ec6a1fe4e0391d1cdbce8c68a"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "len_in_bytes": "0x80",
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "msg_prime": "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000613531325f6161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161008000515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
+      "uniform_bytes": "546aff5444b5b79aa6148bd81728704c32decb73a3ba76e9e75885cad9def1d06d6792f8a7d12794e90efed817d96920d728896a4510864370c207f99bd4a608ea121700ef01ed879745ee3e4ceef777eda6d9e5e38b90c86ea6fb0b36504ba4a45d22e86f6db5dd43d98a294bebb9125d5b794e9d2a81181066eb954966a487"
+    }
+  ]
+}

test/hash-to-curve/expand_message_xmd_SHA512_38.json

@@ -0,0 +1,78 @@
+{
+  "DST": "QUUX-V01-CS02-with-expander-SHA512-256",
+  "hash": "SHA512",
+  "k": 256,
+  "name": "expand_message_xmd",
+  "tests": [
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "len_in_bytes": "0x20",
+      "msg": "",
+      "msg_prime": "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002000515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "uniform_bytes": "6b9a7312411d92f921c6f68ca0b6380730a1a4d982c507211a90964c394179ba"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "len_in_bytes": "0x20",
+      "msg": "abc",
+      "msg_prime": "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000616263002000515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "uniform_bytes": "0da749f12fbe5483eb066a5f595055679b976e93abe9be6f0f6318bce7aca8dc"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "len_in_bytes": "0x20",
+      "msg": "abcdef0123456789",
+      "msg_prime": "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000061626364656630313233343536373839002000515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "uniform_bytes": "087e45a86e2939ee8b91100af1583c4938e0f5fc6c9db4b107b83346bc967f58"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "len_in_bytes": "0x20",
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "msg_prime": "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000713132385f7171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171002000515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "uniform_bytes": "7336234ee9983902440f6bc35b348352013becd88938d2afec44311caf8356b3"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "len_in_bytes": "0x20",
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "msg_prime": "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000613531325f6161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161002000515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "uniform_bytes": "57b5f7e766d5be68a6bfe1768e3c2b7f1228b3e4b3134956dd73a59b954c66f4"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "len_in_bytes": "0x80",
+      "msg": "",
+      "msg_prime": "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000008000515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "uniform_bytes": "41b037d1734a5f8df225dd8c7de38f851efdb45c372887be655212d07251b921b052b62eaed99b46f72f2ef4cc96bfaf254ebbbec091e1a3b9e4fb5e5b619d2e0c5414800a1d882b62bb5cd1778f098b8eb6cb399d5d9d18f5d5842cf5d13d7eb00a7cff859b605da678b318bd0e65ebff70bec88c753b159a805d2c89c55961"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "len_in_bytes": "0x80",
+      "msg": "abc",
+      "msg_prime": "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000616263008000515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "uniform_bytes": "7f1dddd13c08b543f2e2037b14cefb255b44c83cc397c1786d975653e36a6b11bdd7732d8b38adb4a0edc26a0cef4bb45217135456e58fbca1703cd6032cb1347ee720b87972d63fbf232587043ed2901bce7f22610c0419751c065922b488431851041310ad659e4b23520e1772ab29dcdeb2002222a363f0c2b1c972b3efe1"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "len_in_bytes": "0x80",
+      "msg": "abcdef0123456789",
+      "msg_prime": "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000061626364656630313233343536373839008000515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "uniform_bytes": "3f721f208e6199fe903545abc26c837ce59ac6fa45733f1baaf0222f8b7acb0424814fcb5eecf6c1d38f06e9d0a6ccfbf85ae612ab8735dfdf9ce84c372a77c8f9e1c1e952c3a61b7567dd0693016af51d2745822663d0c2367e3f4f0bed827feecc2aaf98c949b5ed0d35c3f1023d64ad1407924288d366ea159f46287e61ac"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "len_in_bytes": "0x80",
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "msg_prime": "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000713132385f7171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171008000515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "uniform_bytes": "b799b045a58c8d2b4334cf54b78260b45eec544f9f2fb5bd12fb603eaee70db7317bf807c406e26373922b7b8920fa29142703dd52bdf280084fb7ef69da78afdf80b3586395b433dc66cde048a258e476a561e9deba7060af40adf30c64249ca7ddea79806ee5beb9a1422949471d267b21bc88e688e4014087a0b592b695ed"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "len_in_bytes": "0x80",
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "msg_prime": "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000613531325f6161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161008000515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
+      "uniform_bytes": "05b0bfef265dcee87654372777b7c44177e2ae4c13a27f103340d9cd11c86cb2426ffcad5bd964080c2aee97f03be1ca18e30a1f14e27bc11ebbd650f305269cc9fb1db08bf90bfc79b42a952b46daf810359e7bc36452684784a64952c343c52e5124cd1f71d474d5197fefc571a92929c9084ffe1112cf5eea5192ebff330b"
+    }
+  ]
+}

test/hash-to-curve/expand_message_xof_SHAKE128_256.json

@@ -0,0 +1,78 @@
+{
+  "DST": "QUUX-V01-CS02-with-expander-SHAKE128-long-DST-111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111",
+  "hash": "SHAKE128",
+  "k": 128,
+  "name": "expand_message_xof",
+  "tests": [
+    {
+      "DST_prime": "acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "len_in_bytes": "0x20",
+      "msg": "",
+      "msg_prime": "0020acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "uniform_bytes": "827c6216330a122352312bccc0c8d6e7a146c5257a776dbd9ad9d75cd880fc53"
+    },
+    {
+      "DST_prime": "acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "len_in_bytes": "0x20",
+      "msg": "abc",
+      "msg_prime": "6162630020acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "uniform_bytes": "690c8d82c7213b4282c6cb41c00e31ea1d3e2005f93ad19bbf6da40f15790c5c"
+    },
+    {
+      "DST_prime": "acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "len_in_bytes": "0x20",
+      "msg": "abcdef0123456789",
+      "msg_prime": "616263646566303132333435363738390020acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "uniform_bytes": "979e3a15064afbbcf99f62cc09fa9c85028afcf3f825eb0711894dcfc2f57057"
+    },
+    {
+      "DST_prime": "acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "len_in_bytes": "0x20",
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "msg_prime": "713132385f71717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171710020acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "uniform_bytes": "c5a9220962d9edc212c063f4f65b609755a1ed96e62f9db5d1fd6adb5a8dc52b"
+    },
+    {
+      "DST_prime": "acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "len_in_bytes": "0x20",
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "msg_prime": "613531325f61616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161610020acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "uniform_bytes": "f7b96a5901af5d78ce1d071d9c383cac66a1dfadb508300ec6aeaea0d62d5d62"
+    },
+    {
+      "DST_prime": "acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "len_in_bytes": "0x80",
+      "msg": "",
+      "msg_prime": "0080acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "uniform_bytes": "3890dbab00a2830be398524b71c2713bbef5f4884ac2e6f070b092effdb19208c7df943dc5dcbaee3094a78c267ef276632ee2c8ea0c05363c94b6348500fae4208345dd3475fe0c834c2beac7fa7bc181692fb728c0a53d809fc8111495222ce0f38468b11becb15b32060218e285c57a60162c2c8bb5b6bded13973cd41819"
+    },
+    {
+      "DST_prime": "acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "len_in_bytes": "0x80",
+      "msg": "abc",
+      "msg_prime": "6162630080acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "uniform_bytes": "41b7ffa7a301b5c1441495ebb9774e2a53dbbf4e54b9a1af6a20fd41eafd69ef7b9418599c5545b1ee422f363642b01d4a53449313f68da3e49dddb9cd25b97465170537d45dcbdf92391b5bdff344db4bd06311a05bca7dcd360b6caec849c299133e5c9194f4e15e3e23cfaab4003fab776f6ac0bfae9144c6e2e1c62e7d57"
+    },
+    {
+      "DST_prime": "acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "len_in_bytes": "0x80",
+      "msg": "abcdef0123456789",
+      "msg_prime": "616263646566303132333435363738390080acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "uniform_bytes": "55317e4a21318472cd2290c3082957e1242241d9e0d04f47026f03401643131401071f01aa03038b2783e795bdfa8a3541c194ad5de7cb9c225133e24af6c86e748deb52e560569bd54ef4dac03465111a3a44b0ea490fb36777ff8ea9f1a8a3e8e0de3cf0880b4b2f8dd37d3a85a8b82375aee4fa0e909f9763319b55778e71"
+    },
+    {
+      "DST_prime": "acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "len_in_bytes": "0x80",
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "msg_prime": "713132385f71717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171710080acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "uniform_bytes": "19fdd2639f082e31c77717ac9bb032a22ff0958382b2dbb39020cdc78f0da43305414806abf9a561cb2d0067eb2f7bc544482f75623438ed4b4e39dd9e6e2909dd858bd8f1d57cd0fce2d3150d90aa67b4498bdf2df98c0100dd1a173436ba5d0df6be1defb0b2ce55ccd2f4fc05eb7cb2c019c35d5398b85adc676da4238bc7"
+    },
+    {
+      "DST_prime": "acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "len_in_bytes": "0x80",
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "msg_prime": "613531325f61616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161610080acb9736c0867fdfbd6385519b90fc8c034b5af04a958973212950132d035792f20",
+      "uniform_bytes": "945373f0b3431a103333ba6a0a34f1efab2702efde41754c4cb1d5216d5b0a92a67458d968562bde7fa6310a83f53dda1383680a276a283438d58ceebfa7ab7ba72499d4a3eddc860595f63c93b1c5e823ea41fc490d938398a26db28f61857698553e93f0574eb8c5017bfed6249491f9976aaa8d23d9485339cc85ca329308"
+    }
+  ]
+}

test/hash-to-curve/expand_message_xof_SHAKE128_36.json

@@ -0,0 +1,78 @@
+{
+  "DST": "QUUX-V01-CS02-with-expander-SHAKE128",
+  "hash": "SHAKE128",
+  "k": 128,
+  "name": "expand_message_xof",
+  "tests": [
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "len_in_bytes": "0x20",
+      "msg": "",
+      "msg_prime": "0020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "uniform_bytes": "86518c9cd86581486e9485aa74ab35ba150d1c75c88e26b7043e44e2acd735a2"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "len_in_bytes": "0x20",
+      "msg": "abc",
+      "msg_prime": "6162630020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "uniform_bytes": "8696af52a4d862417c0763556073f47bc9b9ba43c99b505305cb1ec04a9ab468"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "len_in_bytes": "0x20",
+      "msg": "abcdef0123456789",
+      "msg_prime": "616263646566303132333435363738390020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "uniform_bytes": "912c58deac4821c3509dbefa094df54b34b8f5d01a191d1d3108a2c89077acca"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "len_in_bytes": "0x20",
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "msg_prime": "713132385f71717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171710020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "uniform_bytes": "1adbcc448aef2a0cebc71dac9f756b22e51839d348e031e63b33ebb50faeaf3f"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "len_in_bytes": "0x20",
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "msg_prime": "613531325f61616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161610020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "uniform_bytes": "df3447cc5f3e9a77da10f819218ddf31342c310778e0e4ef72bbaecee786a4fe"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "len_in_bytes": "0x80",
+      "msg": "",
+      "msg_prime": "0080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "uniform_bytes": "7314ff1a155a2fb99a0171dc71b89ab6e3b2b7d59e38e64419b8b6294d03ffee42491f11370261f436220ef787f8f76f5b26bdcd850071920ce023f3ac46847744f4612b8714db8f5db83205b2e625d95afd7d7b4d3094d3bdde815f52850bb41ead9822e08f22cf41d615a303b0d9dde73263c049a7b9898208003a739a2e57"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "len_in_bytes": "0x80",
+      "msg": "abc",
+      "msg_prime": "6162630080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "uniform_bytes": "c952f0c8e529ca8824acc6a4cab0e782fc3648c563ddb00da7399f2ae35654f4860ec671db2356ba7baa55a34a9d7f79197b60ddae6e64768a37d699a78323496db3878c8d64d909d0f8a7de4927dcab0d3dbbc26cb20a49eceb0530b431cdf47bc8c0fa3e0d88f53b318b6739fbed7d7634974f1b5c386d6230c76260d5337a"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "len_in_bytes": "0x80",
+      "msg": "abcdef0123456789",
+      "msg_prime": "616263646566303132333435363738390080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "uniform_bytes": "19b65ee7afec6ac06a144f2d6134f08eeec185f1a890fe34e68f0e377b7d0312883c048d9b8a1d6ecc3b541cb4987c26f45e0c82691ea299b5e6889bbfe589153016d8131717ba26f07c3c14ffbef1f3eff9752e5b6183f43871a78219a75e7000fbac6a7072e2b83c790a3a5aecd9d14be79f9fd4fb180960a3772e08680495"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "len_in_bytes": "0x80",
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "msg_prime": "713132385f71717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171710080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "uniform_bytes": "ca1b56861482b16eae0f4a26212112362fcc2d76dcc80c93c4182ed66c5113fe41733ed68be2942a3487394317f3379856f4822a611735e50528a60e7ade8ec8c71670fec6661e2c59a09ed36386513221688b35dc47e3c3111ee8c67ff49579089d661caa29db1ef10eb6eace575bf3dc9806e7c4016bd50f3c0e2a6481ee6d"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "len_in_bytes": "0x80",
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "msg_prime": "613531325f61616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161610080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
+      "uniform_bytes": "9d763a5ce58f65c91531b4100c7266d479a5d9777ba761693d052acd37d149e7ac91c796a10b919cd74a591a1e38719fb91b7203e2af31eac3bff7ead2c195af7d88b8bc0a8adf3d1e90ab9bed6ddc2b7f655dd86c730bdeaea884e73741097142c92f0e3fc1811b699ba593c7fbd81da288a29d423df831652e3a01a9374999"
+    }
+  ]
+}

test/hash-to-curve/expand_message_xof_SHAKE256_36.json

@@ -0,0 +1,78 @@
+{
+  "DST": "QUUX-V01-CS02-with-expander-SHAKE256",
+  "hash": "SHAKE256",
+  "k": 256,
+  "name": "expand_message_xof",
+  "tests": [
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "len_in_bytes": "0x20",
+      "msg": "",
+      "msg_prime": "0020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "uniform_bytes": "2ffc05c48ed32b95d72e807f6eab9f7530dd1c2f013914c8fed38c5ccc15ad76"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "len_in_bytes": "0x20",
+      "msg": "abc",
+      "msg_prime": "6162630020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "uniform_bytes": "b39e493867e2767216792abce1f2676c197c0692aed061560ead251821808e07"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "len_in_bytes": "0x20",
+      "msg": "abcdef0123456789",
+      "msg_prime": "616263646566303132333435363738390020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "uniform_bytes": "245389cf44a13f0e70af8665fe5337ec2dcd138890bb7901c4ad9cfceb054b65"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "len_in_bytes": "0x20",
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "msg_prime": "713132385f71717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171710020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "uniform_bytes": "719b3911821e6428a5ed9b8e600f2866bcf23c8f0515e52d6c6c019a03f16f0e"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "len_in_bytes": "0x20",
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "msg_prime": "613531325f61616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161610020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "uniform_bytes": "9181ead5220b1963f1b5951f35547a5ea86a820562287d6ca4723633d17ccbbc"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "len_in_bytes": "0x80",
+      "msg": "",
+      "msg_prime": "0080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "uniform_bytes": "7a1361d2d7d82d79e035b8880c5a3c86c5afa719478c007d96e6c88737a3f631dd74a2c88df79a4cb5e5d9f7504957c70d669ec6bfedc31e01e2bacc4ff3fdf9b6a00b17cc18d9d72ace7d6b81c2e481b4f73f34f9a7505dccbe8f5485f3d20c5409b0310093d5d6492dea4e18aa6979c23c8ea5de01582e9689612afbb353df"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "len_in_bytes": "0x80",
+      "msg": "abc",
+      "msg_prime": "6162630080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "uniform_bytes": "a54303e6b172909783353ab05ef08dd435a558c3197db0c132134649708e0b9b4e34fb99b92a9e9e28fc1f1d8860d85897a8e021e6382f3eea10577f968ff6df6c45fe624ce65ca25932f679a42a404bc3681efe03fcd45ef73bb3a8f79ba784f80f55ea8a3c367408f30381299617f50c8cf8fbb21d0f1e1d70b0131a7b6fbe"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "len_in_bytes": "0x80",
+      "msg": "abcdef0123456789",
+      "msg_prime": "616263646566303132333435363738390080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "uniform_bytes": "e42e4d9538a189316e3154b821c1bafb390f78b2f010ea404e6ac063deb8c0852fcd412e098e231e43427bd2be1330bb47b4039ad57b30ae1fc94e34993b162ff4d695e42d59d9777ea18d3848d9d336c25d2acb93adcad009bcfb9cde12286df267ada283063de0bb1505565b2eb6c90e31c48798ecdc71a71756a9110ff373"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "len_in_bytes": "0x80",
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "msg_prime": "713132385f71717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171710080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "uniform_bytes": "4ac054dda0a38a65d0ecf7afd3c2812300027c8789655e47aecf1ecc1a2426b17444c7482c99e5907afd9c25b991990490bb9c686f43e79b4471a23a703d4b02f23c669737a886a7ec28bddb92c3a98de63ebf878aa363a501a60055c048bea11840c4717beae7eee28c3cfa42857b3d130188571943a7bd747de831bd6444e0"
+    },
+    {
+      "DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "len_in_bytes": "0x80",
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "msg_prime": "613531325f61616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161610080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
+      "uniform_bytes": "09afc76d51c2cccbc129c2315df66c2be7295a231203b8ab2dd7f95c2772c68e500bc72e20c602abc9964663b7a03a389be128c56971ce81001a0b875e7fd17822db9d69792ddf6a23a151bf470079c518279aef3e75611f8f828994a9988f4a8a256ddb8bae161e658d5a2a09bcfe839c6396dc06ee5c8ff3c22d3b1f9deb7e"
+    }
+  ]
+}

test/hash-to-curve/secp256k1_XMD:SHA-256_SSWU_NU_.json

@@ -0,0 +1,90 @@
+{
+  "L": "0x30",
+  "Z": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc24",
+  "ciphersuite": "secp256k1_XMD:SHA-256_SSWU_NU_",
+  "curve": "secp256k1",
+  "dst": "QUUX-V01-CS02-with-secp256k1_XMD:SHA-256_SSWU_NU_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x1",
+    "p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f"
+  },
+  "hash": "sha256",
+  "k": "0x80",
+  "map": {
+    "name": "SSWU"
+  },
+  "randomOracle": false,
+  "vectors": [
+    {
+      "P": {
+        "x": "0xa4792346075feae77ac3b30026f99c1441b4ecf666ded19b7522cf65c4c55c5b",
+        "y": "0x62c59e2a6aeed1b23be5883e833912b08ba06be7f57c0e9cdc663f31639ff3a7"
+      },
+      "Q": {
+        "x": "0xa4792346075feae77ac3b30026f99c1441b4ecf666ded19b7522cf65c4c55c5b",
+        "y": "0x62c59e2a6aeed1b23be5883e833912b08ba06be7f57c0e9cdc663f31639ff3a7"
+      },
+      "msg": "",
+      "u": [
+        "0x0137fcd23bc3da962e8808f97474d097a6c8aa2881fceef4514173635872cf3b"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x3f3b5842033fff837d504bb4ce2a372bfeadbdbd84a1d2b678b6e1d7ee426b9d",
+        "y": "0x902910d1fef15d8ae2006fc84f2a5a7bda0e0407dc913062c3a493c4f5d876a5"
+      },
+      "Q": {
+        "x": "0x3f3b5842033fff837d504bb4ce2a372bfeadbdbd84a1d2b678b6e1d7ee426b9d",
+        "y": "0x902910d1fef15d8ae2006fc84f2a5a7bda0e0407dc913062c3a493c4f5d876a5"
+      },
+      "msg": "abc",
+      "u": [
+        "0xe03f894b4d7caf1a50d6aa45cac27412c8867a25489e32c5ddeb503229f63a2e"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x07644fa6281c694709f53bdd21bed94dab995671e4a8cd1904ec4aa50c59bfdf",
+        "y": "0xc79f8d1dad79b6540426922f7fbc9579c3018dafeffcd4552b1626b506c21e7b"
+      },
+      "Q": {
+        "x": "0x07644fa6281c694709f53bdd21bed94dab995671e4a8cd1904ec4aa50c59bfdf",
+        "y": "0xc79f8d1dad79b6540426922f7fbc9579c3018dafeffcd4552b1626b506c21e7b"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0xe7a6525ae7069ff43498f7f508b41c57f80563c1fe4283510b322446f32af41b"
+      ]
+    },
+    {
+      "P": {
+        "x": "0xb734f05e9b9709ab631d960fa26d669c4aeaea64ae62004b9d34f483aa9acc33",
+        "y": "0x03fc8a4a5a78632e2eb4d8460d69ff33c1d72574b79a35e402e801f2d0b1d6ee"
+      },
+      "Q": {
+        "x": "0xb734f05e9b9709ab631d960fa26d669c4aeaea64ae62004b9d34f483aa9acc33",
+        "y": "0x03fc8a4a5a78632e2eb4d8460d69ff33c1d72574b79a35e402e801f2d0b1d6ee"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0xd97cf3d176a2f26b9614a704d7d434739d194226a706c886c5c3c39806bc323c"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x17d22b867658977b5002dbe8d0ee70a8cfddec3eec50fb93f36136070fd9fa6c",
+        "y": "0xe9178ff02f4dab73480f8dd590328aea99856a7b6cc8e5a6cdf289ecc2a51718"
+      },
+      "Q": {
+        "x": "0x17d22b867658977b5002dbe8d0ee70a8cfddec3eec50fb93f36136070fd9fa6c",
+        "y": "0xe9178ff02f4dab73480f8dd590328aea99856a7b6cc8e5a6cdf289ecc2a51718"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0xa9ffbeee1d6e41ac33c248fb3364612ff591b502386c1bf6ac4aaf1ea51f8c3b"
+      ]
+    }
+  ]
+}

test/hash-to-curve/secp256k1_XMD:SHA-256_SSWU_RO_.json

@@ -0,0 +1,115 @@
+{
+  "L": "0x30",
+  "Z": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc24",
+  "ciphersuite": "secp256k1_XMD:SHA-256_SSWU_RO_",
+  "curve": "secp256k1",
+  "dst": "QUUX-V01-CS02-with-secp256k1_XMD:SHA-256_SSWU_RO_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x1",
+    "p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f"
+  },
+  "hash": "sha256",
+  "k": "0x80",
+  "map": {
+    "name": "SSWU"
+  },
+  "randomOracle": true,
+  "vectors": [
+    {
+      "P": {
+        "x": "0xc1cae290e291aee617ebaef1be6d73861479c48b841eaba9b7b5852ddfeb1346",
+        "y": "0x64fa678e07ae116126f08b022a94af6de15985c996c3a91b64c406a960e51067"
+      },
+      "Q0": {
+        "x": "0x74519ef88b32b425a095e4ebcc84d81b64e9e2c2675340a720bb1a1857b99f1e",
+        "y": "0xc174fa322ab7c192e11748beed45b508e9fdb1ce046dee9c2cd3a2a86b410936"
+      },
+      "Q1": {
+        "x": "0x44548adb1b399263ded3510554d28b4bead34b8cf9a37b4bd0bd2ba4db87ae63",
+        "y": "0x96eb8e2faf05e368efe5957c6167001760233e6dd2487516b46ae725c4cce0c6"
+      },
+      "msg": "",
+      "u": [
+        "0x6b0f9910dd2ba71c78f2ee9f04d73b5f4c5f7fc773a701abea1e573cab002fb3",
+        "0x1ae6c212e08fe1a5937f6202f929a2cc8ef4ee5b9782db68b0d5799fd8f09e16"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x3377e01eab42db296b512293120c6cee72b6ecf9f9205760bd9ff11fb3cb2c4b",
+        "y": "0x7f95890f33efebd1044d382a01b1bee0900fb6116f94688d487c6c7b9c8371f6"
+      },
+      "Q0": {
+        "x": "0x07dd9432d426845fb19857d1b3a91722436604ccbbbadad8523b8fc38a5322d7",
+        "y": "0x604588ef5138cffe3277bbd590b8550bcbe0e523bbaf1bed4014a467122eb33f"
+      },
+      "Q1": {
+        "x": "0xe9ef9794d15d4e77dde751e06c182782046b8dac05f8491eb88764fc65321f78",
+        "y": "0xcb07ce53670d5314bf236ee2c871455c562dd76314aa41f012919fe8e7f717b3"
+      },
+      "msg": "abc",
+      "u": [
+        "0x128aab5d3679a1f7601e3bdf94ced1f43e491f544767e18a4873f397b08a2b61",
+        "0x5897b65da3b595a813d0fdcc75c895dc531be76a03518b044daaa0f2e4689e00"
+      ]
+    },
+    {
+      "P": {
+        "x": "0xbac54083f293f1fe08e4a70137260aa90783a5cb84d3f35848b324d0674b0e3a",
+        "y": "0x4436476085d4c3c4508b60fcf4389c40176adce756b398bdee27bca19758d828"
+      },
+      "Q0": {
+        "x": "0x576d43ab0260275adf11af990d130a5752704f79478628761720808862544b5d",
+        "y": "0x643c4a7fb68ae6cff55edd66b809087434bbaff0c07f3f9ec4d49bb3c16623c3"
+      },
+      "Q1": {
+        "x": "0xf89d6d261a5e00fe5cf45e827b507643e67c2a947a20fd9ad71039f8b0e29ff8",
+        "y": "0xb33855e0cc34a9176ead91c6c3acb1aacb1ce936d563bc1cee1dcffc806caf57"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0xea67a7c02f2cd5d8b87715c169d055a22520f74daeb080e6180958380e2f98b9",
+        "0x7434d0d1a500d38380d1f9615c021857ac8d546925f5f2355319d823a478da18"
+      ]
+    },
+    {
+      "P": {
+        "x": "0xe2167bc785333a37aa562f021f1e881defb853839babf52a7f72b102e41890e9",
+        "y": "0xf2401dd95cc35867ffed4f367cd564763719fbc6a53e969fb8496a1e6685d873"
+      },
+      "Q0": {
+        "x": "0x9c91513ccfe9520c9c645588dff5f9b4e92eaf6ad4ab6f1cd720d192eb58247a",
+        "y": "0xc7371dcd0134412f221e386f8d68f49e7fa36f9037676e163d4a063fbf8a1fb8"
+      },
+      "Q1": {
+        "x": "0x10fee3284d7be6bd5912503b972fc52bf4761f47141a0015f1c6ae36848d869b",
+        "y": "0x0b163d9b4bf21887364332be3eff3c870fa053cf508732900fc69a6eb0e1b672"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0xeda89a5024fac0a8207a87e8cc4e85aa3bce10745d501a30deb87341b05bcdf5",
+        "0xdfe78cd116818fc2c16f3837fedbe2639fab012c407eac9dfe9245bf650ac51d"
+      ]
+    },
+    {
+      "P": {
+        "x": "0xe3c8d35aaaf0b9b647e88a0a0a7ee5d5bed5ad38238152e4e6fd8c1f8cb7c998",
+        "y": "0x8446eeb6181bf12f56a9d24e262221cc2f0c4725c7e3803024b5888ee5823aa6"
+      },
+      "Q0": {
+        "x": "0xb32b0ab55977b936f1e93fdc68cec775e13245e161dbfe556bbb1f72799b4181",
+        "y": "0x2f5317098360b722f132d7156a94822641b615c91f8663be69169870a12af9e8"
+      },
+      "Q1": {
+        "x": "0x148f98780f19388b9fa93e7dc567b5a673e5fca7079cd9cdafd71982ec4c5e12",
+        "y": "0x3989645d83a433bc0c001f3dac29af861f33a6fd1e04f4b36873f5bff497298a"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x8d862e7e7e23d7843fe16d811d46d7e6480127a6b78838c277bca17df6900e9f",
+        "0x68071d2530f040f081ba818d3c7188a94c900586761e9115efa47ae9bd847938"
+      ]
+    }
+  ]
+}

test/index.test.js

@@ -0,0 +1,14 @@
+import { should } from 'micro-should';
+
+// Should be first to catch obvious things
+import './basic.test.js';
+import './nist.test.js';
+import './ed448.test.js';
+import './ed25519.test.js';
+import './secp256k1.test.js';
+import './stark/stark.test.js';
+import './jubjub.test.js';
+import './bls12-381.test.js';
+import './hash-to-curve.test.js';
+
+should.run();

test/jubjub.test.js

@@ -0,0 +1,74 @@
+import { jubjub, findGroupHash } from '../lib/esm/jubjub.js';
+import { should } from 'micro-should';
+import { deepStrictEqual, throws } from 'assert';
+import { hexToBytes, bytesToHex } from '@noble/hashes/utils';
+
+const G_SPEND = new jubjub.ExtendedPoint(
+  0x055f1f24f0f0512287e51c3c5a0a6903fc0baf8711de9eafd7c0e66f69d8d2dbn,
+  0x566178b2505fdd52132a5007d80a04652842e78ffb376897588f406278214ed7n,
+  0x0141fafa1f11088a3b2007c14d652375888f3b37838ba6bdffae096741ceddfen,
+  0x12eada93c0b7d595f5f04f5ebfb4b7d033ef2884136475cab5e41ce17db5be9cn
+);
+const G_PROOF = new jubjub.ExtendedPoint(
+  0x0174d54ce9fad258a2f8a86a1deabf15c7a2b51106b0fbcd9d29020f78936f71n,
+  0x16871d6d877dcd222e4ec3bccb3f37cb1865a2d37dd3a5dcbc032a69b62b4445n,
+  0x57a3cd31e496d82bd4aa78bd5ecd751cfb76d54a5d3f4560866379f9fc11c9b3n,
+  0x42cc53f6b519d1f4f52c47ff1256463a616c2c2f49ffe77765481eca04c72081n
+);
+
+const getXY = (p) => ({ x: p.x, y: p.y });
+
+should('toHex/fromHex', () => {
+  // More than field
+  throws(() =>
+    jubjub.Point.fromHex(
+      new Uint8Array([
+        255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
+        255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
+      ])
+    )
+  );
+  // Multiplicative generator (sqrt == null), not on curve.
+  throws(() =>
+    jubjub.Point.fromHex(
+      new Uint8Array([
+        7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+        0,
+      ])
+    )
+  );
+  const tmp = jubjub.Point.fromHex(
+    new Uint8Array([
+      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+      0,
+    ])
+  );
+  deepStrictEqual(tmp.x, 0x8d51ccce760304d0ec030002760300000001000000000000n);
+  deepStrictEqual(tmp.y, 0n);
+
+  const S = G_SPEND.toAffine().toRawBytes();
+  const S2 = G_SPEND.double().toAffine().toRawBytes();
+  const P = G_PROOF.toAffine().toRawBytes();
+  const P2 = G_PROOF.double().toAffine().toRawBytes();
+  const S_exp = jubjub.Point.fromHex(S);
+  const S2_exp = jubjub.Point.fromHex(S2);
+  const P_exp = jubjub.Point.fromHex(P);
+  const P2_exp = jubjub.Point.fromHex(P2);
+  deepStrictEqual(getXY(G_SPEND.toAffine()), getXY(S_exp));
+  deepStrictEqual(getXY(G_SPEND.double().toAffine()), getXY(S2_exp));
+  deepStrictEqual(getXY(G_PROOF.toAffine()), getXY(P_exp));
+  deepStrictEqual(getXY(G_PROOF.double().toAffine()), getXY(P2_exp));
+});
+
+should('Find generators', () => {
+  const spend = findGroupHash(new Uint8Array(), new Uint8Array([90, 99, 97, 115, 104, 95, 71, 95]));
+  const proof = findGroupHash(new Uint8Array(), new Uint8Array([90, 99, 97, 115, 104, 95, 72, 95]));
+  deepStrictEqual(getXY(spend.toAffine()), getXY(G_SPEND.toAffine()));
+  deepStrictEqual(getXY(proof.toAffine()), getXY(G_PROOF.toAffine()));
+});
+
+// ESM is broken.
+import url from 'url';
+if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
+  should.run();
+}

test/nist.test.js

@@ -0,0 +1,386 @@
+import { deepStrictEqual, throws } from 'assert';
+import { should } from 'micro-should';
+import { secp192r1, P192 } from '../lib/esm/p192.js';
+import { secp224r1, P224 } from '../lib/esm/p224.js';
+import { secp256r1, P256 } from '../lib/esm/p256.js';
+import { secp384r1, P384 } from '../lib/esm/p384.js';
+import { secp521r1, P521 } from '../lib/esm/p521.js';
+import { secp256k1 } from '../lib/esm/secp256k1.js';
+import { hexToBytes, bytesToHex } from '../lib/esm/abstract/utils.js';
+import { default as ecdsa } from './wycheproof/ecdsa_test.json' assert { type: 'json' };
+import { default as ecdh } from './wycheproof/ecdh_test.json' assert { type: 'json' };
+import { default as rfc6979 } from './fixtures/rfc6979.json' assert { type: 'json' };
+
+const hex = bytesToHex;
+
+// prettier-ignore
+const NIST = {
+  secp192r1, P192,
+  secp224r1, P224,
+  secp256r1, P256,
+  secp384r1, P384,
+  secp521r1, P521,
+  secp256k1,
+};
+
+should('Curve Fields', () => {
+  const vectors = {
+    secp192r1: 0xfffffffffffffffffffffffffffffffeffffffffffffffffn,
+    secp224r1: 0xffffffffffffffffffffffffffffffff000000000000000000000001n,
+    secp256r1: 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffffn,
+    secp256k1: 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2fn,
+    secp384r1:
+      0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffffn,
+    secp521r1:
+      0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffn,
+  };
+  for (const n in vectors) deepStrictEqual(NIST[n].CURVE.Fp.ORDER, vectors[n]);
+});
+
+should('wychenproof ECDSA vectors', () => {
+  for (const group of ecdsa.testGroups) {
+    // Tested in secp256k1.test.js
+    if (group.key.curve === 'secp256k1') continue;
+    let CURVE = NIST[group.key.curve];
+    if (!CURVE) continue;
+    if (group.key.curve === 'secp224r1' && group.sha !== 'SHA-224') {
+      if (group.sha === 'SHA-256') CURVE = CURVE.create(sha256);
+    }
+    const pubKey = CURVE.Point.fromHex(group.key.uncompressed);
+    deepStrictEqual(pubKey.x, BigInt(`0x${group.key.wx}`));
+    deepStrictEqual(pubKey.y, BigInt(`0x${group.key.wy}`));
+    for (const test of group.tests) {
+      if (['Hash weaker than DL-group'].includes(test.comment)) {
+        continue;
+      }
+      const m = CURVE.CURVE.hash(hexToBytes(test.msg));
+      if (test.result === 'valid' || test.result === 'acceptable') {
+        try {
+          CURVE.Signature.fromDER(test.sig);
+        } catch (e) {
+          // Some test has invalid signature which we don't accept
+          if (e.message.includes('Invalid signature: incorrect length')) continue;
+          throw e;
+        }
+        const verified = CURVE.verify(test.sig, m, pubKey);
+        deepStrictEqual(verified, true, 'valid');
+      } else if (test.result === 'invalid') {
+        let failed = false;
+        try {
+          failed = !CURVE.verify(test.sig, m, pubKey);
+        } catch (error) {
+          failed = true;
+        }
+        deepStrictEqual(failed, true, 'invalid');
+      } else throw new Error('unknown test result');
+    }
+  }
+});
+
+should('wychenproof ECDH vectors', () => {
+  for (const group of ecdh.testGroups) {
+    // // Tested in secp256k1.test.js
+    // if (group.key.curve === 'secp256k1') continue;
+    // We don't have SHA-224
+    const CURVE = NIST[group.curve];
+    if (!CURVE) continue;
+    for (const test of group.tests) {
+      if (test.result === 'valid' || test.result === 'acceptable') {
+        try {
+          const pub = CURVE.Point.fromHex(test.public);
+        } catch (e) {
+          if (e.message.includes('Point.fromHex: received invalid point.')) continue;
+          throw e;
+        }
+        const shared = CURVE.getSharedSecret(test.private, test.public);
+        deepStrictEqual(shared, test.shared, 'valid');
+      } else if (test.result === 'invalid') {
+        let failed = false;
+        try {
+          CURVE.getSharedSecret(test.private, test.public);
+        } catch (error) {
+          failed = true;
+        }
+        deepStrictEqual(failed, true, 'invalid');
+      } else throw new Error('unknown test result');
+    }
+  }
+});
+
+import { default as ecdh_secp224r1_test } from './wycheproof/ecdh_secp224r1_test.json' assert { type: 'json' };
+import { default as ecdh_secp256r1_test } from './wycheproof/ecdh_secp256r1_test.json' assert { type: 'json' };
+import { default as ecdh_secp256k1_test } from './wycheproof/ecdh_secp256k1_test.json' assert { type: 'json' };
+import { default as ecdh_secp384r1_test } from './wycheproof/ecdh_secp384r1_test.json' assert { type: 'json' };
+import { default as ecdh_secp521r1_test } from './wycheproof/ecdh_secp521r1_test.json' assert { type: 'json' };
+
+// More per curve tests
+const WYCHEPROOF_ECDH = {
+  P224: {
+    curve: P224,
+    tests: [ecdh_secp224r1_test],
+  },
+  P256: {
+    curve: P256,
+    tests: [ecdh_secp256r1_test],
+  },
+  secp256k1: {
+    curve: secp256k1,
+    tests: [ecdh_secp256k1_test],
+  },
+  P384: {
+    curve: P384,
+    tests: [ecdh_secp384r1_test],
+  },
+  P521: {
+    curve: P521,
+    tests: [ecdh_secp521r1_test],
+  },
+};
+
+for (const name in WYCHEPROOF_ECDH) {
+  const { curve, tests } = WYCHEPROOF_ECDH[name];
+  for (let i = 0; i < tests.length; i++) {
+    const test = tests[i];
+    for (let j = 0; j < test.testGroups.length; j++) {
+      const group = test.testGroups[j];
+      should(`Wycheproof/ECDH ${name} (${i}/${j})`, () => {
+        for (const test of group.tests) {
+          if (test.result === 'valid' || test.result === 'acceptable') {
+            try {
+              const pub = curve.Point.fromHex(test.public);
+            } catch (e) {
+              if (e.message.includes('Point.fromHex: received invalid point.')) continue;
+              throw e;
+            }
+            const shared = curve.getSharedSecret(test.private, test.public);
+            deepStrictEqual(hex(shared), test.shared, 'valid');
+          } else if (test.result === 'invalid') {
+            let failed = false;
+            try {
+              curve.getSharedSecret(test.private, test.public);
+            } catch (error) {
+              failed = true;
+            }
+            deepStrictEqual(failed, true, 'invalid');
+          } else throw new Error('unknown test result');
+        }
+      });
+    }
+  }
+}
+
+// Tests with custom hashes
+import { default as secp224r1_sha224_test } from './wycheproof/ecdsa_secp224r1_sha224_test.json' assert { type: 'json' };
+import { default as secp224r1_sha256_test } from './wycheproof/ecdsa_secp224r1_sha256_test.json' assert { type: 'json' };
+import { default as secp224r1_sha3_224_test } from './wycheproof/ecdsa_secp224r1_sha3_224_test.json' assert { type: 'json' };
+import { default as secp224r1_sha3_256_test } from './wycheproof/ecdsa_secp224r1_sha3_256_test.json' assert { type: 'json' };
+import { default as secp224r1_sha3_512_test } from './wycheproof/ecdsa_secp224r1_sha3_512_test.json' assert { type: 'json' };
+import { default as secp224r1_sha512_test } from './wycheproof/ecdsa_secp224r1_sha512_test.json' assert { type: 'json' };
+
+import { default as secp256k1_sha256_test } from './wycheproof/ecdsa_secp256k1_sha256_test.json' assert { type: 'json' };
+import { default as secp256k1_sha3_256_test } from './wycheproof/ecdsa_secp256k1_sha3_256_test.json' assert { type: 'json' };
+import { default as secp256k1_sha3_512_test } from './wycheproof/ecdsa_secp256k1_sha3_512_test.json' assert { type: 'json' };
+import { default as secp256k1_sha512_test } from './wycheproof/ecdsa_secp256k1_sha512_test.json' assert { type: 'json' };
+
+import { default as secp256r1_sha256_test } from './wycheproof/ecdsa_secp256r1_sha256_test.json' assert { type: 'json' };
+import { default as secp256r1_sha3_256_test } from './wycheproof/ecdsa_secp256r1_sha3_256_test.json' assert { type: 'json' };
+import { default as secp256r1_sha3_512_test } from './wycheproof/ecdsa_secp256r1_sha3_512_test.json' assert { type: 'json' };
+import { default as secp256r1_sha512_test } from './wycheproof/ecdsa_secp256r1_sha512_test.json' assert { type: 'json' };
+
+import { default as secp384r1_sha384_test } from './wycheproof/ecdsa_secp384r1_sha384_test.json' assert { type: 'json' };
+import { default as secp384r1_sha3_384_test } from './wycheproof/ecdsa_secp384r1_sha3_384_test.json' assert { type: 'json' };
+import { default as secp384r1_sha3_512_test } from './wycheproof/ecdsa_secp384r1_sha3_512_test.json' assert { type: 'json' };
+import { default as secp384r1_sha512_test } from './wycheproof/ecdsa_secp384r1_sha512_test.json' assert { type: 'json' };
+
+import { default as secp521r1_sha3_512_test } from './wycheproof/ecdsa_secp521r1_sha3_512_test.json' assert { type: 'json' };
+import { default as secp521r1_sha512_test } from './wycheproof/ecdsa_secp521r1_sha512_test.json' assert { type: 'json' };
+
+import { sha3_224, sha3_256, sha3_384, sha3_512 } from '@noble/hashes/sha3';
+import { sha512, sha384 } from '@noble/hashes/sha512';
+import { sha224, sha256 } from '@noble/hashes/sha256';
+
+const WYCHEPROOF_ECDSA = {
+  P224: {
+    curve: P224,
+    hashes: {
+      sha224: {
+        hash: sha224,
+        tests: [secp224r1_sha224_test],
+      },
+      sha256: {
+        hash: sha256,
+        tests: [secp224r1_sha256_test],
+      },
+      sha3_224: {
+        hash: sha3_224,
+        tests: [secp224r1_sha3_224_test],
+      },
+      sha3_256: {
+        hash: sha3_256,
+        tests: [secp224r1_sha3_256_test],
+      },
+      sha3_512: {
+        hash: sha3_512,
+        tests: [secp224r1_sha3_512_test],
+      },
+      sha512: {
+        hash: sha512,
+        tests: [secp224r1_sha512_test],
+      },
+    },
+  },
+  secp256k1: {
+    curve: secp256k1,
+    hashes: {
+      // TODO: debug why fails, can be bug
+      sha256: {
+        hash: sha256,
+        tests: [secp256k1_sha256_test],
+      },
+      sha3_256: {
+        hash: sha3_256,
+        tests: [secp256k1_sha3_256_test],
+      },
+      sha3_512: {
+        hash: sha3_512,
+        tests: [secp256k1_sha3_512_test],
+      },
+      sha512: {
+        hash: sha512,
+        tests: [secp256k1_sha512_test],
+      },
+    },
+  },
+  P256: {
+    curve: P256,
+    hashes: {
+      sha256: {
+        hash: sha256,
+        tests: [secp256r1_sha256_test],
+      },
+      sha3_256: {
+        hash: sha3_256,
+        tests: [secp256r1_sha3_256_test],
+      },
+      sha3_512: {
+        hash: sha3_512,
+        tests: [secp256r1_sha3_512_test],
+      },
+      sha512: {
+        hash: sha512,
+        tests: [secp256r1_sha512_test],
+      },
+    },
+  },
+  P384: {
+    curve: P384,
+    hashes: {
+      sha384: {
+        hash: sha384,
+        tests: [secp384r1_sha384_test],
+      },
+      sha3_384: {
+        hash: sha3_384,
+        tests: [secp384r1_sha3_384_test],
+      },
+      sha3_512: {
+        hash: sha3_512,
+        tests: [secp384r1_sha3_512_test],
+      },
+      sha512: {
+        hash: sha512,
+        tests: [secp384r1_sha512_test],
+      },
+    },
+  },
+  P521: {
+    curve: P521,
+    hashes: {
+      sha3_512: {
+        hash: sha3_512,
+        tests: [secp521r1_sha3_512_test],
+      },
+      sha512: {
+        hash: sha512,
+        tests: [secp521r1_sha512_test],
+      },
+    },
+  },
+};
+
+function runWycheproof(name, CURVE, group, index) {
+  const pubKey = CURVE.Point.fromHex(group.key.uncompressed);
+  deepStrictEqual(pubKey.x, BigInt(`0x${group.key.wx}`));
+  deepStrictEqual(pubKey.y, BigInt(`0x${group.key.wy}`));
+  for (const test of group.tests) {
+    const m = CURVE.CURVE.hash(hexToBytes(test.msg));
+
+    if (test.result === 'valid' || test.result === 'acceptable') {
+      try {
+        CURVE.Signature.fromDER(test.sig);
+      } catch (e) {
+        // Some tests has invalid signature which we don't accept
+        if (e.message.includes('Invalid signature: incorrect length')) continue;
+        throw e;
+      }
+      const verified = CURVE.verify(test.sig, m, pubKey);
+      if (name === 'secp256k1') {
+        // lowS: true for secp256k1
+        deepStrictEqual(verified, !CURVE.Signature.fromDER(test.sig).hasHighS(), `${index}: valid`);
+      } else {
+        deepStrictEqual(verified, true, `${index}: valid`);
+      }
+    } else if (test.result === 'invalid') {
+      let failed = false;
+      try {
+        failed = !CURVE.verify(test.sig, m, pubKey);
+      } catch (error) {
+        failed = true;
+      }
+      deepStrictEqual(failed, true, `${index}: invalid`);
+    } else throw new Error('unknown test result');
+  }
+}
+
+for (const name in WYCHEPROOF_ECDSA) {
+  const { curve, hashes } = WYCHEPROOF_ECDSA[name];
+  for (const hName in hashes) {
+    const { hash, tests } = hashes[hName];
+    const CURVE = curve.create(hash);
+    should(`Wycheproof/WYCHEPROOF_ECDSA ${name}/${hName}`, () => {
+      for (let i = 0; i < tests.length; i++) {
+        const groups = tests[i].testGroups;
+        for (let j = 0; j < groups.length; j++) {
+          const group = groups[j];
+          runWycheproof(name, CURVE, group, `${i}/${j}`);
+        }
+      }
+    });
+  }
+}
+
+const hexToBigint = (hex) => BigInt(`0x${hex}`);
+should('RFC6979', () => {
+  for (const v of rfc6979) {
+    const curve = NIST[v.curve];
+    deepStrictEqual(curve.CURVE.n, hexToBigint(v.q));
+    const pubKey = curve.getPublicKey(v.private);
+    const pubPoint = curve.Point.fromHex(pubKey);
+    deepStrictEqual(pubPoint.x, hexToBigint(v.Ux));
+    deepStrictEqual(pubPoint.y, hexToBigint(v.Uy));
+    for (const c of v.cases) {
+      const h = curve.CURVE.hash(c.message);
+      const sigObj = curve.sign(h, v.private);
+      deepStrictEqual(sigObj.r, hexToBigint(c.r), 'R');
+      deepStrictEqual(sigObj.s, hexToBigint(c.s), 'S');
+      deepStrictEqual(curve.verify(sigObj.toDERRawBytes(), h, pubKey), true, 'verify(1)');
+      deepStrictEqual(curve.verify(sigObj, h, pubKey), true, 'verify(2)');
+    }
+  }
+});
+
+// ESM is broken.
+import url from 'url';
+if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
+  should.run();
+}

test/package.json

@@ -0,0 +1,7 @@
+{
+  "type": "module",
+  "browser": {
+    "crypto": false,
+    "./crypto": "./esm/cryptoBrowser.js"
+  }
+}

test/secp256k1.test.js

@@ -1,5 +1,5 @@
 import * as fc from 'fast-check';
-import * as nist from '../lib/nist.js';
+import { secp256k1, schnorr } from '../lib/esm/secp256k1.js';
 import { readFileSync } from 'fs';
 import { default as ecdsa } from './vectors/ecdsa.json' assert { type: 'json' };
 import { default as ecdh } from './vectors/ecdh.json' assert { type: 'json' };
@@ -7,15 +7,16 @@ import { default as privates } from './vectors/privates.json' assert { type: 'js
 import { default as points } from './vectors/points.json' assert { type: 'json' };
 import { default as wp } from './vectors/wychenproof.json' assert { type: 'json' };
 import { should } from 'micro-should';
-import { deepStrictEqual, throws, rejects } from 'assert';
+import { deepStrictEqual, throws } from 'assert';
 import { hexToBytes, bytesToHex } from '@noble/hashes/utils';
 
 const hex = bytesToHex;
-const secp = nist.secp256k1;
+const secp = secp256k1;
 const privatesTxt = readFileSync('./test/vectors/privates-2.txt', 'utf-8');
 const schCsv = readFileSync('./test/vectors/schnorr.csv', 'utf-8');
 
 const FC_BIGINT = fc.bigInt(1n + 1n, secp.CURVE.n - 1n);
+const P = secp.CURVE.Fp.ORDER;
 // prettier-ignore
 const INVALID_ITEMS = ['deadbeef', Math.pow(2, 53), [1], 'xyzxyzxyxyzxyzxyxyzxyzxyxyzxyzxyxyzxyzxyxyzxyzxyxyzxyzxyxyzxyzxy', secp.CURVE.n + 2n];
 
@@ -163,15 +164,15 @@ should('secp256k1.Point#multiply(privateKey)', () => {
 });
 
 // multiply() should equal multiplyUnsafe()
-// should('JacobianPoint#multiplyUnsafe', () => {
-//   const p0 = new secp.JacobianPoint(
+// should('ProjectivePoint#multiplyUnsafe', () => {
+//   const p0 = new secp.ProjectivePoint(
 //     55066263022277343669578718895168534326250603453777594175500187360389116729240n,
 //     32670510020758816978083085130507043184471273380659243275938904335757337482424n,
 //     1n
 //   );
 //   const z = 106011723082030650010038151861333186846790370053628296836951575624442507889495n;
 //   console.log(p0.multiply(z));
-//   console.log(secp.JacobianPoint.normalizeZ([p0.multiplyUnsafe(z)])[0])
+//   console.log(secp.ProjectivePoint.normalizeZ([p0.multiplyUnsafe(z)])[0])
 // });
 
 should('secp256k1.Signature.fromCompactHex() roundtrip', () => {
@@ -192,35 +193,28 @@ should('secp256k1.Signature.fromDERHex() roundtrip', () => {
   );
 });
 
-should('secp256k1.sign()/should create deterministic signatures with RFC 6979', async () => {
+should('secp256k1.sign()/should create deterministic signatures with RFC 6979', () => {
   for (const vector of ecdsa.valid) {
-    let usig = await secp.sign(vector.m, vector.d);
-    let sig = (usig.toCompactHex());
+    let usig = secp.sign(vector.m, vector.d);
+    let sig = usig.toCompactHex();
     const vsig = vector.signature;
     deepStrictEqual(sig.slice(0, 64), vsig.slice(0, 64));
     deepStrictEqual(sig.slice(64, 128), vsig.slice(64, 128));
   }
 });
 
-should(
-  'secp256k1.sign()/should not create invalid deterministic signatures with RFC 6979',
-  async () => {
+should('secp256k1.sign()/should not create invalid deterministic signatures with RFC 6979', () => {
   for (const vector of ecdsa.invalid.sign) {
-      throws(() => {
-        return secp.sign(vector.m, vector.d);
-      });
+    throws(() => secp.sign(vector.m, vector.d));
   }
-  }
-);
-
-should('secp256k1.sign()/edge cases', () => {
-  // @ts-ignore
-  rejects(async () => await secp.sign());
-  // @ts-ignore
-  rejects(async () => await secp.sign(''));
 });
 
-should('secp256k1.sign()/should create correct DER encoding against libsecp256k1', async () => {
+should('secp256k1.sign()/edge cases', () => {
+  throws(() => secp.sign());
+  throws(() => secp.sign(''));
+});
+
+should('secp256k1.sign()/should create correct DER encoding against libsecp256k1', () => {
   const CASES = [
     [
       'd1a9dc8ed4e46a6a3e5e594615ca351d7d7ef44df1e4c94c1802f3592183794b',
@@ -236,14 +230,14 @@ should('secp256k1.sign()/should create correct DER encoding against libsecp256k1
     ],
   ];
   const privKey = hexToBytes('0101010101010101010101010101010101010101010101010101010101010101');
-  for (let [msg, exp] of CASES) {
-    const res = await secp.sign(msg, privKey, { extraEntropy: undefined });
-    deepStrictEqual((res.toDERHex()), exp);
+  for (const [msg, exp] of CASES) {
+    const res = secp.sign(msg, privKey, { extraEntropy: undefined });
+    deepStrictEqual(res.toDERHex(), exp);
     const rs = secp.Signature.fromDER(res.toDERHex()).toCompactHex();
     deepStrictEqual(secp.Signature.fromCompact(rs).toDERHex(), exp);
   }
 });
-should('secp256k1.sign()/sign ecdsa extraData', async () => {
+should('secp256k1.sign()/sign ecdsa extraData', () => {
   const ent1 = '0000000000000000000000000000000000000000000000000000000000000000';
   const ent2 = '0000000000000000000000000000000000000000000000000000000000000001';
   const ent3 = '6e723d3fd94ed5d2b6bdd4f123364b0f3ca52af829988a63f8afe91d29db1c33';
@@ -251,56 +245,52 @@ should('secp256k1.sign()/sign ecdsa extraData', async () => {
   const ent5 = 'ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff';
 
   for (const e of ecdsa.extraEntropy) {
-    const sign = async (extraEntropy) => {
-      const s = secp.sign(e.m, e.d, {extraEntropy }).toCompactHex();
+    const sign = (extraEntropy) => {
+      const s = secp.sign(e.m, e.d, { extraEntropy }).toCompactHex();
       return s;
     };
-    deepStrictEqual(await sign(), e.signature);
-    deepStrictEqual(await sign(ent1), e.extraEntropy0);
-    deepStrictEqual(await sign(ent2), e.extraEntropy1);
-    deepStrictEqual(await sign(ent3), e.extraEntropyRand);
-    deepStrictEqual(await sign(ent4), e.extraEntropyN);
-    deepStrictEqual(await sign(ent5), e.extraEntropyMax);
+    deepStrictEqual(sign(), e.signature);
+    deepStrictEqual(sign(ent1), e.extraEntropy0);
+    deepStrictEqual(sign(ent2), e.extraEntropy1);
+    deepStrictEqual(sign(ent3), e.extraEntropyRand);
+    deepStrictEqual(sign(ent4), e.extraEntropyN);
+    deepStrictEqual(sign(ent5), e.extraEntropyMax);
   }
 });
 
-should('secp256k1.verify()/should verify signature', async () => {
+should('secp256k1.verify()/should verify signature', () => {
   const MSG = '01'.repeat(32);
   const PRIV_KEY = 0x2n;
-  const signature = await secp.sign(MSG, PRIV_KEY);
+  const signature = secp.sign(MSG, PRIV_KEY);
   const publicKey = secp.getPublicKey(PRIV_KEY);
   deepStrictEqual(publicKey.length, 65);
   deepStrictEqual(secp.verify(signature, MSG, publicKey), true);
 });
-should('secp256k1.verify()/should not verify signature with wrong public key', async () => {
+should('secp256k1.verify()/should not verify signature with wrong public key', () => {
   const MSG = '01'.repeat(32);
   const PRIV_KEY = 0x2n;
   const WRONG_PRIV_KEY = 0x22n;
-  const signature = await secp.sign(MSG, PRIV_KEY);
+  const signature = secp.sign(MSG, PRIV_KEY);
   const publicKey = secp.Point.fromPrivateKey(WRONG_PRIV_KEY).toHex();
   deepStrictEqual(publicKey.length, 130);
   deepStrictEqual(secp.verify(signature, MSG, publicKey), false);
 });
-should('secp256k1.verify()/should not verify signature with wrong hash', async () => {
+should('secp256k1.verify()/should not verify signature with wrong hash', () => {
   const MSG = '01'.repeat(32);
   const PRIV_KEY = 0x2n;
   const WRONG_MSG = '11'.repeat(32);
-  const signature = await secp.sign(MSG, PRIV_KEY);
+  const signature = secp.sign(MSG, PRIV_KEY);
   const publicKey = secp.getPublicKey(PRIV_KEY);
   deepStrictEqual(publicKey.length, 65);
   deepStrictEqual(secp.verify(signature, WRONG_MSG, publicKey), false);
 });
-should('secp256k1.verify()/should verify random signatures', async () =>
+should('secp256k1.verify()/should verify random signatures', () =>
   fc.assert(
-    fc.asyncProperty(
-      FC_BIGINT,
-      fc.hexaString({ minLength: 64, maxLength: 64 }),
-      async (privKey, msg) => {
+    fc.property(FC_BIGINT, fc.hexaString({ minLength: 64, maxLength: 64 }), (privKey, msg) => {
       const pub = secp.getPublicKey(privKey);
-        const sig = await secp.sign(msg, privKey);
+      const sig = secp.sign(msg, privKey);
       deepStrictEqual(secp.verify(sig, msg, pub), true);
-      }
-    )
+    })
   )
 );
 should('secp256k1.verify()/should not verify signature with invalid r/s', () => {
@@ -315,16 +305,14 @@ should('secp256k1.verify()/should not verify signature with invalid r/s', () =>
 
   const pub = new secp.Point(x, y);
   const signature = new secp.Signature(2n, 2n);
-  // @ts-ignore
   signature.r = r;
-  // @ts-ignore
   signature.s = s;
 
   const verified = secp.verify(signature, msg, pub);
   // Verifies, but it shouldn't, because signature S > curve order
   deepStrictEqual(verified, false);
 });
-should('secp256k1.verify()/should not verify msg = curve order', async () => {
+should('secp256k1.verify()/should not verify msg = curve order', () => {
   const msg = 'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141';
   const x = 55066263022277343669578718895168534326250603453777594175500187360389116729240n;
   const y = 32670510020758816978083085130507043184471273380659243275938904335757337482424n;
@@ -334,7 +322,7 @@ should('secp256k1.verify()/should not verify msg = curve order', async () => {
   const sig = new secp.Signature(r, s);
   deepStrictEqual(secp.verify(sig, msg, pub), false);
 });
-should('secp256k1.verify()/should verify non-strict msg bb5a...', async () => {
+should('secp256k1.verify()/should verify non-strict msg bb5a...', () => {
   const msg = 'bb5a52f42f9c9261ed4361f59422a1e30036e7c32b270c8807a419feca605023';
   const x = 3252872872578928810725465493269682203671229454553002637820453004368632726370n;
   const y = 17482644437196207387910659778872952193236850502325156318830589868678978890912n;
@@ -354,47 +342,35 @@ should(
   }
 );
 
-// describe('schnorr', () => {
-//   // index,secret key,public key,aux_rand,message,signature,verification result,comment
-//   const vectors = schCsv
-//     .split('\n')
-//     .map((line: string) => line.split(','))
-//     .slice(1, -1);
-//   for (let vec of vectors) {
-//     const [index, sec, pub, rnd, msg, expSig, passes, comment] = vec;
-//     it(`should sign with Schnorr scheme vector ${index}`, async () => {
-//       if (sec) {
-//         expect(hex(secp.schnorr.getPublicKey(sec))).toBe(pub.toLowerCase());
-//         const sig = await secp.schnorr.sign(msg, sec, rnd);
-//         const sigS = secp.schnorr.signSync(msg, sec, rnd);
-//         expect(hex(sig)).toBe(expSig.toLowerCase());
-//         expect(hex(sigS)).toBe(expSig.toLowerCase());
-//         expect(await secp.schnorr.verify(sigS, msg, pub)).toBe(true);
-//         expect(secp.schnorr.verifySync(sig, msg, pub)).toBe(true);
-//       } else {
-//         const passed = await secp.schnorr.verify(expSig, msg, pub);
-//         const passedS = secp.schnorr.verifySync(expSig, msg, pub);
-//         if (passes === 'TRUE') {
-//           expect(passed).toBeTruthy();
-//           expect(passedS).toBeTruthy();
-//         } else {
-//           expect(passed).toBeFalsy();
-//           expect(passedS).toBeFalsy();
-//         }
-//       }
-//     });
-//   }
-// });
+// index,secret key,public key,aux_rand,message,signature,verification result,comment
+const vectors = schCsv
+  .split('\n')
+  .map((line) => line.split(','))
+  .slice(1, -1);
+for (let vec of vectors) {
+  const [index, sec, pub, rnd, msg, expSig, passes, comment] = vec;
+  should(`sign with Schnorr scheme vector ${index}`, () => {
+    if (sec) {
+      deepStrictEqual(hex(schnorr.getPublicKey(sec)), pub.toLowerCase());
+      const sig = schnorr.sign(msg, sec, rnd);
+      deepStrictEqual(hex(sig), expSig.toLowerCase());
+      deepStrictEqual(schnorr.verify(sig, msg, pub), true);
+    } else {
+      const passed = schnorr.verify(expSig, msg, pub);
+      deepStrictEqual(passed, passes === 'TRUE');
+    }
+  });
+}
 
-should('secp256k1.recoverPublicKey()/should recover public key from recovery bit', async () => {
+should('secp256k1.recoverPublicKey()/should recover public key from recovery bit', () => {
   const message = '00000000000000000000000000000000000000000000000000000000deadbeef';
   const privateKey = 123456789n;
   const publicKey = secp.Point.fromHex(secp.getPublicKey(privateKey)).toHex(false);
-  const sig = await secp.sign(message, privateKey);
+  const sig = secp.sign(message, privateKey);
   const recoveredPubkey = sig.recoverPublicKey(message);
   // const recoveredPubkey = secp.recoverPublicKey(message, signature, recovery);
   deepStrictEqual(recoveredPubkey !== null, true);
-  deepStrictEqual((recoveredPubkey).toHex(), publicKey);
+  deepStrictEqual(recoveredPubkey.toHex(), publicKey);
   deepStrictEqual(secp.verify(sig, message, publicKey), true);
 });
 should('secp256k1.recoverPublicKey()/should not recover zero points', () => {
@@ -404,22 +380,21 @@ should('secp256k1.recoverPublicKey()/should not recover zero points', () => {
   const recovery = 0;
   throws(() => secp.recoverPublicKey(msgHash, sig, recovery));
 });
-should('secp256k1.recoverPublicKey()/should handle all-zeros msghash', async () => {
+should('secp256k1.recoverPublicKey()/should handle all-zeros msghash', () => {
   const privKey = secp.utils.randomPrivateKey();
   const pub = secp.getPublicKey(privKey);
   const zeros = '0000000000000000000000000000000000000000000000000000000000000000';
-  const sig = await secp.sign(zeros, privKey, { recovered: true });
+  const sig = secp.sign(zeros, privKey, { recovered: true });
   const recoveredKey = sig.recoverPublicKey(zeros);
   deepStrictEqual(recoveredKey.toRawBytes(), pub);
 });
-should('secp256k1.recoverPublicKey()/should handle RFC 6979 vectors', async () => {
+should('secp256k1.recoverPublicKey()/should handle RFC 6979 vectors', () => {
   for (const vector of ecdsa.valid) {
-    if (secp.utils.mod(hexToNumber(vector.m), secp.CURVE.n) === 0n) continue;
     let usig = secp.sign(vector.m, vector.d);
-    let sig = (usig).toDERHex();
+    let sig = usig.toDERHex();
     const vpub = secp.getPublicKey(vector.d);
     const recovered = usig.recoverPublicKey(vector.m);
-    deepStrictEqual((recovered).toHex(), hex(vpub));
+    deepStrictEqual(recovered.toHex(), hex(vpub));
   }
 });
 
@@ -431,8 +406,6 @@ should('secp256k1.getSharedSecret()/should produce correct results', () => {
   // TODO: Once der is there, run all tests.
   for (const vector of ecdh.testGroups[0].tests.slice(0, 230)) {
     if (vector.result === 'invalid' || vector.private.length !== 64) {
-      // We support eth-like hexes
-      if (vector.private.length < 64) continue;
       throws(() => {
         secp.getSharedSecret(vector.private, derToPub(vector.public), true);
       });
@@ -556,4 +529,8 @@ should('secp256k1.wychenproof vectors', () => {
   }
 });
 
-should.run();
+// ESM is broken.
+import url from 'url';
+if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
+  should.run();
+}

test/stark/basic.test.js

@@ -1,6 +1,6 @@
 import { deepStrictEqual, throws } from 'assert';
 import { should } from 'micro-should';
-import * as starknet from '../../lib/starknet.js';
+import * as starknet from '../../lib/esm/stark.js';
 import { default as issue2 } from './fixtures/issue2.json' assert { type: 'json' };
 
 should('Basic elliptic sanity check', () => {

test/stark/benchmark/index.js

@@ -1,4 +1,4 @@
-import * as microStark from '../../../lib/starknet.js';
+import * as microStark from '../../../lib/esm/stark.js';
 import * as starkwareCrypto from '@starkware-industries/starkware-crypto-utils';
 import * as bench from 'micro-bmark';
 const { run, mark } = bench; // or bench.mark

test/stark/index.test.js

@@ -1,5 +1,5 @@
 
 import './basic.test.js';
-import './starknet.test.js';
+import './stark.test.js';
 import './property.test.js';