Release 1.2.0.

Update lockfile for 1.2
Release 1.2.0.
2023-08-23 20:00:32 +02:00 · 2023-08-23 19:58:55 +02:00 · 2023-08-23 19:55:35 +02:00 · 2023-08-23 19:48:52 +02:00 · 2023-08-23 19:45:47 +02:00 · 2023-08-23 19:43:55 +02:00
41 changed files with 1644 additions and 730 deletions
--- a/.github/workflows/nodejs.yml
+++ b/.github/workflows/nodejs.yml
@@ -3,15 +3,18 @@ name: Node CI
 on: [push, pull_request]
 jobs:
  test:
-    name: v18 @ ubuntu-latest
+    name: v${{ matrix.node }} @ ubuntu-latest
    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        node: [18, 20]
    steps:
    - uses: actions/checkout@v3
    - name: Use Node.js ${{ matrix.node }}
      uses: actions/setup-node@v3
      with:
-        node-version: 18
+        node-version: ${{ matrix.node }}
    - run: npm install
    - run: npm run build --if-present
-    - run: npm run lint --if-present
    - run: npm test
+    - run: npm run lint --if-present
--- a/.github/workflows/publish-npm.yml
+++ b/.github/workflows/publish-npm.yml
@@ -0,0 +1,23 @@
+name: Publish Package to npm
+on:
+ release:
+   types: [created]
+jobs:
+ build:
+   runs-on: ubuntu-latest
+   permissions:
+     contents: read
+     id-token: write
+   steps:
+     - uses: actions/checkout@8e5e7e5ab8b370d6c329ec480221332ada57f0ab # v3
+     - uses: actions/setup-node@64ed1c7eab4cce3362f8c340dee64e5eaeef8f7c # v3
+       with:
+         node-version: 20
+         registry-url: 'https://registry.npmjs.org'
+         cache: npm
+     - run: npm install -g npm
+     - run: npm ci
+     - run: npm run build
+     - run: npm publish --provenance --access public
+       env:
+         NODE_AUTH_TOKEN: ${{ secrets.NPM_PUBLISH_TOKEN }}
--- a/README.md
+++ b/README.md
@@ -8,70 +8,80 @@ Audited & minimal JS implementation of elliptic curve cryptography.
 - 🔍 Unique tests ensure correctness: property-based, cross-library and Wycheproof vectors, fuzzing
 - ➰ Short Weierstrass, Edwards, Montgomery curves
 - ✍️ ECDSA, EdDSA, Schnorr, BLS signature schemes, ECDH key agreement
- #️⃣ Hash-to-curve
-  for encoding or hashing an arbitrary string to an elliptic curve point
+- 🔖 SUF-CMA and SBS (non-repudiation) for ed25519, ed448 and others
+- #️⃣ hash-to-curve for encoding or hashing an arbitrary string to an elliptic curve point
 - 🧜‍♂️ Poseidon ZK-friendly hash

-Check out [Upgrading](#upgrading) if you've previously used single-feature noble
-packages. See [Resources](#resources) for articles and real-world software that uses curves.
-
 ### This library belongs to _noble_ crypto

 > **noble-crypto** — high-security, easily auditable set of contained cryptographic libraries and tools.

 - No dependencies, protection against supply chain attacks
 - Auditable TypeScript / JS code
- Supported in all major browsers and stable node.js versions
- All releases are signed with PGP keys
+- Supported on all major platforms
+- Releases are signed with PGP keys and built transparently with NPM provenance
 - Check out [homepage](https://paulmillr.com/noble/) & all libraries:
-  [curves](https://github.com/paulmillr/noble-curves)
-  (4kb versions [secp256k1](https://github.com/paulmillr/noble-secp256k1),
-  [ed25519](https://github.com/paulmillr/noble-ed25519)),
-  [hashes](https://github.com/paulmillr/noble-hashes)
+  [ciphers](https://github.com/paulmillr/noble-ciphers),
+  [curves](https://github.com/paulmillr/noble-curves),
+  [hashes](https://github.com/paulmillr/noble-hashes),
+  4kb [secp256k1](https://github.com/paulmillr/noble-secp256k1) /
+  [ed25519](https://github.com/paulmillr/noble-ed25519)

 ## Usage

-Browser, deno and node.js are supported:
-
 > npm install @noble/curves

-For [Deno](https://deno.land), use it with
-[npm specifier](https://deno.land/manual@v1.28.0/node/npm_specifiers).
-In browser, you could also include the single file from
-[GitHub's releases page](https://github.com/paulmillr/noble-curves/releases).
+We support all major platforms and runtimes.
+For [Deno](https://deno.land), ensure to use [npm specifier](https://deno.land/manual@v1.28.0/node/npm_specifiers).
+For React Native, you may need a [polyfill for crypto.getRandomValues](https://github.com/LinusU/react-native-get-random-values).
+If you don't like NPM, a standalone [noble-curves.js](https://github.com/paulmillr/noble-curves/releases) is also available.

-The library is tree-shaking-friendly and does NOT expose root entry point as
-`import c from '@noble/curves'`. Instead, you need to import specific primitives.
-This is done to ensure small size of your apps.
-
-Package consists of two parts:
-
-1. [Implementations](#implementations), utilizing one dependency [noble-hashes](https://github.com/paulmillr/noble-hashes),
-   providing ready-to-use:
-   - NIST curves secp256r1 / p256, secp384r1 / p384, secp521r1 / p521
-   - SECG curve secp256k1
-   - ed25519 / curve25519 / x25519 / ristretto255,
-     edwards448 / curve448 / x448
-     implementing
-     [RFC7748](https://www.rfc-editor.org/rfc/rfc7748) /
-     [RFC8032](https://www.rfc-editor.org/rfc/rfc8032) /
-     [FIPS 186-5](https://csrc.nist.gov/publications/detail/fips/186/5/final) /
-     [ZIP215](https://zips.z.cash/zip-0215) standards
-   - pairing-friendly curves bls12-381, bn254
-   - [pasta](https://electriccoin.co/blog/the-pasta-curves-for-halo-2-and-beyond/) curves
-2. [Abstract](#abstract-api), zero-dependency EC algorithms
+- [Implementations](#implementations)
+  - [ECDSA signature scheme](#ecdsa-signature-scheme)
+  - [ECDSA public key recovery & extra entropy](#ecdsa-public-key-recovery--extra-entropy)
+  - [ECDH (Elliptic Curve Diffie-Hellman)](#ecdh-elliptic-curve-diffie-hellman)
+  - [Schnorr signatures over secp256k1, BIP340](#schnorr-signatures-over-secp256k1-bip340)
+  - [ed25519, X25519, ristretto255](#ed25519-x25519-ristretto255)
+  - [ed448, X448, decaf448](#ed448-x448-decaf448)
+  - [bls12-381](#bls12-381)
+  - [All available imports](#all-available-imports)
+  - [Accessing a curve's variables](#accessing-a-curves-variables)
+- [Abstract API](#abstract-api)
+  - [abstract/weierstrass: Short Weierstrass curve](#abstractweierstrass-short-weierstrass-curve)
+  - [abstract/edwards: Twisted Edwards curve](#abstractedwards-twisted-edwards-curve)
+  - [abstract/montgomery: Montgomery curve](#abstractmontgomery-montgomery-curve)
+  - [abstract/bls: Barreto-Lynn-Scott curves](#abstractbls-barreto-lynn-scott-curves)
+  - [abstract/hash-to-curve: Hashing strings to curve points](#abstracthash-to-curve-hashing-strings-to-curve-points)
+  - [abstract/poseidon: Poseidon hash](#abstractposeidon-poseidon-hash)
+  - [abstract/modular: Modular arithmetics utilities](#abstractmodular-modular-arithmetics-utilities)
+    - [Creating private keys from hashes](#creating-private-keys-from-hashes)
+  - [abstract/utils: Useful utilities](#abstractutils-useful-utilities)
+- [Security](#security)
+- [Speed](#speed)
+- [Contributing & testing](#contributing--testing)
+- [Upgrading](#upgrading)
+- [Resources](#resources)
+  - [Demos](#demos)
+  - [Projects using curves](#projects-using-curves)
+- [License](#license)

 ### Implementations

-Each curve can be used in the following way:
+Implementations are utilizing [noble-hashes](https://github.com/paulmillr/noble-hashes).
+[Abstract API](#abstract-api) doesn't depend on them: you can use a different hashing library.
+
+#### ECDSA signature scheme
+
+Generic example that works for all curves, shown for secp256k1:

 ```ts
+// import * from '@noble/curves'; // Error: use sub-imports, to ensure small app size
 import { secp256k1 } from '@noble/curves/secp256k1'; // ESM and Common.js
 // import { secp256k1 } from 'npm:@noble/curves@1.2.0/secp256k1'; // Deno
 const priv = secp256k1.utils.randomPrivateKey();
 const pub = secp256k1.getPublicKey(priv);
-const msg = new Uint8Array(32).fill(1);
-const sig = secp256k1.sign(msg, priv);
+const msg = new Uint8Array(32).fill(1); // message hash (not message) in ecdsa
+const sig = secp256k1.sign(msg, priv); // `{prehash: true}` option is available
 const isValid = secp256k1.verify(sig, msg, pub) === true;

 // hex strings are also supported besides Uint8Arrays:
@@ -79,33 +89,25 @@ const privHex = '46c930bc7bb4db7f55da20798697421b98c4175a52c630294d75a84b9c12623
 const pub2 = secp256k1.getPublicKey(privHex);
 ```

-All curves:
-
-```typescript
-import { secp256k1, schnorr } 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 { bls12_381 } from '@noble/curves/bls12-381';
-import { bn254 } from '@noble/curves/bn254';
-import { jubjub } from '@noble/curves/jubjub';
-```
-
-Recovering public keys from weierstrass ECDSA signatures; using ECDH:
+#### ECDSA public key recovery & extra entropy

 ```ts
+sig.recoverPublicKey(msg).toRawBytes(); // === pub; // public key recovery
+
 // extraEntropy https://moderncrypto.org/mail-archive/curves/2017/000925.html
 const sigImprovedSecurity = secp256k1.sign(msg, priv, { extraEntropy: true });
-sig.recoverPublicKey(msg) === pub; // public key recovery
-const someonesPub = secp256k1.getPublicKey(secp256k1.utils.randomPrivateKey());
-const shared = secp256k1.getSharedSecret(priv, someonesPub); // ECDH
 ```

-Schnorr signatures over secp256k1 following
-[BIP340](https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki):
+#### ECDH (Elliptic Curve Diffie-Hellman)
+
+```ts
+// 1. The output includes parity byte. Strip it using shared.slice(1)
+// 2. The output is not hashed. More secure way is sha256(shared) or hkdf(shared)
+const someonesPub = secp256k1.getPublicKey(secp256k1.utils.randomPrivateKey());
+const shared = secp256k1.getSharedSecret(priv, someonesPub);
+```
+
+#### Schnorr signatures over secp256k1 (BIP340)

 ```ts
 import { schnorr } from '@noble/curves/secp256k1';
@@ -116,12 +118,7 @@ const sig = schnorr.sign(msg, priv);
 const isValid = schnorr.verify(sig, msg, pub);
 ```

-ed25519 module has ed25519ctx / ed25519ph variants,
-x25519 ECDH and [ristretto255](https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-ristretto255-decaf448).
-
-Default `verify` behavior follows [ZIP215](https://zips.z.cash/zip-0215) and
-[can be used in consensus-critical applications](https://hdevalence.ca/blog/2020-10-04-its-25519am).
-`zip215: false` option switches verification criteria to RFC8032 / FIPS 186-5.
+#### ed25519, X25519, ristretto255

 ```ts
 import { ed25519 } from '@noble/curves/ed25519';
@@ -131,7 +128,18 @@ const msg = new TextEncoder().encode('hello');
 const sig = ed25519.sign(msg, priv);
 ed25519.verify(sig, msg, pub); // Default mode: follows ZIP215
 ed25519.verify(sig, msg, pub, { zip215: false }); // RFC8032 / FIPS 186-5
+```

+Default `verify` behavior follows [ZIP215](https://zips.z.cash/zip-0215) and
+[can be used in consensus-critical applications](https://hdevalence.ca/blog/2020-10-04-its-25519am).
+It has SUF-CMA (strong unforgeability under chosen message attacks).
+`zip215: false` option switches verification criteria to strict
+[RFC8032](https://www.rfc-editor.org/rfc/rfc8032) / [FIPS 186-5](https://csrc.nist.gov/publications/detail/fips/186/5/final)
+and additionally provides non-repudiation with SBS [(Strongly Binding Signatures)](https://eprint.iacr.org/2020/1244).
+
+X25519 follows [RFC7748](https://www.rfc-editor.org/rfc/rfc7748).
+
+```ts
 // Variants from RFC8032: with context, prehashed
 import { ed25519ctx, ed25519ph } from '@noble/curves/ed25519';

@@ -141,31 +149,119 @@ const priv = 'a546e36bf0527c9d3b16154b82465edd62144c0ac1fc5a18506a2244ba449ac4';
 const pub = 'e6db6867583030db3594c1a424b15f7c726624ec26b3353b10a903a6d0ab1c4c';
 x25519.getSharedSecret(priv, pub) === x25519.scalarMult(priv, pub); // aliases
 x25519.getPublicKey(priv) === x25519.scalarMultBase(priv);
+x25519.getPublicKey(x25519.utils.randomPrivateKey());

-// hash-to-curve
-import { hashToCurve, encodeToCurve } from '@noble/curves/ed25519';
+// ed25519 => x25519 conversion
+import { edwardsToMontgomeryPub, edwardsToMontgomeryPriv } from '@noble/curves/ed25519';
+edwardsToMontgomeryPub(ed25519.getPublicKey(ed25519.utils.randomPrivateKey()));
+edwardsToMontgomeryPriv(ed25519.utils.randomPrivateKey());
+```
+
+ristretto255 follows [irtf draft](https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-ristretto255-decaf448).
+
+```ts
+// hash-to-curve, ristretto255
+import { utf8ToBytes } from '@noble/hashes/utils';
+import { sha512 } from '@noble/hashes/sha512';
+import {
+  hashToCurve,
+  encodeToCurve,
+  RistrettoPoint,
+  hashToRistretto255,
+} from '@noble/curves/ed25519';
+
+const msg = utf8ToBytes('Ristretto is traditionally a short shot of espresso coffee');
+hashToCurve(msg);

-import { RistrettoPoint } from '@noble/curves/ed25519';
 const rp = RistrettoPoint.fromHex(
  '6a493210f7499cd17fecb510ae0cea23a110e8d5b901f8acadd3095c73a3b919'
 );
-RistrettoPoint.hashToCurve('Ristretto is traditionally a short shot of espresso coffee');
-// also has add(), equals(), multiply(), toRawBytes() methods
+RistrettoPoint.BASE.multiply(2n).add(rp).subtract(RistrettoPoint.BASE).toRawBytes();
+RistrettoPoint.ZERO.equals(dp) === false;
+// pre-hashed hash-to-curve
+RistrettoPoint.hashToCurve(sha512(msg));
+// full hash-to-curve including domain separation tag
+hashToRistretto255(msg, { DST: 'ristretto255_XMD:SHA-512_R255MAP_RO_' });
 ```

-ed448 is similar:
+#### ed448, X448, decaf448

 ```ts
+import { ed448 } from '@noble/curves/ed448';
+const priv = ed448.utils.randomPrivateKey();
+const pub = ed448.getPublicKey(priv);
+const msg = new TextEncoder().encode('whatsup');
+const sig = ed448.sign(msg, priv);
+ed448.verify(sig, msg, pub);
+
+// Variants from RFC8032: prehashed
+import { ed448ph } from '@noble/curves/ed448';
+```
+
+ECDH using Curve448 aka X448, follows [RFC7748](https://www.rfc-editor.org/rfc/rfc7748).
+
+```ts
+import { x448 } from '@noble/curves/ed448';
+x448.getSharedSecret(priv, pub) === x448.scalarMult(priv, pub); // aliases
+x448.getPublicKey(priv) === x448.scalarMultBase(priv);
+
+// ed448 => x448 conversion
+import { edwardsToMontgomeryPub } from '@noble/curves/ed448';
+edwardsToMontgomeryPub(ed448.getPublicKey(ed448.utils.randomPrivateKey()));
+```
+
+decaf448 follows [irtf draft](https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-ristretto255-decaf448).
+
+```ts
+import { utf8ToBytes } from '@noble/hashes/utils';
+import { shake256 } from '@noble/hashes/sha3';
+import { hashToCurve, encodeToCurve, DecafPoint, hashToDecaf448 } from '@noble/curves/ed448';
+
+const msg = utf8ToBytes('Ristretto is traditionally a short shot of espresso coffee');
+hashToCurve(msg);
+
+const dp = DecafPoint.fromHex(
+  'c898eb4f87f97c564c6fd61fc7e49689314a1f818ec85eeb3bd5514ac816d38778f69ef347a89fca817e66defdedce178c7cc709b2116e75'
+);
+DecafPoint.BASE.multiply(2n).add(dp).subtract(DecafPoint.BASE).toRawBytes();
+DecafPoint.ZERO.equals(dp) === false;
+// pre-hashed hash-to-curve
+DecafPoint.hashToCurve(shake256(msg, { dkLen: 112 }));
+// full hash-to-curve including domain separation tag
+hashToDecaf448(msg, { DST: 'decaf448_XOF:SHAKE256_D448MAP_RO_' });
+```
+
+Same RFC7748 / RFC8032 / IRTF draft are followed.
+
+#### bls12-381
+
+See [abstract/bls](#abstractbls-barreto-lynn-scott-curves).
+
+#### All available imports
+
+```typescript
+import { secp256k1, schnorr } from '@noble/curves/secp256k1';
+import { ed25519, ed25519ph, ed25519ctx, x25519, RistrettoPoint } from '@noble/curves/ed25519';
 import { ed448, ed448ph, ed448ctx, x448 } from '@noble/curves/ed448';
-import { hashToCurve, encodeToCurve } from '@noble/curves/ed448';
-ed448.getPublicKey(ed448.utils.randomPrivateKey());
+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 { bls12_381 } from '@noble/curves/bls12-381';
+import { bn254 } from '@noble/curves/bn254'; // also known as alt_bn128
+import { jubjub } from '@noble/curves/jubjub';
+import { bytesToHex, hexToBytes, concatBytes, utf8ToBytes } from '@noble/curves/abstract/utils';
 ```

-Every curve has `CURVE` object that contains its parameters, field, and others:
+#### Accessing a curve's variables

 ```ts
-import { secp256k1 } from '@noble/curves/secp256k1'; // ESM and Common.js
-console.log(secp256k1.CURVE.p, secp256k1.CURVE.n, secp256k1.CURVE.a, secp256k1.CURVE.b);
+import { secp256k1 } from '@noble/curves/secp256k1';
+// Every curve has `CURVE` object that contains its parameters, field, and others
+console.log(secp256k1.CURVE.p); // field modulus
+console.log(secp256k1.CURVE.n); // curve order
+console.log(secp256k1.CURVE.a, secp256k1.CURVE.b); // equation params
+console.log(secp256k1.CURVE.Gx, secp256k1.CURVE.Gy); // base point coordinates
 ```

 ## Abstract API
@@ -178,17 +274,6 @@ Precomputes are enabled for weierstrass and edwards BASE points of a curve. You
 could precompute any other point (e.g. for ECDH) using `utils.precompute()`
 method: check out examples.

-There are following zero-dependency algorithms:
-
- [abstract/weierstrass: Short Weierstrass curve](#abstractweierstrass-short-weierstrass-curve)
- [abstract/edwards: Twisted Edwards curve](#abstractedwards-twisted-edwards-curve)
- [abstract/montgomery: Montgomery curve](#abstractmontgomery-montgomery-curve)
- [abstract/bls: Barreto-Lynn-Scott curves](#abstractbls-barreto-lynn-scott-curves)
- [abstract/hash-to-curve: Hashing strings to curve points](#abstracthash-to-curve-hashing-strings-to-curve-points)
- [abstract/poseidon: Poseidon hash](#abstractposeidon-poseidon-hash)
- [abstract/modular: Modular arithmetics utilities](#abstractmodular-modular-arithmetics-utilities)
- [abstract/utils: General utilities](#abstractutils-general-utilities)
-
 ### abstract/weierstrass: Short Weierstrass curve

 ```ts
@@ -212,7 +297,7 @@ const secq256k1 = weierstrass({
  randomBytes,
 });

-// Replace weierstrass with weierstrassPoints if you don't need ECDSA, hash, hmac, randomBytes
+// Replace weierstrass() with weierstrassPoints() if you don't need ECDSA, hash, hmac, randomBytes
 ```

 Short Weierstrass curve's formula is `y² = x³ + ax + b`. `weierstrass`
@@ -233,6 +318,11 @@ type CHash = {
 };
 ```

+**Message hash** is expected instead of message itself:
+
+- `sign(msgHash, privKey)` is default behavior, assuming you pre-hash msg with sha2, or other hash
+- `sign(msg, privKey, {prehash: true})` option can be used if you want to pass the message itself
+
 **Weierstrass points:**

 1. Exported as `ProjectivePoint`
@@ -328,6 +418,7 @@ More examples:
 const priv = secq256k1.utils.randomPrivateKey();
 secq256k1.getPublicKey(priv); // Convert private key to public.
 const sig = secq256k1.sign(msg, priv); // Sign msg with private key.
+const sig2 = secq256k1.sign(msg, priv, { prehash: true }); // hash(msg)
 secq256k1.verify(sig, msg, priv); // Verify if sig is correct.

 const Point = secq256k1.ProjectivePoint;
@@ -475,6 +566,8 @@ use aggregated, batch-verifiable
 [threshold signatures](https://medium.com/snigirev.stepan/bls-signatures-better-than-schnorr-5a7fe30ea716),
 using Boneh-Lynn-Shacham signature scheme.

+The module doesn't expose `CURVE` property: use `G1.CURVE`, `G2.CURVE` instead.
+
 Main methods and properties are:

 - `getPublicKey(privateKey)`
@@ -518,7 +611,12 @@ const aggSignature3 = bls.aggregateSignatures(signatures3);
 const isValid3 = bls.verifyBatch(aggSignature3, messages, publicKeys);
 console.log({ publicKeys, signatures3, aggSignature3, isValid3 });

-// bls.pairing(PointG1, PointG2) // pairings
+// Pairings, with and without final exponentiation
+// bls.pairing(PointG1, PointG2);
+// bls.pairing(PointG1, PointG2, false);
+// bls.fields.Fp12.finalExponentiate(bls.fields.Fp12.mul(eGS, ePHm));
+
+// Others
 // bls.G1.ProjectivePoint.BASE, bls.G2.ProjectivePoint.BASE
 // bls.fields.Fp, bls.fields.Fp2, bls.fields.Fp12, bls.fields.Fr

@@ -577,7 +675,7 @@ utils: {

 ### abstract/hash-to-curve: Hashing strings to curve points

-The module allows to hash arbitrary strings to elliptic curve points. Implements [hash-to-curve v16](https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16).
+The module allows to hash arbitrary strings to elliptic curve points. Implements [RFC 9380](https://www.rfc-editor.org/rfc/rfc9380).

 Every curve has exported `hashToCurve` and `encodeToCurve` methods. You should always prefer `hashToCurve` for security:

@@ -593,19 +691,17 @@ bls12_381.G1.hashToCurve(randomBytes(), { DST: 'another' });
 bls12_381.G2.hashToCurve(randomBytes(), { DST: 'custom' });
 ```

-If you need low-level methods from spec:
-
-`expand_message_xmd` [(spec)](https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-5.4.1) produces a uniformly random byte string using a cryptographic hash function H that outputs b bits.
-
-Hash must conform to `CHash` interface (see [weierstrass section](#abstractweierstrass-short-weierstrass-curve)).
+Low-level methods from the spec:

 ```ts
+// produces a uniformly random byte string using a cryptographic hash function H that outputs b bits.
 function expand_message_xmd(
  msg: Uint8Array,
  DST: Uint8Array,
  lenInBytes: number,
-  H: CHash
+  H: CHash // For CHash see abstract/weierstrass docs section
 ): Uint8Array;
+// produces a uniformly random byte string using an extendable-output function (XOF) H.
 function expand_message_xof(
  msg: Uint8Array,
  DST: Uint8Array,
@@ -613,13 +709,9 @@ function expand_message_xof(
  k: number,
  H: CHash
 ): Uint8Array;
-```
+// Hashes arbitrary-length byte strings to a list of one or more elements of a finite field F
+function hash_to_field(msg: Uint8Array, count: number, options: Opts): bigint[][];

-`hash_to_field(msg, count, options)`
-[(spec)](https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-5.3)
-hashes arbitrary-length byte strings to a list of one or more elements of a finite field F.
-
-```ts
 /**
 * * `DST` is a domain separation tag, defined in section 2.2.5
 * * `p` characteristic of F, where F is a finite field of characteristic p and order q = p^m
@@ -630,23 +722,13 @@ hashes arbitrary-length byte strings to a list of one or more elements of a fini
 */
 type UnicodeOrBytes = string | Uint8Array;
 type Opts = {
-    DST: UnicodeOrBytes;
-    p: bigint;
-    m: number;
-    k: number;
-    expand?: 'xmd' | 'xof';
-    hash: CHash;
+  DST: UnicodeOrBytes;
+  p: bigint;
+  m: number;
+  k: number;
+  expand?: 'xmd' | 'xof';
+  hash: CHash;
 };
-
-/**
- * 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
- * @param msg a byte string containing the message to hash
- * @param count the number of elements of F to output
- * @param options `{DST: string, p: bigint, m: number, k: number, expand: 'xmd' | 'xof', hash: H}`, see above
- * @returns [u_0, ..., u_(count - 1)], a list of field elements.
- */
-function hash_to_field(msg: Uint8Array, count: number, options: Opts): bigint[][];
 ```

 ### abstract/poseidon: Poseidon hash
@@ -689,30 +771,40 @@ mod.invert(17n, 10n); // invert(17) mod 10; modular multiplicative inverse
 mod.invertBatch([1n, 2n, 4n], 21n); // => [1n, 11n, 16n] in one inversion
 ```

+Field operations are not constant-time: they are using JS bigints, see [security](#security).
+The fact is mostly irrelevant, but the important method to keep in mind is `pow`,
+which may leak exponent bits, when used naïvely.
+
+`mod.Field` is always **field over prime**. Non-prime fields aren't supported for now.
+We don't test for prime-ness for speed and because algorithms are probabilistic anyway.
+Initializing a non-prime field could make your app suspectible to
+DoS (infilite loop) on Tonelli-Shanks square root calculation.
+
+Unlike `mod.invert`, `mod.invertBatch` won't throw on `0`: make sure to throw an error yourself.
+
 #### Creating private keys from hashes

-Suppose you have `sha256(something)` (e.g. from HMAC) and you want to make a private key from it.
-Even though p256 or secp256k1 may have 32-byte private keys,
-and sha256 output is also 32-byte, you can't just use it and reduce it modulo `CURVE.n`.
+You can't simply make a 32-byte private key from a 32-byte hash.
+Doing so will make the key [biased](https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/).

-Doing so will make the result key [biased](https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/).
+To make the bias negligible, we follow [FIPS 186-5 A.2](https://csrc.nist.gov/publications/detail/fips/186/5/final)
+and [RFC 9380](https://www.rfc-editor.org/rfc/rfc9380#section-5.2).
+This means, for 32-byte key, we would need 48-byte hash to get 2^-128 bias, which matches curve security level.

-To avoid the bias, we implement FIPS 186 B.4.1, which allows to take arbitrary
-byte array and produce valid scalars / private keys with bias being neglible.
-
-Use [hash-to-curve](#abstracthash-to-curve-hashing-strings-to-curve-points) if you need
-hashing to **public keys**; the function in the module instead operates on **private keys**.
+`hashToPrivateScalar()` that hashes to **private key** was created for this purpose.
+Use [abstract/hash-to-curve](#abstracthash-to-curve-hashing-strings-to-curve-points)
+if you need to hash to **public key**.

 ```ts
 import { p256 } from '@noble/curves/p256';
 import { sha256 } from '@noble/hashes/sha256';
 import { hkdf } from '@noble/hashes/hkdf';
 const someKey = new Uint8Array(32).fill(2); // Needs to actually be random, not .fill(2)
-const derived = hkdf(sha256, someKey, undefined, 'application', 40); // 40 bytes
+const derived = hkdf(sha256, someKey, undefined, 'application', 48); // 48 bytes for 32-byte priv
 const validPrivateKey = mod.hashToPrivateScalar(derived, p256.CURVE.n);
 ```

-### abstract/utils: General utilities
+### abstract/utils: Useful utilities

 ```ts
 import * as utils from '@noble/curves/abstract/utils';
@@ -734,96 +826,122 @@ utils.equalBytes(Uint8Array.from([0xde]), Uint8Array.from([0xde]));

 ## Security

-1. The library has been audited during Jan-Feb 2023 by an independent security firm [Trail of Bits](https://www.trailofbits.com):
-[PDF](https://github.com/trailofbits/publications/blob/master/reviews/2023-01-ryanshea-noblecurveslibrary-securityreview.pdf).
-The audit has been funded by Ryan Shea. Audit scope was abstract modules `curve`, `hash-to-curve`, `modular`, `poseidon`, `utils`, `weierstrass`, and top-level modules `_shortw_utils` and `secp256k1`. See [changes since audit](https://github.com/paulmillr/noble-curves/compare/0.7.3..main).
-2. The library has been fuzzed by [Guido Vranken's cryptofuzz](https://github.com/guidovranken/cryptofuzz). You can run the fuzzer by yourself to check it.
-3. [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.
+1. The library has been independently audited:

-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. As for devDependencies used by the library:
+- in Feb 2023 by [Trail of Bits](https://www.trailofbits.com):
+  [PDF](https://github.com/trailofbits/publications/blob/master/reviews/2023-01-ryanshea-noblecurveslibrary-securityreview.pdf).
+  The audit has been funded by [Ryan Shea](https://www.shea.io).
+  Audit scope was abstract modules `curve`, `hash-to-curve`, `modular`, `poseidon`, `utils`, `weierstrass`,
+  and top-level modules `_shortw_utils` and `secp256k1`.
+  See [changes since v0.7.3 audit](https://github.com/paulmillr/noble-curves/compare/0.7.3..main).

- `@scure` base, bip32, bip39 (used in tests), micro-bmark (benchmark), micro-should (testing) are developed by us
-  and follow the same practices such as: minimal library size, auditability, signed releases
- prettier (linter), fast-check (property-based testing),
-  typescript versions are locked and rarely updated. Every update is checked with `npm-diff`.
+2. The library has been fuzzed by [Guido Vranken's cryptofuzz](https://github.com/guidovranken/cryptofuzz).
+   You can run the fuzzer by yourself to check it.
+3. [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.
+As for devDependencies used by the library:
+
+- `@scure` base, bip32, bip39 (used in tests), micro-bmark (benchmark), micro-should (testing)
+  are developed by us and follow the same practices such as: minimal library size, auditability,
+  signed releases
+- prettier (linter), fast-check (property-based testing), typescript versions
+  are locked and rarely updated. Every update is checked with `npm-diff`.
  The packages are big, which makes it hard to audit their source code thoroughly and fully.
 - They are only used if you clone the git repo and want to add some feature to it. End-users won't use them.

+As for key generation, we're deferring to built-in
+[crypto.getRandomValues](https://developer.mozilla.org/en-US/docs/Web/API/Crypto/getRandomValues)
+which is considered cryptographically secure (CSPRNG).
+
 ## Speed

-Benchmark results on Apple M2 with node v19:
+Benchmark results on Apple M2 with node v20:

 ```
 secp256k1
-init x 58 ops/sec @ 17ms/op
-getPublicKey x 5,640 ops/sec @ 177μs/op
-sign x 4,471 ops/sec @ 223μs/op
-verify x 780 ops/sec @ 1ms/op
-getSharedSecret x 465 ops/sec @ 2ms/op
-recoverPublicKey x 740 ops/sec @ 1ms/op
-schnorr.sign x 597 ops/sec @ 1ms/op
-schnorr.verify x 775 ops/sec @ 1ms/op
+init x 68 ops/sec @ 14ms/op
+getPublicKey x 6,750 ops/sec @ 148μs/op
+sign x 5,206 ops/sec @ 192μs/op
+verify x 880 ops/sec @ 1ms/op
+getSharedSecret x 536 ops/sec @ 1ms/op
+recoverPublicKey x 852 ops/sec @ 1ms/op
+schnorr.sign x 685 ops/sec @ 1ms/op
+schnorr.verify x 908 ops/sec @ 1ms/op

-P256
-init x 31 ops/sec @ 31ms/op
-getPublicKey x 5,607 ops/sec @ 178μs/op
-sign x 4,583 ops/sec @ 218μs/op
-verify x 540 ops/sec @ 1ms/op
+p256
+init x 38 ops/sec @ 26ms/op
+getPublicKey x 6,530 ops/sec @ 153μs/op
+sign x 5,074 ops/sec @ 197μs/op
+verify x 626 ops/sec @ 1ms/op

-P384
-init x 15 ops/sec @ 63ms/op
-getPublicKey x 2,622 ops/sec @ 381μs/op
-sign x 2,106 ops/sec @ 474μs/op
-verify x 222 ops/sec @ 4ms/op
+p384
+init x 17 ops/sec @ 57ms/op
+getPublicKey x 2,883 ops/sec @ 346μs/op
+sign x 2,358 ops/sec @ 424μs/op
+verify x 245 ops/sec @ 4ms/op

-P521
-init x 8 ops/sec @ 119ms/op
-getPublicKey x 1,371 ops/sec @ 729μs/op
-sign x 1,164 ops/sec @ 858μs/op
-verify x 118 ops/sec @ 8ms/op
+p521
+init x 9 ops/sec @ 109ms/op
+getPublicKey x 1,516 ops/sec @ 659μs/op
+sign x 1,271 ops/sec @ 786μs/op
+verify x 123 ops/sec @ 8ms/op

 ed25519
-init x 47 ops/sec @ 20ms/op
-getPublicKey x 9,414 ops/sec @ 106μs/op
-sign x 4,516 ops/sec @ 221μs/op
-verify x 912 ops/sec @ 1ms/op
+init x 54 ops/sec @ 18ms/op
+getPublicKey x 10,269 ops/sec @ 97μs/op
+sign x 5,110 ops/sec @ 195μs/op
+verify x 1,049 ops/sec @ 952μs/op

 ed448
-init x 17 ops/sec @ 56ms/op
-getPublicKey x 3,363 ops/sec @ 297μs/op
-sign x 1,615 ops/sec @ 619μs/op
-verify x 319 ops/sec @ 3ms/op
+init x 19 ops/sec @ 51ms/op
+getPublicKey x 3,775 ops/sec @ 264μs/op
+sign x 1,771 ops/sec @ 564μs/op
+verify x 351 ops/sec @ 2ms/op

 ecdh
-├─x25519 x 1,337 ops/sec @ 747μs/op
-├─secp256k1 x 461 ops/sec @ 2ms/op
-├─P256 x 441 ops/sec @ 2ms/op
-├─P384 x 179 ops/sec @ 5ms/op
-├─P521 x 93 ops/sec @ 10ms/op
-└─x448 x 496 ops/sec @ 2ms/op
+├─x25519 x 1,466 ops/sec @ 682μs/op
+├─secp256k1 x 539 ops/sec @ 1ms/op
+├─p256 x 511 ops/sec @ 1ms/op
+├─p384 x 199 ops/sec @ 5ms/op
+├─p521 x 103 ops/sec @ 9ms/op
+└─x448 x 548 ops/sec @ 1ms/op

 bls12-381
-init x 32 ops/sec @ 30ms/op
-getPublicKey 1-bit x 858 ops/sec @ 1ms/op
-getPublicKey x 858 ops/sec @ 1ms/op
-sign x 49 ops/sec @ 20ms/op
-verify x 34 ops/sec @ 28ms/op
-pairing x 94 ops/sec @ 10ms/op
-aggregatePublicKeys/8 x 116 ops/sec @ 8ms/op
-aggregatePublicKeys/32 x 31 ops/sec @ 31ms/op
-aggregatePublicKeys/128 x 7 ops/sec @ 125ms/op
-aggregateSignatures/8 x 45 ops/sec @ 22ms/op
-aggregateSignatures/32 x 11 ops/sec @ 84ms/op
-aggregateSignatures/128 x 3 ops/sec @ 332ms/opp
+init x 36 ops/sec @ 27ms/op
+getPublicKey 1-bit x 973 ops/sec @ 1ms/op
+getPublicKey x 970 ops/sec @ 1ms/op
+sign x 55 ops/sec @ 17ms/op
+verify x 39 ops/sec @ 25ms/op
+pairing x 106 ops/sec @ 9ms/op
+aggregatePublicKeys/8 x 129 ops/sec @ 7ms/op
+aggregatePublicKeys/32 x 34 ops/sec @ 28ms/op
+aggregatePublicKeys/128 x 8 ops/sec @ 112ms/op
+aggregatePublicKeys/512 x 2 ops/sec @ 446ms/op
+aggregatePublicKeys/2048 x 0 ops/sec @ 1778ms/op
+aggregateSignatures/8 x 50 ops/sec @ 19ms/op
+aggregateSignatures/32 x 13 ops/sec @ 74ms/op
+aggregateSignatures/128 x 3 ops/sec @ 296ms/op
+aggregateSignatures/512 x 0 ops/sec @ 1180ms/op
+aggregateSignatures/2048 x 0 ops/sec @ 4715ms/op

 hash-to-curve
-hash_to_field x 850,340 ops/sec @ 1μs/op
-secp256k1 x 2,143 ops/sec @ 466μs/op
-P256 x 3,861 ops/sec @ 258μs/op
-P384 x 1,526 ops/sec @ 655μs/op
-P521 x 748 ops/sec @ 1ms/op
-ed25519 x 2,772 ops/sec @ 360μs/op
-ed448 x 1,146 ops/sec @ 871μs/op
+hash_to_field x 91,600 ops/sec @ 10μs/op
+secp256k1 x 2,373 ops/sec @ 421μs/op
+p256 x 4,310 ops/sec @ 231μs/op
+p384 x 1,664 ops/sec @ 600μs/op
+p521 x 807 ops/sec @ 1ms/op
+ed25519 x 3,088 ops/sec @ 323μs/op
+ed448 x 1,247 ops/sec @ 801μs/op
 ```

 ## Contributing & testing
@@ -836,33 +954,37 @@ ed448 x 1,146 ops/sec @ 871μs/op
 ## Upgrading

 Previously, the library was split into single-feature packages
-noble-secp256k1 and noble-ed25519. curves can be thought as a continuation of their
-original work. The libraries now changed their direction towards providing
-minimal 4kb implementations of cryptography and are not as feature-complete.
+[noble-secp256k1](https://github.com/paulmillr/noble-secp256k1),
+[noble-ed25519](https://github.com/paulmillr/noble-ed25519) and
+[noble-bls12-381](https://github.com/paulmillr/noble-bls12-381).

-Upgrading from @noble/secp256k1 2.0 or @noble/ed25519 2.0: no changes, libraries are compatible.
+Curves continue their original work. The single-feature packages changed their
+direction towards providing minimal 4kb implementations of cryptography,
+which means they have less features.

-Upgrading from [@noble/secp256k1](https://github.com/paulmillr/noble-secp256k1) 1.7:
+Upgrading from noble-secp256k1 2.0 or noble-ed25519 2.0: no changes, libraries are compatible.
+
+Upgrading from noble-secp256k1 1.7:

 - `getPublicKey`
-    - now produce 33-byte compressed signatures by default
-    - to use old behavior, which produced 65-byte uncompressed keys, set
-      argument `isCompressed` to `false`: `getPublicKey(priv, false)`
+  - now produce 33-byte compressed signatures by default
+  - to use old behavior, which produced 65-byte uncompressed keys, set
+    argument `isCompressed` to `false`: `getPublicKey(priv, false)`
 - `sign`
-    - is now sync; use `signAsync` for async version
-    - now returns `Signature` instance with `{ r, s, recovery }` properties
-    - `canonical` option was renamed to `lowS`
-    - `recovered` option has been removed because recovery bit is always returned now
-    - `der` option has been removed. There are 2 options:
-        1. Use compact encoding: `fromCompact`, `toCompactRawBytes`, `toCompactHex`.
-           Compact encoding is simply a concatenation of 32-byte r and 32-byte s.
-        2. If you must use DER encoding, switch to noble-curves (see above).
+  - is now sync; use `signAsync` for async version
+  - now returns `Signature` instance with `{ r, s, recovery }` properties
+  - `canonical` option was renamed to `lowS`
+  - `recovered` option has been removed because recovery bit is always returned now
+  - `der` option has been removed. There are 2 options:
+    1. Use compact encoding: `fromCompact`, `toCompactRawBytes`, `toCompactHex`.
+       Compact encoding is simply a concatenation of 32-byte r and 32-byte s.
+    2. If you must use DER encoding, switch to noble-curves (see above).
 - `verify`
-    - `strict` option was renamed to `lowS`
+  - `strict` option was renamed to `lowS`
 - `getSharedSecret`
-    - now produce 33-byte compressed signatures by default
-    - to use old behavior, which produced 65-byte uncompressed keys, set
-      argument `isCompressed` to `false`: `getSharedSecret(a, b, false)`
+  - now produce 33-byte compressed signatures by default
+  - to use old behavior, which produced 65-byte uncompressed keys, set
+    argument `isCompressed` to `false`: `getSharedSecret(a, b, false)`
 - `recoverPublicKey(msg, sig, rec)` was changed to `sig.recoverPublicKey(msg)`
 - `number` type for private keys have been removed: use `bigint` instead
 - `Point` (2d xy) has been changed to `ProjectivePoint` (3d xyz)
@@ -878,40 +1000,70 @@ Upgrading from [@noble/ed25519](https://github.com/paulmillr/noble-ed25519) 1.7:
 - `utils` were split into `utils` (same api as in noble-curves) and
  `etc` (`sha512Sync` and others)
 - `getSharedSecret` was moved to `x25519` module
+- `toX25519` has been moved to `edwardsToMontgomeryPub` and `edwardsToMontgomeryPriv` methods

 Upgrading from [@noble/bls12-381](https://github.com/paulmillr/noble-bls12-381):

 - Methods and classes were renamed:
-    - PointG1 -> G1.Point, PointG2 -> G2.Point
-    - PointG2.fromSignature -> Signature.decode, PointG2.toSignature ->  Signature.encode
+  - PointG1 -> G1.Point, PointG2 -> G2.Point
+  - PointG2.fromSignature -> Signature.decode, PointG2.toSignature -> Signature.encode
 - Fp2 ORDER was corrected

 ## Resources

-Useful articles about the library or its primitives:
-
 - [Learning fast elliptic-curve cryptography](https://paulmillr.com/posts/noble-secp256k1-fast-ecc/)
+- EdDSA
+  - [A Deep dive into Ed25519 Signatures](https://cendyne.dev/posts/2022-03-06-ed25519-signatures.html)
+  - [Ed25519 Deep Dive Addendum](https://cendyne.dev/posts/2022-09-11-ed25519-deep-dive-addendum.html)
+  - [It’s 255:19AM. Do you know what your validation criteria are?](https://hdevalence.ca/blog/2020-10-04-its-25519am)
+  - [Taming the many EdDSAs](https://csrc.nist.gov/csrc/media/Presentations/2023/crclub-2023-03-08/images-media/20230308-crypto-club-slides--taming-the-many-EdDSAs.pdf)
+    that describes concepts of Strong UnForgeability under Chosen Message Attacks and Strongly Binding Signatures
+  - [Cofactor Explained: Clearing Elliptic Curves’ dirty little secret](https://loup-vaillant.fr/tutorials/cofactor)
+  - [Surrounded by Elligators](https://loup-vaillant.fr/articles/implementing-elligator)
 - Pairings and BLS
-    - [BLS12-381 for the rest of us](https://hackmd.io/@benjaminion/bls12-381)
-    - [Key concepts of pairings](https://medium.com/@alonmuroch_65570/bls-signatures-part-2-key-concepts-of-pairings-27a8a9533d0c)
-    - Pairing over bls12-381:
-      [part 1](https://research.nccgroup.com/2020/07/06/pairing-over-bls12-381-part-1-fields/),
-      [part 2](https://research.nccgroup.com/2020/07/13/pairing-over-bls12-381-part-2-curves/),
-      [part 3](https://research.nccgroup.com/2020/08/13/pairing-over-bls12-381-part-3-pairing/)
-    - [Estimating the bit security of pairing-friendly curves](https://research.nccgroup.com/2022/02/03/estimating-the-bit-security-of-pairing-friendly-curves/)
+  - [BLS signatures for busy people](https://gist.github.com/paulmillr/18b802ad219b1aee34d773d08ec26ca2)
+  - [BLS12-381 for the rest of us](https://hackmd.io/@benjaminion/bls12-381)
+  - [Key concepts of pairings](https://medium.com/@alonmuroch_65570/bls-signatures-part-2-key-concepts-of-pairings-27a8a9533d0c)
+  - Pairing over bls12-381:
+    [fields](https://research.nccgroup.com/2020/07/06/pairing-over-bls12-381-part-1-fields/),
+    [curves](https://research.nccgroup.com/2020/07/13/pairing-over-bls12-381-part-2-curves/),
+    [pairings](https://research.nccgroup.com/2020/08/13/pairing-over-bls12-381-part-3-pairing/)
+  - [Estimating the bit security of pairing-friendly curves](https://research.nccgroup.com/2022/02/03/estimating-the-bit-security-of-pairing-friendly-curves/)

-Real-world software that uses curves:
+### Demos

- [Elliptic Curve Calculator](https://paulmillr.com/noble) online demo: add / multiply points, sign messages
- Signers for web3 projects:
-  [btc-signer](https://github.com/paulmillr/scure-btc-signer), [eth-signer](https://github.com/paulmillr/micro-eth-signer),
-  [sol-signer](https://github.com/paulmillr/micro-sol-signer) for Solana
- [scure-bip32](https://github.com/paulmillr/scure-bip32) and separate [bip32](https://github.com/bitcoinjs/bip32) HDkey libraries
+- [Elliptic Curve Calculator](https://paulmillr.com/noble): add / multiply points, sign messages
+- [BLS threshold signatures](https://genthresh.com)
+
+### Projects using curves
+
+- HDkey libraries: [scure-bip32](https://github.com/paulmillr/scure-bip32), [bip32](https://github.com/bitcoinjs/bip32)
+- Social networks: [nostr](https://github.com/nbd-wtf/nostr-tools), [bluesky](https://github.com/bluesky-social/atproto)
+- Ethereum libraries:
+  - [ethereum-cryptography](https://github.com/ethereum/js-ethereum-cryptography)
+  - [micro-eth-signer](https://github.com/paulmillr/micro-eth-signer),
+    [ethers](https://github.com/ethers-io/ethers.js) (old noble),
+    [viem.sh](https://viem.sh),
+    [@ethereumjs](https://github.com/ethereumjs/ethereumjs-monorepo)
+  - [metamask's eth-sig-util](https://github.com/MetaMask/eth-sig-util)
+  - [gridplus lattice sdk](https://github.com/GridPlus/lattice-eth2-utils)
+- Bitcoin libraries:
+  - [scure-btc-signer](https://github.com/paulmillr/scure-btc-signer)
+  - [tapscript](https://github.com/cmdruid/tapscript)
+- Solana libraries: [micro-sol-signer](https://github.com/paulmillr/micro-sol-signer), [solana-web3.js](https://github.com/solana-labs/solana-web3.js)
+- Other web3 stuff:
+  - [scure-starknet](https://github.com/paulmillr/scure-starknet)
+  - [aztec](https://github.com/AztecProtocol/aztec-packages)
+  - [polkadot.js](https://github.com/polkadot-js/common), [drand-client](https://github.com/drand/drand-client), [moneroj](https://github.com/beritani/moneroj), [tronlib](https://github.com/CoinSpace/tronlib)
+- [protonmail](https://github.com/ProtonMail/WebClients) (old noble for now)
+- [did-jwt](https://github.com/decentralized-identity/did-jwt), [hpke-js](https://github.com/dajiaji/hpke-js),
+  [js-libp2p-noise](https://github.com/ChainSafe/js-libp2p-noise)
 - [ed25519-keygen](https://github.com/paulmillr/ed25519-keygen) SSH, PGP, TOR key generation
- [micro-starknet](https://github.com/paulmillr/micro-starknet) stark-friendly elliptic curve algorithms.
- BLS threshold sigs demo [genthresh.com](https://genthresh.com)
- BLS BBS signatures [github.com/Wind4Greg/BBS-Draft-Checks](https://github.com/Wind4Greg/BBS-Draft-Checks) following [draft-irtf-cfrg-bbs-signatures-latest](https://identity.foundation/bbs-signature/draft-irtf-cfrg-bbs-signatures.html)
+- [secp256k1 compatibility layer](https://github.com/ethereum/js-ethereum-cryptography/blob/2.0.0/src/secp256k1-compat.ts)
+  for users who want to switch from secp256k1-node or tiny-secp256k1. Allows to see which methods map to corresponding noble code.
+- [BLS BBS signatures](https://github.com/Wind4Greg/BBS-Draft-Checks) following [draft-irtf-cfrg-bbs-signatures-latest](https://identity.foundation/bbs-signature/draft-irtf-cfrg-bbs-signatures.html)
 - [KZG trusted setup ceremony](https://github.com/dsrvlabs/czg-keremony)
+- See [full list of projects on GitHub](https://github.com/paulmillr/noble-curves/network/dependents).

 ## License

--- a/benchmark/bls.js
+++ b/benchmark/bls.js
@@ -39,6 +39,21 @@ run(async () => {
  await mark('sign', 50, () => bls.sign('09', priv));
  await mark('verify', 50, () => bls.verify(sig, '09', pub));
  await mark('pairing', 100, () => bls.pairing(p1, p2));
+
+  const scalars1 = Array(4096).fill(0).map(i => 2n ** 235n - BigInt(i));
+  const scalars2 = Array(4096).fill(0).map(i => 2n ** 241n + BigInt(i));
+  const points = scalars1.map(s => bls.G1.ProjectivePoint.BASE.multiply(s));
+  await mark('MSM 4096 scalars x points', 1, () => {
+    // naive approach, not using multi-scalar-multiplication
+    let sum = bls.G1.ProjectivePoint.ZERO;
+    for (let i = 0; i < 4096; i++) {
+      const scalar = scalars2[i];
+      const G1 = points[i];
+      const mutliplied = G1.multiplyUnsafe(scalar);
+      sum = sum.add(mutliplied);
+    }
+  });
+
  await mark('aggregatePublicKeys/8', 100, () => bls.aggregatePublicKeys(pubs.slice(0, 8)));
  await mark('aggregatePublicKeys/32', 50, () => bls.aggregatePublicKeys(pub32));
  await mark('aggregatePublicKeys/128', 20, () => bls.aggregatePublicKeys(pub128));
--- a/benchmark/curves.js
+++ b/benchmark/curves.js
@@ -8,7 +8,7 @@ import { ed448 } from '../ed448.js';

 run(async () => {
  const RAM = false
-  for (let kv of Object.entries({ p256, p384, p521, ed25519, ed448 })) {
+  for (let kv of Object.entries({ ed25519, ed448, p256, p384, p521 })) {
    const [name, curve] = kv;
    console.log();
    console.log(`\x1b[36m${name}\x1b[0m`);
--- a/benchmark/decaf448.js
+++ b/benchmark/decaf448.js
@@ -0,0 +1,18 @@
+import { run, mark, utils } from 'micro-bmark';
+import { shake256 } from '@noble/hashes/sha3';
+import * as mod from '../abstract/modular.js';
+import { ed448, DecafPoint } from '../ed448.js';
+
+run(async () => {
+  const RAM = false;
+  if (RAM) utils.logMem();
+  console.log(`\x1b[36mdecaf448\x1b[0m`);
+  const priv = mod.hashToPrivateScalar(shake256(ed448.utils.randomPrivateKey(), { dkLen: 112 }), ed448.CURVE.n);
+  const pub = DecafPoint.BASE.multiply(priv);
+  const encoded = pub.toRawBytes();
+  await mark('add', 1000000, () => pub.add(DecafPoint.BASE));
+  await mark('multiply', 1000, () => DecafPoint.BASE.multiply(priv));
+  await mark('encode', 10000, () => DecafPoint.BASE.toRawBytes());
+  await mark('decode', 10000, () => DecafPoint.fromHex(encoded));
+  if (RAM) utils.logMem();
+});
--- a/benchmark/hash-to-curve.js
+++ b/benchmark/hash-to-curve.js
@@ -8,8 +8,8 @@ import { hashToCurve as secp256k1 } from '../secp256k1.js';
 import { hashToCurve as p256 } from '../p256.js';
 import { hashToCurve as p384 } from '../p384.js';
 import { hashToCurve as p521 } from '../p521.js';
-import { hashToCurve as ed25519 } from '../ed25519.js';
-import { hashToCurve as ed448 } from '../ed448.js';
+import { hashToCurve as ed25519, hash_to_ristretto255 } from '../ed25519.js';
+import { hashToCurve as ed448, hash_to_decaf448 } from '../ed448.js';
 import { utf8ToBytes } from '../abstract/utils.js';

 const N = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141n;
@@ -26,4 +26,7 @@ run(async () => {
  for (let [title, fn] of Object.entries({ secp256k1, p256, p384, p521, ed25519, ed448 })) {
    await mark(`hashToCurve ${title}`, 1000, () => fn(msg));
  }
+
+  await mark('hash_to_ristretto255', 1000, () => hash_to_ristretto255(msg, { DST: 'ristretto255_XMD:SHA-512_R255MAP_RO_' }));
+  await mark('hash_to_decaf448', 1000, () => hash_to_decaf448(msg, { DST: 'decaf448_XOF:SHAKE256_D448MAP_RO_' }));
 });
--- a/benchmark/ristretto255.js
+++ b/benchmark/ristretto255.js
@@ -0,0 +1,18 @@
+import { run, mark, utils } from 'micro-bmark';
+import { sha512 } from '@noble/hashes/sha512';
+import * as mod from '../abstract/modular.js';
+import { ed25519, RistrettoPoint } from '../ed25519.js';
+
+run(async () => {
+  const RAM = false;
+  if (RAM) utils.logMem();
+  console.log(`\x1b[36mristretto255\x1b[0m`);
+  const priv = mod.hashToPrivateScalar(sha512(ed25519.utils.randomPrivateKey()), ed25519.CURVE.n);
+  const pub = RistrettoPoint.BASE.multiply(priv);
+  const encoded = pub.toRawBytes();
+  await mark('add', 1000000, () => pub.add(RistrettoPoint.BASE));
+  await mark('multiply', 10000, () => RistrettoPoint.BASE.multiply(priv));
+  await mark('encode', 10000, () => RistrettoPoint.BASE.toRawBytes());
+  await mark('decode', 10000, () => RistrettoPoint.fromHex(encoded));
+  if (RAM) utils.logMem();
+});
--- a/build/README.md
+++ b/build/README.md
@@ -0,0 +1,7 @@
+# build
+
+The directory is used to build a single file `noble-curves.js` which contains everything.
+
+The output file uses iife wrapper and can be used in browsers as-is.
+
+Don't use it unless you can't use NPM/ESM, which support tree shaking.
--- a/build/input.js
+++ b/build/input.js
@@ -0,0 +1,11 @@
+import { bytesToHex, concatBytes, hexToBytes } from '@noble/curves/abstract/utils';
+
+export { secp256k1 } from '@noble/curves/secp256k1';
+export { ed25519, x25519 } from '@noble/curves/ed25519';
+export { ed448, x448 } from '@noble/curves/ed448';
+export { p256 } from '@noble/curves/p256';
+export { p384 } from '@noble/curves/p384';
+export { p521 } from '@noble/curves/p521';
+export { bls12_381 } from '@noble/curves/bls12-381';
+
+export const utils = { bytesToHex, concatBytes, hexToBytes };
--- a/build/package.json
+++ b/build/package.json
@@ -0,0 +1,18 @@
+{
+  "name": "build",
+  "private": true,
+  "version": "1.0.0",
+  "description": "Used to build a single file",
+  "main": "input.js",
+  "keywords": [],
+  "type": "module",
+  "author": "",
+  "license": "MIT",
+  "devDependencies": {
+    "@noble/curves": "..",
+    "esbuild": "0.18.11"
+  },
+  "scripts": {
+    "build": "npx esbuild --bundle input.js --outfile=noble-curves.js --global-name=nobleCurves"
+  }
+}
--- a/esm/package.json
+++ b/esm/package.json
@@ -1,7 +1,4 @@
 {
  "type": "module",
-  "browser": {
-    "crypto": false,
-    "./crypto": "./esm/crypto.js"
-  }
+  "sideEffects": false
 }
--- a/package-lock.json
+++ b/package-lock.json
@@ -1,21 +1,15 @@
 {
  "name": "@noble/curves",
-  "version": "1.0.0",
+  "version": "1.2.0",
  "lockfileVersion": 3,
  "requires": true,
  "packages": {
    "": {
      "name": "@noble/curves",
-      "version": "1.0.0",
-      "funding": [
-        {
-          "type": "individual",
-          "url": "https://paulmillr.com/funding/"
-        }
-      ],
+      "version": "1.2.0",
      "license": "MIT",
      "dependencies": {
-        "@noble/hashes": "1.3.0"
+        "@noble/hashes": "1.3.2"
      },
      "devDependencies": {
        "fast-check": "3.0.0",
@@ -23,18 +17,21 @@
        "micro-should": "0.4.0",
        "prettier": "2.8.4",
        "typescript": "5.0.2"
+      },
+      "funding": {
+        "url": "https://paulmillr.com/funding/"
      }
    },
    "node_modules/@noble/hashes": {
-      "version": "1.3.0",
-      "resolved": "https://registry.npmjs.org/@noble/hashes/-/hashes-1.3.0.tgz",
-      "integrity": "sha512-ilHEACi9DwqJB0pw7kv+Apvh50jiiSyR/cQ3y4W7lOR5mhvn/50FLUfsnfJz0BDZtl/RR16kXvptiv6q1msYZg==",
-      "funding": [
-        {
-          "type": "individual",
-          "url": "https://paulmillr.com/funding/"
-        }
-      ]
+      "version": "1.3.2",
+      "resolved": "https://registry.npmjs.org/@noble/hashes/-/hashes-1.3.2.tgz",
+      "integrity": "sha512-MVC8EAQp7MvEcm30KWENFjgR+Mkmf+D189XJTkFIlwohU5hcBbn1ZkKq7KVTi2Hme3PMGF390DaL52beVrIihQ==",
+      "engines": {
+        "node": ">= 16"
+      },
+      "funding": {
+        "url": "https://paulmillr.com/funding/"
+      }
    },
    "node_modules/fast-check": {
      "version": "3.0.0",
--- a/package.json
+++ b/package.json
@@ -1,6 +1,6 @@
 {
  "name": "@noble/curves",
-  "version": "1.0.0",
+  "version": "1.2.0",
  "description": "Audited & minimal JS implementation of elliptic curve cryptography",
  "files": [
    "abstract",
@@ -12,7 +12,7 @@
    "*.d.ts.map"
  ],
  "scripts": {
-    "bench": "cd benchmark; node secp256k1.js; node curves.js; node ecdh.js; node hash-to-curve.js; node modular.js; node bls.js",
+    "bench": "cd benchmark; node secp256k1.js; node curves.js; node ecdh.js; node hash-to-curve.js; node modular.js; node bls.js; node ristretto255.js; node decaf448.js",
    "build": "tsc && tsc -p tsconfig.esm.json",
    "build:release": "rollup -c rollup.config.js",
    "build:clean": "rm *.{js,d.ts,d.ts.map,js.map} esm/*.{js,d.ts,d.ts.map,js.map} 2> /dev/null",
@@ -28,7 +28,7 @@
  },
  "license": "MIT",
  "dependencies": {
-    "@noble/hashes": "1.3.0"
+    "@noble/hashes": "1.3.2"
  },
  "devDependencies": {
    "fast-check": "3.0.0",
@@ -37,6 +37,7 @@
    "prettier": "2.8.4",
    "typescript": "5.0.2"
  },
+  "sideEffects": false,
  "main": "index.js",
  "exports": {
    ".": {
@@ -164,6 +165,8 @@
    "secp256k1",
    "ed25519",
    "ed448",
+    "x25519",
+    "ed25519",
    "bls12-381",
    "bn254",
    "pasta",
@@ -174,10 +177,5 @@
    "eddsa",
    "schnorr"
  ],
-  "funding": [
-    {
-      "type": "individual",
-      "url": "https://paulmillr.com/funding/"
-    }
-  ]
+  "funding": "https://paulmillr.com/funding/"
 }
--- a/src/abstract/bls.ts
+++ b/src/abstract/bls.ts
@@ -12,7 +12,7 @@
 * Some projects may prefer to swap this relation, it is not supported for now.
 */
 import { AffinePoint } from './curve.js';
-import { IField, hashToPrivateScalar } from './modular.js';
+import { IField, getMinHashLength, mapHashToField } from './modular.js';
 import { Hex, PrivKey, CHash, bitLen, bitGet, ensureBytes } from './utils.js';
 import * as htf from './hash-to-curve.js';
 import {
@@ -122,7 +122,6 @@ export function bls<Fp2, Fp6, Fp12>(
  // Fields are specific for curve, so for now we'll need to pass them with opts
  const { Fp, Fr, Fp2, Fp6, Fp12 } = CURVE.fields;
  const BLS_X_LEN = bitLen(CURVE.params.x);
-  const groupLen = 32; // TODO: calculate; hardcoded for now

  // Pre-compute coefficients for sparse multiplication
  // Point addition and point double calculations is reused for coefficients
@@ -189,7 +188,8 @@ export function bls<Fp2, Fp6, Fp12>(

  const utils = {
    randomPrivateKey: (): Uint8Array => {
-      return Fr.toBytes(hashToPrivateScalar(CURVE.randomBytes(groupLen + 8), CURVE.params.r));
+      const length = getMinHashLength(Fr.ORDER);
+      return mapHashToField(CURVE.randomBytes(length), Fr.ORDER);
    },
    calcPairingPrecomputes,
  };
--- a/src/abstract/edwards.ts
+++ b/src/abstract/edwards.ts
@@ -75,8 +75,13 @@ export interface ExtPointConstructor extends GroupConstructor<ExtPointType> {
 export type CurveFn = {
  CURVE: ReturnType<typeof validateOpts>;
  getPublicKey: (privateKey: Hex) => Uint8Array;
-  sign: (message: Hex, privateKey: Hex) => Uint8Array;
-  verify: (sig: Hex, message: Hex, publicKey: Hex) => boolean;
+  sign: (message: Hex, privateKey: Hex, options?: { context?: Hex }) => Uint8Array;
+  verify: (
+    sig: Hex,
+    message: Hex,
+    publicKey: Hex,
+    options?: { context?: Hex; zip215: boolean }
+  ) => boolean;
  ExtendedPoint: ExtPointConstructor;
  utils: {
    randomPrivateKey: () => Uint8Array;
@@ -102,7 +107,7 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
    nByteLength,
    h: cofactor,
  } = CURVE;
-  const MASK = _2n ** BigInt(nByteLength * 8);
+  const MASK = _2n << (BigInt(nByteLength * 8) - _1n);
  const modP = Fp.create; // Function overrides

  // sqrt(u/v)
@@ -379,7 +384,10 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
      let { isValid, value: x } = uvRatio(u, v); // √(u/v)
      if (!isValid) throw new Error('Point.fromHex: invalid y coordinate');
      const isXOdd = (x & _1n) === _1n; // There are 2 square roots. Use x_0 bit to select proper
-      const isLastByteOdd = (lastByte & 0x80) !== 0; // if x=0 and x_0 = 1, fail
+      const isLastByteOdd = (lastByte & 0x80) !== 0; // x_0, last bit
+      if (!zip215 && x === _0n && isLastByteOdd)
+        // if x=0 and x_0 = 1, fail
+        throw new Error('Point.fromHex: x=0 and x_0=1');
      if (isLastByteOdd !== isXOdd) x = modP(-x); // if x_0 != x mod 2, set x = p-x
      return Point.fromAffine({ x, y });
    }
@@ -466,6 +474,7 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
    } catch (error) {
      return false;
    }
+    if (!zip215 && A.isSmallOrder()) return false;

    const k = hashDomainToScalar(context, R.toRawBytes(), A.toRawBytes(), msg);
    const RkA = R.add(A.multiplyUnsafe(k));
--- a/src/abstract/hash-to-curve.ts
+++ b/src/abstract/hash-to-curve.ts
@@ -59,7 +59,7 @@ function isNum(item: unknown): void {
 }

 // 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
+// https://www.rfc-editor.org/rfc/rfc9380#section-5.3.1
 export function expand_message_xmd(
  msg: Uint8Array,
  DST: Uint8Array,
@@ -69,7 +69,7 @@ export function expand_message_xmd(
  isBytes(msg);
  isBytes(DST);
  isNum(lenInBytes);
-  // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16#section-5.3.3
+  // https://www.rfc-editor.org/rfc/rfc9380#section-5.3.3
  if (DST.length > 255) DST = H(concatBytes(utf8ToBytes('H2C-OVERSIZE-DST-'), DST));
  const { outputLen: b_in_bytes, blockLen: r_in_bytes } = H;
  const ell = Math.ceil(lenInBytes / b_in_bytes);
@@ -88,6 +88,11 @@ export function expand_message_xmd(
  return pseudo_random_bytes.slice(0, lenInBytes);
 }

+// Produces a uniformly random byte string using an extendable-output function (XOF) H.
+// 1. The collision resistance of H MUST be at least k bits.
+// 2. H MUST be an XOF that has been proved indifferentiable from
+//    a random oracle under a reasonable cryptographic assumption.
+// https://www.rfc-editor.org/rfc/rfc9380#section-5.3.2
 export function expand_message_xof(
  msg: Uint8Array,
  DST: Uint8Array,
@@ -98,7 +103,7 @@ export function expand_message_xof(
  isBytes(msg);
  isBytes(DST);
  isNum(lenInBytes);
-  // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16#section-5.3.3
+  // https://www.rfc-editor.org/rfc/rfc9380#section-5.3.3
  // DST = H('H2C-OVERSIZE-DST-' || a_very_long_DST, Math.ceil((lenInBytes * k) / 8));
  if (DST.length > 255) {
    const dkLen = Math.ceil((2 * k) / 8);
@@ -119,7 +124,7 @@ export function expand_message_xof(

 /**
 * 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
+ * https://www.rfc-editor.org/rfc/rfc9380#section-5.2
 * @param msg a byte string containing the message to hash
 * @param count the number of elements of F to output
 * @param options `{DST: string, p: bigint, m: number, k: number, expand: 'xmd' | 'xof', hash: H}`, see above
@@ -127,7 +132,7 @@ export function expand_message_xof(
 */
 export function hash_to_field(msg: Uint8Array, count: number, options: Opts): bigint[][] {
  validateObject(options, {
-    DST: 'string',
+    DST: 'stringOrUint8Array',
    p: 'bigint',
    m: 'isSafeInteger',
    k: 'isSafeInteger',
@@ -201,8 +206,8 @@ export function createHasher<T>(
 ) {
  if (typeof mapToCurve !== 'function') throw new Error('mapToCurve() must be defined');
  return {
-    // Encodes byte string to elliptic curve
-    // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16#section-3
+    // Encodes byte string to elliptic curve.
+    // hash_to_curve from https://www.rfc-editor.org/rfc/rfc9380#section-3
    hashToCurve(msg: Uint8Array, options?: htfBasicOpts) {
      const u = hash_to_field(msg, 2, { ...def, DST: def.DST, ...options } as Opts);
      const u0 = Point.fromAffine(mapToCurve(u[0]));
@@ -212,7 +217,8 @@ export function createHasher<T>(
      return P;
    },

-    // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16#section-3
+    // Encodes byte string to elliptic curve.
+    // encode_to_curve from https://www.rfc-editor.org/rfc/rfc9380#section-3
    encodeToCurve(msg: Uint8Array, options?: htfBasicOpts) {
      const u = hash_to_field(msg, 1, { ...def, DST: def.encodeDST, ...options } as Opts);
      const P = Point.fromAffine(mapToCurve(u[0])).clearCofactor();
--- a/src/abstract/modular.ts
+++ b/src/abstract/modular.ts
@@ -22,10 +22,10 @@ export function mod(a: bigint, b: bigint): bigint {
  return result >= _0n ? result : b + result;
 }
 /**
- * Efficiently exponentiate num to power and do modular division.
+ * Efficiently raise 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
+ * pow(2n, 6n, 11n) // 64n % 11n == 9n
 */
 // TODO: use field version && remove
 export function pow(num: bigint, power: bigint, modulo: bigint): bigint {
@@ -55,7 +55,7 @@ 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/
+  // Euclidean GCD https://brilliant.org/wiki/extended-euclidean-algorithm/
  // Fermat's little theorem "CT-like" version inv(n) = n^(m-2) mod m is 30x slower.
  let a = mod(number, modulo);
  let b = modulo;
@@ -75,9 +75,14 @@ export function invert(number: bigint, modulo: bigint): bigint {
  return mod(x, modulo);
 }

-// Tonelli-Shanks algorithm
-// Paper 1: https://eprint.iacr.org/2012/685.pdf (page 12)
-// Paper 2: Square Roots from 1; 24, 51, 10 to Dan Shanks
+/**
+ * Tonelli-Shanks square root search algorithm.
+ * 1. https://eprint.iacr.org/2012/685.pdf (page 12)
+ * 2. Square Roots from 1; 24, 51, 10 to Dan Shanks
+ * Will start an infinite loop if field order P is not prime.
+ * @param P field order
+ * @returns function that takes field Fp (created from P) and number n
+ */
 export function tonelliShanks(P: bigint) {
  // Legendre constant: used to calculate Legendre symbol (a | p),
  // which denotes the value of a^((p-1)/2) (mod p).
@@ -198,11 +203,7 @@ export function FpSqrt(P: bigint) {
 // 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
+// Field is not always over prime: for example, Fp2 has ORDER(q)=p^m
 export interface IField<T> {
  ORDER: bigint;
  BYTES: number;
@@ -232,7 +233,8 @@ export interface IField<T> {
  sqrN(num: T): T;

  // Optional
-  // Should be same as sgn0 function in https://datatracker.ietf.org/doc/draft-irtf-cfrg-hash-to-curve/
+  // Should be same as sgn0 function in
+  // [RFC9380](https://www.rfc-editor.org/rfc/rfc9380#section-4.1).
  // NOTE: sgn0 is 'negative in LE', which is same as odd. And negative in LE is kinda strange definition anyway.
  isOdd?(num: T): boolean; // Odd instead of even since we have it for Fp2
  // legendre?(num: T): T;
@@ -264,6 +266,11 @@ export function validateField<T>(field: IField<T>) {
 }

 // Generic field functions
+
+/**
+ * Same as `pow` but for Fp: non-constant-time.
+ * Unsafe in some contexts: uses ladder, so can expose bigint bits.
+ */
 export function FpPow<T>(f: IField<T>, num: T, power: bigint): T {
  // Should have same speed as pow for bigints
  // TODO: benchmark!
@@ -280,7 +287,10 @@ export function FpPow<T>(f: IField<T>, num: T, power: bigint): T {
  return p;
 }

-// 0 is non-invertible: non-batched version will throw on 0
+/**
+ * Efficiently invert an array of Field elements.
+ * `inv(0)` will return `undefined` here: make sure to throw an error.
+ */
 export function FpInvertBatch<T>(f: IField<T>, nums: T[]): T[] {
  const tmp = new Array(nums.length);
  // Walk from first to last, multiply them by each other MOD p
@@ -323,12 +333,12 @@ export function nLength(n: bigint, nBitLength?: number) {

 type FpField = IField<bigint> & Required<Pick<IField<bigint>, 'isOdd'>>;
 /**
- * Initializes a galois field over prime. Non-primes are not supported for now.
- * Do not init in loop: slow. Very fragile: always run a benchmark on change.
- * Major performance gains:
- * a) non-normalized operations like mulN instead of mul
- * b) `Object.freeze`
- * c) Same object shape: never add or remove keys
+ * Initializes a finite field over prime. **Non-primes are not supported.**
+ * Do not init in loop: slow. Very fragile: always run a benchmark on a change.
+ * Major performance optimizations:
+ * * a) denormalized operations like mulN instead of mul
+ * * b) same object shape: never add or remove keys
+ * * c) Object.freeze
 * @param ORDER prime positive bigint
 * @param bitLen how many bits the field consumes
 * @param isLE (def: false) if encoding / decoding should be in little-endian
@@ -340,7 +350,7 @@ export function Field(
  isLE = false,
  redef: Partial<IField<bigint>> = {}
 ): Readonly<FpField> {
-  if (ORDER <= _0n) throw new Error(`Expected Fp ORDER > 0, got ${ORDER}`);
+  if (ORDER <= _0n) throw new Error(`Expected Field ORDER > 0, got ${ORDER}`);
  const { nBitLength: BITS, nByteLength: BYTES } = nLength(ORDER, bitLen);
  if (BYTES > 2048) throw new Error('Field lengths over 2048 bytes are not supported');
  const sqrtP = FpSqrt(ORDER);
@@ -404,13 +414,10 @@ export function FpSqrtEven<T>(Fp: IField<T>, elm: T) {
 }

 /**
- * FIPS 186 B.4.1-compliant "constant-time" private key generation utility.
- * 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.
- * Needs at least 40 bytes of input for 32-byte private key.
- * https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
- * @param hash hash output from SHA3 or a similar function
- * @returns valid private scalar
+ * "Constant-time" private key generation utility.
+ * Same as mapKeyToField, but accepts less bytes (40 instead of 48 for 32-byte field).
+ * Which makes it slightly more biased, less secure.
+ * @deprecated use mapKeyToField instead
 */
 export function hashToPrivateScalar(
  hash: string | Uint8Array,
@@ -425,3 +432,53 @@ export function hashToPrivateScalar(
  const num = isLE ? bytesToNumberLE(hash) : bytesToNumberBE(hash);
  return mod(num, groupOrder - _1n) + _1n;
 }
+
+/**
+ * Returns total number of bytes consumed by the field element.
+ * For example, 32 bytes for usual 256-bit weierstrass curve.
+ * @param fieldOrder number of field elements, usually CURVE.n
+ * @returns byte length of field
+ */
+export function getFieldBytesLength(fieldOrder: bigint): number {
+  if (typeof fieldOrder !== 'bigint') throw new Error('field order must be bigint');
+  const bitLength = fieldOrder.toString(2).length;
+  return Math.ceil(bitLength / 8);
+}
+
+/**
+ * Returns minimal amount of bytes that can be safely reduced
+ * by field order.
+ * Should be 2^-128 for 128-bit curve such as P256.
+ * @param fieldOrder number of field elements, usually CURVE.n
+ * @returns byte length of target hash
+ */
+export function getMinHashLength(fieldOrder: bigint): number {
+  const length = getFieldBytesLength(fieldOrder);
+  return length + Math.ceil(length / 2);
+}
+
+/**
+ * "Constant-time" private key generation utility.
+ * Can take (n + n/2) or more bytes of uniform input e.g. from CSPRNG or KDF
+ * and convert them into private scalar, with the modulo bias being negligible.
+ * Needs at least 48 bytes of input for 32-byte private key.
+ * https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
+ * FIPS 186-5, A.2 https://csrc.nist.gov/publications/detail/fips/186/5/final
+ * RFC 9380, https://www.rfc-editor.org/rfc/rfc9380#section-5
+ * @param hash hash output from SHA3 or a similar function
+ * @param groupOrder size of subgroup - (e.g. secp256k1.CURVE.n)
+ * @param isLE interpret hash bytes as LE num
+ * @returns valid private scalar
+ */
+export function mapHashToField(key: Uint8Array, fieldOrder: bigint, isLE = false): Uint8Array {
+  const len = key.length;
+  const fieldLen = getFieldBytesLength(fieldOrder);
+  const minLen = getMinHashLength(fieldOrder);
+  // No small numbers: need to understand bias story. No huge numbers: easier to detect JS timings.
+  if (len < 16 || len < minLen || len > 1024)
+    throw new Error(`expected ${minLen}-1024 bytes of input, got ${len}`);
+  const num = isLE ? bytesToNumberBE(key) : bytesToNumberLE(key);
+  // `mod(x, 11)` can sometimes produce 0. `mod(x, 10) + 1` is the same, but no 0
+  const reduced = mod(num, fieldOrder - _1n) + _1n;
+  return isLE ? numberToBytesLE(reduced, fieldLen) : numberToBytesBE(reduced, fieldLen);
+}
--- a/src/abstract/poseidon.ts
+++ b/src/abstract/poseidon.ts
@@ -15,34 +15,36 @@ export type PoseidonOpts = {
 };

 export function validateOpts(opts: PoseidonOpts) {
-  const { Fp } = opts;
+  const { Fp, mds, reversePartialPowIdx: rev, roundConstants: rc } = opts;
+  const { roundsFull, roundsPartial, sboxPower, t } = opts;
+
  validateField(Fp);
  for (const i of ['t', 'roundsFull', 'roundsPartial'] as const) {
    if (typeof opts[i] !== 'number' || !Number.isSafeInteger(opts[i]))
      throw new Error(`Poseidon: invalid param ${i}=${opts[i]} (${typeof opts[i]})`);
  }
-  if (opts.reversePartialPowIdx !== undefined && typeof opts.reversePartialPowIdx !== 'boolean')
-    throw new Error(`Poseidon: invalid param reversePartialPowIdx=${opts.reversePartialPowIdx}`);
-  // Default is 5, but by some reasons stark uses 3
-  let sboxPower = opts.sboxPower;
-  if (sboxPower === undefined) sboxPower = 5;
-  if (typeof sboxPower !== 'number' || !Number.isSafeInteger(sboxPower))
-    throw new Error(`Poseidon wrong sboxPower=${sboxPower}`);

-  const _sboxPower = BigInt(sboxPower);
-  let sboxFn = (n: bigint) => FpPow(Fp, n, _sboxPower);
-  // Unwrapped sbox power for common cases (195->142μs)
-  if (sboxPower === 3) sboxFn = (n: bigint) => Fp.mul(Fp.sqrN(n), n);
-  else if (sboxPower === 5) sboxFn = (n: bigint) => Fp.mul(Fp.sqrN(Fp.sqrN(n)), n);
+  // MDS is TxT matrix
+  if (!Array.isArray(mds) || mds.length !== t) throw new Error('Poseidon: wrong MDS matrix');
+  const _mds = mds.map((mdsRow) => {
+    if (!Array.isArray(mdsRow) || mdsRow.length !== t)
+      throw new Error(`Poseidon MDS matrix row: ${mdsRow}`);
+    return mdsRow.map((i) => {
+      if (typeof i !== 'bigint') throw new Error(`Poseidon MDS matrix value=${i}`);
+      return Fp.create(i);
+    });
+  });

-  if (opts.roundsFull % 2 !== 0)
-    throw new Error(`Poseidon roundsFull is not even: ${opts.roundsFull}`);
-  const rounds = opts.roundsFull + opts.roundsPartial;
+  if (rev !== undefined && typeof rev !== 'boolean')
+    throw new Error(`Poseidon: invalid param reversePartialPowIdx=${rev}`);

-  if (!Array.isArray(opts.roundConstants) || opts.roundConstants.length !== rounds)
+  if (roundsFull % 2 !== 0) throw new Error(`Poseidon roundsFull is not even: ${roundsFull}`);
+  const rounds = roundsFull + roundsPartial;
+
+  if (!Array.isArray(rc) || rc.length !== rounds)
    throw new Error('Poseidon: wrong round constants');
-  const roundConstants = opts.roundConstants.map((rc) => {
-    if (!Array.isArray(rc) || rc.length !== opts.t)
+  const roundConstants = rc.map((rc) => {
+    if (!Array.isArray(rc) || rc.length !== t)
      throw new Error(`Poseidon wrong round constants: ${rc}`);
    return rc.map((i) => {
      if (typeof i !== 'bigint' || !Fp.isValid(i))
@@ -50,18 +52,16 @@ export function validateOpts(opts: PoseidonOpts) {
      return Fp.create(i);
    });
  });
-  // MDS is TxT matrix
-  if (!Array.isArray(opts.mds) || opts.mds.length !== opts.t)
-    throw new Error('Poseidon: wrong MDS matrix');
-  const mds = opts.mds.map((mdsRow) => {
-    if (!Array.isArray(mdsRow) || mdsRow.length !== opts.t)
-      throw new Error(`Poseidon MDS matrix row: ${mdsRow}`);
-    return mdsRow.map((i) => {
-      if (typeof i !== 'bigint') throw new Error(`Poseidon MDS matrix value=${i}`);
-      return Fp.create(i);
-    });
-  });
-  return Object.freeze({ ...opts, rounds, sboxFn, roundConstants, mds });
+
+  if (!sboxPower || ![3, 5, 7].includes(sboxPower))
+    throw new Error(`Poseidon wrong sboxPower=${sboxPower}`);
+  const _sboxPower = BigInt(sboxPower);
+  let sboxFn = (n: bigint) => FpPow(Fp, n, _sboxPower);
+  // Unwrapped sbox power for common cases (195->142μs)
+  if (sboxPower === 3) sboxFn = (n: bigint) => Fp.mul(Fp.sqrN(n), n);
+  else if (sboxPower === 5) sboxFn = (n: bigint) => Fp.mul(Fp.sqrN(Fp.sqrN(n)), n);
+
+  return Object.freeze({ ...opts, rounds, sboxFn, roundConstants, mds: _mds });
 }

 export function splitConstants(rc: bigint[], t: number) {
@@ -80,18 +80,17 @@ export function splitConstants(rc: bigint[], t: number) {
 }

 export function poseidon(opts: PoseidonOpts) {
-  const { t, Fp, rounds, sboxFn, reversePartialPowIdx } = validateOpts(opts);
-  const halfRoundsFull = Math.floor(opts.roundsFull / 2);
-  const partialIdx = reversePartialPowIdx ? t - 1 : 0;
+  const _opts = validateOpts(opts);
+  const { Fp, mds, roundConstants, rounds, roundsPartial, sboxFn, t } = _opts;
+  const halfRoundsFull = _opts.roundsFull / 2;
+  const partialIdx = _opts.reversePartialPowIdx ? t - 1 : 0;
  const poseidonRound = (values: bigint[], isFull: boolean, idx: number) => {
-    values = values.map((i, j) => Fp.add(i, opts.roundConstants[idx][j]));
+    values = values.map((i, j) => Fp.add(i, roundConstants[idx][j]));

    if (isFull) values = values.map((i) => sboxFn(i));
    else values[partialIdx] = sboxFn(values[partialIdx]);
    // Matrix multiplication
-    values = opts.mds.map((i) =>
-      i.reduce((acc, i, j) => Fp.add(acc, Fp.mulN(i, values[j])), Fp.ZERO)
-    );
+    values = mds.map((i) => i.reduce((acc, i, j) => Fp.add(acc, Fp.mulN(i, values[j])), Fp.ZERO));
    return values;
  };
  const poseidonHash = function poseidonHash(values: bigint[]) {
@@ -105,7 +104,7 @@ export function poseidon(opts: PoseidonOpts) {
    // Apply r_f/2 full rounds.
    for (let i = 0; i < halfRoundsFull; i++) values = poseidonRound(values, true, round++);
    // Apply r_p partial rounds.
-    for (let i = 0; i < opts.roundsPartial; i++) values = poseidonRound(values, false, round++);
+    for (let i = 0; i < roundsPartial; i++) values = poseidonRound(values, false, round++);
    // Apply r_f/2 full rounds.
    for (let i = 0; i < halfRoundsFull; i++) values = poseidonRound(values, true, round++);

@@ -114,6 +113,6 @@ export function poseidon(opts: PoseidonOpts) {
    return values;
  };
  // For verification in tests
-  poseidonHash.roundConstants = opts.roundConstants;
+  poseidonHash.roundConstants = roundConstants;
  return poseidonHash;
 }
--- a/src/abstract/utils.ts
+++ b/src/abstract/utils.ts
@@ -1,13 +1,14 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+// 100 lines of code in the file are duplicated from noble-hashes (utils).
+// This is OK: `abstract` directory does not use noble-hashes.
+// User may opt-in into using different hashing library. This way, noble-hashes
+// won't be included into their bundle.
 const _0n = BigInt(0);
 const _1n = BigInt(1);
 const _2n = BigInt(2);
 const u8a = (a: any): a is Uint8Array => a instanceof Uint8Array;
-
-// 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;
+export type Hex = Uint8Array | string; // hex strings are accepted for simplicity
+export type PrivKey = Hex | bigint; // bigints are accepted to ease learning curve
 export type CHash = {
  (message: Uint8Array | string): Uint8Array;
  blockLen: number;
@@ -16,7 +17,12 @@ export type CHash = {
 };
 export type FHash = (message: Uint8Array | string) => Uint8Array;

-const hexes = Array.from({ length: 256 }, (v, i) => i.toString(16).padStart(2, '0'));
+const hexes = /* @__PURE__ */ Array.from({ length: 256 }, (_, i) =>
+  i.toString(16).padStart(2, '0')
+);
+/**
+ * @example bytesToHex(Uint8Array.from([0xca, 0xfe, 0x01, 0x23])) // 'cafe0123'
+ */
 export function bytesToHex(bytes: Uint8Array): string {
  if (!u8a(bytes)) throw new Error('Uint8Array expected');
  // pre-caching improves the speed 6x
@@ -38,22 +44,25 @@ export function hexToNumber(hex: string): bigint {
  return BigInt(hex === '' ? '0' : `0x${hex}`);
 }

-// Caching slows it down 2-3x
+/**
+ * @example hexToBytes('cafe0123') // Uint8Array.from([0xca, 0xfe, 0x01, 0x23])
+ */
 export function hexToBytes(hex: string): Uint8Array {
  if (typeof hex !== 'string') throw new Error('hex string expected, got ' + typeof hex);
-  if (hex.length % 2) throw new Error('hex string is invalid: unpadded ' + hex.length);
-  const array = new Uint8Array(hex.length / 2);
+  const len = hex.length;
+  if (len % 2) throw new Error('padded hex string expected, got unpadded hex of length ' + len);
+  const array = new Uint8Array(len / 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');
+    if (Number.isNaN(byte) || byte < 0) throw new Error('Invalid byte sequence');
    array[i] = byte;
  }
  return array;
 }

-// Big Endian
+// BE: Big Endian, LE: Little Endian
 export function bytesToNumberBE(bytes: Uint8Array): bigint {
  return hexToNumber(bytesToHex(bytes));
 }
@@ -62,12 +71,26 @@ export function bytesToNumberLE(bytes: Uint8Array): bigint {
  return hexToNumber(bytesToHex(Uint8Array.from(bytes).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();
-// Returns variable number bytes (minimal bigint encoding?)
-export const numberToVarBytesBE = (n: bigint) => hexToBytes(numberToHexUnpadded(n));
+export function numberToBytesBE(n: number | bigint, len: number): Uint8Array {
+  return hexToBytes(n.toString(16).padStart(len * 2, '0'));
+}
+export function numberToBytesLE(n: number | bigint, len: number): Uint8Array {
+  return numberToBytesBE(n, len).reverse();
+}
+// Unpadded, rarely used
+export function numberToVarBytesBE(n: number | bigint): Uint8Array {
+  return hexToBytes(numberToHexUnpadded(n));
+}

+/**
+ * Takes hex string or Uint8Array, converts to Uint8Array.
+ * Validates output length.
+ * Will throw error for other types.
+ * @param title descriptive title for an error e.g. 'private key'
+ * @param hex hex string or Uint8Array
+ * @param expectedLength optional, will compare to result array's length
+ * @returns
+ */
 export function ensureBytes(title: string, hex: Hex, expectedLength?: number): Uint8Array {
  let res: Uint8Array;
  if (typeof hex === 'string') {
@@ -89,11 +112,13 @@ export function ensureBytes(title: string, hex: Hex, expectedLength?: number): U
  return res;
 }

-// Copies several Uint8Arrays into one.
-export function concatBytes(...arrs: Uint8Array[]): Uint8Array {
-  const r = new Uint8Array(arrs.reduce((sum, a) => sum + a.length, 0));
+/**
+ * Copies several Uint8Arrays into one.
+ */
+export function concatBytes(...arrays: Uint8Array[]): Uint8Array {
+  const r = new Uint8Array(arrays.reduce((sum, a) => sum + a.length, 0));
  let pad = 0; // walk through each item, ensure they have proper type
-  arrs.forEach((a) => {
+  arrays.forEach((a) => {
    if (!u8a(a)) throw new Error('Uint8Array expected');
    r.set(a, pad);
    pad += a.length;
@@ -111,29 +136,47 @@ export function equalBytes(b1: Uint8Array, b2: Uint8Array) {
 // Global symbols in both browsers and Node.js since v11
 // See https://github.com/microsoft/TypeScript/issues/31535
 declare const TextEncoder: any;
+
+/**
+ * @example utf8ToBytes('abc') // new Uint8Array([97, 98, 99])
+ */
 export function utf8ToBytes(str: string): Uint8Array {
-  if (typeof str !== 'string') {
-    throw new Error(`utf8ToBytes expected string, got ${typeof str}`);
-  }
-  return new TextEncoder().encode(str);
+  if (typeof str !== 'string') throw new Error(`utf8ToBytes expected string, got ${typeof str}`);
+  return new Uint8Array(new TextEncoder().encode(str)); // https://bugzil.la/1681809
 }

 // Bit operations

-// Amount of bits inside bigint (Same as n.toString(2).length)
+/**
+ * Calculates amount of bits in a 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${Array(i).fill('1').join('')}`))
-// Not using ** operator with bigints for old engines.
+
+/**
+ * Gets single bit at position.
+ * NOTE: first bit position is 0 (same as arrays)
+ * Same as `!!+Array.from(n.toString(2)).reverse()[pos]`
+ */
+export function bitGet(n: bigint, pos: number) {
+  return (n >> BigInt(pos)) & _1n;
+}
+
+/**
+ * Sets single bit at position.
+ */
+export const bitSet = (n: bigint, pos: number, value: boolean) => {
+  return n | ((value ? _1n : _0n) << BigInt(pos));
+};
+
+/**
+ * Calculate mask for N bits. Not using ** operator with bigints because of old engines.
+ * Same as BigInt(`0b${Array(i).fill('1').join('')}`)
+ */
 export const bitMask = (n: number) => (_2n << BigInt(n - 1)) - _1n;

 // DRBG
@@ -205,6 +248,7 @@ const validatorFns = {
  function: (val: any) => typeof val === 'function',
  boolean: (val: any) => typeof val === 'boolean',
  string: (val: any) => typeof val === 'string',
+  stringOrUint8Array: (val: any) => typeof val === 'string' || val instanceof Uint8Array,
  isSafeInteger: (val: any) => Number.isSafeInteger(val),
  array: (val: any) => Array.isArray(val),
  field: (val: any, object: any) => (object as any).Fp.isValid(val),
--- a/src/abstract/weierstrass.ts
+++ b/src/abstract/weierstrass.ts
@@ -193,7 +193,7 @@ export function weierstrassPoints<T>(opts: CurvePointsType<T>) {

  const toBytes =
    CURVE.toBytes ||
-    ((c: ProjConstructor<T>, point: ProjPointType<T>, isCompressed: boolean) => {
+    ((_c: ProjConstructor<T>, point: ProjPointType<T>, _isCompressed: boolean) => {
      const a = point.toAffine();
      return ut.concatBytes(Uint8Array.from([0x04]), Fp.toBytes(a.x), Fp.toBytes(a.y));
    });
@@ -333,9 +333,11 @@ export function weierstrassPoints<T>(opts: CurvePointsType<T>) {

    // A point on curve is valid if it conforms to equation.
    assertValidity(): void {
-      // Zero is valid point too!
      if (this.is0()) {
-        if (CURVE.allowInfinityPoint) return;
+        // (0, 1, 0) aka ZERO is invalid in most contexts.
+        // In BLS, ZERO can be serialized, so we allow it.
+        // (0, 0, 0) is wrong representation of ZERO and is always invalid.
+        if (CURVE.allowInfinityPoint && !Fp.is0(this.py)) return;
        throw new Error('bad point: ZERO');
      }
      // Some 3rd-party test vectors require different wording between here & `fromCompressedHex`
@@ -618,7 +620,7 @@ export interface SignatureType {
  readonly s: bigint;
  readonly recovery?: number;
  assertValidity(): void;
-  addRecoveryBit(recovery: number): SignatureType;
+  addRecoveryBit(recovery: number): RecoveredSignatureType;
  hasHighS(): boolean;
  normalizeS(): SignatureType;
  recoverPublicKey(msgHash: Hex): ProjPointType<bigint>;
@@ -628,6 +630,9 @@ export interface SignatureType {
  toDERRawBytes(isCompressed?: boolean): Uint8Array;
  toDERHex(isCompressed?: boolean): string;
 }
+export type RecoveredSignatureType = SignatureType & {
+  readonly recovery: number;
+};
 // Static methods
 export type SignatureConstructor = {
  new (r: bigint, s: bigint): SignatureType;
@@ -669,7 +674,7 @@ export type CurveFn = {
  CURVE: ReturnType<typeof validateOpts>;
  getPublicKey: (privateKey: PrivKey, isCompressed?: boolean) => Uint8Array;
  getSharedSecret: (privateA: PrivKey, publicB: Hex, isCompressed?: boolean) => Uint8Array;
-  sign: (msgHash: Hex, privKey: PrivKey, opts?: SignOpts) => SignatureType;
+  sign: (msgHash: Hex, privKey: PrivKey, opts?: SignOpts) => RecoveredSignatureType;
  verify: (signature: Hex | SignatureLike, msgHash: Hex, publicKey: Hex, opts?: VerOpts) => boolean;
  ProjectivePoint: ProjConstructor<bigint>;
  Signature: SignatureConstructor;
@@ -704,7 +709,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
    isWithinCurveOrder,
  } = weierstrassPoints({
    ...CURVE,
-    toBytes(c, point, isCompressed: boolean): Uint8Array {
+    toBytes(_c, point, isCompressed: boolean): Uint8Array {
      const a = point.toAffine();
      const x = Fp.toBytes(a.x);
      const cat = ut.concatBytes;
@@ -782,8 +787,8 @@ export function weierstrass(curveDef: CurveType): CurveFn {
      if (!isWithinCurveOrder(this.s)) throw new Error('s must be 0 < s < CURVE.n');
    }

-    addRecoveryBit(recovery: number) {
-      return new Signature(this.r, this.s, recovery);
+    addRecoveryBit(recovery: number): RecoveredSignature {
+      return new Signature(this.r, this.s, recovery) as RecoveredSignature;
    }

    recoverPublicKey(msgHash: Hex): typeof Point.BASE {
@@ -828,6 +833,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
      return numToNByteStr(this.r) + numToNByteStr(this.s);
    }
  }
+  type RecoveredSignature = Signature & { recovery: number };

  const utils = {
    isValidPrivateKey(privateKey: PrivKey) {
@@ -841,13 +847,12 @@ export function weierstrass(curveDef: CurveType): CurveFn {
    normPrivateKeyToScalar: normPrivateKeyToScalar,

    /**
-     * Produces cryptographically secure private key from random of size (nBitLength+64)
-     * as per FIPS 186 B.4.1 with modulo bias being neglible.
+     * Produces cryptographically secure private key from random of size
+     * (groupLen + ceil(groupLen / 2)) with modulo bias being negligible.
     */
    randomPrivateKey: (): Uint8Array => {
-      const rand = CURVE.randomBytes(Fp.BYTES + 8);
-      const num = mod.hashToPrivateScalar(rand, CURVE_ORDER);
-      return ut.numberToBytesBE(num, CURVE.nByteLength);
+      const length = mod.getMinHashLength(CURVE.n);
+      return mod.mapHashToField(CURVE.randomBytes(length), CURVE.n);
    },

    /**
@@ -960,12 +965,12 @@ export function weierstrass(curveDef: CurveType): CurveFn {
    if (ent != null) {
      // K = HMAC_K(V || 0x00 || int2octets(x) || bits2octets(h1) || k')
      const e = ent === true ? randomBytes(Fp.BYTES) : ent; // generate random bytes OR pass as-is
-      seedArgs.push(ensureBytes('extraEntropy', e, Fp.BYTES)); // check for being of size BYTES
+      seedArgs.push(ensureBytes('extraEntropy', e)); // check for being bytes
    }
    const seed = ut.concatBytes(...seedArgs); // Step D of RFC6979 3.2
    const m = h1int; // NOTE: no need to call bits2int second time here, it is inside truncateHash!
    // Converts signature params into point w r/s, checks result for validity.
-    function k2sig(kBytes: Uint8Array): Signature | undefined {
+    function k2sig(kBytes: Uint8Array): RecoveredSignature | undefined {
      // RFC 6979 Section 3.2, step 3: k = bits2int(T)
      const k = bits2int(kBytes); // Cannot use fields methods, since it is group element
      if (!isWithinCurveOrder(k)) return; // Important: all mod() calls here must be done over N
@@ -984,7 +989,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
        normS = normalizeS(s); // if lowS was passed, ensure s is always
        recovery ^= 1; // // in the bottom half of N
      }
-      return new Signature(r, normS, recovery); // use normS, not s
+      return new Signature(r, normS, recovery) as RecoveredSignature; // use normS, not s
    }
    return { seed, k2sig };
  }
@@ -992,18 +997,22 @@ export function weierstrass(curveDef: CurveType): CurveFn {
  const defaultVerOpts: VerOpts = { lowS: CURVE.lowS, prehash: false };

  /**
-   * Signs message hash (not message: you need to hash it by yourself).
+   * Signs message hash with a private key.
   * ```
   * sign(m, d, k) where
   *   (x, y) = G × k
   *   r = x mod n
   *   s = (m + dr)/k mod n
   * ```
-   * @param opts `lowS, extraEntropy, prehash`
+   * @param msgHash NOT message. msg needs to be hashed to `msgHash`, or use `prehash`.
+   * @param privKey private key
+   * @param opts lowS for non-malleable sigs. extraEntropy for mixing randomness into k. prehash will hash first arg.
+   * @returns signature with recovery param
   */
-  function sign(msgHash: Hex, privKey: PrivKey, opts = defaultSigOpts): Signature {
+  function sign(msgHash: Hex, privKey: PrivKey, opts = defaultSigOpts): RecoveredSignature {
    const { seed, k2sig } = prepSig(msgHash, privKey, opts); // Steps A, D of RFC6979 3.2.
-    const drbg = ut.createHmacDrbg<Signature>(CURVE.hash.outputLen, CURVE.nByteLength, CURVE.hmac);
+    const C = CURVE;
+    const drbg = ut.createHmacDrbg<RecoveredSignature>(C.hash.outputLen, C.nByteLength, C.hmac);
    return drbg(seed, k2sig); // Steps B, C, D, E, F, G
  }

@@ -1084,20 +1093,29 @@ export function weierstrass(curveDef: CurveType): CurveFn {
  };
 }

-// Implementation of the Shallue and van de Woestijne method for any Weierstrass curve
-// TODO: check if there is a way to merge this with uvRatio in Edwards && move to modular?
-// b = True and y = sqrt(u / v) if (u / v) is square in F, and
-// b = False and y = sqrt(Z * (u / v)) otherwise.
+/**
+ * Implementation of the Shallue and van de Woestijne method for any weierstrass curve.
+ * TODO: check if there is a way to merge this with uvRatio in Edwards; move to modular.
+ * b = True and y = sqrt(u / v) if (u / v) is square in F, and
+ * b = False and y = sqrt(Z * (u / v)) otherwise.
+ * @param Fp
+ * @param Z
+ * @returns
+ */
 export function SWUFpSqrtRatio<T>(Fp: mod.IField<T>, Z: T) {
  // Generic implementation
  const q = Fp.ORDER;
  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
+  // We need 2n ** c1 and 2n ** (c1-1). We can't use **; but we can use <<.
+  // 2n ** c1 == 2n << (c1-1)
+  const _2n_pow_c1_1 = _2n << (c1 - _1n - _1n);
+  const _2n_pow_c1 = _2n_pow_c1_1 * _2n;
+  const c2 = (q - _1n) / _2n_pow_c1; // 2. c2 = (q - 1) / (2^c1)  # Integer arithmetic
  const c3 = (c2 - _1n) / _2n; // 3. c3 = (c2 - 1) / 2            # Integer arithmetic
-  const c4 = _2n ** c1 - _1n; // 4. c4 = 2^c1 - 1                # Integer arithmetic
-  const c5 = _2n ** (c1 - _1n); // 5. c5 = 2^(c1 - 1)              # Integer arithmetic
+  const c4 = _2n_pow_c1 - _1n; // 4. c4 = 2^c1 - 1                # Integer arithmetic
+  const c5 = _2n_pow_c1_1; // 5. c5 = 2^(c1 - 1)                  # Integer arithmetic
  const c6 = Fp.pow(Z, c2); // 6. c6 = Z^c2
  const c7 = Fp.pow(Z, (c2 + _1n) / _2n); // 7. c7 = Z^((c2 + 1) / 2)
  let sqrtRatio = (u: T, v: T): { isValid: boolean; value: T } => {
@@ -1119,7 +1137,8 @@ export function SWUFpSqrtRatio<T>(Fp: mod.IField<T>, Z: T) {
    tv4 = Fp.cmov(tv5, tv4, isQR); // 16. tv4 = CMOV(tv5, tv4, isQR)
    // 17. for i in (c1, c1 - 1, ..., 2):
    for (let i = c1; i > _1n; i--) {
-      let tv5 = _2n ** (i - _2n); // 18.    tv5 = i - 2;    19.    tv5 = 2^tv5
+      let tv5 = i - _2n; // 18.    tv5 = i - 2
+      tv5 = _2n << (tv5 - _1n); // 19.    tv5 = 2^tv5
      let tvv5 = Fp.pow(tv4, tv5); // 20.    tv5 = tv4^tv5
      const e1 = Fp.eql(tvv5, Fp.ONE); // 21.    e1 = tv5 == 1
      tv2 = Fp.mul(tv3, tv1); // 22.    tv2 = tv3 * tv1
@@ -1151,7 +1170,10 @@ export function SWUFpSqrtRatio<T>(Fp: mod.IField<T>, Z: T) {
  // if (Fp.ORDER % _8n === _5n) // sqrt_ratio_5mod8
  return sqrtRatio;
 }
-// From draft-irtf-cfrg-hash-to-curve-16
+/**
+ * Simplified Shallue-van de Woestijne-Ulas Method
+ * https://www.rfc-editor.org/rfc/rfc9380#section-6.6.2
+ */
 export function mapToCurveSimpleSWU<T>(
  Fp: mod.IField<T>,
  opts: {
--- a/src/bls12-381.ts
+++ b/src/bls12-381.ts
@@ -8,8 +8,8 @@
 // The library uses G1 for public keys and G2 for signatures. Support for G1 signatures is planned.
 // Compatible with Algorand, Chia, Dfinity, Ethereum, FIL, Zcash. Matches specs
 // [pairing-curves-11](https://tools.ietf.org/html/draft-irtf-cfrg-pairing-friendly-curves-11),
-// [bls-sigs-04](https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-04),
-// [hash-to-curve-12](https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-12).
+// [bls-sigs-04](https:/cfrg-hash-to/tools.ietf.org/html/draft-irtf-cfrg-bls-signature-04),
+// [hash-to-curve-12](https://tools.ietf.org/html/draft-irtf--curve-12).
 //
 // ### Summary
 // 1. BLS Relies on Bilinear Pairing (expensive)
@@ -60,11 +60,10 @@ const _8n = BigInt(8), _16n = BigInt(16);

 // CURVE FIELDS
 // Finite field over p.
-const Fp = mod.Field(
-  BigInt(
-    '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab'
-  )
+const Fp_raw = BigInt(
+  '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab'
 );
+const Fp = mod.Field(Fp_raw);
 type Fp = bigint;
 // Finite field over r.
 // This particular field is not used anywhere in bls12-381, but it is still useful.
@@ -110,10 +109,7 @@ type Fp2Utils = {
 // G² - 1
 // h2q
 // NOTE: ORDER was wrong!
-const FP2_ORDER =
-  BigInt(
-    '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab'
-  ) ** _2n;
+const FP2_ORDER = Fp_raw * Fp_raw;

 const Fp2: mod.IField<Fp2> & Fp2Utils = {
  ORDER: FP2_ORDER,
@@ -181,7 +177,7 @@ const Fp2: mod.IField<Fp2> & Fp2Utils = {
    if (im1 > im2 || (im1 === im2 && re1 > re2)) return x1;
    return x2;
  },
-  // Same as sgn0_fp2 in draft-irtf-cfrg-hash-to-curve-16
+  // Same as sgn0_m_eq_2 in RFC 9380
  isOdd: (x: Fp2) => {
    const { re: x0, im: x1 } = Fp2.reim(x);
    const sign_0 = x0 % _2n;
@@ -784,8 +780,7 @@ const FP12_FROBENIUS_COEFFICIENTS = [

 // HashToCurve

-// 3-isogeny map from E' to E
-// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#appendix-E.3
+// 3-isogeny map from E' to E https://www.rfc-editor.org/rfc/rfc9380#appendix-E.3
 const isogenyMapG2 = isogenyMap(
  Fp2,
  [
@@ -989,7 +984,7 @@ function G2psi2(c: ProjConstructor<Fp2>, P: ProjPointType<Fp2>) {
 //
 // Parameter definitions are in section 5.3 of the spec unless otherwise noted.
 // Parameter values come from section 8.8.2 of the spec.
-// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-8.8.2
+// https://www.rfc-editor.org/rfc/rfc9380#section-8.8.2
 //
 // Base field F is GF(p^m)
 // p = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab
@@ -1044,7 +1039,7 @@ function signatureG2ToRawBytes(point: ProjPointType<Fp2>) {
 }

 // To verify curve parameters, see pairing-friendly-curves spec:
-// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-pairing-friendly-curves-09
+// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-pairing-friendly-curves-11
 // Basic math is done over finite fields over p.
 // More complicated math is done over polynominal extension fields.
 // To simplify calculations in Fp12, we construct extension tower:
@@ -1112,7 +1107,7 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
    },
    // Clear cofactor of G1
    // https://eprint.iacr.org/2019/403
-    clearCofactor: (c, point) => {
+    clearCofactor: (_c, point) => {
      // return this.multiplyUnsafe(CURVE.h);
      return point.multiplyUnsafe(bls12_381.params.x).add(point); // x*P + P
    },
@@ -1197,7 +1192,7 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
      ),
    ]),
    a: Fp2.ZERO,
-    b: Fp2.fromBigTuple([4n, _4n]),
+    b: Fp2.fromBigTuple([_4n, _4n]),
    hEff: BigInt(
      '0xbc69f08f2ee75b3584c6a0ea91b352888e2a8e9145ad7689986ff031508ffe1329c2f178731db956d82bf015d1212b02ec0ec69d7477c1ae954cbc06689f6a359894c0adebbf6b4e8020005aaa95551'
    ),
--- a/src/ed25519.ts
+++ b/src/ed25519.ts
@@ -1,18 +1,18 @@
 /*! 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, ExtPointType } from './abstract/edwards.js';
+import { ExtPointType, twistedEdwards } from './abstract/edwards.js';
 import { montgomery } from './abstract/montgomery.js';
-import { mod, pow2, isNegativeLE, Field, FpSqrtEven } from './abstract/modular.js';
+import { Field, FpSqrtEven, isNegativeLE, mod, pow2 } from './abstract/modular.js';
 import {
-  equalBytes,
  bytesToHex,
  bytesToNumberLE,
-  numberToBytesLE,
-  Hex,
  ensureBytes,
+  equalBytes,
+  Hex,
+  numberToBytesLE,
 } from './abstract/utils.js';
-import * as htf from './abstract/hash-to-curve.js';
+import { createHasher, htfBasicOpts, expand_message_xmd } from './abstract/hash-to-curve.js';
 import { AffinePoint } from './abstract/curve.js';

 /**
@@ -34,6 +34,7 @@ const ED25519_SQRT_M1 = BigInt(
 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;
@@ -51,6 +52,7 @@ function ed25519_pow_2_252_3(x: bigint) {
  // ^ 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
@@ -61,6 +63,7 @@ function adjustScalarBytes(bytes: Uint8Array): Uint8Array {
  bytes[31] |= 64; // 0b0100_0000
  return bytes;
 }
+
 // sqrt(u/v)
 function uvRatio(u: bigint, v: bigint): { isValid: boolean; value: bigint } {
  const P = ED25519_P;
@@ -101,10 +104,10 @@ const ed25519Defaults = {
  // d is 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
+  // Finite field 𝔽p over which we'll do calculations; 2n**255n - 19n
  Fp,
  // Subgroup order: how many points curve has
-  // 2n ** 252n + 27742317777372353535851937790883648493n;
+  // 2n**252n + 27742317777372353535851937790883648493n;
  n: BigInt('7237005577332262213973186563042994240857116359379907606001950938285454250989'),
  // Cofactor
  h: BigInt(8),
@@ -120,7 +123,8 @@ const ed25519Defaults = {
  uvRatio,
 } as const;

-export const ed25519 = twistedEdwards(ed25519Defaults);
+export const ed25519 = /* @__PURE__ */ twistedEdwards(ed25519Defaults);
+
 function ed25519_domain(data: Uint8Array, ctx: Uint8Array, phflag: boolean) {
  if (ctx.length > 255) throw new Error('Context is too big');
  return concatBytes(
@@ -130,41 +134,60 @@ function ed25519_domain(data: Uint8Array, ctx: Uint8Array, phflag: boolean) {
    data
  );
 }
-export const ed25519ctx = twistedEdwards({ ...ed25519Defaults, domain: ed25519_domain });
-export const ed25519ph = twistedEdwards({
+
+export const ed25519ctx = /* @__PURE__ */ twistedEdwards({
+  ...ed25519Defaults,
+  domain: ed25519_domain,
+});
+export const ed25519ph = /* @__PURE__ */ twistedEdwards({
  ...ed25519Defaults,
  domain: ed25519_domain,
  prehash: sha512,
 });

-export const x25519 = montgomery({
-  P: ED25519_P,
-  a: BigInt(486662),
-  montgomeryBits: 255, // n is 253 bits
-  nByteLength: 32,
-  Gu: BigInt(9),
-  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,
-  randomBytes,
-});
+export const x25519 = /* @__PURE__ */ (() =>
+  montgomery({
+    P: ED25519_P,
+    a: BigInt(486662),
+    montgomeryBits: 255, // n is 253 bits
+    nByteLength: 32,
+    Gu: BigInt(9),
+    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,
+    randomBytes,
+  }))();

 /**
 * Converts ed25519 public key to x25519 public key. Uses formula:
 * * `(u, v) = ((1+y)/(1-y), sqrt(-486664)*u/x)`
 * * `(x, y) = (sqrt(-486664)*u/v, (u-1)/(u+1))`
 * @example
- *   const aPub = ed25519.getPublicKey(utils.randomPrivateKey());
- *   x25519.getSharedSecret(edwardsToMontgomery(aPub), edwardsToMontgomery(someonesPub))
+ *   const someonesPub = ed25519.getPublicKey(ed25519.utils.randomPrivateKey());
+ *   const aPriv = x25519.utils.randomPrivateKey();
+ *   x25519.getSharedSecret(aPriv, edwardsToMontgomeryPub(someonesPub))
 */
-export function edwardsToMontgomery(edwardsPub: Hex): Uint8Array {
+export function edwardsToMontgomeryPub(edwardsPub: Hex): Uint8Array {
  const { y } = ed25519.ExtendedPoint.fromHex(edwardsPub);
  const _1n = BigInt(1);
-  return Fp.toBytes(Fp.create((y - _1n) * Fp.inv(y + _1n)));
+  return Fp.toBytes(Fp.create((_1n + y) * Fp.inv(_1n - y)));
+}
+export const edwardsToMontgomery = edwardsToMontgomeryPub; // deprecated
+
+/**
+ * Converts ed25519 secret key to x25519 secret key.
+ * @example
+ *   const someonesPub = x25519.getPublicKey(x25519.utils.randomPrivateKey());
+ *   const aPriv = ed25519.utils.randomPrivateKey();
+ *   x25519.getSharedSecret(edwardsToMontgomeryPriv(aPriv), someonesPub)
+ */
+export function edwardsToMontgomeryPriv(edwardsPriv: Uint8Array): Uint8Array {
+  const hashed = ed25519Defaults.hash(edwardsPriv.subarray(0, 32));
+  return ed25519Defaults.adjustScalarBytes(hashed).subarray(0, 32);
 }

 // Hash To Curve Elligator2 Map (NOTE: different from ristretto255 elligator)
@@ -223,7 +246,8 @@ function map_to_curve_elligator2_curve25519(u: bigint) {

 const ELL2_C1_EDWARDS = FpSqrtEven(Fp, Fp.neg(BigInt(486664))); // sgn0(c1) MUST equal 0
 function map_to_curve_elligator2_edwards25519(u: bigint) {
-  const { xMn, xMd, yMn, yMd } = map_to_curve_elligator2_curve25519(u); //  1.  (xMn, xMd, yMn, yMd) = map_to_curve_elligator2_curve25519(u)
+  const { xMn, xMd, yMn, yMd } = map_to_curve_elligator2_curve25519(u); //  1.  (xMn, xMd, yMn, yMd) =
+  // map_to_curve_elligator2_curve25519(u)
  let xn = Fp.mul(xMn, yMd); //  2.  xn = xMn * yMd
  xn = Fp.mul(xn, ELL2_C1_EDWARDS); //  3.  xn = xn * c1
  let xd = Fp.mul(xMd, yMn); //  4.  xd = xMd * yMn    # xn / xd = c1 * xM / yM
@@ -239,28 +263,30 @@ function map_to_curve_elligator2_edwards25519(u: bigint) {
  const inv = Fp.invertBatch([xd, yd]); // batch division
  return { x: Fp.mul(xn, inv[0]), y: Fp.mul(yn, inv[1]) }; //  13. return (xn, xd, yn, yd)
 }
-const { hashToCurve, encodeToCurve } = htf.createHasher(
-  ed25519.ExtendedPoint,
-  (scalars: bigint[]) => map_to_curve_elligator2_edwards25519(scalars[0]),
-  {
-    DST: 'edwards25519_XMD:SHA-512_ELL2_RO_',
-    encodeDST: 'edwards25519_XMD:SHA-512_ELL2_NU_',
-    p: Fp.ORDER,
-    m: 1,
-    k: 128,
-    expand: 'xmd',
-    hash: sha512,
-  }
-);
-export { hashToCurve, encodeToCurve };
+
+const htf = /* @__PURE__ */ (() =>
+  createHasher(
+    ed25519.ExtendedPoint,
+    (scalars: bigint[]) => map_to_curve_elligator2_edwards25519(scalars[0]),
+    {
+      DST: 'edwards25519_XMD:SHA-512_ELL2_RO_',
+      encodeDST: 'edwards25519_XMD:SHA-512_ELL2_NU_',
+      p: Fp.ORDER,
+      m: 1,
+      k: 128,
+      expand: 'xmd',
+      hash: sha512,
+    }
+  ))();
+export const hashToCurve = /* @__PURE__ */ (() => htf.hashToCurve)();
+export const encodeToCurve = /* @__PURE__ */ (() => htf.encodeToCurve)();

 function assertRstPoint(other: unknown) {
-  if (!(other instanceof RistrettoPoint)) throw new Error('RistrettoPoint expected');
+  if (!(other instanceof RistPoint)) throw new Error('RistrettoPoint expected');
 }
+
 // √(-1) aka √(a) aka 2^((p-1)/4)
-const SQRT_M1 = BigInt(
-  '19681161376707505956807079304988542015446066515923890162744021073123829784752'
-);
+const SQRT_M1 = ED25519_SQRT_M1;
 // √(ad - 1)
 const SQRT_AD_MINUS_ONE = BigInt(
  '25063068953384623474111414158702152701244531502492656460079210482610430750235'
@@ -317,32 +343,31 @@ function calcElligatorRistrettoMap(r0: bigint): 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);
-
+class RistPoint {
+  static BASE: RistPoint;
+  static ZERO: RistPoint;
  // Private property to discourage combining ExtendedPoint + RistrettoPoint
  // Always use Ristretto encoding/decoding instead.
  constructor(private readonly ep: ExtendedPoint) {}

  static fromAffine(ap: AffinePoint<bigint>) {
-    return new RistrettoPoint(ed25519.ExtendedPoint.fromAffine(ap));
+    return new RistPoint(ed25519.ExtendedPoint.fromAffine(ap));
  }

  /**
-   * Takes uniform output of 64-bit hash function like sha512 and converts it to `RistrettoPoint`.
+   * Takes uniform output of 64-byte 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
+   * @param hex 64-byte output of a hash function
   */
-  static hashToCurve(hex: Hex): RistrettoPoint {
+  static hashToCurve(hex: Hex): RistPoint {
    hex = ensureBytes('ristrettoHash', 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));
+    return new RistPoint(R1.add(R2));
  }

  /**
@@ -350,7 +375,7 @@ export class RistrettoPoint {
   * 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 {
+  static fromHex(hex: Hex): RistPoint {
    hex = ensureBytes('ristrettoHex', hex, 32);
    const { a, d } = ed25519.CURVE;
    const P = ed25519.CURVE.Fp.ORDER;
@@ -374,7 +399,7 @@ export class RistrettoPoint {
    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));
+    return new RistPoint(new ed25519.ExtendedPoint(x, y, _1n, t));
  }

  /**
@@ -418,7 +443,7 @@ export class RistrettoPoint {
  }

  // Compare one point to another.
-  equals(other: RistrettoPoint): boolean {
+  equals(other: RistPoint): boolean {
    assertRstPoint(other);
    const { ex: X1, ey: Y1 } = this.ep;
    const { ex: X2, ey: Y2 } = other.ep;
@@ -429,31 +454,36 @@ export class RistrettoPoint {
    return one || two;
  }

-  add(other: RistrettoPoint): RistrettoPoint {
+  add(other: RistPoint): RistPoint {
    assertRstPoint(other);
-    return new RistrettoPoint(this.ep.add(other.ep));
+    return new RistPoint(this.ep.add(other.ep));
  }

-  subtract(other: RistrettoPoint): RistrettoPoint {
+  subtract(other: RistPoint): RistPoint {
    assertRstPoint(other);
-    return new RistrettoPoint(this.ep.subtract(other.ep));
+    return new RistPoint(this.ep.subtract(other.ep));
  }

-  multiply(scalar: bigint): RistrettoPoint {
-    return new RistrettoPoint(this.ep.multiply(scalar));
+  multiply(scalar: bigint): RistPoint {
+    return new RistPoint(this.ep.multiply(scalar));
  }

-  multiplyUnsafe(scalar: bigint): RistrettoPoint {
-    return new RistrettoPoint(this.ep.multiplyUnsafe(scalar));
+  multiplyUnsafe(scalar: bigint): RistPoint {
+    return new RistPoint(this.ep.multiplyUnsafe(scalar));
  }
 }
+export const RistrettoPoint = /* @__PURE__ */ (() => {
+  if (!RistPoint.BASE) RistPoint.BASE = new RistPoint(ed25519.ExtendedPoint.BASE);
+  if (!RistPoint.ZERO) RistPoint.ZERO = new RistPoint(ed25519.ExtendedPoint.ZERO);
+  return RistPoint;
+})();

-// https://datatracker.ietf.org/doc/draft-irtf-cfrg-hash-to-curve/14/
-// Appendix B.  Hashing to ristretto255
-export const hash_to_ristretto255 = (msg: Uint8Array, options: htf.htfBasicOpts) => {
+// Hashing to ristretto255. https://www.rfc-editor.org/rfc/rfc9380#appendix-B
+export const hashToRistretto255 = (msg: Uint8Array, options: htfBasicOpts) => {
  const d = options.DST;
  const DST = typeof d === 'string' ? utf8ToBytes(d) : d;
-  const uniform_bytes = htf.expand_message_xmd(msg, DST, 64, sha512);
-  const P = RistrettoPoint.hashToCurve(uniform_bytes);
+  const uniform_bytes = expand_message_xmd(msg, DST, 64, sha512);
+  const P = RistPoint.hashToCurve(uniform_bytes);
  return P;
 };
+export const hash_to_ristretto255 = hashToRistretto255; // legacy
--- a/src/ed448.ts
+++ b/src/ed448.ts
@@ -1,14 +1,25 @@
 /*! 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, Field } from './abstract/modular.js';
+import { ExtPointType, twistedEdwards } from './abstract/edwards.js';
+import { mod, pow2, Field, isNegativeLE } from './abstract/modular.js';
 import { montgomery } from './abstract/montgomery.js';
-import * as htf from './abstract/hash-to-curve.js';
+import { createHasher, htfBasicOpts, expand_message_xof } from './abstract/hash-to-curve.js';
+import {
+  bytesToHex,
+  bytesToNumberLE,
+  ensureBytes,
+  equalBytes,
+  Hex,
+  numberToBytesLE,
+} from './abstract/utils.js';
+import { AffinePoint } from './abstract/curve.js';

 /**
 * Edwards448 (not Ed448-Goldilocks) curve with following addons:
- * * X448 ECDH
+ * - X448 ECDH
+ * - Decaf cofactor elimination
+ * - Elligator hash-to-group / point indistinguishability
 * Conforms to RFC 8032 https://www.rfc-editor.org/rfc/rfc8032.html#section-5.2
 */

@@ -18,15 +29,16 @@ const ed448P = BigInt(
  '726838724295606890549323807888004534353641360687318060281490199180612328166730772686396383698676545930088884461843637361053498018365439'
 );

+// prettier-ignore
+const _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3), _4n = BigInt(4), _11n = BigInt(11);
+// prettier-ignore
+const _22n = BigInt(22), _44n = BigInt(44), _88n = BigInt(88), _223n = BigInt(223);
+
 // 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;
@@ -53,8 +65,29 @@ function adjustScalarBytes(bytes: Uint8Array): Uint8Array {
  return bytes;
 }

+// Constant-time ratio of u to v. Allows to combine inversion and square root u/√v.
+// Uses algo from RFC8032 5.1.3.
+function uvRatio(u: bigint, v: bigint): { isValid: boolean; value: bigint } {
+  const P = ed448P;
+  // https://www.rfc-editor.org/rfc/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 };
+}
+
 const Fp = Field(ed448P, 456, true);
-const _4n = BigInt(4);

 const ED448_DEF = {
  // Param: a
@@ -63,7 +96,7 @@ const ED448_DEF = {
  d: BigInt(
    '726838724295606890549323807888004534353641360687318060281490199180612328166730772686396383698676545930088884461843637361053498018326358'
  ),
-  // Finite field 𝔽p over which we'll do calculations; 2n ** 448n - 2n ** 224n - 1n
+  // Finite field 𝔽p over which we'll do calculations; 2n**448n - 2n**224n - 1n
  Fp,
  // Subgroup order: how many points curve has;
  // 2n**446n - 13818066809895115352007386748515426880336692474882178609894547503885n
@@ -94,49 +127,29 @@ const ED448_DEF = {
      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 };
-  },
+  uvRatio,
 } as const;

-export const ed448 = twistedEdwards(ED448_DEF);
+export const ed448 = /* @__PURE__ */ 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 ed448ph = /* @__PURE__ */ twistedEdwards({ ...ED448_DEF, prehash: shake256_64 });

-export const x448 = montgomery({
-  a: BigInt(156326),
-  montgomeryBits: 448,
-  nByteLength: 57,
-  P: ed448P,
-  Gu: BigInt(5),
-  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,
-  randomBytes,
-});
+export const x448 = /* @__PURE__ */ (() =>
+  montgomery({
+    a: BigInt(156326),
+    montgomeryBits: 448,
+    nByteLength: 57,
+    P: ed448P,
+    Gu: BigInt(5),
+    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,
+    randomBytes,
+  }))();

 /**
 * Converts edwards448 public key to x448 public key. Uses formula:
@@ -146,11 +159,12 @@ export const x448 = montgomery({
 *   const aPub = ed448.getPublicKey(utils.randomPrivateKey());
 *   x448.getSharedSecret(edwardsToMontgomery(aPub), edwardsToMontgomery(someonesPub))
 */
-export function edwardsToMontgomery(edwardsPub: string | Uint8Array): Uint8Array {
+export function edwardsToMontgomeryPub(edwardsPub: string | Uint8Array): Uint8Array {
  const { y } = ed448.ExtendedPoint.fromHex(edwardsPub);
  const _1n = BigInt(1);
  return Fp.toBytes(Fp.create((y - _1n) * Fp.inv(y + _1n)));
 }
+export const edwardsToMontgomery = edwardsToMontgomeryPub; // deprecated

 // Hash To Curve Elligator2 Map
 const ELL2_C1 = (Fp.ORDER - BigInt(3)) / BigInt(4); // 1. c1 = (q - 3) / 4         # Integer arithmetic
@@ -227,17 +241,225 @@ function map_to_curve_elligator2_edwards448(u: bigint) {
  return { x: Fp.mul(xEn, inv[0]), y: Fp.mul(yEn, inv[1]) }; // 38. return (xEn, xEd, yEn, yEd)
 }

-const { hashToCurve, encodeToCurve } = htf.createHasher(
-  ed448.ExtendedPoint,
-  (scalars: bigint[]) => map_to_curve_elligator2_edwards448(scalars[0]),
-  {
-    DST: 'edwards448_XOF:SHAKE256_ELL2_RO_',
-    encodeDST: 'edwards448_XOF:SHAKE256_ELL2_NU_',
-    p: Fp.ORDER,
-    m: 1,
-    k: 224,
-    expand: 'xof',
-    hash: shake256,
-  }
+const htf = /* @__PURE__ */ (() =>
+  createHasher(
+    ed448.ExtendedPoint,
+    (scalars: bigint[]) => map_to_curve_elligator2_edwards448(scalars[0]),
+    {
+      DST: 'edwards448_XOF:SHAKE256_ELL2_RO_',
+      encodeDST: 'edwards448_XOF:SHAKE256_ELL2_NU_',
+      p: Fp.ORDER,
+      m: 1,
+      k: 224,
+      expand: 'xof',
+      hash: shake256,
+    }
+  ))();
+export const hashToCurve = /* @__PURE__ */ (() => htf.hashToCurve)();
+export const encodeToCurve = /* @__PURE__ */ (() => htf.encodeToCurve)();
+
+function assertDcfPoint(other: unknown) {
+  if (!(other instanceof DcfPoint)) throw new Error('DecafPoint expected');
+}
+
+// 1-d
+const ONE_MINUS_D = BigInt('39082');
+// 1-2d
+const ONE_MINUS_TWO_D = BigInt('78163');
+// √(-d)
+const SQRT_MINUS_D = BigInt(
+  '98944233647732219769177004876929019128417576295529901074099889598043702116001257856802131563896515373927712232092845883226922417596214'
 );
-export { hashToCurve, encodeToCurve };
+// 1 / √(-d)
+const INVSQRT_MINUS_D = BigInt(
+  '315019913931389607337177038330951043522456072897266928557328499619017160722351061360252776265186336876723201881398623946864393857820716'
+);
+// Calculates 1/√(number)
+const invertSqrt = (number: bigint) => uvRatio(_1n, number);
+
+const MAX_448B = BigInt(
+  '0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff'
+);
+const bytes448ToNumberLE = (bytes: Uint8Array) =>
+  ed448.CURVE.Fp.create(bytesToNumberLE(bytes) & MAX_448B);
+
+type ExtendedPoint = ExtPointType;
+
+// Computes Elligator map for Decaf
+// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-ristretto255-decaf448-07#name-element-derivation-2
+function calcElligatorDecafMap(r0: bigint): ExtendedPoint {
+  const { d } = ed448.CURVE;
+  const P = ed448.CURVE.Fp.ORDER;
+  const mod = ed448.CURVE.Fp.create;
+
+  const r = mod(-(r0 * r0)); // 1
+  const u0 = mod(d * (r - _1n)); // 2
+  const u1 = mod((u0 + _1n) * (u0 - r)); // 3
+
+  const { isValid: was_square, value: v } = uvRatio(ONE_MINUS_TWO_D, mod((r + _1n) * u1)); // 4
+
+  let v_prime = v; // 5
+  if (!was_square) v_prime = mod(r0 * v);
+
+  let sgn = _1n; // 6
+  if (!was_square) sgn = mod(-_1n);
+
+  const s = mod(v_prime * (r + _1n)); // 7
+  let s_abs = s;
+  if (isNegativeLE(s, P)) s_abs = mod(-s);
+
+  const s2 = s * s;
+  const W0 = mod(s_abs * _2n); // 8
+  const W1 = mod(s2 + _1n); // 9
+  const W2 = mod(s2 - _1n); // 10
+  const W3 = mod(v_prime * s * (r - _1n) * ONE_MINUS_TWO_D + sgn); // 11
+  return new ed448.ExtendedPoint(mod(W0 * W3), mod(W2 * W1), mod(W1 * W3), mod(W0 * W2));
+}
+
+/**
+ * Each ed448/ExtendedPoint has 4 different equivalent points. This can be
+ * a source of bugs for protocols like ring signatures. Decaf was created to solve this.
+ * Decaf 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
+ */
+class DcfPoint {
+  static BASE: DcfPoint;
+  static ZERO: DcfPoint;
+  // Private property to discourage combining ExtendedPoint + DecafPoint
+  // Always use Decaf encoding/decoding instead.
+  constructor(private readonly ep: ExtendedPoint) {}
+
+  static fromAffine(ap: AffinePoint<bigint>) {
+    return new DcfPoint(ed448.ExtendedPoint.fromAffine(ap));
+  }
+
+  /**
+   * Takes uniform output of 112-byte hash function like shake256 and converts it to `DecafPoint`.
+   * 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://datatracker.ietf.org/doc/html/draft-irtf-cfrg-ristretto255-decaf448-07#name-element-derivation-2
+   * @param hex 112-byte output of a hash function
+   */
+  static hashToCurve(hex: Hex): DcfPoint {
+    hex = ensureBytes('decafHash', hex, 112);
+    const r1 = bytes448ToNumberLE(hex.slice(0, 56));
+    const R1 = calcElligatorDecafMap(r1);
+    const r2 = bytes448ToNumberLE(hex.slice(56, 112));
+    const R2 = calcElligatorDecafMap(r2);
+    return new DcfPoint(R1.add(R2));
+  }
+
+  /**
+   * Converts decaf-encoded string to decaf point.
+   * https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-ristretto255-decaf448-07#name-decode-2
+   * @param hex Decaf-encoded 56 bytes. Not every 56-byte string is valid decaf encoding
+   */
+  static fromHex(hex: Hex): DcfPoint {
+    hex = ensureBytes('decafHex', hex, 56);
+    const { d } = ed448.CURVE;
+    const P = ed448.CURVE.Fp.ORDER;
+    const mod = ed448.CURVE.Fp.create;
+    const emsg = 'DecafPoint.fromHex: the hex is not valid encoding of DecafPoint';
+    const s = bytes448ToNumberLE(hex);
+
+    // 1. Check that s_bytes is the canonical encoding of a field element, or else abort.
+    // 2. Check that s is non-negative, or else abort
+    if (!equalBytes(numberToBytesLE(s, 56), hex) || isNegativeLE(s, P)) throw new Error(emsg);
+
+    const s2 = mod(s * s); // 1
+    const u1 = mod(_1n + s2); // 2
+    const u1sq = mod(u1 * u1);
+    const u2 = mod(u1sq - _4n * d * s2); // 3
+
+    const { isValid, value: invsqrt } = invertSqrt(mod(u2 * u1sq)); // 4
+
+    let u3 = mod((s + s) * invsqrt * u1 * SQRT_MINUS_D); // 5
+    if (isNegativeLE(u3, P)) u3 = mod(-u3);
+
+    const x = mod(u3 * invsqrt * u2 * INVSQRT_MINUS_D); // 6
+    const y = mod((_1n - s2) * invsqrt * u1); // 7
+    const t = mod(x * y); // 8
+
+    if (!isValid) throw new Error(emsg);
+    return new DcfPoint(new ed448.ExtendedPoint(x, y, _1n, t));
+  }
+
+  /**
+   * Encodes decaf point to Uint8Array.
+   * https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-ristretto255-decaf448-07#name-encode-2
+   */
+  toRawBytes(): Uint8Array {
+    let { ex: x, ey: _y, ez: z, et: t } = this.ep;
+    const P = ed448.CURVE.Fp.ORDER;
+    const mod = ed448.CURVE.Fp.create;
+
+    const u1 = mod(mod(x + t) * mod(x - t)); // 1
+    const x2 = mod(x * x);
+    const { value: invsqrt } = invertSqrt(mod(u1 * ONE_MINUS_D * x2)); // 2
+
+    let ratio = mod(invsqrt * u1 * SQRT_MINUS_D); // 3
+    if (isNegativeLE(ratio, P)) ratio = mod(-ratio);
+
+    const u2 = mod(INVSQRT_MINUS_D * ratio * z - t); // 4
+
+    let s = mod(ONE_MINUS_D * invsqrt * x * u2); // 5
+    if (isNegativeLE(s, P)) s = mod(-s);
+
+    return numberToBytesLE(s, 56);
+  }
+
+  toHex(): string {
+    return bytesToHex(this.toRawBytes());
+  }
+
+  toString(): string {
+    return this.toHex();
+  }
+
+  // Compare one point to another.
+  // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-ristretto255-decaf448-07#name-equals-2
+  equals(other: DcfPoint): boolean {
+    assertDcfPoint(other);
+    const { ex: X1, ey: Y1 } = this.ep;
+    const { ex: X2, ey: Y2 } = other.ep;
+    const mod = ed448.CURVE.Fp.create;
+    // (x1 * y2 == y1 * x2)
+    return mod(X1 * Y2) === mod(Y1 * X2);
+  }
+
+  add(other: DcfPoint): DcfPoint {
+    assertDcfPoint(other);
+    return new DcfPoint(this.ep.add(other.ep));
+  }
+
+  subtract(other: DcfPoint): DcfPoint {
+    assertDcfPoint(other);
+    return new DcfPoint(this.ep.subtract(other.ep));
+  }
+
+  multiply(scalar: bigint): DcfPoint {
+    return new DcfPoint(this.ep.multiply(scalar));
+  }
+
+  multiplyUnsafe(scalar: bigint): DcfPoint {
+    return new DcfPoint(this.ep.multiplyUnsafe(scalar));
+  }
+}
+export const DecafPoint = /* @__PURE__ */ (() => {
+  // decaf448 base point is ed448 base x 2
+  // https://github.com/dalek-cryptography/curve25519-dalek/blob/59837c6ecff02b77b9d5ff84dbc239d0cf33ef90/vendor/ristretto.sage#L699
+  if (!DcfPoint.BASE) DcfPoint.BASE = new DcfPoint(ed448.ExtendedPoint.BASE).multiply(_2n);
+  if (!DcfPoint.ZERO) DcfPoint.ZERO = new DcfPoint(ed448.ExtendedPoint.ZERO);
+  return DcfPoint;
+})();
+
+// Hashing to decaf448. https://www.rfc-editor.org/rfc/rfc9380#appendix-C
+export const hashToDecaf448 = (msg: Uint8Array, options: htfBasicOpts) => {
+  const d = options.DST;
+  const DST = typeof d === 'string' ? utf8ToBytes(d) : d;
+  const uniform_bytes = expand_message_xof(msg, DST, 112, 224, shake256);
+  const P = DcfPoint.hashToCurve(uniform_bytes);
+  return P;
+};
+export const hash_to_decaf448 = hashToDecaf448; // legacy
--- a/src/jubjub.ts
+++ b/src/jubjub.ts
@@ -11,7 +11,7 @@ import { Field } from './abstract/modular.js';
 * jubjub does not use EdDSA, so `hash`/sha512 params are passed because interface expects them.
 */

-export const jubjub = twistedEdwards({
+export const jubjub = /* @__PURE__ */ twistedEdwards({
  // Params: a, d
  a: BigInt('0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000000'),
  d: BigInt('0x2a9318e74bfa2b48f5fd9207e6bd7fd4292d7f6d37579d2601065fd6d6343eb1'),
--- a/src/p256.ts
+++ b/src/p256.ts
@@ -3,7 +3,7 @@ import { createCurve } from './_shortw_utils.js';
 import { sha256 } from '@noble/hashes/sha256';
 import { Field } from './abstract/modular.js';
 import { mapToCurveSimpleSWU } from './abstract/weierstrass.js';
-import * as htf from './abstract/hash-to-curve.js';
+import { createHasher } from './abstract/hash-to-curve.js';

 // NIST secp256r1 aka p256
 // https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-256
@@ -12,12 +12,6 @@ const Fp = Field(BigInt('0xffffffff00000001000000000000000000000000fffffffffffff
 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')),
-});
-
 // prettier-ignore
 export const p256 = createCurve({
  a: CURVE_A, // Equation params: a, b
@@ -33,10 +27,15 @@ export const p256 = createCurve({
 } as const, sha256);
 export const secp256r1 = p256;

-const { hashToCurve, encodeToCurve } = htf.createHasher(
-  secp256r1.ProjectivePoint,
-  (scalars: bigint[]) => mapSWU(scalars[0]),
-  {
+const mapSWU = /* @__PURE__ */ (() =>
+  mapToCurveSimpleSWU(Fp, {
+    A: CURVE_A,
+    B: CURVE_B,
+    Z: Fp.create(BigInt('-10')),
+  }))();
+
+const htf = /* @__PURE__ */ (() =>
+  createHasher(secp256r1.ProjectivePoint, (scalars: bigint[]) => mapSWU(scalars[0]), {
    DST: 'P256_XMD:SHA-256_SSWU_RO_',
    encodeDST: 'P256_XMD:SHA-256_SSWU_NU_',
    p: Fp.ORDER,
@@ -44,6 +43,6 @@ const { hashToCurve, encodeToCurve } = htf.createHasher(
    k: 128,
    expand: 'xmd',
    hash: sha256,
-  }
-);
-export { hashToCurve, encodeToCurve };
+  }))();
+export const hashToCurve = /* @__PURE__ */ (() => htf.hashToCurve)();
+export const encodeToCurve = /* @__PURE__ */ (() => htf.encodeToCurve)();
--- a/src/p384.ts
+++ b/src/p384.ts
@@ -3,7 +3,7 @@ import { createCurve } from './_shortw_utils.js';
 import { sha384 } from '@noble/hashes/sha512';
 import { Field } from './abstract/modular.js';
 import { mapToCurveSimpleSWU } from './abstract/weierstrass.js';
-import * as htf from './abstract/hash-to-curve.js';
+import { createHasher } from './abstract/hash-to-curve.js';

 // NIST secp384r1 aka p384
 // https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-384
@@ -31,16 +31,15 @@ export const p384 = createCurve({
 } as const, sha384);
 export const secp384r1 = p384;

-const mapSWU = mapToCurveSimpleSWU(Fp, {
-  A: CURVE_A,
-  B: CURVE_B,
-  Z: Fp.create(BigInt('-12')),
-});
+const mapSWU = /* @__PURE__ */ (() =>
+  mapToCurveSimpleSWU(Fp, {
+    A: CURVE_A,
+    B: CURVE_B,
+    Z: Fp.create(BigInt('-12')),
+  }))();

-const { hashToCurve, encodeToCurve } = htf.createHasher(
-  secp384r1.ProjectivePoint,
-  (scalars: bigint[]) => mapSWU(scalars[0]),
-  {
+const htf = /* @__PURE__ */ (() =>
+  createHasher(secp384r1.ProjectivePoint, (scalars: bigint[]) => mapSWU(scalars[0]), {
    DST: 'P384_XMD:SHA-384_SSWU_RO_',
    encodeDST: 'P384_XMD:SHA-384_SSWU_NU_',
    p: Fp.ORDER,
@@ -48,6 +47,6 @@ const { hashToCurve, encodeToCurve } = htf.createHasher(
    k: 192,
    expand: 'xmd',
    hash: sha384,
-  }
-);
-export { hashToCurve, encodeToCurve };
+  }))();
+export const hashToCurve = /* @__PURE__ */ (() => htf.hashToCurve)();
+export const encodeToCurve = /* @__PURE__ */ (() => htf.encodeToCurve)();
--- a/src/p521.ts
+++ b/src/p521.ts
@@ -3,7 +3,7 @@ import { createCurve } from './_shortw_utils.js';
 import { sha512 } from '@noble/hashes/sha512';
 import { Field } from './abstract/modular.js';
 import { mapToCurveSimpleSWU } from './abstract/weierstrass.js';
-import * as htf from './abstract/hash-to-curve.js';
+import { createHasher } from './abstract/hash-to-curve.js';

 // NIST secp521r1 aka p521
 // Note that it's 521, which differs from 512 of its hash function.
@@ -47,16 +47,15 @@ export const p521 = createCurve({
 } as const, sha512);
 export const secp521r1 = p521;

-const mapSWU = mapToCurveSimpleSWU(Fp, {
-  A: CURVE.a,
-  B: CURVE.b,
-  Z: Fp.create(BigInt('-4')),
-});
+const mapSWU = /* @__PURE__ */ (() =>
+  mapToCurveSimpleSWU(Fp, {
+    A: CURVE.a,
+    B: CURVE.b,
+    Z: Fp.create(BigInt('-4')),
+  }))();

-const { hashToCurve, encodeToCurve } = htf.createHasher(
-  secp521r1.ProjectivePoint,
-  (scalars: bigint[]) => mapSWU(scalars[0]),
-  {
+const htf = /* @__PURE__ */ (() =>
+  createHasher(secp521r1.ProjectivePoint, (scalars: bigint[]) => mapSWU(scalars[0]), {
    DST: 'P521_XMD:SHA-512_SSWU_RO_',
    encodeDST: 'P521_XMD:SHA-512_SSWU_NU_',
    p: Fp.ORDER,
@@ -64,6 +63,6 @@ const { hashToCurve, encodeToCurve } = htf.createHasher(
    k: 256,
    expand: 'xmd',
    hash: sha512,
-  }
-);
-export { hashToCurve, encodeToCurve };
+  }))();
+export const hashToCurve = /* @__PURE__ */ (() => htf.hashToCurve)();
+export const encodeToCurve = /* @__PURE__ */ (() => htf.encodeToCurve)();
--- a/src/secp256k1.ts
+++ b/src/secp256k1.ts
@@ -5,7 +5,7 @@ import { Field, mod, pow2 } from './abstract/modular.js';
 import { ProjPointType as PointType, mapToCurveSimpleSWU } from './abstract/weierstrass.js';
 import type { Hex, PrivKey } from './abstract/utils.js';
 import { bytesToNumberBE, concatBytes, ensureBytes, numberToBytesBE } from './abstract/utils.js';
-import * as htf from './abstract/hash-to-curve.js';
+import { createHasher, isogenyMap } from './abstract/hash-to-curve.js';
 import { createCurve } from './_shortw_utils.js';

 const secp256k1P = BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f');
@@ -199,7 +199,7 @@ function schnorrVerify(signature: Hex, message: Hex, publicKey: Hex): boolean {
  }
 }

-export const schnorr = {
+export const schnorr = /* @__PURE__ */ (() => ({
  getPublicKey: schnorrGetPublicKey,
  sign: schnorrSign,
  verify: schnorrVerify,
@@ -212,58 +212,63 @@ export const schnorr = {
    taggedHash,
    mod,
  },
-};
+}))();

-const isoMap = htf.isogenyMap(
-  Fp,
-  [
-    // xNum
+const isoMap = /* @__PURE__ */ (() =>
+  isogenyMap(
+    Fp,
    [
-      '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 [bigint[], bigint[], bigint[], bigint[]]
-);
-const mapSWU = mapToCurveSimpleSWU(Fp, {
-  A: BigInt('0x3f8731abdd661adca08a5558f0f5d272e953d363cb6f0e5d405447c01a444533'),
-  B: BigInt('1771'),
-  Z: Fp.create(BigInt('-11')),
-});
-export const { hashToCurve, encodeToCurve } = htf.createHasher(
-  secp256k1.ProjectivePoint,
-  (scalars: bigint[]) => {
-    const { x, y } = mapSWU(Fp.create(scalars[0]));
-    return isoMap(x, y);
-  },
-  {
-    DST: 'secp256k1_XMD:SHA-256_SSWU_RO_',
-    encodeDST: 'secp256k1_XMD:SHA-256_SSWU_NU_',
-    p: Fp.ORDER,
-    m: 1,
-    k: 128,
-    expand: 'xmd',
-    hash: sha256,
-  }
-);
+      // 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 [bigint[], bigint[], bigint[], bigint[]]
+  ))();
+const mapSWU = /* @__PURE__ */ (() =>
+  mapToCurveSimpleSWU(Fp, {
+    A: BigInt('0x3f8731abdd661adca08a5558f0f5d272e953d363cb6f0e5d405447c01a444533'),
+    B: BigInt('1771'),
+    Z: Fp.create(BigInt('-11')),
+  }))();
+const htf = /* @__PURE__ */ (() =>
+  createHasher(
+    secp256k1.ProjectivePoint,
+    (scalars: bigint[]) => {
+      const { x, y } = mapSWU(Fp.create(scalars[0]));
+      return isoMap(x, y);
+    },
+    {
+      DST: 'secp256k1_XMD:SHA-256_SSWU_RO_',
+      encodeDST: 'secp256k1_XMD:SHA-256_SSWU_NU_',
+      p: Fp.ORDER,
+      m: 1,
+      k: 128,
+      expand: 'xmd',
+      hash: sha256,
+    }
+  ))();
+export const hashToCurve = /* @__PURE__ */ (() => htf.hashToCurve)();
+export const encodeToCurve = /* @__PURE__ */ (() => htf.encodeToCurve)();
--- a/test/bls12-381.test.js
+++ b/test/bls12-381.test.js
@@ -37,6 +37,11 @@ const B_192_40 = '40'.padEnd(192, '0');
 const B_384_40 = '40'.padEnd(384, '0'); // [0x40, 0, 0...]

 const getPubKey = (priv) => bls.getPublicKey(priv);
+function replaceZeroPoint(item) {
+  const zeros = '0000000000000000000000000000000000000000000000000000000000000000';
+  const ones = '1000000000000000000000000000000000000000000000000000000000000001';
+  return item === zeros ? ones : item;
+}

 function equal(a, b, comment) {
  deepStrictEqual(a.equals(b), true, `eq(${comment})`);
@@ -1234,6 +1239,7 @@ describe('verify()', () => {
    should('verify multi-signature as simple signature', () => {
      fc.assert(
        fc.property(FC_MSG, FC_BIGINT_5, (message, privateKeys) => {
+          message = replaceZeroPoint(message);
          const publicKey = privateKeys.map(getPubKey);
          const signatures = privateKeys.map((privateKey) => bls.sign(message, privateKey));
          const aggregatedSignature = bls.aggregateSignatures(signatures);
@@ -1245,6 +1251,7 @@ describe('verify()', () => {
    should('not verify wrong multi-signature as simple signature', () => {
      fc.assert(
        fc.property(FC_MSG, FC_MSG, FC_BIGINT_5, (message, wrongMessage, privateKeys) => {
+          message = replaceZeroPoint(message);
          const publicKey = privateKeys.map(getPubKey);
          const signatures = privateKeys.map((privateKey) => bls.sign(message, privateKey));
          const aggregatedSignature = bls.aggregateSignatures(signatures);
--- a/test/ed25519-addons.test.js
+++ b/test/ed25519-addons.test.js
@@ -1,10 +1,18 @@
 import { sha512 } from '@noble/hashes/sha512';
-import { hexToBytes, bytesToHex as hex } from '@noble/hashes/utils';
+import { bytesToHex as hex, hexToBytes } from '@noble/hashes/utils';
 import { deepStrictEqual, throws } from 'assert';
 import { describe, should } from 'micro-should';
 import { bytesToNumberLE, numberToBytesLE } from '../esm/abstract/utils.js';
 import { default as x25519vectors } from './wycheproof/x25519_test.json' assert { type: 'json' };
-import { ed25519ctx, ed25519ph, RistrettoPoint, x25519 } from '../esm/ed25519.js';
+import {
+  ed25519,
+  ed25519ctx,
+  ed25519ph,
+  edwardsToMontgomeryPub,
+  edwardsToMontgomeryPriv,
+  RistrettoPoint,
+  x25519,
+} from '../esm/ed25519.js';

 const VECTORS_RFC8032_CTX = [
  {
@@ -141,6 +149,56 @@ describe('RFC7748 X25519 ECDH', () => {
    deepStrictEqual(hex(x25519.scalarMult(bobPrivate, alicePublic)), shared);
  });

+  should('X25519/getSharedSecret() should be commutative', () => {
+    for (let i = 0; i < 512; i++) {
+      const asec = x25519.utils.randomPrivateKey();
+      const apub = x25519.getPublicKey(asec);
+      const bsec = x25519.utils.randomPrivateKey();
+      const bpub = x25519.getPublicKey(bsec);
+      try {
+        deepStrictEqual(x25519.getSharedSecret(asec, bpub), x25519.getSharedSecret(bsec, apub));
+      } catch (error) {
+        console.error('not commutative', { asec, apub, bsec, bpub });
+        throw error;
+      }
+    }
+  });
+
+  should('edwardsToMontgomery should produce correct output', () => {
+    const edSecret = hexToBytes('77076d0a7318a57d3c16c17251b26645df4c2f87ebc0992ab177fba51db92c2a');
+    const edPublic = ed25519.getPublicKey(edSecret);
+    const xPrivate = edwardsToMontgomeryPriv(edSecret);
+    deepStrictEqual(
+      hex(xPrivate),
+      'a8cd44eb8e93319c0570bc11005c0e0189d34ff02f6c17773411ad191293c94f'
+    );
+    const xPublic = edwardsToMontgomeryPub(edPublic);
+    deepStrictEqual(
+      hex(xPublic),
+      'ed7749b4d989f6957f3bfde6c56767e988e21c9f8784d91d610011cd553f9b06'
+    );
+  });
+
+  should('edwardsToMontgomery should produce correct keyPair', () => {
+    const edSecret = ed25519.utils.randomPrivateKey();
+    const edPublic = ed25519.getPublicKey(edSecret);
+    const xSecret = edwardsToMontgomeryPriv(edSecret);
+    const expectedXPublic = x25519.getPublicKey(xSecret);
+    const xPublic = edwardsToMontgomeryPub(edPublic);
+    deepStrictEqual(xPublic, expectedXPublic);
+  });
+
+  should('ECDH through edwardsToMontgomery should be commutative', () => {
+    const edSecret1 = ed25519.utils.randomPrivateKey();
+    const edPublic1 = ed25519.getPublicKey(edSecret1);
+    const edSecret2 = ed25519.utils.randomPrivateKey();
+    const edPublic2 = ed25519.getPublicKey(edSecret2);
+    deepStrictEqual(
+      x25519.getSharedSecret(edwardsToMontgomeryPriv(edSecret1), edwardsToMontgomeryPub(edPublic2)),
+      x25519.getSharedSecret(edwardsToMontgomeryPriv(edSecret2), edwardsToMontgomeryPub(edPublic1))
+    );
+  });
+
  should('base point', () => {
    const { y } = ed25519ph.ExtendedPoint.BASE;
    const { Fp } = ed25519ph.CURVE;
@@ -298,7 +356,7 @@ describe('ristretto255', () => {

 // ESM is broken.
 import url from 'url';
-import { assert } from 'console';
+
 if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
  should.run();
 }
--- a/test/ed25519.test.js
+++ b/test/ed25519.test.js
@@ -1,17 +1,19 @@
 import { deepStrictEqual, strictEqual, throws } from 'assert';
 import { readFileSync } from 'fs';
-import { bytesToHex, concatBytes, hexToBytes, randomBytes } from '@noble/hashes/utils';
+import { bytesToHex, concatBytes, hexToBytes, utf8ToBytes, randomBytes } from '@noble/hashes/utils';
 import * as fc from 'fast-check';
 import { describe, should } from 'micro-should';
-import { ed25519, ED25519_TORSION_SUBGROUP, numberToBytesLE } from './ed25519.helpers.js';
+import { ed25519 as ed, ED25519_TORSION_SUBGROUP, numberToBytesLE } from './ed25519.helpers.js';
 // Old vectors allow to test sign() because they include private key
 import { default as ed25519vectors_OLD } from './ed25519/ed25519_test_OLD.json' assert { type: 'json' };
 import { default as ed25519vectors } from './wycheproof/ed25519_test.json' assert { type: 'json' };
-
 import { default as zip215 } from './ed25519/zip215.json' assert { type: 'json' };
+import { default as edgeCases } from './ed25519/edge-cases.json' assert { type: 'json' };
+
+// Any changes to the file will need to be aware of the fact
+// the file is shared between noble-curves and noble-ed25519.

 describe('ed25519', () => {
-  const ed = ed25519;
  const hex = bytesToHex;
  const Point = ed.ExtendedPoint;

@@ -20,13 +22,6 @@ describe('ed25519', () => {
    return hexToBytes(hex.padStart(64, '0'));
  }

-  function utf8ToBytes(str) {
-    if (typeof str !== 'string') {
-      throw new Error(`utf8ToBytes expected string, got ${typeof str}`);
-    }
-    return new TextEncoder().encode(str);
-  }
-
  ed.utils.precompute(8);

  should('not accept >32byte private keys', () => {
@@ -415,27 +410,36 @@ describe('ed25519', () => {
    }
  });

+  should('have strict SUF-CMA and SBS properties', () => {
+    // https://eprint.iacr.org/2020/1244
+    const list = [0, 1, 6, 7, 8, 9, 10, 11].map((i) => edgeCases[i]);
+    for (let v of list) {
+      const result = ed.verify(v.signature, v.message, v.pub_key, { zip215: false });
+      strictEqual(result, false, `zip215: false must not validate: ${v.signature}`);
+    }
+  });
+
  should('not verify when sig.s >= CURVE.n', () => {
-    const privateKey = ed25519.utils.randomPrivateKey();
+    const privateKey = ed.utils.randomPrivateKey();
    const message = Uint8Array.from([0xab, 0xbc, 0xcd, 0xde]);
-    const publicKey = ed25519.getPublicKey(privateKey);
-    const signature = ed25519.sign(message, privateKey);
+    const publicKey = ed.getPublicKey(privateKey);
+    const signature = ed.sign(message, privateKey);

    const R = signature.slice(0, 32);
    let s = signature.slice(32, 64);

    s = bytesToHex(s.slice().reverse());
    s = BigInt('0x' + s);
-    s = s + ed25519.CURVE.n;
+    s = s + ed.CURVE.n;
    s = numberToBytesLE(s, 32);

    const sig_invalid = concatBytes(R, s);
-    deepStrictEqual(ed25519.verify(sig_invalid, message, publicKey), false);
+    deepStrictEqual(ed.verify(sig_invalid, message, publicKey), false);
  });

  should('not accept point without z, t', () => {
    const t = 81718630521762619991978402609047527194981150691135404693881672112315521837062n;
-    const point = ed25519.ExtendedPoint.fromAffine({ x: t, y: t });
+    const point = Point.fromAffine({ x: t, y: t });
    throws(() => point.assertValidity());
    // Otherwise (without assertValidity):
    // const point2 = point.double();
--- a/test/ed25519/edge-cases.json
+++ b/test/ed25519/edge-cases.json
@@ -0,0 +1 @@
+[{"message":"8c93255d71dcab10e8f379c26200f3c7bd5f09d9bc3068d3ef4edeb4853022b6","pub_key":"c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa","signature":"c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac037a0000000000000000000000000000000000000000000000000000000000000000"},{"message":"9bd9f44f4dcc75bd531b56b2cd280b0bb38fc1cd6d1230e14861d861de092e79","pub_key":"c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa","signature":"f7badec5b8abeaf699583992219b7b223f1df3fbbea919844e3f7c554a43dd43a5bb704786be79fc476f91d3f3f89b03984d8068dcf1bb7dfc6637b45450ac04"},{"message":"aebf3f2601a0c8c5d39cc7d8911642f740b78168218da8471772b35f9d35b9ab","pub_key":"f7badec5b8abeaf699583992219b7b223f1df3fbbea919844e3f7c554a43dd43","signature":"c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa8c4bd45aecaca5b24fb97bc10ac27ac8751a7dfe1baff8b953ec9f5833ca260e"},{"message":"9bd9f44f4dcc75bd531b56b2cd280b0bb38fc1cd6d1230e14861d861de092e79","pub_key":"cdb267ce40c5cd45306fa5d2f29731459387dbf9eb933b7bd5aed9a765b88d4d","signature":"9046a64750444938de19f227bb80485e92b83fdb4b6506c160484c016cc1852f87909e14428a7a1d62e9f22f3d3ad7802db02eb2e688b6c52fcd6648a98bd009"},{"message":"e47d62c63f830dc7a6851a0b1f33ae4bb2f507fb6cffec4011eaccd55b53f56c","pub_key":"cdb267ce40c5cd45306fa5d2f29731459387dbf9eb933b7bd5aed9a765b88d4d","signature":"160a1cb0dc9c0258cd0a7d23e94d8fa878bcb1925f2c64246b2dee1796bed5125ec6bc982a269b723e0668e540911a9a6a58921d6925e434ab10aa7940551a09"},{"message":"e47d62c63f830dc7a6851a0b1f33ae4bb2f507fb6cffec4011eaccd55b53f56c","pub_key":"cdb267ce40c5cd45306fa5d2f29731459387dbf9eb933b7bd5aed9a765b88d4d","signature":"21122a84e0b5fca4052f5b1235c80a537878b38f3142356b2c2384ebad4668b7e40bc836dac0f71076f9abe3a53f9c03c1ceeeddb658d0030494ace586687405"},{"message":"85e241a07d148b41e47d62c63f830dc7a6851a0b1f33ae4bb2f507fb6cffec40","pub_key":"442aad9f089ad9e14647b1ef9099a1ff4798d78589e66f28eca69c11f582a623","signature":"e96f66be976d82e60150baecff9906684aebb1ef181f67a7189ac78ea23b6c0e547f7690a0e2ddcd04d87dbc3490dc19b3b3052f7ff0538cb68afb369ba3a514"},{"message":"85e241a07d148b41e47d62c63f830dc7a6851a0b1f33ae4bb2f507fb6cffec40","pub_key":"442aad9f089ad9e14647b1ef9099a1ff4798d78589e66f28eca69c11f582a623","signature":"8ce5b96c8f26d0ab6c47958c9e68b937104cd36e13c33566acd2fe8d38aa19427e71f98a473474f2f13f06f97c20d58cc3f54b8bd0d272f42b695dd7e89a8c22"},{"message":"9bedc267423725d473888631ebf45988bad3db83851ee85c85e241a07d148b41","pub_key":"f7badec5b8abeaf699583992219b7b223f1df3fbbea919844e3f7c554a43dd43","signature":"ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff03be9678ac102edcd92b0210bb34d7428d12ffc5df5f37e359941266a4e35f0f"},{"message":"9bedc267423725d473888631ebf45988bad3db83851ee85c85e241a07d148b41","pub_key":"f7badec5b8abeaf699583992219b7b223f1df3fbbea919844e3f7c554a43dd43","signature":"ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffca8c5b64cd208982aa38d4936621a4775aa233aa0505711d8fdcfdaa943d4908"},{"message":"e96b7021eb39c1a163b6da4e3093dcd3f21387da4cc4572be588fafae23c155b","pub_key":"ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff","signature":"a9d55260f765261eb9b84e106f665e00b867287a761990d7135963ee0a7d59dca5bb704786be79fc476f91d3f3f89b03984d8068dcf1bb7dfc6637b45450ac04"},{"message":"39a591f5321bbe07fd5a23dc2f39d025d74526615746727ceefd6e82ae65c06f","pub_key":"ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff","signature":"a9d55260f765261eb9b84e106f665e00b867287a761990d7135963ee0a7d59dca5bb704786be79fc476f91d3f3f89b03984d8068dcf1bb7dfc6637b45450ac04"}]
--- a/test/ed448-addons.test.js
+++ b/test/ed448-addons.test.js
@@ -0,0 +1,117 @@
+import { bytesToHex as hex, hexToBytes } from '@noble/hashes/utils';
+import { deepStrictEqual, throws } from 'assert';
+import { describe, should } from 'micro-should';
+import { bytesToNumberLE } from '../esm/abstract/utils.js';
+import { ed448, DecafPoint } from '../esm/ed448.js';
+
+describe('decaf448', () => {
+  should('follow the byte encodings of small multiples', () => {
+    const encodingsOfSmallMultiples = [
+      // This is the identity point
+      '0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000',
+      // This is the basepoint
+      '6666666666666666666666666666666666666666666666666666666633333333333333333333333333333333333333333333333333333333',
+      // These are small multiples of the basepoint
+      'c898eb4f87f97c564c6fd61fc7e49689314a1f818ec85eeb3bd5514ac816d38778f69ef347a89fca817e66defdedce178c7cc709b2116e75',
+      'a0c09bf2ba7208fda0f4bfe3d0f5b29a543012306d43831b5adc6fe7f8596fa308763db15468323b11cf6e4aeb8c18fe44678f44545a69bc',
+      'b46f1836aa287c0a5a5653f0ec5ef9e903f436e21c1570c29ad9e5f596da97eeaf17150ae30bcb3174d04bc2d712c8c7789d7cb4fda138f4',
+      '1c5bbecf4741dfaae79db72dface00eaaac502c2060934b6eaaeca6a20bd3da9e0be8777f7d02033d1b15884232281a41fc7f80eed04af5e',
+      '86ff0182d40f7f9edb7862515821bd67bfd6165a3c44de95d7df79b8779ccf6460e3c68b70c16aaa280f2d7b3f22d745b97a89906cfc476c',
+      '502bcb6842eb06f0e49032bae87c554c031d6d4d2d7694efbf9c468d48220c50f8ca28843364d70cee92d6fe246e61448f9db9808b3b2408',
+      '0c9810f1e2ebd389caa789374d78007974ef4d17227316f40e578b336827da3f6b482a4794eb6a3975b971b5e1388f52e91ea2f1bcb0f912',
+      '20d41d85a18d5657a29640321563bbd04c2ffbd0a37a7ba43a4f7d263ce26faf4e1f74f9f4b590c69229ae571fe37fa639b5b8eb48bd9a55',
+      'e6b4b8f408c7010d0601e7eda0c309a1a42720d6d06b5759fdc4e1efe22d076d6c44d42f508d67be462914d28b8edce32e7094305164af17',
+      'be88bbb86c59c13d8e9d09ab98105f69c2d1dd134dbcd3b0863658f53159db64c0e139d180f3c89b8296d0ae324419c06fa87fc7daaf34c1',
+      'a456f9369769e8f08902124a0314c7a06537a06e32411f4f93415950a17badfa7442b6217434a3a05ef45be5f10bd7b2ef8ea00c431edec5',
+      '186e452c4466aa4383b4c00210d52e7922dbf9771e8b47e229a9b7b73c8d10fd7ef0b6e41530f91f24a3ed9ab71fa38b98b2fe4746d51d68',
+      '4ae7fdcae9453f195a8ead5cbe1a7b9699673b52c40ab27927464887be53237f7f3a21b938d40d0ec9e15b1d5130b13ffed81373a53e2b43',
+      '841981c3bfeec3f60cfeca75d9d8dc17f46cf0106f2422b59aec580a58f342272e3a5e575a055ddb051390c54c24c6ecb1e0aceb075f6056',
+    ];
+    let B = DecafPoint.BASE;
+    let P = DecafPoint.ZERO;
+    for (const encoded of encodingsOfSmallMultiples) {
+      deepStrictEqual(P.toHex(), encoded);
+      deepStrictEqual(DecafPoint.fromHex(encoded).toHex(), encoded);
+      P = P.add(B);
+    }
+  });
+  should('not convert bad bytes encoding', () => {
+    const badEncodings = [
+      // These are all bad because they're non-canonical field encodings.
+      '8e24f838059ee9fef1e209126defe53dcd74ef9b6304601c6966099effffffffffffffffffffffffffffffffffffffffffffffffffffffff',
+      '86fcc7212bd4a0b980928666dc28c444a605ef38e09fb569e28d4443ffffffffffffffffffffffffffffffffffffffffffffffffffffffff',
+      '866d54bd4c4ff41a55d4eefdbeca73cbd653c7bd3135b383708ec0bdffffffffffffffffffffffffffffffffffffffffffffffffffffffff',
+      '4a380ccdab9c86364a89e77a464d64f9157538cfdfa686adc0d5ece4ffffffffffffffffffffffffffffffffffffffffffffffffffffffff',
+      'f22d9d4c945dd44d11e0b1d3d3d358d959b4844d83b08c44e659d79fffffffffffffffffffffffffffffffffffffffffffffffffffffffff',
+      '8cdffc681aa99e9c818c8ef4c3808b58e86acdef1ab68c8477af185bffffffffffffffffffffffffffffffffffffffffffffffffffffffff',
+      '0e1c12ac7b5920effbd044e897c57634e2d05b5c27f8fa3df8a086a1ffffffffffffffffffffffffffffffffffffffffffffffffffffffff',
+      // These are all bad because they're negative field elements.
+      '15141bd2121837ef71a0016bd11be757507221c26542244f23806f3fd3496b7d4c36826276f3bf5deea2c60c4fa4cec69946876da497e795',
+      '455d380238434ab740a56267f4f46b7d2eb2dd8ee905e51d7b0ae8a6cb2bae501e67df34ab21fa45946068c9f233939b1d9521a998b7cb93',
+      '810b1d8e8bf3a9c023294bbfd3d905a97531709bdc0f42390feedd7010f77e98686d400c9c86ed250ceecd9de0a18888ffecda0f4ea1c60d',
+      'd3af9cc41be0e5de83c0c6273bedcb9351970110044a9a41c7b9b2267cdb9d7bf4dc9c2fdb8bed32878184604f1d9944305a8df4274ce301',
+      '9312bcab09009e4330ff89c4bc1e9e000d863efc3c863d3b6c507a40fd2cdefde1bf0892b4b5ed9780b91ed1398fb4a7344c605aa5efda74',
+      '53d11bce9e62a29d63ed82ae93761bdd76e38c21e2822d6ebee5eb1c5b8a03eaf9df749e2490eda9d8ac27d1f71150de93668074d18d1c3a',
+      '697c1aed3cd8858515d4be8ac158b229fe184d79cb2b06e49210a6f3a7cd537bcd9bd390d96c4ab6a4406da5d93640726285370cfa95df80',
+      // These are all bad because they give a nonsquare x².
+      '58ad48715c9a102569b68b88362a4b0645781f5a19eb7e59c6a4686fd0f0750ff42e3d7af1ab38c29d69b670f31258919c9fdbf6093d06c0',
+      '8ca37ee2b15693f06e910cf43c4e32f1d5551dda8b1e48cb6ddd55e440dbc7b296b601919a4e4069f59239ca247ff693f7daa42f086122b1',
+      '982c0ec7f43d9f97c0a74b36db0abd9ca6bfb98123a90782787242c8a523cdc76df14a910d54471127e7662a1059201f902940cd39d57af5',
+      'baa9ab82d07ca282b968a911a6c3728d74bf2fe258901925787f03ee4be7e3cb6684fd1bcfe5071a9a974ad249a4aaa8ca81264216c68574',
+      '2ed9ffe2ded67a372b181ac524996402c42970629db03f5e8636cbaf6074b523d154a7a8c4472c4c353ab88cd6fec7da7780834cc5bd5242',
+      'f063769e4241e76d815800e4933a3a144327a30ec40758ad3723a788388399f7b3f5d45b6351eb8eddefda7d5bff4ee920d338a8b89d8b63',
+      '5a0104f1f55d152ceb68bc138182499891d90ee8f09b40038ccc1e07cb621fd462f781d045732a4f0bda73f0b2acf94355424ff0388d4b9c',
+    ];
+    for (const badBytes of badEncodings) {
+      const b = hexToBytes(badBytes);
+      throws(() => DecafPoint.fromHex(b), badBytes);
+    }
+  });
+  should('create right points from uniform hash', () => {
+    const hashes = [
+      'cbb8c991fd2f0b7e1913462d6463e4fd2ce4ccdd28274dc2ca1f4165d5ee6cdccea57be3416e166fd06718a31af45a2f8e987e301be59ae6673e963001dbbda80df47014a21a26d6c7eb4ebe0312aa6fffb8d1b26bc62ca40ed51f8057a635a02c2b8c83f48fa6a2d70f58a1185902c0',
+      'b6d8da654b13c3101d6634a231569e6b85961c3f4b460a08ac4a5857069576b64428676584baa45b97701be6d0b0ba18ac28d443403b45699ea0fbd1164f5893d39ad8f29e48e399aec5902508ea95e33bc1e9e4620489d684eb5c26bc1ad1e09aba61fabc2cdfee0b6b6862ffc8e55a',
+      '36a69976c3e5d74e4904776993cbac27d10f25f5626dd45c51d15dcf7b3e6a5446a6649ec912a56895d6baa9dc395ce9e34b868d9fb2c1fc72eb6495702ea4f446c9b7a188a4e0826b1506b0747a6709f37988ff1aeb5e3788d5076ccbb01a4bc6623c92ff147a1e21b29cc3fdd0e0f4',
+      'd5938acbba432ecd5617c555a6a777734494f176259bff9dab844c81aadcf8f7abd1a9001d89c7008c1957272c1786a4293bb0ee7cb37cf3988e2513b14e1b75249a5343643d3c5e5545a0c1a2a4d3c685927c38bc5e5879d68745464e2589e000b31301f1dfb7471a4f1300d6fd0f99',
+      '4dec58199a35f531a5f0a9f71a53376d7b4bdd6bbd2904234a8ea65bbacbce2a542291378157a8f4be7b6a092672a34d85e473b26ccfbd4cdc6739783dc3f4f6ee3537b7aed81df898c7ea0ae89a15b5559596c2a5eeacf8b2b362f3db2940e3798b63203cae77c4683ebaed71533e51',
+      'df2aa1536abb4acab26efa538ce07fd7bca921b13e17bc5ebcba7d1b6b733deda1d04c220f6b5ab35c61b6bcb15808251cab909a01465b8ae3fc770850c66246d5a9eae9e2877e0826e2b8dc1bc08009590bc6778a84e919fbd28e02a0f9c49b48dc689eb5d5d922dc01469968ee81b5',
+      'e9fb440282e07145f1f7f5ecf3c273212cd3d26b836b41b02f108431488e5e84bd15f2418b3d92a3380dd66a374645c2a995976a015632d36a6c2189f202fc766e1c82f50ad9189be190a1f0e8f9b9e69c9c18cc98fdd885608f68bf0fdedd7b894081a63f70016a8abf04953affbefa',
+    ];
+    const encodedHashToPoints = [
+      '0c709c9607dbb01c94513358745b7c23953d03b33e39c7234e268d1d6e24f34014ccbc2216b965dd231d5327e591dc3c0e8844ccfd568848',
+      '76ab794e28ff1224c727fa1016bf7f1d329260b7218a39aea2fdb17d8bd9119017b093d641cedf74328c327184dc6f2a64bd90eddccfcdab',
+      'c8d7ac384143500e50890a1c25d643343accce584caf2544f9249b2bf4a6921082be0e7f3669bb5ec24535e6c45621e1f6dec676edd8b664',
+      '62beffc6b8ee11ccd79dbaac8f0252c750eb052b192f41eeecb12f2979713b563caf7d22588eca5e80995241ef963e7ad7cb7962f343a973',
+      'f4ccb31d263731ab88bed634304956d2603174c66da38742053fa37dd902346c3862155d68db63be87439e3d68758ad7268e239d39c4fd3b',
+      '7e79b00e8e0a76a67c0040f62713b8b8c6d6f05e9c6d02592e8a22ea896f5deacc7c7df5ed42beae6fedb9000285b482aa504e279fd49c32',
+      '20b171cb16be977f15e013b9752cf86c54c631c4fc8cbf7c03c4d3ac9b8e8640e7b0e9300b987fe0ab5044669314f6ed1650ae037db853f1',
+    ];
+
+    for (let i = 0; i < hashes.length; i++) {
+      const hash = hexToBytes(hashes[i]);
+      const point = DecafPoint.hashToCurve(hash);
+      deepStrictEqual(point.toHex(), encodedHashToPoints[i]);
+    }
+  });
+  should('have proper equality testing', () => {
+    const MAX_448B = BigInt(
+      '0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff'
+    );
+    const bytes448ToNumberLE = (bytes) => ed448.CURVE.Fp.create(bytesToNumberLE(bytes) & MAX_448B);
+
+    const priv = new Uint8Array([
+      23, 211, 149, 179, 209, 108, 78, 37, 229, 45, 122, 220, 85, 38, 192, 182, 96, 40, 168, 63,
+      175, 194, 73, 202, 14, 175, 78, 15, 117, 175, 40, 32, 218, 221, 151, 58, 158, 91, 250, 141,
+      18, 175, 191, 119, 152, 124, 223, 101, 54, 218, 76, 158, 43, 112, 151, 32,
+    ]);
+    const pub = DecafPoint.BASE.multiply(bytes448ToNumberLE(priv));
+    deepStrictEqual(pub.equals(DecafPoint.ZERO), false);
+  });
+});
+
+// ESM is broken.
+import url from 'url';
+
+if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
+  should.run();
+}
--- a/test/index.test.js
+++ b/test/index.test.js
@@ -4,7 +4,9 @@ import { should } from 'micro-should';
 import './basic.test.js';
 import './nist.test.js';
 import './ed448.test.js';
+import './ed448-addons.test.js';
 import './ed25519.test.js';
+import './ed25519-addons.test.js';
 import './secp256k1.test.js';
 import './secp256k1-schnorr.test.js';
 import './jubjub.test.js';
--- a/test/nist.test.js
+++ b/test/nist.test.js
@@ -10,6 +10,7 @@ import { hexToBytes, bytesToHex } from '../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 './vectors/rfc6979.json' assert { type: 'json' };
+import { default as endoVectors } from './vectors/secp256k1/endomorphism.json' assert { type: 'json' };

 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' };
@@ -438,7 +439,7 @@ describe('RFC6979', () => {
  }
 });

-should('DER Leading zero', () => {
+should('properly add leading zero to DER', () => {
  // Valid DER
  deepStrictEqual(
    DER.toSig(
@@ -465,6 +466,16 @@ should('DER Leading zero', () => {
  );
 });

+should('have proper GLV endomorphism logic in secp256k1', () => {
+  const Point = secp256k1.ProjectivePoint;
+  for (let item of endoVectors) {
+    const point = Point.fromAffine({ x: BigInt(item.ax), y: BigInt(item.ay) });
+    const c = point.multiplyUnsafe(BigInt(item.scalar)).toAffine();
+    deepStrictEqual(c.x, BigInt(item.cx));
+    deepStrictEqual(c.y, BigInt(item.cy));
+  }
+});
+
 // ESM is broken.
 import url from 'url';
 if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
--- a/test/poseidon.test.js
+++ b/test/poseidon.test.js
@@ -163,6 +163,7 @@ should('poseidonperm_x5_255_3', () => {
    t,
    roundsFull: 8,
    roundsPartial: 57,
+    sboxPower: 5,
    mds,
    roundConstants,
  });
@@ -229,6 +230,7 @@ should('poseidonperm_x5_255_5', () => {
    t,
    roundsFull: 8,
    roundsPartial: 60,
+    sboxPower: 5,
    mds,
    roundConstants,
  });
@@ -280,6 +282,7 @@ should('poseidonperm_x5_254_3', () => {
    t,
    roundsFull: 8,
    roundsPartial: 57,
+    sboxPower: 5,
    mds,
    roundConstants,
  });
@@ -347,6 +350,7 @@ should('poseidonperm_x5_254_5', () => {
    t,
    roundsFull: 8,
    roundsPartial: 60,
+    sboxPower: 5,
    mds,
    roundConstants,
  });
--- a/test/secp256k1.test.js
+++ b/test/secp256k1.test.js
@@ -14,6 +14,9 @@ import { default as privates } from './vectors/secp256k1/privates.json' assert {
 import { default as points } from './vectors/secp256k1/points.json' assert { type: 'json' };
 import { default as wp } from './wycheproof/ecdsa_secp256k1_sha256_test.json' assert { type: 'json' };

+// Any changes to the file will need to be aware of the fact
+// the file is shared between noble-curves and noble-secp256k1.
+
 const Point = secp.ProjectivePoint;
 const privatesTxt = readFileSync('./test/vectors/secp256k1/privates-2.txt', 'utf-8');

@@ -265,6 +268,33 @@ describe('secp256k1', () => {
        deepStrictEqual(sign(ent5), e.extraEntropyMax);
      }
    });
+
+    should('handle one byte {extraData}', () => {
+      const extraEntropy = '01';
+      const privKey = hexToBytes(
+        '0101010101010101010101010101010101010101010101010101010101010101'
+      );
+      const msg = 'd1a9dc8ed4e46a6a3e5e594615ca351d7d7ef44df1e4c94c1802f3592183794b';
+      const res = secp.sign(msg, privKey, { extraEntropy }).toCompactHex();
+      deepStrictEqual(
+        res,
+        'a250ec23a54bfdecf0e924cbf484077c5044410f915cdba86731cb2e4e925aaa5b1e4e3553d88be2c48a9a0d8d849ce2cc5720d25b2f97473e02f2550abe9545'
+      );
+    });
+
+    should('handle 48 bytes {extraData}', () => {
+      const extraEntropy =
+        '000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000001';
+      const privKey = hexToBytes(
+        '0101010101010101010101010101010101010101010101010101010101010101'
+      );
+      const msg = 'd1a9dc8ed4e46a6a3e5e594615ca351d7d7ef44df1e4c94c1802f3592183794b';
+      const res = secp.sign(msg, privKey, { extraEntropy }).toCompactHex();
+      deepStrictEqual(
+        res,
+        '2bdf40f42ac0e42ee12750d03bb12b75306dae58eb3c961c5a80d78efae93e595295b66e8eb28f1eb046bb129a976340312159ec0c20b97342667572e4a8379a'
+      );
+    });
  });

  describe('verify()', () => {
--- a/test/vectors/secp256k1/endomorphism.json
+++ b/test/vectors/secp256k1/endomorphism.json
@@ -0,0 +1,26 @@
+[
+  {
+    "desc": "k1neg=true, k2neg=false",
+    "ax": "55066263022277343669578718895168534326250603453777594175500187360389116729240",
+    "ay": "32670510020758816978083085130507043184471273380659243275938904335757337482424",
+    "scalar": "2704427838213584814824020837927043695889",
+    "cx": "70912011419250646761259860556624974262679413898110209707622032756145750038852",
+    "cy": "46481114889376149700487001434152190585794282401306514438088690968308506923285"
+  },
+  {
+    "desc": "k1neg=false, k2neg=true",
+    "ax": "55066263022277343669578718895168534326250603453777594175500187360389116729240",
+    "ay": "32670510020758816978083085130507043184471273380659243275938904335757337482424",
+    "scalar": "367917413016453100223835821029139468248",
+    "cx": "10322688129782350538653828383726187034025074756440739323015371090593152139135",
+    "cy": "68793242610611269092604721689053086352541804982835045879816374698216278704126"
+  },
+  {
+    "desc": "k1neg=true, k2neg=true",
+    "ax": "55066263022277343669578718895168534326250603453777594175500187360389116729240",
+    "ay": "32670510020758816978083085130507043184471273380659243275938904335757337482424",
+    "scalar": "3808180077262944115495528301014462100633",
+    "cx": "14215418389480067884450074673878587420586762919133643262861030012154939932102",
+    "cy": "29847359538023735520768762420255189621104408153695873716448888266404867737302"
+  }
+]
--- a/tsconfig.esm.json
+++ b/tsconfig.esm.json
@@ -1,20 +1,24 @@
 {
-    "compilerOptions": {
-        "strict": true,
-        "outDir": "esm",
-        "target": "es2020",
-        "module": "es6",
-        "moduleResolution": "node16",
-        "noUnusedLocals": true,
-        "sourceMap": true,
-        "baseUrl": ".",
-        "paths": {
-            "@noble/hashes/crypto": [ "src/crypto" ]
-        },
+  "compilerOptions": {
+    "outDir": "esm",
+    "target": "es2020",
+    "module": "es6",
+    "moduleResolution": "node16",
+    "baseUrl": ".",
+    "paths": {
+      "@noble/hashes/crypto": ["src/crypto"]
    },
-    "include": ["src"],
-    "exclude": [
-        "node_modules",
-        "lib",
-    ],
+    "sourceMap": true,
+    "strict": true,
+    "allowSyntheticDefaultImports": false,
+    "allowUnreachableCode": false,
+    "esModuleInterop": false,
+    "noFallthroughCasesInSwitch": true,
+    "noImplicitReturns": true,
+    "noUncheckedIndexedAccess": false,
+    "noUnusedLocals": true,
+    "noUnusedParameters": true,
+  },
+  "include": ["src"],
+  "exclude": ["node_modules", "lib"]
 }
--- a/tsconfig.json
+++ b/tsconfig.json
@@ -1,20 +1,24 @@
 {
-    "compilerOptions": {
-        "strict": true,
-        "declaration": true,
-        "declarationMap": true,
-        "sourceMap": true,
-        "outDir": ".",
-        "target": "es2020",
-        "lib": ["es2020"], // Set explicitly to remove DOM
-        "module": "commonjs",
-        "moduleResolution": "node",
-        "noUnusedLocals": true,
-        "baseUrl": ".",
-    },
-    "include": ["src"],
-    "exclude": [
-        "node_modules",
-        "*.d.ts"
-    ],
+  "compilerOptions": {
+    "outDir": ".",
+    "target": "es2020",
+    "lib": ["es2020"], // Set explicitly to remove DOM
+    "module": "commonjs",
+    "moduleResolution": "node",
+    "baseUrl": ".",
+    "sourceMap": true,
+    "declaration": true,
+    "declarationMap": true,
+    "strict": true,
+    "allowSyntheticDefaultImports": false,
+    "allowUnreachableCode": false,
+    "esModuleInterop": false,
+    "noFallthroughCasesInSwitch": true,
+    "noImplicitReturns": true,
+    "noUncheckedIndexedAccess": false,
+    "noUnusedLocals": true,
+    "noUnusedParameters": true
+  },
+  "include": ["src"],
+  "exclude": ["node_modules", "*.d.ts"]
 }
Author	SHA1	Message	Date
Paul Miller	0d7756dceb	Release 1.2.0.	2023-08-23 20:00:32 +02:00
Paul Miller	b716b4603f	Update lockfile for 1.2	2023-08-23 19:58:55 +02:00
Paul Miller	d7a139822d	Release 1.2.0.	2023-08-23 19:55:35 +02:00
Paul Miller	fb6c379a26	Update README	2023-08-23 19:48:52 +02:00
Paul Miller	eeac255c88	update noble-hashes to 1.3.2	2023-08-23 19:45:47 +02:00
Paul Miller	925fc3f810	modular: adjust getFieldsBytseLength	2023-08-23 19:43:55 +02:00
Paul Miller	eb8e7ec964	hash-to-curve, weierstrass, bls, ed: upgrade h2c comments to rfc 9380	2023-08-23 19:43:14 +02:00
Paul Miller	e7ac5e85d3	poseidon: refactor params	2023-08-21 18:16:40 +02:00
Paul Miller	d285fcce06	modular: Document FpPow	2023-08-21 17:52:21 +02:00
Paul Miller	ef667bb404	poseidon: refactor validateOpts, fix tests	2023-08-21 17:48:34 +02:00
Paul Miller	62749382e7	poseidon: remove default sboxPower: 5	2023-08-21 17:04:58 +02:00
Paul Miller	f90e871725	weierstrass: prohibit (0, 0, 0) in assertValidity	2023-08-21 16:05:53 +02:00
Paul Miller	f049398718	modular: bring back 1.1.0 hashToPrivateScalar for clean diff	2023-08-18 23:14:08 +02:00
Paul Miller	ca99179bd8	bls, modular: lint	2023-08-18 23:09:53 +02:00
Paul Miller	1545230ee5	modular, weierstrass, bls: use new mapHashToField	2023-08-18 23:08:46 +02:00
Paul Miller	2ce3b825f8	readme	2023-08-16 02:36:24 +02:00
Paul Miller	8315fe3580	readme	2023-08-16 02:33:10 +02:00
Paul Miller	9b7889e16f	README: improve docs for ecdh	2023-08-16 02:14:41 +02:00
Paul Miller	e8b9509c16	abstract/modular: add more comments everywhere	2023-08-11 12:23:52 +02:00
Paul Miller	d92c9d14ad	README: update Field documentation, reformat with prettier	2023-08-11 12:23:19 +02:00
Paul Miller	05794c0283	weierstrass, bls: improve randomPrivateKey security and decrease bias	2023-08-11 12:22:37 +02:00
Paul Miller	ca5583f713	ed25519, ed448: rename hash_to_ristretto to hashToRistretto. And decaf	2023-08-10 20:01:13 +02:00
Paul Miller	8c48abe16a	Lint	2023-08-08 15:43:31 +02:00
Paul Miller	08bb00cc8f	poseidon: prohibit sBoxPower other than 3, 5, 7	2023-08-08 15:43:14 +02:00
Paul Miller	1ef16033fe	readme	2023-08-07 13:54:02 +02:00
Paul Miller	113b6d7c00	readme	2023-08-07 13:48:18 +02:00
Paul Miller	5c3dc0be50	README: more blog posts	2023-08-07 13:45:38 +02:00
Paul Miller	e7d01f4038	Update README.md	2023-08-07 13:11:30 +02:00
Paul Miller	9a39625eda	test: lint	2023-08-05 11:25:56 +02:00
Paul Miller	af8462b09e	tests/bls12: fix crashes on zero messages	2023-08-05 10:56:52 +02:00
Paul Miller	bfd9ae040d	readme: add alt_bn128	2023-08-05 01:19:42 +02:00
Paul Miller	2bd437df4e	readme	2023-08-05 00:47:59 +02:00
Paul Miller	b0af0a8977	readme	2023-08-05 00:31:41 +02:00
Paul Miller	aee10c8141	readme	2023-07-18 09:11:24 +02:00
Paul Miller	ff92bafb6f	readme	2023-07-18 09:09:01 +02:00
Paul Miller	54679ff788	Usage	2023-07-18 09:08:28 +02:00
Paul Miller	ee4571c7a1	readme: toc	2023-07-18 09:07:11 +02:00
Paul Miller	fe7afdd392	readme	2023-07-16 06:31:52 +02:00
Paul Miller	dba2f0e732	lint	2023-07-12 23:58:30 +02:00
Paul Miller	52c5df0264	utils: add PURE flag	2023-07-12 20:28:45 +02:00
Paul Miller	ebea4a4bcd	weierstrass, bls12-381: adjust var names for typescript flag	2023-07-12 20:28:38 +02:00
Paul Miller	33a53006f7	build: update esbuild	2023-07-12 20:28:11 +02:00
Paul Miller	549e286ef0	package.json: declare side-effects free	2023-07-12 20:26:12 +02:00
Paul Miller	3f0c0b59f1	readme	2023-07-11 19:00:56 +02:00
Paul Miller	62205347e1	readme for finalExponentiate	2023-07-11 18:59:40 +02:00
Paul Miller	476e75104f	Merge pull request #62 from steveluscher/pure-and-twisted Add pure annotation to all calls to `twistedEdwards`	2023-07-01 04:27:31 +02:00
steveluscher	413725cfb3	Add pure annotation to all calls to `twistedEdwards` This PR makes it so that if you only use _one_ export: ```ts import { ed25519 } from '@noble/curves`; ``` …then only the `twistedEdwards` call that constructs that export will remain after bundling and tree-shaking. Before this change, the compiled bundle contains all the code that constructs `ed25519ph` and `ed25519ctx` remains. ```js var ed25519 = twistedEdwards(ed25519Defaults); function ed25519_domain(data, ctx, phflag) { 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); } twistedEdwards({ ...ed25519Defaults, domain: ed25519_domain }); twistedEdwards({ ...ed25519Defaults, domain: ed25519_domain, prehash: sha512 }); ``` ```js var ed25519 = twistedEdwards(ed25519Defaults); ```	2023-06-30 17:36:16 +00:00
Paul Miller	cf17f7fe01	readme	2023-06-28 17:33:13 +02:00
Paul Miller	49fb90ae9a	Add README link to new library noble-ciphers	2023-06-28 16:04:09 +02:00
Paul Miller	309d29a084	Merge pull request #56 from CoinSpace/extraentropy fix: check extraEntropy according to the spec	2023-06-28 14:44:56 +02:00
Evgeny Vlasenko	d3aa051770	feat: tests for extraEntropy	2023-06-28 16:12:44 +04:00
Paul Miller	5609ec7644	Adjust readme docs on sig key recovery	2023-06-27 01:38:02 +02:00
Paul Miller	af8c1eebee	Merge pull request #59 from stknob/decaf448 Add decaf448	2023-06-27 00:32:53 +02:00
Stefan Knoblich	08ea57ce5c	Expand ristretto255 and ed448 + decaf448 README section Signed-off-by: Stefan Knoblich <stkn@bitplumber.de>	2023-06-26 22:48:48 +02:00
Stefan Knoblich	ee3d3815b4	Add benchmarks for hash_to_ristretto255 and hash_to_decaf448 Signed-off-by: Stefan Knoblich <stkn@bitplumber.de>	2023-06-26 22:48:48 +02:00
Stefan Knoblich	f471405798	Add benchmarks for ristretto255 and decaf448 Signed-off-by: Stefan Knoblich <stkn@bitplumber.de>	2023-06-26 22:48:48 +02:00
Stefan Knoblich	e3a4bbffe9	Add decaf448 Based on draft-irtf-cfrg-ristretto255-decaf448-07, draft-irtf-cfrg-hash-to-curve-16 and the ristretto255 implementation. Signed-off-by: Stefan Knoblich <stkn@bitplumber.de>	2023-06-26 22:48:48 +02:00
Paul Miller	c2edc97868	Merge pull request #58 from sublimator/nd-validate-dst-as-stringoruint8array-closes-57-2023-06-22 fix: validate hash_to_field DST as stringOrUint8Array (closes #57)	2023-06-23 00:27:24 +02:00
Nicholas Dudfield	bf70ba9776	fix: validate hash_to_field DST as stringOrUint8Array (closes #57 )	2023-06-22 07:19:08 +07:00
Evgeny Vlasenko	c71920722c	fix: check extraEntropy according to the spec	2023-06-16 19:43:12 +04:00
Paul Miller	62e806cfaf	Release 1.1.0.	2023-06-03 14:31:43 +02:00
Paul Miller	6a72821185	readme	2023-06-03 14:27:05 +02:00
Paul Miller	8cee1f559f	Bump noble-hashes to 1.3.1	2023-06-03 14:23:18 +02:00
Paul Miller	6f10632ac0	Add build directory that allows to test tree-shaking	2023-06-02 17:16:56 +02:00
Paul Miller	b281167e8d	Fix utf8ToBytes in firefox extension context	2023-06-02 15:57:46 +02:00
Paul Miller	c6b4aadafb	utils: harmonize with noble-hashes	2023-06-02 15:35:37 +02:00
Paul Miller	aade023e48	pkg.json: Adjust funding field	2023-05-27 16:10:58 +02:00
Paul Miller	2e04d96ce9	readme	2023-05-26 13:27:41 +02:00
Paul Miller	79dd7d3426	readme	2023-05-20 12:34:51 +02:00
Paul Miller	ff5b231e31	secp256k1 & other implementations: reduce bundle size by 20% by using PURE. PURE annotation helps bundlers during tree-shaking and eliminates dead code. * secp256k1: 75.4kb => 62.3kb * ed25519: 67.5kb => 51.1kb * ed448: 55.1kb => 44.0kb * p256: 67.8kb => 59.8kb * p384: 75.4kb => 67.4kb * p521: 75.8kb => 67.8kb	2023-05-20 10:49:50 +02:00
Paul Miller	648fd2cc07	benchmark: curves should bench ed25519 first	2023-05-19 09:58:30 +02:00
Paul Miller	f67134ca86	benchmark: add msm to bls	2023-05-19 09:58:13 +02:00
Paul Miller	6d0678b076	readme	2023-05-14 06:54:17 +02:00
Paul Miller	53ebde19ea	readme	2023-05-14 06:48:22 +02:00
Paul Miller	a7755332c8	readme	2023-05-14 06:40:09 +02:00
Paul Miller	5f0007ab24	readme	2023-05-13 01:31:55 +02:00
Paul Miller	1ee5a5c07f	CI: auto-publish to NPM on GH release	2023-05-12 20:53:24 +02:00
Paul Miller	708c0e14d5	readme	2023-05-12 19:03:17 +02:00
Paul Miller	624d7c9910	Merge pull request #46 from sublimator/nd-sort-few-typos-things-editor-nagging-about-2023-05-09 docs(modular): sort few typos/things editor nagging about	2023-05-09 18:01:35 +02:00
Nicholas Dudfield	665ef2dd93	docs(modular): sort few typos/things editor nagging about	2023-05-09 07:35:33 +07:00
Paul Miller	acc1f26acf	readme	2023-05-07 23:32:41 +02:00
Paul Miller	3c4a25263e	readme	2023-05-06 22:05:33 +02:00
Paul Miller	e887d516ab	readme	2023-05-06 21:20:38 +02:00
Paul Miller	90e87f7ab1	weierstrass: adjust SWUFpSqrtRatio to not use exp operator	2023-05-06 14:38:53 +02:00
Paul Miller	5edafbac97	Merge pull request #42 from sublimator/patch-1 ed25519: fix ristrettoHash size typo in hashToCurve	2023-05-05 17:48:08 +02:00
Nicholas Dudfield	554c94509e	ed25519: fix ristrettoHash size typo in hashToCurve	2023-05-05 18:17:40 +07:00
Paul Miller	7c11a021c0	Drop v16 from ci, it will be out in 4 months	2023-05-05 03:54:16 +02:00
Paul Miller	531b6a3a48	Adjust CI	2023-05-05 03:53:35 +02:00
Paul Miller	fb5cd9df39	README	2023-05-05 03:52:49 +02:00
Paul Miller	53a6d636d4	Merge pull request #38 from legobeat/ci-node-version-matrix ci: test nodejs v16/v18/v20	2023-05-05 03:50:00 +02:00
Paul Miller	42de620010	edwards: make zip215 false Strongly Binding Signature (SBS) secure. gh-40	2023-05-05 03:37:13 +02:00
Paul Miller	6621053c7d	edwards: ensure Point.fromHex fails when x=0 and first x bit is 1. gh-40	2023-05-05 01:39:53 +02:00
Paul Miller	9bee88888f	weierstrass: improve return type of sign(). Clarify comments.	2023-05-03 18:28:35 +02:00
legobt	103ba5f0a7	ci: test nodejs v16/v18/v20	2023-05-02 11:59:54 +09:00
Paul Miller	d5de5d2659	README: add more projects using curves	2023-04-28 02:46:07 +02:00
Paul Miller	217cf8c654	readme: more resources	2023-04-27 01:58:29 +02:00
Paul Miller	8e307d8f89	readme	2023-04-27 01:01:42 +02:00
Paul Miller	8c0018d57f	readme	2023-04-27 00:54:41 +02:00
Paul Miller	ca7f202839	Add secp256k1 compatibility layer URL to readme	2023-04-27 00:16:29 +02:00
Paul Miller	816077ac0a	README	2023-04-24 13:00:43 +02:00
Paul Miller	bc03a07043	readme	2023-04-23 20:31:29 +02:00
Paul Miller	63653255e1	ed448: rename to edwardsToMontgomeryPub	2023-04-23 20:29:17 +02:00
Paul Miller	895ee3a1a4	bls: refactor slightly	2023-04-23 20:29:03 +02:00
Paul Miller	16b31b9087	edwards: use bitmask instead of exp	2023-04-23 20:28:47 +02:00
Paul Miller	213796db4b	ed25519: rename to edwardsToMontgomeryPub	2023-04-23 20:28:28 +02:00
Paul Miller	049d3bce54	CI: node.js 20	2023-04-23 20:17:45 +02:00
Paul Miller	b2a04c2393	Merge pull request #32 from mirceanis/31-fix-edwardsToMontgomery ed25519: fix edwardsToMontgomery formula; implement edwardsToMontgomeryPriv	2023-04-23 20:16:22 +02:00
Paul Miller	cb5e9a6e96	Update benchmarks	2023-04-22 03:20:11 +02:00
Paul Miller	36af62357f	test: adjust ed and secp tests a bit	2023-04-22 02:24:41 +02:00
Mircea Nistor	88291eba33	ed25519: fix edwardsToMontgomery formula; implement edwardsToMontgomeryPriv; add tests	2023-04-20 13:37:21 +02:00
Paul Miller	848a1b0226	nist tests: add endomorphism test	2023-04-14 19:53:20 +02:00
Paul Miller	972e549dde	bls: no bigint literals	2023-04-13 17:18:39 +02:00
				`@@ -0,0 +1 @@`
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