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README.md
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README.md
@ -35,10 +35,16 @@ For [Deno](https://deno.land), ensure to use [npm specifier](https://deno.land/m
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For React Native, you may need a [polyfill for getRandomValues](https://github.com/LinusU/react-native-get-random-values).
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A standalone file [noble-curves.js](https://github.com/paulmillr/noble-curves/releases) is also available.
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```js
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// import * from '@noble/curves'; // Error: use sub-imports, to ensure small app size
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import { secp256k1 } from '@noble/curves/secp256k1'; // ESM and Common.js
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// import { secp256k1 } from 'npm:@noble/curves@1.2.0/secp256k1'; // Deno
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```
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- [Implementations](#implementations)
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- [ECDSA signature scheme](#ecdsa-signature-scheme)
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- [ECDSA public key recovery & extra entropy](#ecdsa-public-key-recovery--extra-entropy)
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- [ECDH (Elliptic Curve Diffie-Hellman)](#ecdh-elliptic-curve-diffie-hellman)
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- [ECDH: Elliptic Curve Diffie-Hellman](#ecdh-elliptic-curve-diffie-hellman)
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- [Schnorr signatures over secp256k1, BIP340](#schnorr-signatures-over-secp256k1-bip340)
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- [ed25519, X25519, ristretto255](#ed25519-x25519-ristretto255)
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- [ed448, X448, decaf448](#ed448-x448-decaf448)
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@ -46,15 +52,15 @@ A standalone file [noble-curves.js](https://github.com/paulmillr/noble-curves/re
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- [All available imports](#all-available-imports)
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- [Accessing a curve's variables](#accessing-a-curves-variables)
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- [Abstract API](#abstract-api)
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- [weierstrass: Short Weierstrass curve](#abstractweierstrass-short-weierstrass-curve)
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- [edwards: Twisted Edwards curve](#abstractedwards-twisted-edwards-curve)
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- [montgomery: Montgomery curve](#abstractmontgomery-montgomery-curve)
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- [bls: Barreto-Lynn-Scott curves](#abstractbls-barreto-lynn-scott-curves)
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- [hash-to-curve: Hashing strings to curve points](#abstracthash-to-curve-hashing-strings-to-curve-points)
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- [poseidon: Poseidon hash](#abstractposeidon-poseidon-hash)
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- [modular: Modular arithmetics utilities](#abstractmodular-modular-arithmetics-utilities)
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- [weierstrass: Short Weierstrass curve](#weierstrass-short-weierstrass-curve)
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- [edwards: Twisted Edwards curve](#edwards-twisted-edwards-curve)
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- [montgomery: Montgomery curve](#montgomery-montgomery-curve)
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- [bls: Barreto-Lynn-Scott curves](#bls-barreto-lynn-scott-curves)
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- [hash-to-curve: Hashing strings to curve points](#hash-to-curve-hashing-strings-to-curve-points)
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- [poseidon: Poseidon hash](#poseidon-poseidon-hash)
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- [modular: Modular arithmetics utilities](#modular-modular-arithmetics-utilities)
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- [Creating private keys from hashes](#creating-private-keys-from-hashes)
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- [utils: Useful utilities](#abstractutils-useful-utilities)
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- [utils: Useful utilities](#utils-useful-utilities)
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- [Security](#security)
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- [Speed](#speed)
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- [Upgrading](#upgrading)
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@ -71,9 +77,7 @@ Implementations are utilizing [noble-hashes](https://github.com/paulmillr/noble-
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Generic example that works for all curves, shown for secp256k1:
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```ts
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// import * from '@noble/curves'; // Error: use sub-imports, to ensure small app size
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import { secp256k1 } from '@noble/curves/secp256k1'; // ESM and Common.js
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// import { secp256k1 } from 'npm:@noble/curves@1.2.0/secp256k1'; // Deno
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import { secp256k1 } from '@noble/curves/secp256k1';
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const priv = secp256k1.utils.randomPrivateKey();
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const pub = secp256k1.getPublicKey(priv);
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const msg = new Uint8Array(32).fill(1); // message hash (not message) in ecdsa
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@ -96,7 +100,7 @@ sig.recoverPublicKey(msg).toRawBytes(); // === pub; // public key recovery
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const sigImprovedSecurity = secp256k1.sign(msg, priv, { extraEntropy: true });
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```
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#### ECDH (Elliptic Curve Diffie-Hellman)
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#### ECDH: Elliptic Curve Diffie-Hellman
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```ts
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// 1. The output includes parity byte. Strip it using shared.slice(1)
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@ -272,7 +276,7 @@ Precomputes are enabled for weierstrass and edwards BASE points of a curve. You
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could precompute any other point (e.g. for ECDH) using `utils.precompute()`
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method: check out examples.
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### abstract/weierstrass: Short Weierstrass curve
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### weierstrass: Short Weierstrass curve
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```ts
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import { weierstrass } from '@noble/curves/abstract/weierstrass';
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@ -443,7 +447,7 @@ const fast = secq256k1.utils.precompute(8, Point.fromHex(someonesPubKey));
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fast.multiply(privKey); // much faster ECDH now
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```
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### abstract/edwards: Twisted Edwards curve
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### edwards: Twisted Edwards curve
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```ts
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import { twistedEdwards } from '@noble/curves/abstract/edwards';
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@ -533,7 +537,7 @@ interface ExtPointConstructor extends GroupConstructor<ExtPointType> {
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}
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```
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### abstract/montgomery: Montgomery curve
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### montgomery: Montgomery curve
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```typescript
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import { montgomery } from '@noble/curves/abstract/montgomery';
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@ -560,7 +564,7 @@ Proper Elliptic Curve Points are not implemented yet.
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You must specify curve params `Fp`, `a`, `Gu` coordinate of u, `montgomeryBits` and `nByteLength`.
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### abstract/bls: Barreto-Lynn-Scott curves
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### bls: Barreto-Lynn-Scott curves
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The module abstracts BLS (Barreto-Lynn-Scott) pairing-friendly elliptic curve construction.
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They allow to construct [zk-SNARKs](https://z.cash/technology/zksnarks/) and
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@ -633,7 +637,7 @@ bls.params.x, bls.params.r, bls.params.G1b, bls.params.G2b
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// hash-to-curve examples can be seen below
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```
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### abstract/hash-to-curve: Hashing strings to curve points
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### hash-to-curve: Hashing strings to curve points
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The module allows to hash arbitrary strings to elliptic curve points. Implements [RFC 9380](https://www.rfc-editor.org/rfc/rfc9380).
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@ -691,7 +695,7 @@ type Opts = {
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};
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```
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### abstract/poseidon: Poseidon hash
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### poseidon: Poseidon hash
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Implements [Poseidon](https://www.poseidon-hash.info) ZK-friendly hash.
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@ -715,7 +719,7 @@ type PoseidonOpts = {
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const instance = poseidon(opts: PoseidonOpts);
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```
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### abstract/modular: Modular arithmetics utilities
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### modular: Modular arithmetics utilities
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```ts
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import * as mod from '@noble/curves/abstract/modular';
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@ -765,7 +769,7 @@ const derived = hkdf(sha256, someKey, undefined, 'application', 48); // 48 bytes
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const validPrivateKey = mod.hashToPrivateScalar(derived, p256.CURVE.n);
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```
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### abstract/utils: Useful utilities
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### utils: Useful utilities
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```ts
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import * as utils from '@noble/curves/abstract/utils';
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