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