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@ -46,23 +46,19 @@ If you don't like NPM, a standalone [noble-curves.js](https://github.com/paulmil
- [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)
- [weierstrass: Short Weierstrass curve](#abstractweierstrass-short-weierstrass-curve)
- [edwards: Twisted Edwards curve](#abstractedwards-twisted-edwards-curve)
- [montgomery: Montgomery curve](#abstractmontgomery-montgomery-curve)
- [bls: Barreto-Lynn-Scott curves](#abstractbls-barreto-lynn-scott-curves)
- [hash-to-curve: Hashing strings to curve points](#abstracthash-to-curve-hashing-strings-to-curve-points)
- [poseidon: Poseidon hash](#abstractposeidon-poseidon-hash)
- [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)
- [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
@ -572,6 +568,8 @@ use aggregated, batch-verifiable
using Boneh-Lynn-Shacham signature scheme.
The module doesn't expose `CURVE` property: use `G1.CURVE`, `G2.CURVE` instead.
Only BLS12-381 is implemented currently.
Defining BLS12-377 and BLS24 should be straightforward.
Main methods and properties are:
@ -592,9 +590,6 @@ Short signatures (public keys in G2 and signatures in G1) is also supported, usi
- `verifyShortSignature(signature, message, publicKey)`
- `aggregateShortSignatures(signatures)`
Right now we only implement BLS12-381 (compatible with ETH and others),
but in theory defining BLS12-377, BLS24 should be straightforward. An example:
```ts
import { bls12_381 as bls } from '@noble/curves/bls12-381';
const privateKey = '67d53f170b908cabb9eb326c3c337762d59289a8fec79f7bc9254b584b73265c';
@ -625,81 +620,18 @@ const isValid3 = bls.verifyBatch(aggSignature3, messages, publicKeys);
console.log({ publicKeys, signatures3, aggSignature3, isValid3 });
// 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));
bls.pairing(PointG1, PointG2);
bls.pairing(PointG1, PointG2, false);
bls.fields.Fp12.finalExponentiate(bls.fields.Fp12.mul(PointG1, PointG2));
// Others
// bls.G1.ProjectivePoint.BASE, bls.G2.ProjectivePoint.BASE
// bls.fields.Fp, bls.fields.Fp2, bls.fields.Fp12, bls.fields.Fr
bls.G1.ProjectivePoint.BASE, bls.G2.ProjectivePoint.BASE
bls.fields.Fp, bls.fields.Fp2, bls.fields.Fp12, bls.fields.Fr
bls.params.x, bls.params.r, bls.params.G1b, bls.params.G2b
// hash-to-curve examples can be seen below
```
Full types:
```ts
getPublicKey: (privateKey: PrivKey) => Uint8Array;
getPublicKeyForShortSignatures: (privateKey: PrivKey) => Uint8Array;
sign: {
(message: Hex, privateKey: PrivKey): Uint8Array;
(message: ProjPointType<Fp2>, privateKey: PrivKey): ProjPointType<Fp2>;
};
signShortSignature: {
(message: Hex, privateKey: PrivKey): Uint8Array;
(message: ProjPointType<Fp>, privateKey: PrivKey): ProjPointType<Fp>;
};
verify: (
signature: Hex | ProjPointType<Fp2>,
message: Hex | ProjPointType<Fp2>,
publicKey: Hex | ProjPointType<Fp>
) => boolean;
verifyShortSignature: (
signature: Hex | ProjPointType<Fp>,
message: Hex | ProjPointType<Fp>,
publicKey: Hex | ProjPointType<Fp2>
) => boolean;
verifyBatch: (
signature: Hex | ProjPointType<Fp2>,
messages: (Hex | ProjPointType<Fp2>)[],
publicKeys: (Hex | ProjPointType<Fp>)[]
) => boolean;
aggregatePublicKeys: {
(publicKeys: Hex[]): Uint8Array;
(publicKeys: ProjPointType<Fp>[]): ProjPointType<Fp>;
};
aggregateSignatures: {
(signatures: Hex[]): Uint8Array;
(signatures: ProjPointType<Fp2>[]): ProjPointType<Fp2>;
};
aggregateShortSignatures: {
(signatures: Hex[]): Uint8Array;
(signatures: ProjPointType<Fp>[]): ProjPointType<Fp>;
};
millerLoop: (ell: [Fp2, Fp2, Fp2][], g1: [Fp, Fp]) => Fp12;
pairing: (P: ProjPointType<Fp>, Q: ProjPointType<Fp2>, withFinalExponent?: boolean) => Fp12;
G1: CurvePointsRes<Fp> & ReturnType<typeof htf.createHasher<Fp>>;
G2: CurvePointsRes<Fp2> & ReturnType<typeof htf.createHasher<Fp2>>;
Signature: SignatureCoder<Fp2>;
params: {
x: bigint;
r: bigint;
G1b: bigint;
G2b: Fp2;
};
fields: {
Fp: IField<Fp>;
Fp2: IField<Fp2>;
Fp6: IField<Fp6>;
Fp12: IField<Fp12>;
Fr: IField<bigint>;
};
utils: {
randomPrivateKey: () => Uint8Array;
calcPairingPrecomputes: (p: AffinePoint<Fp2>) => [Fp2, Fp2, Fp2][];
};
```
### abstract/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).
@ -1060,60 +992,9 @@ Upgrading from [@noble/bls12-381](https://github.com/paulmillr/noble-bls12-381):
## Resources
- [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
- [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/)
### Demos
- [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)
- [crystals-kyber-js](https://github.com/dajiaji/crystals-kyber-js), a post-quantum cryptography algorithm
- [ed25519-keygen](https://github.com/paulmillr/ed25519-keygen) SSH, PGP, TOR key generation
- [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).
Check out [paulmillr.com/noble](https://paulmillr.com/noble/)
for useful resources, articles, documentation and demos
related to the library.
## License