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noble-bls12-381

[!WARNING]
The repository has been merged into noble-curves. Please head to the new repo for updates.

npm install @noble/curves

import { bls12_381 } from '@noble/curves/bls12-381';

Fastest JS implementation of BLS12-381. Auditable, secure, 0-dependency aggregated signatures & pairings.

The pairing-friendly Barreto-Lynn-Scott elliptic curve construction allows to:

Compatible with Algorand, Chia, Dfinity, Ethereum, FIL, Zcash. Matches specs pairing-curves-10, bls-sigs-04, hash-to-curve-12. To learn more about internals, navigate to utilities section.

This library belongs to noble crypto

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

Usage

Use NPM in node.js / browser, or include single file from GitHub's releases page:

npm install @noble/bls12-381

const bls = require('@noble/bls12-381');
// If you're using single file, use global variable instead: `window.nobleBls12381`

(async () => {
  // keys, messages & other inputs can be Uint8Arrays or hex strings
  const privateKey = '67d53f170b908cabb9eb326c3c337762d59289a8fec79f7bc9254b584b73265c';
  const message = '64726e3da8';
  const publicKey = bls.getPublicKey(privateKey);
  const signature = await bls.sign(message, privateKey);
  const isValid = await bls.verify(signature, message, publicKey);
  console.log({ publicKey, signature, isValid });

  // Sign 1 msg with 3 keys
  const privateKeys = [
    '18f020b98eb798752a50ed0563b079c125b0db5dd0b1060d1c1b47d4a193e1e4',
    'ed69a8c50cf8c9836be3b67c7eeff416612d45ba39a5c099d48fa668bf558c9c',
    '16ae669f3be7a2121e17d0c68c05a8f3d6bef21ec0f2315f1d7aec12484e4cf5'
  ];
  const messages = ['d2', '0d98', '05caf3'];
  const publicKeys = privateKeys.map(bls.getPublicKey);
  const signatures2 = await Promise.all(privateKeys.map(p => bls.sign(message, p)));
  const aggPubKey2 = bls.aggregatePublicKeys(publicKeys);
  const aggSignature2 = bls.aggregateSignatures(signatures2);
  const isValid2 = await bls.verify(aggSignature2, message, aggPubKey2);
  console.log({ signatures2, aggSignature2, isValid2 });

  // Sign 3 msgs with 3 keys
  const signatures3 = await Promise.all(privateKeys.map((p, i) => bls.sign(messages[i], p)));
  const aggSignature3 = bls.aggregateSignatures(signatures3);
  const isValid3 = await bls.verifyBatch(aggSignature3, messages, publicKeys);
  console.log({ publicKeys, signatures3, aggSignature3, isValid3 });
})();

To use the module with Deno, you will need import map:

API

getPublicKey(privateKey)
function getPublicKey(privateKey: Uint8Array | string | bigint): Uint8Array;

Note: if you need EIP2333-compliant KeyGen (eth2/fil), use paulmillr/bls12-381-keygen.

sign(message, privateKey)
function sign(message: Uint8Array | string, privateKey: Uint8Array | string): Promise<Uint8Array>;
function sign(message: PointG2, privateKey: Uint8Array | string | bigint): Promise<PointG2>;

Check out Utilities section on instructions about domain separation tag (DST).

verify(signature, message, publicKey)
function verify(
  signature: Uint8Array | string | PointG2,
  message: Uint8Array | string | PointG2,
  publicKey: Uint8Array | string | PointG1
): Promise<boolean>
aggregatePublicKeys(publicKeys)
function aggregatePublicKeys(publicKeys: (Uint8Array | string)[]): Uint8Array;
function aggregatePublicKeys(publicKeys: PointG1[]): PointG1;
aggregateSignatures(signatures)
function aggregateSignatures(signatures: (Uint8Array | string)[]): Uint8Array;
function aggregateSignatures(signatures: PointG2[]): PointG2;
verifyBatch(signature, messages, publicKeys)
function verifyBatch(
  signature: Uint8Array | string | PointG2,
  messages: (Uint8Array | string | PointG2)[],
  publicKeys: (Uint8Array | string | PointG1)[]
): Promise<boolean>
pairing(pointG1, pointG2)
function pairing(
  pointG1: PointG1,
  pointG2: PointG2,
  withFinalExponent: boolean = true
): Fp12

Utilities

Resources that help to understand bls12-381:

The library uses G1 for public keys and G2 for signatures. Adding support for G1 signatures is planned.

Formulas:

The BLS parameters for the library are:

Filecoin uses little endian byte arrays for private keys - so ensure to reverse byte order if you'll use it with FIL.

// Exports `CURVE`, `utils`, `PointG1`, `PointG2`, `Fp`, `Fp2`, `Fp12` helpers

const utils: {
  hashToField(msg: Uint8Array, count: number, options = {}): Promise<bigint[][]>;
  bytesToHex: (bytes: Uint8Array): string;
  randomBytes: (bytesLength?: number) => Uint8Array;
  randomPrivateKey: () => Uint8Array;
  sha256: (message: Uint8Array) => Promise<Uint8Array>;
  mod: (a: bigint, b = CURVE.P): bigint;
  getDSTLabel(): string;
  setDSTLabel(newLabel: string): void;
};

// characteristic; z + (z⁴ - z² + 1)(z - 1)²/3
CURVE.P // 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab
CURVE.r // curve order; z⁴ − z² + 1, 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
curve.h // cofactor; (z - 1)²/3, 0x396c8c005555e1568c00aaab0000aaab
CURVE.Gx, CURVE.Gy   // G1 base point coordinates (x, y)
CURVE.G2x, CURVE.G2y // G2 base point coordinates (x₁, x₂+i), (y₁, y₂+i)

// Classes
bls.Fp   // field over Fp
bls.Fp2  // field over Fp₂
bls.Fp12 // finite extension field over irreducible polynominal

// for hashToCurve static method
declare const htfDefaults: {
  DST: string;
  p: bigint;
  m: number;
  k: number;
  expand: boolean;
  hash: Hash;
};

// projective point (xyz) at G1
class PointG1 extends ProjectivePoint<Fp> {
  constructor(x: Fp, y: Fp, z?: Fp);
  static BASE: PointG1;
  static ZERO: PointG1;
  static fromHex(bytes: Bytes): PointG1;
  static fromPrivateKey(privateKey: PrivateKey): PointG1;
  static hashToCurve(msg: Hex, options?: Partial<typeof htfDefaults>): Promise<PointG1>;
  toRawBytes(isCompressed?: boolean): Uint8Array;
  toHex(isCompressed?: boolean): string;
  assertValidity(): this;
  millerLoop(P: PointG2): Fp12;
  clearCofactor(): PointG1;
}
// projective point (xyz) at G2
class PointG2 extends ProjectivePoint<Fp2> {
  constructor(x: Fp2, y: Fp2, z?: Fp2);
  static BASE: PointG2;
  static ZERO: PointG2;
  static hashToCurve(msg: Hex, options?: Partial<typeof htfDefaults>): Promise<PointG2>;
  static fromSignature(hex: Bytes): PointG2;
  static fromHex(bytes: Bytes): PointG2;
  static fromPrivateKey(privateKey: PrivateKey): PointG2;
  toSignature(): Uint8Array;
  toRawBytes(isCompressed?: boolean): Uint8Array;
  toHex(isCompressed?: boolean): string;
  assertValidity(): this;
  clearCofactor(): PointG2;
}

Speed

To achieve the best speed out of all JS / Python implementations, the library employs different optimizations:

Benchmarks measured with Apple M2 on macOS 12.5 with node.js 18.8:

getPublicKey x 818 ops/sec @ 1ms/op
sign x 44 ops/sec @ 22ms/op
verify x 34 ops/sec @ 29ms/op
pairing x 84 ops/sec @ 11ms/op
aggregatePublicKeys/8 x 117 ops/sec @ 8ms/op
aggregateSignatures/8 x 45 ops/sec @ 21ms/op

with compression / decompression disabled:
sign/nc x 60 ops/sec @ 16ms/op
verify/nc x 57 ops/sec @ 17ms/op ± 1.05% (min: 17ms, max: 19ms)
aggregatePublicKeys/32 x 1,163 ops/sec @ 859μs/op
aggregatePublicKeys/128 x 758 ops/sec @ 1ms/op
aggregatePublicKeys/512 x 318 ops/sec @ 3ms/op
aggregatePublicKeys/2048 x 96 ops/sec @ 10ms/op
aggregateSignatures/32 x 516 ops/sec @ 1ms/op
aggregateSignatures/128 x 269 ops/sec @ 3ms/op
aggregateSignatures/512 x 93 ops/sec @ 10ms/op
aggregateSignatures/2048 x 25 ops/sec @ 38ms/op

Security

Noble is production-ready.

  1. No public audits have been done yet. Our goal is to crowdfund the audit.
  2. It was developed in a similar fashion to noble-secp256k1, which was audited by a third-party firm.
  3. It was fuzzed by Guido Vranken's cryptofuzz, no serious issues have been found. You can run the fuzzer by yourself to check it.

We're using built-in JS BigInt, which is potentially vulnerable to timing attacks as per official spec. But, JIT-compiler and Garbage Collector make "constant time" extremely hard to achieve in a scripting language. Which means any other JS library doesn't use constant-time bigints. Including bn.js or anything else. Even statically typed Rust, a language without GC, makes it harder to achieve constant-time 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.

We however 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.

Contributing

  1. Clone the repository.
  2. npm install to install build dependencies like TypeScript
  3. npm run build to compile TypeScript code
  4. npm run test to run jest on test/index.ts

Special thanks to Roman Koblov, who have helped to improve pairing speed.

License

MIT (c) 2019 Paul Miller (https://paulmillr.com), see LICENSE file.