noble-bls12-381

bls12-381, a pairing-friendly Barreto-Lynn-Scott elliptic curve construction. Allows to:

• Construct zk-SNARKs at the 128-bit security
• Use threshold signatures, which allows a user to sign lots of messages with one signature and verify them swiftly in a batch, using Boneh-Lynn-Shacham signature scheme.

The fastest implementation written in a scripting language. Matches following specs:

• Pairing-friendly curves 09
• BLS signatures 04
• Hash to curve 10

Check out BLS12-381 For The Rest Of Us & key concepts of pairings to get started with the primitives.

This library belongs to noble crypto

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

• No dependencies
• Easily auditable TypeScript/JS code
• Uses es2020 bigint. Supported in Chrome, Firefox, Safari, node 10+
• All releases are signed and trusted
• Check out all libraries: secp256k1, ed25519, bls12-381, ripemd160

Usage

Node.js and browser:

npm install noble-bls12-381

import * as bls from "bls12-381";

// Use hex or Uint8Arrays
const privateKey = '67d53f170b908cabb9eb326c3c337762d59289a8fec79f7bc9254b584b73265c';
const msg = 'hello';

(async () => {
  const publicKey = bls.getPublicKey(privateKey);
  const signature1 = await bls.sign(msg, privateKey);
  const isCorrect1 = await bls.verify(msg, publicKey, signature);

  // Sign 1 msg with 3 keys
  const privateKeys = [
    '18f020b98eb798752a50ed0563b079c125b0db5dd0b1060d1c1b47d4a193e1e4',
    'ed69a8c50cf8c9836be3b67c7eeff416612d45ba39a5c099d48fa668bf558c9c',
    '16ae669f3be7a2121e17d0c68c05a8f3d6bef21ec0f2315f1d7aec12484e4cf5'
  ];
  const publicKeys = privateKeys.map(bls.getPublicKey);
  const signatures = await Promise.all(privateKeys.map(p => bls.sign(msg, p)));
  const aggPubKey = bls.aggregatePublicKeys(publicKeys);
  const aggSignature = bls.aggregateSignatures(signatures);
  const isCorrect2 = await bls.verify(signature, msg, aggPubKey);

  // Sign 3 msgs with 3 keys
  const messages = ['whatsup', 'all good', 'thanks'];
  const signatures2 = await Promise.all(privateKeys.map((p, i) => bls.sign(messages[i], p)));
  const aggSignature2 = bls.aggregateSignatures(signatures);
  const isCorrect3 = await bls.verifyBatch(signature, messages, publicKeys);
})();

API

• getPublicKey(privateKey)
• sign(message, privateKey)
• verify(signature, hash, publicKey)
• aggregatePublicKeys(publicKeys)
• aggregateSignatures(signatures)
• verifyBatch(messages, publicKeys, signature)
• pairing(G1Point, G2Point)

getPublicKey(privateKey)

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

• privateKey: Uint8Array | string | bigint will be used to generate public key. Public key is generated by executing scalar multiplication of a base Point(x, y) by a fixed integer. The result is another Point(x, y) which we will by default encode to hex Uint8Array.
• Returns Uint8Array: encoded publicKey for signature verification

sign(message, privateKey)

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

• message: Uint8Array | string - message which would be hashed & signed
• privateKey: Uint8Array | string | bigint - private key which will sign the hash
• Returns Uint8Array | string | PointG2: encoded signature

Default domain (DST) is BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_NUL_, use bls.DST to change it.

verify(signature, hash, publicKey)

function verify(
  signature: Uint8Array | string | PointG2,
  hash: Uint8Array | string | PointG2,
  publicKey: Uint8Array | string | PointG1
): Promise<boolean>

• hash: Uint8Array | string - message hash that needs to be verified
• publicKey: Uint8Array | string - e.g. that was generated from privateKey by getPublicKey
• signature: Uint8Array | string - object returned by the sign or aggregateSignatures function
• Returns Promise<boolean>: true / false whether the signature matches hash

aggregatePublicKeys(publicKeys)

function aggregatePublicKeys(publicKeys: (Uint8Array | string)[]): Uint8Array;
function aggregatePublicKeys(publicKeys: PointG1[]): PointG1;

• publicKeys: (Uint8Array | string | PointG1)[] - e.g. that have been generated from privateKey by getPublicKey
• Returns Uint8Array | PointG1: one aggregated public key which calculated from public keys

aggregateSignatures(signatures)

function aggregateSignatures(signatures: (Uint8Array | string)[]): Uint8Array;
function aggregateSignatures(signatures: PointG2[]): PointG2;

• signatures: (Uint8Array | string | PointG2)[] - e.g. that have been generated by sign
• Returns Uint8Array | PointG2: one aggregated signature which calculated from signatures

verifyBatch(hashes, publicKeys, signature)

function verifyBatch(
  hashes: (Uint8Array | string | PointG2)[],
  publicKeys: (Uint8Array | string | PointG1)[],
  signature: Uint8Array | string | PointG2
): Promise<boolean>

• hashes: (Uint8Array | string | PointG2)[] - messages hashes that needs to be verified
• publicKeys: (Uint8Array | string | PointG1)[] - e.g. that were generated from privateKeys by getPublicKey
• signature: Uint8Array | string | PointG2 - object returned by the aggregateSignatures function
• Returns Promise<boolean>: true / false whether the signature matches hashes

pairing(G1Point, G2Point)

function pairing(
  g1Point: PointG1,
  g2Point: PointG2,
  withFinalExponent: boolean = true
): Fq12

• g1Point: PointG1 - simple point, x, y are bigints
• g2Point: PointG2 - point over curve with imaginary numbers ((x, x_1), (y, y_1))
• withFinalExponent: boolean - should the result be powered by curve order. Very slow.
• Returns Fq12: paired point over 12-degree extension field.

Helpers

// 𝔽p
bls.CURVE.P // 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaabn

// Prime order
bls.CURVE.r // 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001n

// Hash base point (x, y)
bls.CURVE.Gx // 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001n
// x = 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507
// y = 1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569

// Signature base point ((x_1, x_2), (y_1, y_2))
bls.CURVE.Gy
// x = 3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758, 352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160
// y = 927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582, 1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905

// Classes
bls.Fq
bls.Fq2
bls.Fq12
bls.G1Point
bls.G2Point

Internals

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

• BLS Relies on Bilinear Pairing (expensive)
• Private Keys: 32 bytes
• Public Keys: 48 bytes: 381 bit affine x coordinate, encoded into 48 big-endian bytes.
• Signatures: 96 bytes: two 381 bit integers (affine x coordinate), encoded into two 48 big-endian byte arrays.
  • The signature is a point on the G2 subgroup, which is defined over a finite field with elements twice as big as the G1 curve (G2 is over Fq2 rather than Fq. Fq2 is analogous to the complex numbers).
• The 12 stands for the Embedding degree.

Formulas:

• P = pk x G - public keys
• S = pk x H(m) - signing
• e(P, H(m)) == e(G,S) - verification using pairings
• e(G, S) = e(G, SUM(n)(Si)) = MUL(n)(e(G, Si)) - signature aggregation

Speed

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

• cyclotomic exponentation
• frobenius coefficients
• endomorphism for clearing cofactor

Benchmarks measured with 2.9Ghz i9-8950HK:

getPublicKey x 1114 ops/sec @ 897μs/op
sign x 14 ops/sec @ 70ms/op
verify x 22 ops/sec @ 45ms/op
pairing x 54 ops/sec @ 18ms/op
aggregatePublicKeys/8 x 248 ops/sec @ 4ms/op
aggregateSignatures/8 x 50 ops/sec @ 19ms/op

with compression / decompression disabled:
sign/nc x 18 ops/sec @ 54ms/op
verify/nc x 39 ops/sec @ 25ms/op
aggregatePublicKeys/32 x 3966 ops/sec @ 252μs/op
aggregatePublicKeys/128 x 825 ops/sec @ 1ms/op
aggregatePublicKeys/512 x 235 ops/sec @ 4ms/op
aggregatePublicKeys/2048 x 58 ops/sec @ 16ms/op
aggregateSignatures/32 x 1048 ops/sec @ 953μs/op
aggregateSignatures/128 x 252 ops/sec @ 3ms/op
aggregateSignatures/512 x 60 ops/sec @ 16ms/op
aggregateSignatures/2048 x 15 ops/sec @ 65ms/op

Security

Noble is production-ready & secure. Our goal is to have it audited by a good security expert.

We're using built-in JS BigInt, which is "unsuitable for use in cryptography" as per official spec. This means that the lib is potentially vulnerable to timing attacks. But:

1. JIT-compiler and Garbage Collector make "constant time" extremely hard to achieve in a scripting language.
2. 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.
3. If your goal is absolute security, don't use any JS lib — including bindings to native ones. Use low-level libraries & languages.
4. 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 rootkits 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 compile 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) Paul Miller (https://paulmillr.com), see LICENSE file.