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https://github.com/paulmillr/noble-bls12-381
DEPRECATED. Use noble-curves instead. Fastest JS implementation of BLS12-381.
https://github.com/paulmillr/noble-bls12-381
barreto-lynn-scott bls-signature bls12 bls12-381 boneh-lynn-shacham crypto curve ecc elliptic-curve-cryptography eth2 noble pairing signature-aggregation signatures zk-snarks
Last synced: 3 months ago
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DEPRECATED. Use noble-curves instead. Fastest JS implementation of BLS12-381.
- Host: GitHub
- URL: https://github.com/paulmillr/noble-bls12-381
- Owner: paulmillr
- License: mit
- Archived: true
- Created: 2019-08-22T22:46:31.000Z (about 5 years ago)
- Default Branch: main
- Last Pushed: 2023-09-21T14:36:48.000Z (about 1 year ago)
- Last Synced: 2024-05-08T17:03:02.756Z (6 months ago)
- Topics: barreto-lynn-scott, bls-signature, bls12, bls12-381, boneh-lynn-shacham, crypto, curve, ecc, elliptic-curve-cryptography, eth2, noble, pairing, signature-aggregation, signatures, zk-snarks
- Language: TypeScript
- Homepage: https://paulmillr.com/noble/
- Size: 1.98 MB
- Stars: 197
- Watchers: 8
- Forks: 44
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Funding: .github/funding.yml
- License: LICENSE
- Security: SECURITY.md
Awesome Lists containing this project
README
# noble-bls12-381
> [!WARNING]
> The repository has been merged into [noble-curves](https://github.com/paulmillr/noble-curves). Please head to the new repo for updates.
npm install @noble/curves
```js
import { bls12_381 } from '@noble/curves/bls12-381';
```
---
[Fastest](#speed) JS implementation of BLS12-381. Auditable, secure, 0-dependency aggregated signatures & pairings.
The pairing-friendly Barreto-Lynn-Scott elliptic curve construction allows to:
- Construct [zk-SNARKs](https://z.cash/technology/zksnarks/) at the 128-bit security
- Use [threshold signatures](https://medium.com/snigirev.stepan/bls-signatures-better-than-schnorr-5a7fe30ea716),
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.
Compatible with Algorand, Chia, Dfinity, Ethereum, FIL, Zcash. Matches specs [pairing-curves-10](https://tools.ietf.org/html/draft-irtf-cfrg-pairing-friendly-curves-10), [bls-sigs-04](https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-04), [hash-to-curve-12](https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-12). To learn more about internals, navigate to
[utilities](#utilities) section.
### This library belongs to *noble* crypto
> **noble-crypto** — high-security, easily auditable set of contained cryptographic libraries and tools.
- No dependencies, protection against supply chain attacks
- Auditable TypeScript / JS code
- Supported in all major browsers and stable node.js versions
- All releases are signed with PGP keys
- Check out [homepage](https://paulmillr.com/noble/) & all libraries:
[curves](https://github.com/paulmillr/noble-curves)
(4kb versions [secp256k1](https://github.com/paulmillr/noble-secp256k1),
[ed25519](https://github.com/paulmillr/noble-ed25519)),
[hashes](https://github.com/paulmillr/noble-hashes)
## Usage
Use NPM in node.js / browser, or include single file from
[GitHub's releases page](https://github.com/paulmillr/noble-bls12-381/releases):
> npm install @noble/bls12-381
```js
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](https://deno.land),
you will need [import map](https://deno.land/manual/linking_to_external_code/import_maps):
- `deno run --import-map=imports.json app.ts`
- app.ts: `import * as bls from "https://deno.land/x/bls12_381/mod.ts";`
- imports.json: `{"imports": {"crypto": "https://deno.land/[email protected]/node/crypto.ts"}}`
## API
- [`getPublicKey(privateKey)`](#getpublickeyprivatekey)
- [`sign(message, privateKey)`](#signmessage-privatekey)
- [`verify(signature, message, publicKey)`](#verifysignature-message-publickey)
- [`aggregatePublicKeys(publicKeys)`](#aggregatepublickeyspublickeys)
- [`aggregateSignatures(signatures)`](#aggregatesignaturessignatures)
- [`verifyBatch(signature, messages, publicKeys)`](#verifybatchsignature-messages-publickeys)
- [`pairing(G1Point, G2Point)`](#pairingg1point-g2point)
- [Utilities](#utilities)
##### `getPublicKey(privateKey)`
```typescript
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
**Note:** if you need EIP2333-compliant `KeyGen` (eth2/fil), use [paulmillr/bls12-381-keygen](https://github.com/paulmillr/bls12-381-keygen).
##### `sign(message, privateKey)`
```typescript
function sign(message: Uint8Array | string, privateKey: Uint8Array | string): Promise;
function sign(message: PointG2, privateKey: Uint8Array | string | bigint): Promise;
```
- `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
Check out [Utilities](#utilities) section on instructions about domain separation tag (DST).
##### `verify(signature, message, publicKey)`
```typescript
function verify(
signature: Uint8Array | string | PointG2,
message: Uint8Array | string | PointG2,
publicKey: Uint8Array | string | PointG1
): Promise
```
- `signature: Uint8Array | string` - object returned by the `sign` or `aggregateSignatures` function
- `message: Uint8Array | string` - message hash that needs to be verified
- `publicKey: Uint8Array | string` - e.g. that was generated from `privateKey` by `getPublicKey`
- Returns `Promise`: `true` / `false` whether the signature matches hash
##### `aggregatePublicKeys(publicKeys)`
```typescript
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)`
```typescript
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(signature, messages, publicKeys)`
```typescript
function verifyBatch(
signature: Uint8Array | string | PointG2,
messages: (Uint8Array | string | PointG2)[],
publicKeys: (Uint8Array | string | PointG1)[]
): Promise
```
- `signature: Uint8Array | string | PointG2` - object returned by the `aggregateSignatures` function
- `messages: (Uint8Array | string | PointG2)[]` - messages hashes that needs to be verified
- `publicKeys: (Uint8Array | string | PointG1)[]` - e.g. that were generated from `privateKeys` by `getPublicKey`
- Returns `Promise`: `true` / `false` whether the signature matches hashes
##### `pairing(pointG1, pointG2)`
```typescript
function pairing(
pointG1: PointG1,
pointG2: PointG2,
withFinalExponent: boolean = true
): Fp12
```
- `pointG1: PointG1` - simple point, `x, y` are bigints
- `pointG2: PointG2` - point over curve with complex numbers (`(x₁, x₂+i), (y₁, y₂+i)`) - pairs of bigints
- `withFinalExponent: boolean` - should the result be powered by curve order; very slow
- Returns `Fp12`: paired point over 12-degree extension field.
### Utilities
Resources that help to understand bls12-381:
- [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: [part 1](https://research.nccgroup.com/2020/07/06/pairing-over-bls12-381-part-1-fields/),
[part 2](https://research.nccgroup.com/2020/07/13/pairing-over-bls12-381-part-2-curves/),
[part 3](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/)
- Check out [the online demo](https://paulmillr.com/ecc) and [threshold sigs demo](https://genthresh.com)
- See [BBS signatures implementation](https://github.com/Wind4Greg/BBS-Draft-Checks) based on the library, following [draft-irtf-cfrg-bbs-signatures-latest](https://identity.foundation/bbs-signature/draft-irtf-cfrg-bbs-signatures.html)
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 Fp2 rather than Fp. Fp2 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
The BLS parameters for the library are:
- `PK_IN` `G1`
- `HASH_OR_ENCODE` `true`
- `DST` `BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_NUL_` - use `bls.utils.getDSTLabel()` & `bls.utils.setDSTLabel("...")` to read/change the Domain Separation Tag label
- `RAND_BITS` `64`
Filecoin uses little endian byte arrays for private keys - so ensure to reverse byte order if you'll use it with FIL.
```typescript
// Exports `CURVE`, `utils`, `PointG1`, `PointG2`, `Fp`, `Fp2`, `Fp12` helpers
const utils: {
hashToField(msg: Uint8Array, count: number, options = {}): Promise;
bytesToHex: (bytes: Uint8Array): string;
randomBytes: (bytesLength?: number) => Uint8Array;
randomPrivateKey: () => Uint8Array;
sha256: (message: Uint8Array) => Promise;
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 {
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): Promise;
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 {
constructor(x: Fp2, y: Fp2, z?: Fp2);
static BASE: PointG2;
static ZERO: PointG2;
static hashToCurve(msg: Hex, options?: Partial): Promise;
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:
- cyclotomic exponentation
- endomorphism for clearing cofactor
- pairing precomputation
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](https://github.com/paulmillr/noble-secp256k1), which **was** audited by a third-party firm.
3. It was fuzzed by [Guido Vranken's cryptofuzz](https://github.com/guidovranken/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](https://en.wikipedia.org/wiki/Timing_attack) as [per official spec](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#cryptography). 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](https://www.chosenplaintext.ca/open-source/rust-timing-shield/security) 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](https://github.com/romankoblov), who have helped to improve pairing speed.
## License
MIT (c) 2019 Paul Miller [(https://paulmillr.com)](https://paulmillr.com), see LICENSE file.