@aguycalled/noble-bls12-381
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Fastest JS implementation of BLS12-381. Auditable, secure, 0-dependency aggregated signatures & pairings
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# noble-bls12-381  [](https://github.com/prettier/prettier)
**[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, check out [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). To try it live, see [the online demo](https://paulmillr.com/ecc) & [threshold sigs demo](https://genthresh.com).
### This library belongs to *noble* crypto
> **noble-crypto** — high-security, easily auditable set of contained cryptographic libraries and tools.
- Just two files
- No dependencies
- Easily 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:
[secp256k1](https://github.com/paulmillr/noble-secp256k1),
[ed25519](https://github.com/paulmillr/noble-ed25519),
[bls12-381](https://github.com/paulmillr/noble-bls12-381),
[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 nobleBls12381
// You can use Uint8Array, or hex string for readability
const privateKey = '67d53f170b908cabb9eb326c3c337762d59289a8fec79f7bc9254b584b73265c';
const privateKeys = [
'18f020b98eb798752a50ed0563b079c125b0db5dd0b1060d1c1b47d4a193e1e4',
'ed69a8c50cf8c9836be3b67c7eeff416612d45ba39a5c099d48fa668bf558c9c',
'16ae669f3be7a2121e17d0c68c05a8f3d6bef21ec0f2315f1d7aec12484e4cf5'
];
const message = '64726e3da8';
const messages = ['d2', '0d98', '05caf3'];
(async () => {
const publicKey = bls.getPublicKey(privateKey);
const publicKeys = privateKeys.map(bls.getPublicKey);
const signature = await bls.sign(message, privateKey);
const isCorrect = await bls.verify(signature, message, publicKey);
console.log('key', publicKey);
console.log('signature', signature);
console.log('is correct:', isCorrect);
// Sign 1 msg with 3 keys
const signatures2 = await Promise.all(privateKeys.map(p => bls.sign(message, p)));
const aggPubKey2 = bls.aggregatePublicKeys(publicKeys);
const aggSignature2 = bls.aggregateSignatures(signatures2);
const isCorrect2 = await bls.verify(aggSignature2, message, aggPubKey2);
console.log();
console.log('signatures are', signatures2);
console.log('merged to one signature', aggSignature2);
console.log('is correct:', isCorrect2);
// 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 isCorrect3 = await bls.verifyBatch(aggSignature3, messages, publicKeys);
console.log();
console.log('keys', publicKeys);
console.log('signatures', signatures3);
console.log('merged to one signature', aggSignature3);
console.log('is correct:', isCorrect3);
})();
```
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`
```typescript
import * as bls from "https://deno.land/x/bls12_381/mod.ts";
const publicKey = bls.getPublicKey(bls.utils.randomPrivateKey());
console.log(publicKey);
```
- `imports.json`
```json
{
"imports": {
"crypto": "https://deno.land/std@0.119.0/node/crypto.ts",
"./math": "./math.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)
##### `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 spec-based `KeyGen`, use [paulmillr/bls12-381-keygen](https://github.com/paulmillr/bls12-381-keygen). It should work properly with ETH2 and FIL keys.
##### `sign(message, privateKey)`
```typescript
function sign(message: Uint8Array | string, privateKey: Uint8Array | string): Promise<Uint8Array>;
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
Check out **Internals** 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<boolean>
```
- `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<boolean>`: `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<boolean>
```
- `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<boolean>`: `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.
##### Helpers
Use `utils.bytesToHex(str)` to convert byte output to hexademical string.
```typescript
// characteristic; z + (z⁴ - z² + 1)(z - 1)²/3
bls.CURVE.P // 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab
// curve order; z⁴ − z² + 1
bls.CURVE.r // 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
// cofactor; (z - 1)²/3
bls.curve.h // 0x396c8c005555e1568c00aaab0000aaab
// G1 base point coordinates (x, y)
bls.CURVE.Gx
// x = 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507
bls.CURVE.Gy
// y = 1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569
// G2 base point coordinates (x₁, x₂+i), (y₁, y₂+i)
bls.CURVE.G2x
// x =
// 3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758,
// 352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160
bls.CURVE.G2y
// y =
// 927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582,
// 1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905
// Classes
bls.Fp // field over Fp
bls.Fp2 // field over Fp₂
bls.Fp12 // finite extension field over irreducible polynominal
bls.PointG1 // projective point (xyz) at G1
bls.PointG2 // projective point (xyz) at G2
```
## 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 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.
## 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 M1:
```
getPublicKey x 737 ops/sec @ 1ms/op
sign x 37 ops/sec @ 26ms/op
verify x 28 ops/sec @ 34ms/op
pairing x 70 ops/sec @ 14ms/op
aggregatePublicKeys/8 x 102 ops/sec @ 9ms/op
aggregateSignatures/8 x 39 ops/sec @ 25ms/op
with compression / decompression disabled:
sign/nc x 52 ops/sec @ 18ms/op
verify/nc x 47 ops/sec @ 21ms/op
aggregatePublicKeys/32 x 1,014 ops/sec @ 986μs/op
aggregatePublicKeys/128 x 662 ops/sec @ 1ms/op
aggregatePublicKeys/512 x 278 ops/sec @ 3ms/op
aggregatePublicKeys/2048 x 84 ops/sec @ 11ms/op
aggregateSignatures/32 x 444 ops/sec @ 2ms/op
aggregateSignatures/128 x 236 ops/sec @ 4ms/op
aggregateSignatures/512 x 81 ops/sec @ 12ms/op
aggregateSignatures/2048 x 22 ops/sec @ 44ms/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 "unsuitable for use in cryptography" as [per official spec](https://github.com/tc39/proposal-bigint#cryptography). This means that the lib is potentially vulnerable to [timing attacks](https://en.wikipedia.org/wiki/Timing_attack). 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) Paul Miller [(https://paulmillr.com)](https://paulmillr.com), see LICENSE file.