noble-curves
Audited & minimal JS implementation of elliptic curve cryptography.
🔒 Audited by an independent security firm🔻 Tree-shaking-friendly: use only what's necessary, other code won't be included🏎 Ultra-fast, hand-optimized for caveats of JS engines🔍 Unique tests ensure correctness: property-based, cross-library and Wycheproof vectors, fuzzing➰ Short Weierstrass, Edwards, Montgomery curves✍️ ECDSA, EdDSA, Schnorr, BLS signature schemes, ECDH key agreement🔖 SUF-CMA and SBS (non-repudiation) for ed25519, ed448 and others#️⃣ Hash-to-curve for encoding or hashing an arbitrary string to an elliptic curve point🧜♂️ Poseidon ZK-friendly hash
Check out Upgrading if you've previously used single-feature noble packages. See Resources for articles and real-world software that uses curves.
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 & all libraries: curves (4kb versions secp256k1, ed25519), hashes
Usage
npm install @noble/curves
We support all major platforms and runtimes. For Deno, ensure to use npm specifier. For React Native, you may need a polyfill for crypto.getRandomValues. If you don't like NPM, a standalone noble-curves.js is also available.
The library is tree-shaking-friendly and does not expose root entry point as
@noble/curves
. Instead, you need to import specific primitives.
This is done to ensure small size of your apps.
The package consists of two parts:
- Implementations, utilizing one dependency noble-hashes,
providing ready-to-use:
- NIST curves secp256r1 / p256, secp384r1 / p384, secp521r1 / p521
- SECG curve secp256k1
- ed25519 / curve25519 / x25519 / ristretto255, edwards448 / curve448 / x448
- pairing-friendly curves bls12-381, bn254
- pasta curves
- Abstract, zero-dependency elliptic curve algorithms
Implementations
Generic example for all curves, secp256k1
// Each curve has similar methods
import { secp256k1 } from '@noble/curves/secp256k1'; // ESM and Common.js
// import { secp256k1 } from 'npm:@noble/[email protected]/secp256k1'; // Deno
const priv = secp256k1.utils.randomPrivateKey();
const pub = secp256k1.getPublicKey(priv);
const msg = new Uint8Array(32).fill(1);
const sig = secp256k1.sign(msg, priv);
const isValid = secp256k1.verify(sig, msg, pub) === true;
// hex strings are also supported besides Uint8Arrays:
const privHex = '46c930bc7bb4db7f55da20798697421b98c4175a52c630294d75a84b9c126236';
const pub2 = secp256k1.getPublicKey(privHex);
All imports
import { secp256k1, schnorr } from '@noble/curves/secp256k1';
import { ed25519, ed25519ph, ed25519ctx, x25519, RistrettoPoint } from '@noble/curves/ed25519';
import { ed448, ed448ph, ed448ctx, x448 } from '@noble/curves/ed448';
import { p256 } from '@noble/curves/p256';
import { p384 } from '@noble/curves/p384';
import { p521 } from '@noble/curves/p521';
import { pallas, vesta } from '@noble/curves/pasta';
import { bls12_381 } from '@noble/curves/bls12-381';
import { bn254 } from '@noble/curves/bn254';
import { jubjub } from '@noble/curves/jubjub';
ECDSA public key recovery & ECDH
// extraEntropy https://moderncrypto.org/mail-archive/curves/2017/000925.html
const sigImprovedSecurity = secp256k1.sign(msg, priv, { extraEntropy: true });
sig.recoverPublicKey(msg) === pub; // public key recovery
const someonesPub = secp256k1.getPublicKey(secp256k1.utils.randomPrivateKey());
const shared = secp256k1.getSharedSecret(priv, someonesPub); // ECDH
Schnorr signatures over secp256k1 (BIP340)
import { schnorr } from '@noble/curves/secp256k1';
const priv = schnorr.utils.randomPrivateKey();
const pub = schnorr.getPublicKey(priv);
const msg = new TextEncoder().encode('hello');
const sig = schnorr.sign(msg, priv);
const isValid = schnorr.verify(sig, msg, pub);
ed25519, X25519, ristretto255
import { ed25519 } from '@noble/curves/ed25519';
const priv = ed25519.utils.randomPrivateKey();
const pub = ed25519.getPublicKey(priv);
const msg = new TextEncoder().encode('hello');
const sig = ed25519.sign(msg, priv);
ed25519.verify(sig, msg, pub); // Default mode: follows ZIP215
ed25519.verify(sig, msg, pub, { zip215: false }); // RFC8032 / FIPS 186-5
Default verify
behavior follows ZIP215 and
can be used in consensus-critical applications.
It has SUF-CMA (strong unforgeability under chosen message attacks).
zip215: false
option switches verification criteria to strict
RFC8032 / FIPS 186-5
and additionally provides non-repudiation with SBS (Strongly Binding Signatures).
X25519 follows RFC7748. ristretto255 follows irtf draft.
// Variants from RFC8032: with context, prehashed
import { ed25519ctx, ed25519ph } from '@noble/curves/ed25519';
// ECDH using curve25519 aka x25519
import { x25519 } from '@noble/curves/ed25519';
const priv = 'a546e36bf0527c9d3b16154b82465edd62144c0ac1fc5a18506a2244ba449ac4';
const pub = 'e6db6867583030db3594c1a424b15f7c726624ec26b3353b10a903a6d0ab1c4c';
x25519.getSharedSecret(priv, pub) === x25519.scalarMult(priv, pub); // aliases
x25519.getPublicKey(priv) === x25519.scalarMultBase(priv);
x25519.getPublicKey(x25519.utils.randomPrivateKey());
// ed25519 => x25519 conversion
import { edwardsToMontgomeryPub, edwardsToMontgomeryPriv } from '@noble/curves/ed25519';
edwardsToMontgomeryPub(ed25519.getPublicKey(ed25519.utils.randomPrivateKey()));
edwardsToMontgomeryPriv(ed25519.utils.randomPrivateKey());
// hash-to-curve, ristretto255
import { hashToCurve, encodeToCurve, RistrettoPoint } from '@noble/curves/ed25519';
const rp = RistrettoPoint.fromHex(
'6a493210f7499cd17fecb510ae0cea23a110e8d5b901f8acadd3095c73a3b919'
);
RistrettoPoint.hashToCurve('Ristretto is traditionally a short shot of espresso coffee');
// also has add(), equals(), multiply(), toRawBytes() methods
ed448, X448
import { ed448 } from '@noble/curves/ed448';
const priv = ed448.utils.randomPrivateKey();
const pub = ed448.getPublicKey(priv);
const msg = new TextEncoder().encode('whatsup');
const sig = ed448.sign(msg, priv);
ed448.verify(sig, msg, pub);
import { ed448ph, ed448ctx, x448, hashToCurve, encodeToCurve } from '@noble/curves/ed448';
x448.getSharedSecret(priv, pub) === x448.scalarMult(priv, pub); // aliases
x448.getPublicKey(priv) === x448.scalarMultBase(priv);
Same RFC7748 / RFC8032 are followed.
bls12-381
See abstract/bls.
Accessing a curve's variables
import { secp256k1 } from '@noble/curves/secp256k1';
// Every curve has `CURVE` object that contains its parameters, field, and others
console.log(secp256k1.CURVE.p); // field modulus
console.log(secp256k1.CURVE.n); // curve order
console.log(secp256k1.CURVE.a, secp256k1.CURVE.b); // equation params
console.log(secp256k1.CURVE.Gx, secp256k1.CURVE.Gy); // base point coordinates
Abstract API
Abstract API allows to define custom curves. All arithmetics is done with JS
bigints over finite fields, which is defined from modular
sub-module. For
scalar multiplication, we use
precomputed tables with w-ary non-adjacent form (wNAF).
Precomputes are enabled for weierstrass and edwards BASE points of a curve. You
could precompute any other point (e.g. for ECDH) using utils.precompute()
method: check out examples.
There are following zero-dependency algorithms:
- abstract/weierstrass: Short Weierstrass curve
- abstract/edwards: Twisted Edwards curve
- abstract/montgomery: Montgomery curve
- abstract/bls: Barreto-Lynn-Scott curves
- abstract/hash-to-curve: Hashing strings to curve points
- abstract/poseidon: Poseidon hash
- abstract/modular: Modular arithmetics utilities
- abstract/utils: General utilities
abstract/weierstrass: Short Weierstrass curve
import { weierstrass } from '@noble/curves/abstract/weierstrass';
import { Field } from '@noble/curves/abstract/modular'; // finite field for mod arithmetics
import { sha256 } from '@noble/hashes/sha256'; // 3rd-party sha256() of type utils.CHash
import { hmac } from '@noble/hashes/hmac'; // 3rd-party hmac() that will accept sha256()
import { concatBytes, randomBytes } from '@noble/hashes/utils'; // 3rd-party utilities
const secq256k1 = weierstrass({
// secq256k1: cycle of secp256k1 with Fp/N flipped.
// https://personaelabs.org/posts/spartan-ecdsa
// https://zcash.github.io/halo2/background/curves.html#cycles-of-curves
a: 0n,
b: 7n,
Fp: Field(2n ** 256n - 432420386565659656852420866394968145599n),
n: 2n ** 256n - 2n ** 32n - 2n ** 9n - 2n ** 8n - 2n ** 7n - 2n ** 6n - 2n ** 4n - 1n,
Gx: 55066263022277343669578718895168534326250603453777594175500187360389116729240n,
Gy: 32670510020758816978083085130507043184471273380659243275938904335757337482424n,
hash: sha256,
hmac: (key: Uint8Array, ...msgs: Uint8Array[]) => hmac(sha256, key, concatBytes(...msgs)),
randomBytes,
});
// Replace weierstrass with weierstrassPoints if you don't need ECDSA, hash, hmac, randomBytes
Short Weierstrass curve's formula is y² = x³ + ax + b
. weierstrass
expects arguments a
, b
, field Fp
, curve order n
, cofactor h
and coordinates Gx
, Gy
of generator point.
k
generation is done deterministically, following
RFC6979. For this you will need
hmac
& hash
, which in our implementations is provided by noble-hashes. If
you're using different hashing library, make sure to wrap it in the following interface:
type CHash = {
(message: Uint8Array): Uint8Array;
blockLen: number;
outputLen: number;
create(): any;
};
Weierstrass points:
- Exported as
ProjectivePoint
- Represented in projective (homogeneous) coordinates: (x, y, z) ∋ (x=x/z, y=y/z)
- Use complete exception-free formulas for addition and doubling
- Can be decoded/encoded from/to Uint8Array / hex strings using
ProjectivePoint.fromHex
andProjectivePoint#toRawBytes()
- Have
assertValidity()
which checks for being on-curve - Have
toAffine()
andx
/y
getters which convert to 2d xy affine coordinates
// `weierstrassPoints()` returns `CURVE` and `ProjectivePoint`
// `weierstrass()` returns `CurveFn`
type SignOpts = { lowS?: boolean; prehash?: boolean; extraEntropy: boolean | Uint8Array };
type CurveFn = {
CURVE: ReturnType<typeof validateOpts>;
getPublicKey: (privateKey: PrivKey, isCompressed?: boolean) => Uint8Array;
getSharedSecret: (privateA: PrivKey, publicB: Hex, isCompressed?: boolean) => Uint8Array;
sign: (msgHash: Hex, privKey: PrivKey, opts?: SignOpts) => SignatureType;
verify: (
signature: Hex | SignatureType,
msgHash: Hex,
publicKey: Hex,
opts?: { lowS?: boolean; prehash?: boolean }
) => boolean;
ProjectivePoint: ProjectivePointConstructor;
Signature: SignatureConstructor;
utils: {
normPrivateKeyToScalar: (key: PrivKey) => bigint;
isValidPrivateKey(key: PrivKey): boolean;
randomPrivateKey: () => Uint8Array;
precompute: (windowSize?: number, point?: ProjPointType<bigint>) => ProjPointType<bigint>;
};
};
// T is usually bigint, but can be something else like complex numbers in BLS curves
interface ProjPointType<T> extends Group<ProjPointType<T>> {
readonly px: T;
readonly py: T;
readonly pz: T;
get x(): bigint;
get y(): bigint;
multiply(scalar: bigint): ProjPointType<T>;
multiplyUnsafe(scalar: bigint): ProjPointType<T>;
multiplyAndAddUnsafe(Q: ProjPointType<T>, a: bigint, b: bigint): ProjPointType<T> | undefined;
toAffine(iz?: T): AffinePoint<T>;
isTorsionFree(): boolean;
clearCofactor(): ProjPointType<T>;
assertValidity(): void;
hasEvenY(): boolean;
toRawBytes(isCompressed?: boolean): Uint8Array;
toHex(isCompressed?: boolean): string;
}
// Static methods for 3d XYZ points
interface ProjConstructor<T> extends GroupConstructor<ProjPointType<T>> {
new (x: T, y: T, z: T): ProjPointType<T>;
fromAffine(p: AffinePoint<T>): ProjPointType<T>;
fromHex(hex: Hex): ProjPointType<T>;
fromPrivateKey(privateKey: PrivKey): ProjPointType<T>;
}
ECDSA signatures are represented by Signature
instances and can be
described by the interface:
interface SignatureType {
readonly r: bigint;
readonly s: bigint;
readonly recovery?: number;
assertValidity(): void;
addRecoveryBit(recovery: number): SignatureType;
hasHighS(): boolean;
normalizeS(): SignatureType;
recoverPublicKey(msgHash: Hex): ProjPointType<bigint>;
toCompactRawBytes(): Uint8Array;
toCompactHex(): string;
// DER-encoded
toDERRawBytes(): Uint8Array;
toDERHex(): string;
}
type SignatureConstructor = {
new (r: bigint, s: bigint): SignatureType;
fromCompact(hex: Hex): SignatureType;
fromDER(hex: Hex): SignatureType;
};
More examples:
// All curves expose same generic interface.
const priv = secq256k1.utils.randomPrivateKey();
secq256k1.getPublicKey(priv); // Convert private key to public.
const sig = secq256k1.sign(msg, priv); // Sign msg with private key.
secq256k1.verify(sig, msg, priv); // Verify if sig is correct.
const Point = secq256k1.ProjectivePoint;
const point = Point.BASE; // Elliptic curve Point class and BASE point static var.
point.add(point).equals(point.double()); // add(), equals(), double() methods
point.subtract(point).equals(Point.ZERO); // subtract() method, ZERO static var
point.negate(); // Flips point over x/y coordinate.
point.multiply(31415n); // Multiplication of Point by scalar.
point.assertValidity(); // Checks for being on-curve
point.toAffine(); // Converts to 2d affine xy coordinates
secq256k1.CURVE.n;
secq256k1.CURVE.p;
secq256k1.CURVE.Fp.mod();
secq256k1.CURVE.hash();
// precomputes
const fast = secq256k1.utils.precompute(8, Point.fromHex(someonesPubKey));
fast.multiply(privKey); // much faster ECDH now
abstract/edwards: Twisted Edwards curve
import { twistedEdwards } from '@noble/curves/abstract/edwards';
import { Field } from '@noble/curves/abstract/modular';
import { sha512 } from '@noble/hashes/sha512';
import { randomBytes } from '@noble/hashes/utils';
const Fp = Field(2n ** 255n - 19n);
const ed25519 = twistedEdwards({
a: Fp.create(-1n),
d: Fp.div(-121665n, 121666n), // -121665n/121666n mod p
Fp: Fp,
n: 2n ** 252n + 27742317777372353535851937790883648493n,
h: 8n,
Gx: 15112221349535400772501151409588531511454012693041857206046113283949847762202n,
Gy: 46316835694926478169428394003475163141307993866256225615783033603165251855960n,
hash: sha512,
randomBytes,
adjustScalarBytes(bytes) {
// optional; but mandatory in ed25519
bytes[0] &= 248;
bytes[31] &= 127;
bytes[31] |= 64;
return bytes;
},
} as const);
Twisted Edwards curve's formula is ax² + y² = 1 + dx²y²
. You must specify a
, d
, field Fp
, order n
, cofactor h
and coordinates Gx
, Gy
of generator point.
For EdDSA signatures, hash
param required. adjustScalarBytes
which instructs how to change private scalars could be specified.
Edwards points:
- Exported as
ExtendedPoint
- Represented in extended coordinates: (x, y, z, t) ∋ (x=x/z, y=y/z)
- Use complete exception-free formulas for addition and doubling
- Can be decoded/encoded from/to Uint8Array / hex strings using
ExtendedPoint.fromHex
andExtendedPoint#toRawBytes()
- Have
assertValidity()
which checks for being on-curve - Have
toAffine()
andx
/y
getters which convert to 2d xy affine coordinates - Have
isTorsionFree()
,clearCofactor()
andisSmallOrder()
utilities to handle torsions
// `twistedEdwards()` returns `CurveFn` of following type:
type CurveFn = {
CURVE: ReturnType<typeof validateOpts>;
getPublicKey: (privateKey: Hex) => Uint8Array;
sign: (message: Hex, privateKey: Hex, context?: Hex) => Uint8Array;
verify: (sig: SigType, message: Hex, publicKey: Hex, context?: Hex) => boolean;
ExtendedPoint: ExtPointConstructor;
utils: {
randomPrivateKey: () => Uint8Array;
getExtendedPublicKey: (key: PrivKey) => {
head: Uint8Array;
prefix: Uint8Array;
scalar: bigint;
point: PointType;
pointBytes: Uint8Array;
};
};
};
interface ExtPointType extends Group<ExtPointType> {
readonly ex: bigint;
readonly ey: bigint;
readonly ez: bigint;
readonly et: bigint;
get x(): bigint;
get y(): bigint;
assertValidity(): void;
multiply(scalar: bigint): ExtPointType;
multiplyUnsafe(scalar: bigint): ExtPointType;
isSmallOrder(): boolean;
isTorsionFree(): boolean;
clearCofactor(): ExtPointType;
toAffine(iz?: bigint): AffinePoint<bigint>;
toRawBytes(isCompressed?: boolean): Uint8Array;
toHex(isCompressed?: boolean): string;
}
// Static methods of Extended Point with coordinates in X, Y, Z, T
interface ExtPointConstructor extends GroupConstructor<ExtPointType> {
new (x: bigint, y: bigint, z: bigint, t: bigint): ExtPointType;
fromAffine(p: AffinePoint<bigint>): ExtPointType;
fromHex(hex: Hex): ExtPointType;
fromPrivateKey(privateKey: Hex): ExtPointType;
}
abstract/montgomery: Montgomery curve
import { montgomery } from '@noble/curves/abstract/montgomery';
import { Field } from '@noble/curves/abstract/modular';
const x25519 = montgomery({
a: 486662n,
Gu: 9n,
Fp: Field(2n ** 255n - 19n),
montgomeryBits: 255,
nByteLength: 32,
// Optional param
adjustScalarBytes(bytes) {
bytes[0] &= 248;
bytes[31] &= 127;
bytes[31] |= 64;
return bytes;
},
});
The module contains methods for x-only ECDH on Curve25519 / Curve448 from RFC7748. Proper Elliptic Curve Points are not implemented yet.
You must specify curve params Fp
, a
, Gu
coordinate of u, montgomeryBits
and nByteLength
.
abstract/bls: Barreto-Lynn-Scott curves
The module abstracts BLS (Barreto-Lynn-Scott) pairing-friendly elliptic curve construction. They allow to construct zk-SNARKs and use aggregated, batch-verifiable threshold signatures, using Boneh-Lynn-Shacham signature scheme.
Main methods and properties are:
getPublicKey(privateKey)
sign(message, privateKey)
verify(signature, message, publicKey)
aggregatePublicKeys(publicKeys)
aggregateSignatures(signatures)
G1
andG2
curves containingCURVE
andProjectivePoint
Signature
property withfromHex
,toHex
methodsfields
containingFp
,Fp2
,Fp6
,Fp12
,Fr
Right now we only implement BLS12-381 (compatible with ETH and others), but in theory defining BLS12-377, BLS24 should be straightforward. An example:
import { bls12_381 as bls } from '@noble/curves/bls12-381';
const privateKey = '67d53f170b908cabb9eb326c3c337762d59289a8fec79f7bc9254b584b73265c';
const message = '64726e3da8';
const publicKey = bls.getPublicKey(privateKey);
const signature = bls.sign(message, privateKey);
const isValid = 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 = privateKeys.map((p) => bls.sign(message, p));
const aggPubKey2 = bls.aggregatePublicKeys(publicKeys);
const aggSignature2 = bls.aggregateSignatures(signatures2);
const isValid2 = bls.verify(aggSignature2, message, aggPubKey2);
console.log({ signatures2, aggSignature2, isValid2 });
// Sign 3 msgs with 3 keys
const signatures3 = privateKeys.map((p, i) => bls.sign(messages[i], p));
const aggSignature3 = bls.aggregateSignatures(signatures3);
const isValid3 = bls.verifyBatch(aggSignature3, messages, publicKeys);
console.log({ publicKeys, signatures3, aggSignature3, isValid3 });
// bls.pairing(PointG1, PointG2) // pairings
// bls.G1.ProjectivePoint.BASE, bls.G2.ProjectivePoint.BASE
// bls.fields.Fp, bls.fields.Fp2, bls.fields.Fp12, bls.fields.Fr
// hash-to-curve examples can be seen below
Full types:
getPublicKey: (privateKey: PrivKey) => Uint8Array;
sign: {
(message: Hex, privateKey: PrivKey): Uint8Array;
(message: ProjPointType<Fp2>, privateKey: PrivKey): ProjPointType<Fp2>;
};
verify: (
signature: Hex | ProjPointType<Fp2>,
message: Hex | ProjPointType<Fp2>,
publicKey: Hex | ProjPointType<Fp>
) => 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>;
};
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 hash-to-curve v16.
Every curve has exported hashToCurve
and encodeToCurve
methods. You should always prefer hashToCurve
for security:
import { hashToCurve, encodeToCurve } from '@noble/curves/secp256k1';
import { randomBytes } from '@noble/hashes/utils';
hashToCurve('0102abcd');
console.log(hashToCurve(randomBytes()));
console.log(encodeToCurve(randomBytes()));
import { bls12_381 } from '@noble/curves/bls12-381';
bls12_381.G1.hashToCurve(randomBytes(), { DST: 'another' });
bls12_381.G2.hashToCurve(randomBytes(), { DST: 'custom' });
If you need low-level methods from spec:
expand_message_xmd
(spec) produces a uniformly random byte string using a cryptographic hash function H that outputs b bits.
Hash must conform to CHash
interface (see weierstrass section).
function expand_message_xmd(
msg: Uint8Array,
DST: Uint8Array,
lenInBytes: number,
H: CHash
): Uint8Array;
function expand_message_xof(
msg: Uint8Array,
DST: Uint8Array,
lenInBytes: number,
k: number,
H: CHash
): Uint8Array;
hash_to_field(msg, count, options)
(spec)
hashes arbitrary-length byte strings to a list of one or more elements of a finite field F.
/**
* * `DST` is a domain separation tag, defined in section 2.2.5
* * `p` characteristic of F, where F is a finite field of characteristic p and order q = p^m
* * `m` is extension degree (1 for prime fields)
* * `k` is the target security target in bits (e.g. 128), from section 5.1
* * `expand` is `xmd` (SHA2, SHA3, BLAKE) or `xof` (SHAKE, BLAKE-XOF)
* * `hash` conforming to `utils.CHash` interface, with `outputLen` / `blockLen` props
*/
type UnicodeOrBytes = string | Uint8Array;
type Opts = {
DST: UnicodeOrBytes;
p: bigint;
m: number;
k: number;
expand?: 'xmd' | 'xof';
hash: CHash;
};
/**
* Hashes arbitrary-length byte strings to a list of one or more elements of a finite field F
* https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-5.3
* @param msg a byte string containing the message to hash
* @param count the number of elements of F to output
* @param options `{DST: string, p: bigint, m: number, k: number, expand: 'xmd' | 'xof', hash: H}`, see above
* @returns [u_0, ..., u_(count - 1)], a list of field elements.
*/
function hash_to_field(msg: Uint8Array, count: number, options: Opts): bigint[][];
abstract/poseidon: Poseidon hash
Implements Poseidon ZK-friendly hash.
There are many poseidon variants with different constants. We don't provide them: you should construct them manually. Check out micro-starknet package for a proper example.
import { poseidon } from '@noble/curves/abstract/poseidon';
type PoseidonOpts = {
Fp: Field<bigint>;
t: number;
roundsFull: number;
roundsPartial: number;
sboxPower?: number;
reversePartialPowIdx?: boolean;
mds: bigint[][];
roundConstants: bigint[][];
};
const instance = poseidon(opts: PoseidonOpts);
abstract/modular: Modular arithmetics utilities
import * as mod from '@noble/curves/abstract/modular';
const fp = mod.Field(2n ** 255n - 19n); // Finite field over 2^255-19
fp.mul(591n, 932n); // multiplication
fp.pow(481n, 11024858120n); // exponentiation
fp.div(5n, 17n); // division: 5/17 mod 2^255-19 == 5 * invert(17)
fp.sqrt(21n); // square root
// Generic non-FP utils are also available
mod.mod(21n, 10n); // 21 mod 10 == 1n; fixed version of 21 % 10
mod.invert(17n, 10n); // invert(17) mod 10; modular multiplicative inverse
mod.invertBatch([1n, 2n, 4n], 21n); // => [1n, 11n, 16n] in one inversion
Creating private keys from hashes
Suppose you have sha256(something)
(e.g. from HMAC) and you want to make a private key from it.
Even though p256 or secp256k1 may have 32-byte private keys,
and sha256 output is also 32-byte, you can't just use it and reduce it modulo CURVE.n
.
Doing so will make the result key biased.
To avoid the bias, we implement FIPS 186 B.4.1, which allows to take arbitrary byte array and produce valid scalars / private keys with bias being neglible.
Use hash-to-curve if you need hashing to public keys; the function in the module instead operates on private keys.
import { p256 } from '@noble/curves/p256';
import { sha256 } from '@noble/hashes/sha256';
import { hkdf } from '@noble/hashes/hkdf';
const someKey = new Uint8Array(32).fill(2); // Needs to actually be random, not .fill(2)
const derived = hkdf(sha256, someKey, undefined, 'application', 40); // 40 bytes
const validPrivateKey = mod.hashToPrivateScalar(derived, p256.CURVE.n);
abstract/utils: General utilities
import * as utils from '@noble/curves/abstract/utils';
utils.bytesToHex(Uint8Array.from([0xde, 0xad, 0xbe, 0xef]));
utils.hexToBytes('deadbeef');
utils.numberToHexUnpadded(123n);
utils.hexToNumber();
utils.bytesToNumberBE(Uint8Array.from([0xde, 0xad, 0xbe, 0xef]));
utils.bytesToNumberLE(Uint8Array.from([0xde, 0xad, 0xbe, 0xef]));
utils.numberToBytesBE(123n, 32);
utils.numberToBytesLE(123n, 64);
utils.concatBytes(Uint8Array.from([0xde, 0xad]), Uint8Array.from([0xbe, 0xef]));
utils.nLength(255n);
utils.equalBytes(Uint8Array.from([0xde]), Uint8Array.from([0xde]));
Security
- The library has been audited in Feb 2023 by an independent security firm Trail of Bits:
PDF.
The audit has been funded by Ryan Shea. Audit scope was abstract modules
curve
,hash-to-curve
,modular
,poseidon
,utils
,weierstrass
, and top-level modules_shortw_utils
andsecp256k1
. See changes since audit. - The library has been fuzzed by Guido Vranken's cryptofuzz. You can run the fuzzer by yourself to check it.
- Timing attack considerations: JIT-compiler and Garbage Collector make "constant time" extremely hard to achieve in a scripting language. Which means any other JS library can't have constant-timeness. 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. Nonetheless we're targetting algorithmic constant time.
We 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. As for devDependencies used by the library:
@scure
base, bip32, bip39 (used in tests), micro-bmark (benchmark), micro-should (testing) are developed by us and follow the same practices such as: minimal library size, auditability, signed releases- prettier (linter), fast-check (property-based testing),
typescript versions are locked and rarely updated. Every update is checked with
npm-diff
. The packages are big, which makes it hard to audit their source code thoroughly and fully. - They are only used if you clone the git repo and want to add some feature to it. End-users won't use them.
As for key generation, we're deferring to built-in crypto.getRandomValues which is considered cryptographically secure (CSPRNG).
Speed
Benchmark results on Apple M2 with node v20:
secp256k1
init x 68 ops/sec @ 14ms/op
getPublicKey x 6,750 ops/sec @ 148μs/op
sign x 5,206 ops/sec @ 192μs/op
verify x 880 ops/sec @ 1ms/op
getSharedSecret x 536 ops/sec @ 1ms/op
recoverPublicKey x 852 ops/sec @ 1ms/op
schnorr.sign x 685 ops/sec @ 1ms/op
schnorr.verify x 908 ops/sec @ 1ms/op
p256
init x 38 ops/sec @ 26ms/op
getPublicKey x 6,530 ops/sec @ 153μs/op
sign x 5,074 ops/sec @ 197μs/op
verify x 626 ops/sec @ 1ms/op
p384
init x 17 ops/sec @ 57ms/op
getPublicKey x 2,883 ops/sec @ 346μs/op
sign x 2,358 ops/sec @ 424μs/op
verify x 245 ops/sec @ 4ms/op
p521
init x 9 ops/sec @ 109ms/op
getPublicKey x 1,516 ops/sec @ 659μs/op
sign x 1,271 ops/sec @ 786μs/op
verify x 123 ops/sec @ 8ms/op
ed25519
init x 54 ops/sec @ 18ms/op
getPublicKey x 10,269 ops/sec @ 97μs/op
sign x 5,110 ops/sec @ 195μs/op
verify x 1,049 ops/sec @ 952μs/op
ed448
init x 19 ops/sec @ 51ms/op
getPublicKey x 3,775 ops/sec @ 264μs/op
sign x 1,771 ops/sec @ 564μs/op
verify x 351 ops/sec @ 2ms/op
ecdh
├─x25519 x 1,466 ops/sec @ 682μs/op
├─secp256k1 x 539 ops/sec @ 1ms/op
├─p256 x 511 ops/sec @ 1ms/op
├─p384 x 199 ops/sec @ 5ms/op
├─p521 x 103 ops/sec @ 9ms/op
└─x448 x 548 ops/sec @ 1ms/op
bls12-381
init x 36 ops/sec @ 27ms/op
getPublicKey 1-bit x 973 ops/sec @ 1ms/op
getPublicKey x 970 ops/sec @ 1ms/op
sign x 55 ops/sec @ 17ms/op
verify x 39 ops/sec @ 25ms/op
pairing x 106 ops/sec @ 9ms/op
aggregatePublicKeys/8 x 129 ops/sec @ 7ms/op
aggregatePublicKeys/32 x 34 ops/sec @ 28ms/op
aggregatePublicKeys/128 x 8 ops/sec @ 112ms/op
aggregatePublicKeys/512 x 2 ops/sec @ 446ms/op
aggregatePublicKeys/2048 x 0 ops/sec @ 1778ms/op
aggregateSignatures/8 x 50 ops/sec @ 19ms/op
aggregateSignatures/32 x 13 ops/sec @ 74ms/op
aggregateSignatures/128 x 3 ops/sec @ 296ms/op
aggregateSignatures/512 x 0 ops/sec @ 1180ms/op
aggregateSignatures/2048 x 0 ops/sec @ 4715ms/op
hash-to-curve
hash_to_field x 91,600 ops/sec @ 10μs/op
secp256k1 x 2,373 ops/sec @ 421μs/op
p256 x 4,310 ops/sec @ 231μs/op
p384 x 1,664 ops/sec @ 600μs/op
p521 x 807 ops/sec @ 1ms/op
ed25519 x 3,088 ops/sec @ 323μs/op
ed448 x 1,247 ops/sec @ 801μs/op
Contributing & testing
- Clone the repository
npm install
to install build dependencies like TypeScriptnpm run build
to compile TypeScript codenpm run test
will execute all main tests
Upgrading
Previously, the library was split into single-feature packages noble-secp256k1, noble-ed25519 and noble-bls12-381.
Curves continue their original work. The single-feature packages changed their direction towards providing minimal 4kb implementations of cryptography, which means they have less features.
Upgrading from @noble/secp256k1 2.0 or @noble/ed25519 2.0: no changes, libraries are compatible.
Upgrading from @noble/secp256k1 1.7:
getPublicKey
- now produce 33-byte compressed signatures by default
- to use old behavior, which produced 65-byte uncompressed keys, set
argument
isCompressed
tofalse
:getPublicKey(priv, false)
sign
- is now sync; use
signAsync
for async version - now returns
Signature
instance with{ r, s, recovery }
properties canonical
option was renamed tolowS
recovered
option has been removed because recovery bit is always returned nowder
option has been removed. There are 2 options:- Use compact encoding:
fromCompact
,toCompactRawBytes
,toCompactHex
. Compact encoding is simply a concatenation of 32-byte r and 32-byte s. - If you must use DER encoding, switch to noble-curves (see above).
- Use compact encoding:
- is now sync; use
verify
strict
option was renamed tolowS
getSharedSecret
- now produce 33-byte compressed signatures by default
- to use old behavior, which produced 65-byte uncompressed keys, set
argument
isCompressed
tofalse
:getSharedSecret(a, b, false)
recoverPublicKey(msg, sig, rec)
was changed tosig.recoverPublicKey(msg)
number
type for private keys have been removed: usebigint
insteadPoint
(2d xy) has been changed toProjectivePoint
(3d xyz)utils
were split intoutils
(same api as in noble-curves) andetc
(hmacSha256Sync
and others)
Upgrading from @noble/ed25519 1.7:
- Methods are now sync by default
bigint
is no longer allowed ingetPublicKey
,sign
,verify
. Reason: ed25519 is LE, can lead to bugsPoint
(2d xy) has been changed toExtendedPoint
(xyzt)Signature
was removed: just use raw bytes or hex nowutils
were split intoutils
(same api as in noble-curves) andetc
(sha512Sync
and others)getSharedSecret
was moved tox25519
moduletoX25519
has been moved toedwardsToMontgomeryPub
andedwardsToMontgomeryPriv
methods
Upgrading from @noble/bls12-381:
- Methods and classes were renamed:
- PointG1 -> G1.Point, PointG2 -> G2.Point
- PointG2.fromSignature -> Signature.decode, PointG2.toSignature -> Signature.encode
- Fp2 ORDER was corrected
Resources
Useful documentation and articles about the library or its primitives:
- Learning fast elliptic-curve cryptography
- Taming the many EdDSAs that describes concepts of Strong UnForgeability under Chosen Message Attacks and Strongly Binding Signatures
- Pairings and BLS
Online demos:
- Elliptic Curve Calculator: add / multiply points, sign messages
- BLS threshold signatures
Projects using noble-curves:
- scure-bip32 and separate bip32 HDkey libraries
- Ethereum libraries:
- ethereum-cryptography
- @ethereumjs
- micro-eth-signer
- ethers (old noble-secp256k1 for now)
- viem.sh
- metamask's eth-sig-util
- gridplus lattice sdk
- Bitcoin libraries: scure-btc-signer
- Solana libraries: micro-sol-signer, solana-web3.js
- polkadot.js, micro-starknet
- protonmail (old noble-ed25519 for now)
- did-jwt, hpke-js, nostr-tools
- ed25519-keygen SSH, PGP, TOR key generation
- secp256k1 compatibility layer 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 following draft-irtf-cfrg-bbs-signatures-latest
- KZG trusted setup ceremony
License
The MIT License (MIT)
Copyright (c) 2022 Paul Miller (https://paulmillr.com)
See LICENSE file.