@noble/curves
Advanced tools
The @noble/curves npm package is a library that provides a collection of elliptic curves, allowing for the implementation of cryptographic operations such as digital signatures and key agreement protocols. It is part of the noble family of cryptographic libraries, which are known for their focus on security, simplicity, and small bundle size.
Elliptic Curve Cryptography (ECC) Operations
This code demonstrates how to generate a private key, derive its corresponding public key, sign a message, and verify the signature using the P-256 elliptic curve. It showcases the basic cryptographic operations that can be performed with the @noble/curves package.
"use strict";
const curves = require('@noble/curves');
const { p256 } = curves;
async function main() {
const privateKey = p256.utils.randomPrivateKey();
const publicKey = p256.getPublicKey(privateKey);
const message = new TextEncoder().encode('Hello, world!');
const signature = await p256.sign(message, privateKey);
const isValid = await p256.verify(signature, message, publicKey);
console.log('Signature valid:', isValid);
}
main();Elliptic is a popular npm package that provides implementations of various elliptic curve cryptography algorithms. It supports a wide range of curves and cryptographic operations, making it a versatile choice for many applications. Compared to @noble/curves, Elliptic may offer a broader selection of curves but might not have the same focus on minimalism and security.
Bcrypto is a node.js and web cryptography library that supports a variety of cryptographic primitives, including elliptic curve cryptography. It is designed for high performance and security, offering a comprehensive suite of cryptographic functions. Bcrypto and @noble/curves share a focus on security, but bcrypto provides a wider range of cryptographic functionalities beyond just elliptic curves.
Audited & minimal JS implementation of elliptic curve cryptography.
Take a glance at GitHub Discussions for questions and support.
noble cryptography — high-security, easily auditable set of contained cryptographic libraries and tools.
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 getRandomValues. A standalone file noble-curves.js is also available.
// import * from '@noble/curves'; // Error: use sub-imports, to ensure small app size
import { secp256k1 } from '@noble/curves/secp256k1'; // ESM and Common.js
// import { secp256k1 } from 'npm:@noble/curves@1.6.0/secp256k1'; // Deno
Implementations use noble-hashes. If you want to use a different hashing library, abstract API doesn't depend on them.
import { secp256k1 } from '@noble/curves/secp256k1';
// import { p256 } from '@noble/curves/p256'; // or p384 / p521
const priv = secp256k1.utils.randomPrivateKey();
const pub = secp256k1.getPublicKey(priv);
const msg = new Uint8Array(32).fill(1); // message hash (not message) in ecdsa
const sig = secp256k1.sign(msg, priv); // `{prehash: true}` option is available
const isValid = secp256k1.verify(sig, msg, pub) === true;
// hex strings are also supported besides Uint8Array-s:
const privHex = '46c930bc7bb4db7f55da20798697421b98c4175a52c630294d75a84b9c126236';
const pub2 = secp256k1.getPublicKey(privHex);
The same code would work for NIST P256 (secp256r1), P384 (secp384r1) & P521 (secp521r1).
// let sig = secp256k1.Signature.fromCompact(sigHex); // or .fromDER(sigDERHex)
// sig = sig.addRecoveryBit(bit); // bit is not serialized into compact / der format
sig.recoverPublicKey(msg).toRawBytes(); // === pub; // public key recovery
// extraEntropy https://moderncrypto.org/mail-archive/curves/2017/000925.html
const sigImprovedSecurity = secp256k1.sign(msg, priv, { extraEntropy: true });
// 1. The output includes parity byte. Strip it using shared.slice(1)
// 2. The output is not hashed. More secure way is sha256(shared) or hkdf(shared)
const someonesPub = secp256k1.getPublicKey(secp256k1.utils.randomPrivateKey());
const shared = secp256k1.getSharedSecret(priv, someonesPub);
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);
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.
X25519 follows RFC7748.
// 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());
ristretto255 follows irtf draft.
// hash-to-curve, ristretto255
import { utf8ToBytes } from '@noble/hashes/utils';
import { sha512 } from '@noble/hashes/sha512';
import {
hashToCurve,
encodeToCurve,
RistrettoPoint,
hashToRistretto255,
} from '@noble/curves/ed25519';
const msg = utf8ToBytes('Ristretto is traditionally a short shot of espresso coffee');
hashToCurve(msg);
const rp = RistrettoPoint.fromHex(
'6a493210f7499cd17fecb510ae0cea23a110e8d5b901f8acadd3095c73a3b919'
);
RistrettoPoint.BASE.multiply(2n).add(rp).subtract(RistrettoPoint.BASE).toRawBytes();
RistrettoPoint.ZERO.equals(dp) === false;
// pre-hashed hash-to-curve
RistrettoPoint.hashToCurve(sha512(msg));
// full hash-to-curve including domain separation tag
hashToRistretto255(msg, { DST: 'ristretto255_XMD:SHA-512_R255MAP_RO_' });
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);
// Variants from RFC8032: prehashed
import { ed448ph } from '@noble/curves/ed448';
ECDH using Curve448 aka X448, follows RFC7748.
import { x448 } from '@noble/curves/ed448';
x448.getSharedSecret(priv, pub) === x448.scalarMult(priv, pub); // aliases
x448.getPublicKey(priv) === x448.scalarMultBase(priv);
// ed448 => x448 conversion
import { edwardsToMontgomeryPub } from '@noble/curves/ed448';
edwardsToMontgomeryPub(ed448.getPublicKey(ed448.utils.randomPrivateKey()));
decaf448 follows irtf draft.
import { utf8ToBytes } from '@noble/hashes/utils';
import { shake256 } from '@noble/hashes/sha3';
import { hashToCurve, encodeToCurve, DecafPoint, hashToDecaf448 } from '@noble/curves/ed448';
const msg = utf8ToBytes('Ristretto is traditionally a short shot of espresso coffee');
hashToCurve(msg);
const dp = DecafPoint.fromHex(
'c898eb4f87f97c564c6fd61fc7e49689314a1f818ec85eeb3bd5514ac816d38778f69ef347a89fca817e66defdedce178c7cc709b2116e75'
);
DecafPoint.BASE.multiply(2n).add(dp).subtract(DecafPoint.BASE).toRawBytes();
DecafPoint.ZERO.equals(dp) === false;
// pre-hashed hash-to-curve
DecafPoint.hashToCurve(shake256(msg, { dkLen: 112 }));
// full hash-to-curve including domain separation tag
hashToDecaf448(msg, { DST: 'decaf448_XOF:SHAKE256_D448MAP_RO_' });
Same RFC7748 / RFC8032 / IRTF draft are followed.
import { bls12_381 as bls } from '@noble/curves/bls12-381';
// G1 keys, G2 signatures
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 });
// G2 keys, G1 signatures
// getPublicKeyForShortSignatures(privateKey)
// signShortSignature(message, privateKey)
// verifyShortSignature(signature, message, publicKey)
// aggregateShortSignatures(signatures)
// Custom DST
const htfEthereum = { DST: 'BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_POP_' };
const signatureEth = bls.sign(message, privateKey, htfEthereum);
const isValidEth = bls.verify(signature, message, publicKey, htfEthereum);
// Aggregation
const aggregatedKey = bls.aggregatePublicKeys([bls.utils.randomPrivateKey(), bls.utils.randomPrivateKey()])
// const aggregatedSig = bls.aggregateSignatures(sigs)
// Pairings, with and without final exponentiation
// bls.pairing(PointG1, PointG2);
// bls.pairing(PointG1, PointG2, false);
// bls.fields.Fp12.finalExponentiate(bls.fields.Fp12.mul(PointG1, PointG2));
// Others
// bls.G1.ProjectivePoint.BASE, bls.G2.ProjectivePoint.BASE;
// bls.fields.Fp, bls.fields.Fp2, bls.fields.Fp12, bls.fields.Fr;
See abstract/bls. For example usage, check out the implementation of BLS EVM precompiles.
import { bn254 } from '@noble/curves/bn254';
console.log(
bn254.G1,
bn254.G2,
bn254.pairing
)
The API mirrors BLS. The curve was previously called alt_bn128. The implementation is compatible with EIP-196 and EIP-197.
Keep in mind that we don't implement Point methods toHex / toRawBytes. It's because different implementations of bn254 do it differently - there is no standard. Points of divergence:
For example usage, check out the implementation of bn254 EVM precompiles.
import { secp256k1 } from '@noble/curves/secp256k1';
const p = secp256k1.ProjectivePoint;
const points = [p.BASE, p.BASE.multiply(2n), p.BASE.multiply(4n), p.BASE.multiply(8n)];
p.msm(points, [3n, 5n, 7n, 11n]).equals(p.BASE.multiply(129n)); // 129*G
Pippenger algorithm is used underneath.
Multi-scalar-multiplication (MSM) is basically (Pa + Qb + Rc + ...).
It's 10-30x faster vs naive addition for large amount of points.
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'; // also known as alt_bn128
import { jubjub } from '@noble/curves/jubjub';
import { bytesToHex, hexToBytes, concatBytes, utf8ToBytes } from '@noble/curves/abstract/utils';
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 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.
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 hmacSha256 = (key: Uint8Array, ...msgs: Uint8Array[]) => hmac(sha256, key, concatBytes(...msgs));
// 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
const secq256k1 = weierstrass({
// Curve equation params a, b
a: 0n,
b: 7n,
// Field over which we'll do calculations
Fp: Field(2n ** 256n - 432420386565659656852420866394968145599n),
// Curve order, total count of valid points in the field.
n: 2n ** 256n - 2n ** 32n - 2n ** 9n - 2n ** 8n - 2n ** 7n - 2n ** 6n - 2n ** 4n - 1n,
// Base point (x, y) aka generator point
Gx: 55066263022277343669578718895168534326250603453777594175500187360389116729240n,
Gy: 32670510020758816978083085130507043184471273380659243275938904335757337482424n,
hash: sha256,
hmac: hmacSha256,
randomBytes,
});
// NIST secp192r1 aka p192 https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/secg/secp192r1
const secp192r1 = weierstrass({
a: BigInt('0xfffffffffffffffffffffffffffffffefffffffffffffffc'),
b: BigInt('0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1'),
Fp: Field(BigInt('0xfffffffffffffffffffffffffffffffeffffffffffffffff')),
n: BigInt('0xffffffffffffffffffffffff99def836146bc9b1b4d22831'),
Gx: BigInt('0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012'),
Gy: BigInt('0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811'),
h: BigInt(1),
hash: sha256,
hmac: hmacSha256,
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. It is suggested to use extraEntropy
option, which incorporates randomness into signatures to increase their security.
For k generation, specifying hmac & hash is required,
which in our implementations is done 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;
};
// example
function sha256(message: Uint8Array) {
return _internal_lowlvl(message);
}
sha256.outputLen = 32; // 32 bytes of output for sha2-256
Message hash is expected instead of message itself:
sign(msgHash, privKey) is default behavior, assuming you pre-hash msg with sha2, or other hashsign(msg, privKey, {prehash: true}) option can be used if you want to pass the message itselfWeierstrass points:
ProjectivePointProjectivePoint.fromHex and ProjectivePoint#toRawBytes()assertValidity() which checks for being on-curvetoAffine() and x / 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; format?: 'compact' | 'der' }
) => 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>;
msm(points: ProjPointType[], scalars: bigint[]): 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.
const sig2 = secq256k1.sign(msg, priv, { prehash: true }); // hash(msg)
secq256k1.verify(sig, msg, priv); // Verify if sig is correct.
// Default behavior is "try DER, then try compact if fails". Can be explicit:
secq256k1.verify(sig.toCompactHex(), msg, priv, { format: 'compact' });
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
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.
We support non-repudiation, which help in following scenarios:
Edwards points:
ExtendedPointExtendedPoint.fromHex and ExtendedPoint#toRawBytes()assertValidity() which checks for being on-curvetoAffine() and x / y getters which convert to 2d xy affine coordinatesisTorsionFree(), clearCofactor() and isSmallOrder() 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;
msm(points: ExtPointType[], scalars: bigint[]): ExtPointType;
}
import { montgomery } from '@noble/curves/abstract/montgomery';
import { Field } from '@noble/curves/abstract/modular';
const x25519 = montgomery({
a: 486662n,
Gu: 9n,
P: 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.
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.
The module doesn't expose CURVE property: use G1.CURVE, G2.CURVE instead.
Only BLS12-381 is currently implemented.
Defining BLS12-377 and BLS24 should be straightforward.
The default BLS uses short public keys (with public keys in G1 and signatures in G2). Short signatures (public keys in G2 and signatures in G1) are also supported.
The module allows to hash arbitrary strings to elliptic curve points. Implements RFC 9380.
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' });
Low-level methods from the spec:
// produces a uniformly random byte string using a cryptographic hash function H that outputs b bits.
function expand_message_xmd(
msg: Uint8Array,
DST: Uint8Array,
lenInBytes: number,
H: CHash // For CHash see abstract/weierstrass docs section
): Uint8Array;
// produces a uniformly random byte string using an extendable-output function (XOF) H.
function expand_message_xof(
msg: Uint8Array,
DST: Uint8Array,
lenInBytes: number,
k: number,
H: CHash
): Uint8Array;
// Hashes arbitrary-length byte strings to a list of one or more elements of a finite field F
function hash_to_field(msg: Uint8Array, count: number, options: Opts): bigint[][];
/**
* * `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;
};
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);
import * as mod from '@noble/curves/abstract/modular';
// Finite Field utils
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.inv(5n); // modular inverse
fp.sqrt(21n); // square root
// Non-Field generic 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
Field operations are not constant-time: they are using JS bigints, see security.
The fact is mostly irrelevant, but the important method to keep in mind is pow,
which may leak exponent bits, when used naïvely.
mod.Field is always field over prime number. Non-prime fields aren't supported for now.
We don't test for prime-ness for speed and because algorithms are probabilistic anyway.
Initializing a non-prime field could make your app suspectible to
DoS (infilite loop) on Tonelli-Shanks square root calculation.
Unlike mod.inv, mod.invertBatch won't throw on 0: make sure to throw an error yourself.
You can't simply make a 32-byte private key from a 32-byte hash. Doing so will make the key biased.
To make the bias negligible, we follow FIPS 186-5 A.2 and RFC 9380. This means, for 32-byte key, we would need 48-byte hash to get 2^-128 bias, which matches curve security level.
hashToPrivateScalar() that hashes to private key was created for this purpose.
Use abstract/hash-to-curve
if you need to hash to public key.
import { p256 } from '@noble/curves/p256';
import { sha256 } from '@noble/hashes/sha256';
import { hkdf } from '@noble/hashes/hkdf';
import * as mod from '@noble/curves/abstract/modular';
const someKey = new Uint8Array(32).fill(2); // Needs to actually be random, not .fill(2)
const derived = hkdf(sha256, someKey, undefined, 'application', 48); // 48 bytes for 32-byte priv
const validPrivateKey = mod.hashToPrivateScalar(derived, p256.CURVE.n);
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]));
The library has been independently audited:
curve, modular, poseidon, weierstrasscurve, hash-to-curve, modular, poseidon, utils, weierstrass and
top-level modules _shortw_utils and secp256k1It is tested against property-based, cross-library and Wycheproof vectors, and has fuzzing by Guido Vranken's cryptofuzz.
If you see anything unusual: investigate and report.
JIT-compiler and Garbage Collector make "constant time" extremely hard to achieve timing attack resistance 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.
npm-diffWe're deferring to built-in crypto.getRandomValues which is considered cryptographically secure (CSPRNG).
In the past, browsers had bugs that made it weak: it may happen again. Implementing a userspace CSPRNG to get resilient to the weakness is even worse: there is no reliable userspace source of quality entropy.
Benchmark results on Apple M2 with node v22:
secp256k1
init x 68 ops/sec @ 14ms/op
getPublicKey x 6,839 ops/sec @ 146μs/op
sign x 5,226 ops/sec @ 191μs/op
verify x 893 ops/sec @ 1ms/op
getSharedSecret x 538 ops/sec @ 1ms/op
recoverPublicKey x 923 ops/sec @ 1ms/op
schnorr.sign x 700 ops/sec @ 1ms/op
schnorr.verify x 919 ops/sec @ 1ms/op
ed25519
init x 51 ops/sec @ 19ms/op
getPublicKey x 9,809 ops/sec @ 101μs/op
sign x 4,976 ops/sec @ 200μs/op
verify x 1,018 ops/sec @ 981μs/op
ed448
init x 19 ops/sec @ 50ms/op
getPublicKey x 3,723 ops/sec @ 268μs/op
sign x 1,759 ops/sec @ 568μs/op
verify x 344 ops/sec @ 2ms/op
p256
init x 39 ops/sec @ 25ms/op
getPublicKey x 6,518 ops/sec @ 153μs/op
sign x 5,148 ops/sec @ 194μs/op
verify x 609 ops/sec @ 1ms/op
p384
init x 17 ops/sec @ 57ms/op
getPublicKey x 2,933 ops/sec @ 340μs/op
sign x 2,327 ops/sec @ 429μs/op
verify x 244 ops/sec @ 4ms/op
p521
init x 8 ops/sec @ 112ms/op
getPublicKey x 1,484 ops/sec @ 673μs/op
sign x 1,264 ops/sec @ 790μs/op
verify x 124 ops/sec @ 8ms/op
ristretto255
add x 680,735 ops/sec @ 1μs/op
multiply x 10,766 ops/sec @ 92μs/op
encode x 15,835 ops/sec @ 63μs/op
decode x 15,972 ops/sec @ 62μs/op
decaf448
add x 345,303 ops/sec @ 2μs/op
multiply x 300 ops/sec @ 3ms/op
encode x 5,987 ops/sec @ 167μs/op
decode x 5,892 ops/sec @ 169μs/op
ecdh
├─x25519 x 1,477 ops/sec @ 676μs/op
├─secp256k1 x 537 ops/sec @ 1ms/op
├─p256 x 512 ops/sec @ 1ms/op
├─p384 x 198 ops/sec @ 5ms/op
├─p521 x 99 ops/sec @ 10ms/op
└─x448 x 504 ops/sec @ 1ms/op
bls12-381
init x 36 ops/sec @ 27ms/op
getPublicKey x 960 ops/sec @ 1ms/op
sign x 60 ops/sec @ 16ms/op
verify x 47 ops/sec @ 21ms/op
pairing x 125 ops/sec @ 7ms/op
pairing10 x 40 ops/sec @ 24ms/op ± 23.27% (min: 21ms, max: 48ms)
MSM 4096 scalars x points x 0 ops/sec @ 4655ms/op
aggregatePublicKeys/8 x 129 ops/sec @ 7ms/op
aggregatePublicKeys/32 x 34 ops/sec @ 28ms/op
aggregatePublicKeys/128 x 8 ops/sec @ 113ms/op
aggregatePublicKeys/512 x 2 ops/sec @ 449ms/op
aggregatePublicKeys/2048 x 0 ops/sec @ 1792ms/op
aggregateSignatures/8 x 62 ops/sec @ 15ms/op
aggregateSignatures/32 x 16 ops/sec @ 60ms/op
aggregateSignatures/128 x 4 ops/sec @ 238ms/op
aggregateSignatures/512 x 1 ops/sec @ 946ms/op
aggregateSignatures/2048 x 0 ops/sec @ 3774ms/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
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
isCompressed to false: getPublicKey(priv, false)sign
Signature instance with { r, s, recovery } propertiescanonical option was renamed to lowSrecovered option has been removed because recovery bit is always returned nowder option has been removed. There are 2 options:
fromCompact, toCompactRawBytes, toCompactHex.
Compact encoding is simply a concatenation of 32-byte r and 32-byte s.verify
strict option was renamed to lowSgetSharedSecret
isCompressed to false: getSharedSecret(a, b, false)recoverPublicKey(msg, sig, rec) was changed to sig.recoverPublicKey(msg)number type for private keys have been removed: use bigint insteadPoint (2d xy) has been changed to ProjectivePoint (3d xyz)utils were split into utils (same api as in noble-curves) and
etc (hmacSha256Sync and others)Upgrading from @noble/ed25519 1.7:
bigint is no longer allowed in getPublicKey, sign, verify. Reason: ed25519 is LE, can lead to bugsPoint (2d xy) has been changed to ExtendedPoint (xyzt)Signature was removed: just use raw bytes or hex nowutils were split into utils (same api as in noble-curves) and
etc (sha512Sync and others)getSharedSecret was moved to x25519 moduletoX25519 has been moved to edwardsToMontgomeryPub and edwardsToMontgomeryPriv methodsUpgrading from @noble/bls12-381:
npm install to install build dependencies like TypeScriptnpm run build to compile TypeScript codenpm run test will execute all main testsCheck out paulmillr.com/noble for useful resources, articles, documentation and demos related to the library.
The MIT License (MIT)
Copyright (c) 2022 Paul Miller (https://paulmillr.com)
See LICENSE file.
FAQs
Audited & minimal JS implementation of elliptic curve cryptography
We found that @noble/curves demonstrated a healthy version release cadence and project activity because the last version was released less than a year ago. It has 1 open source maintainer collaborating on the project.
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