Audited & minimal JS implementation of elliptic curve cryptography.

• 🔒 Audited by independent security firms
• 🔻 Tree-shakeable: unused code is excluded from your builds
• 🏎 Fast: hand-optimized for caveats of JS engines
• 🔍 Reliable: cross-library / wycheproof tests and fuzzing ensure correctness
• ➰ Weierstrass, Edwards, Montgomery curves; ECDSA, EdDSA, Schnorr, BLS signatures
• ✍️ ECDH, hash-to-curve, OPRF, Poseidon ZK-friendly hash
• 🔖 Non-repudiation (SUF-CMA, SBS) & consensus-friendliness (ZIP215) in ed25519, ed448
• 🥈 Optional, friendly wrapper over native WebCrypto
• 🪶 36KB (gzipped) including bundled hashes, 11KB for single-curve build

Curves have 4KB sister projects secp256k1 & ed25519. They have smaller attack surface, but less features.

Take a glance at GitHub Discussions for questions and support.

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

• Zero or minimal dependencies
• Highly readable TypeScript / JS code
• PGP-signed releases and transparent NPM builds
• All libraries: ciphers, curves, hashes, post-quantum, 4kb secp256k1 / ed25519
• Check out homepage for reading resources, documentation and apps built with noble

npm install @noble/curves

deno add jsr:@noble/curves

deno doc jsr:@noble/curves # command-line documentation

We support all major platforms and runtimes. 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, schnorr } from '@noble/curves/secp256k1.js';
import { ed25519, ed25519ph, ed25519ctx, x25519, ristretto255 } from '@noble/curves/ed25519.js';
import { ed448, ed448ph, ed448ctx, x448, decaf448 } from '@noble/curves/ed448.js';
import { p256, p384, p521 } from '@noble/curves/nist.js';
import { bls12_381 } from '@noble/curves/bls12-381.js';
import { bn254 } from '@noble/curves/bn254.js';
import { jubjub, babyjubjub, brainpoolP256r1, brainpoolP384r1, brainpoolP512r1 } from '@noble/curves/misc.js';

// hash-to-curve
import { secp256k1_hasher } from '@noble/curves/secp256k1.js';
import { p256_hasher, p384_hasher, p521_hasher } from '@noble/curves/nist.js';
import { ristretto255_hasher } from '@noble/curves/ed25519.js';
import { decaf448_hasher } from '@noble/curves/ed448.js';

// OPRFs
import { p256_oprf, p384_oprf, p521_oprf } from '@noble/curves/nist.js';
import { ristretto255_oprf } from '@noble/curves/ed25519.js';
import { decaf448_orpf } from '@noble/curves/ed448.js';

// utils
import { weierstrass, ecdsa } from '@noble/curves/abstract/weierstrass.js';
import { edwards, eddsa } from '@noble/curves/abstract/edwards.js';
import { poseidon, poseidonSponge } from '@noble/curves/abstract/poseidon.js';
import { Field, mod, pow } from '@noble/curves/abstract/modular.js';
import { FFT, poly } from '@noble/curves/abstract/fft.js';
import { bytesToHex, hexToBytes, concatBytes, utf8ToBytes } from '@noble/curves/abstract/utils.js';

import { secp256k1, schnorr } from '@noble/curves/secp256k1.js';
import { p256, p384, p521 } from '@noble/curves/nist.js';
import { ed25519 } from '@noble/curves/ed25519.js';
import { ed448 } from '@noble/curves/ed448.js';
import { brainpoolP256r1, brainpoolP384r1, brainpoolP512r1 } from '@noble/curves/misc.js';

import { hexToBytes, utf8ToBytes } from '@noble/curves/utils.js';

for (const curve of [
  secp256k1, schnorr,
  p256, p384, p521,
  ed25519, ed448,
  brainpoolP256r1, brainpoolP384r1, brainpoolP512r1
]) {
  const { secretKey, publicKey } = curve.keygen();
  const msg = utf8ToBytes('hello noble');
  const sig = curve.sign(msg, secretKey);
  const isValid = curve.verify(sig, msg, publicKey);
  console.log(curve, secretKey, publicKey, sig);
}

// Specific private key
const priv2 = hexToBytes('46c930bc7bb4db7f55da20798697421b98c4175a52c630294d75a84b9c126236');
const pub2 = secp256k1.getPublicKey(priv2);

• We provide NIST P256 (same as secp256r1 / prime256v1), P384 (secp384r1) & P521 (secp521r1), their hash-to-curve methods, and OPRFs.
• ECDSA signatures conform to ....
• EdDSA conform to RFC8032.
• Schnorr is only available for secp256k1 and conforms to BIP340.

import { ristretto255, ristretto255_hasher, ristretto255_oprf } from '@noble/curves/ed25519.js';
import { decaf448, decaf448_hasher, decaf448_oprf } from '@noble/curves/ed448.js';

import { sha512 } from '@noble/hashes/sha2.js';
import { shake256 } from '@noble/hashes/sha3.js';

const msg = new TextEncoder().encode('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).toBytes();
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_' });

Check out RFC9496 more info on ristretto255 & decaf448.

const sig2 = curve.sign(msg, secretKey, { prehash: false })
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;

const isValid = ed25519.verify(sig, msg, pub); // Default mode: follows ZIP215

// SBS / e-voting / RFC8032 / FIPS 186-5
const isValidRfc = ed25519.verify(sig, msg, pub, { zip215: false });

// Variants from RFC8032: with context, prehashed
import { ed25519ctx, ed25519ph } from '@noble/curves/ed25519.js';


import { secp256k1 } from '@noble/curves/secp256k1.js';
// random entropy
const sigNoisy = secp256k1.sign(msg, priv, { extraEntropy: true });
// set custom entropy
const ent = new Uint8Array(32).fill(3);
const sigNoisy2 = secp256k1.sign(msg, priv, { extraEntropy: ent });

• Hedged ECDSA is add-on, providing improved protection against fault attacks. It adds noise to signatures. The technique is used by default in BIP340; we also implement them optionally for ECDSA. Check out blog post Deterministic signatures are not your friends and cfrg-det-sigs-with-noise draft.
• In ed25519 & ed448, default verify behavior follows ZIP215 and can be used in consensus-critical applications. If you need SBS (Strongly Binding Signatures) and FIPS 186-5 compliance, use zip215: false. Check out Edwards Signatures section for more info. Both options have SUF-CMA (strong unforgeability under chosen message attacks).

import { secp256k1 } from '@noble/curves/secp256k1.js';
import { x25519 } from '@noble/curves/ed25519.js';
import { x448 } from '@noble/curves/ed448.js';
import { p256, p384, p521 } from '@noble/curves/nist.js';

for (const curve of [secp256k1, schnorr, x25519, x448, p256, p384, p521]) {
  const alice = curve.keygen();
  const bob = curve.keygen();
  const sharedKey = curve.getSharedSecret(alice.secretKey, bob.publicKey);
  console.log('alice', alice, 'bob', bob, 'shared', sharedKey);
}

x25519.getSharedSecret(priv, pub) === x25519.scalarMult(priv, pub); // aliases
x25519.getPublicKey(priv) === x25519.scalarMultBase(priv);
// ed25519 => x25519 conversion
import { edwardsToMontgomeryPub, edwardsToMontgomeryPriv } from '@noble/curves/ed25519.js';
edwardsToMontgomeryPub(ed25519.getPublicKey(ed25519.utils.randomPrivateKey()));
edwardsToMontgomeryPriv(ed25519.utils.randomPrivateKey());

• X25519 aka ECDH on Curve25519 from RFC7748.
• X448 aka ECDH on Curve448 from RFC7748

import { bls12_381 } from '@noble/curves/bls12-381.js';
import { hexToBytes } from '@noble/curves/abstract/utils.js';

// private keys are 32 bytes
const privKey = hexToBytes('67d53f170b908cabb9eb326c3c337762d59289a8fec79f7bc9254b584b73265c');
// const privKey = bls12_381.utils.randomPrivateKey();

// Long signatures (G2), short public keys (G1)
const blsl = bls12_381.longSignatures;
const publicKey = blsl.getPublicKey(privateKey);
// Sign msg with custom (Ethereum) DST
const msg = new TextEncoder().encode('hello');
const DST = 'BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_POP_';
const msgp = blsl.hash(msg, DST);
const signature = blsl.sign(msgp, privateKey);
const isValid = blsl.verify(signature, msgp, publicKey);
console.log({ publicKey, signature, isValid });

// Short signatures (G1), long public keys (G2)
const blss = bls12_381.shortSignatures;
const publicKey2 = blss.getPublicKey(privateKey);
const msgp2 = blss.hash(new TextEncoder().encode('hello'), 'BLS_SIG_BLS12381G1_XMD:SHA-256_SSWU_RO_NUL_')
const signature2 = blss.sign(msgp2, privateKey);
const isValid2 = blss.verify(signature2, msgp2, publicKey);
console.log({ publicKey2, signature2, isValid2 });

// Aggregation
const aggregatedKey = bls12_381.longSignatures.aggregatePublicKeys([
  bls12_381.utils.randomPrivateKey(),
  bls12_381.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.

The BN254 API mirrors BLS. The curve was previously called alt_bn128. The implementation is compatible with EIP-196 and EIP-197.

We don't implement Point methods toBytes. To work around this limitation, has to initialize points on their own from BigInts. Reason it's not implemented is because there is no standard. Points of divergence:

• Endianness: LE vs BE (byte-swapped)
• Flags as first hex bits (similar to BLS) vs no-flags
• Imaginary part last in G2 vs first (c0, c1 vs c1, c0)

For example usage, check out the implementation of bn254 EVM precompiles.

import { secp256k1, schnorr } from '@noble/curves/secp256k1.js';
import { p256, p384, p521 } from '@noble/curves/nist.js';
import { ed25519, ristretto255 } from '@noble/curves/ed25519.js';
import { ed448, decaf448 } from '@noble/curves/ed448.js';
import { bls12_381 } from '@noble/curves/bls12-381.js'
import { bn254 } from '@noble/curves/bn254.js';
import { jubjub, babyjubjub } from '@noble/curves/misc.js';

const curves = [
  secp256k1, schnorr, p256, p384, p521, ed25519, ed448,
  ristretto255, decaf448,
  bls12_381.G1, bls12_381.G2, bn254.G1, bn254.G2,
  jubjub, babyjubjub
];
for (const curve of curves) {
  const { info, Point } = curve;
  const { BASE, ZERO, Fp, Fn } = Point;
  const p = BASE.multiply(2n);

  // Initialization
  if (info.type === 'weierstrass') {
    // projective (homogeneous) coordinates: (X, Y, Z) ∋ (x=X/Z, y=Y/Z)
    const p_ = new Point(BASE.X, BASE.Y, BASE.Z);
  } else if (info.type === 'edwards') {
    // extended coordinates: (X, Y, Z, T) ∋ (x=X/Z, y=Y/Z)
    const p_ = new Point(BASE.X, BASE.Y, BASE.Z, BASE.T);
  }

  // Math
  const p1 = p.add(p);
  const p2 = p.double();
  const p3 = p.subtract(p);
  const p4 = p.negate();
  const p5 = p.multiply(451n);

  // MSM (multi-scalar multiplication)
  const pa = [BASE, BASE.multiply(2n), BASE.multiply(4n), BASE.multiply(8n)];
  const p6 = Point.msm(pa, [3n, 5n, 7n, 11n]);
  const _true3 = p6.equals(BASE.multiply(129n)); // 129*G

  const pcl = p.clearCofactor();
  console.log(p.isTorsionFree(), p.isSmallOrder());

  const r1 = p.toBytes();
  const r1_ = Point.fromBytes(r1);
  const r2 = p.toAffine();
  const { x, y } = r2;
  const r2_ = Point.fromAffine(r2);
}

import { mod, invert, Field } from '@noble/curves/abstract/modular.js';

// Finite Field utils
const fp = 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(21n, 10n); // 21 mod 10 == 1n; fixed version of 21 % 10
invert(17n, 10n); // invert(17) mod 10; modular multiplicative inverse

ECDSA signatures:

• Are represented by Signature instances with r, s and optional recovery properties
• Have recoverPublicKey(), toBytes() with optional format: 'compact' | 'der'
• Can be prehashed, or non-prehashed:
  • sign(msgHash, privKey) (default, prehash: false) - you did hashing before
  • sign(msg, privKey, {prehash: true}) - curves will do hashing for you
• Are generated deterministically, following RFC6979.
  • Consider hedged ECDSA with noise for adding randomness into for signatures, to get improved security against fault attacks.

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. 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.

We define ed25519, ed448; user can use custom curves with EdDSA, but EdDSA in general is not defined. Check out edwards.ts source code.

For EdDSA signatures:

• zip215: true is default behavior. It has slightly looser verification logic to be consensus-friendly, following ZIP215 rules
• zip215: false switches verification criteria to strict RFC8032 / FIPS 186-5 and additionally provides non-repudiation with SBS, which is useful for:
  • Contract Signing: if A signed an agreement with B using key that allows repudiation, it can later claim that it signed a different contract
  • E-voting: malicious voters may pick keys that allow repudiation in order to deny results
  • Blockchains: transaction of amount X might also be valid for a different amount Y
• Both modes have SUF-CMA (strong unforgeability under chosen message attacks).

• Short Weierstrass curve's formula is y² = x³ + ax + b. weierstrass expects arguments a, b, field characteristic p, curve order n, cofactor h and coordinates Gx, Gy of generator point.
• Twisted Edwards curve's formula is ax² + y² = 1 + dx²y². You must specify a, d, field characteristic p, curve order n (sometimes named as L), cofactor h and coordinates Gx, Gy of generator point.

import { weierstrass } from '@noble/curves/abstract/weierstrass.js';
// NIST secp192r1 aka p192. https://www.secg.org/sec2-v2.pdf
const p192_CURVE = {
  p: 0xfffffffffffffffffffffffffffffffeffffffffffffffffn,
  n: 0xffffffffffffffffffffffff99def836146bc9b1b4d22831n,
  h: 1n,
  a: 0xfffffffffffffffffffffffffffffffefffffffffffffffcn,
  b: 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1n,
  Gx: 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012n,
  Gy: 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811n,
};
const p192_Point = weierstrass(p192_CURVE);

import { edwards } from '@noble/curves/abstract/edwards.js';
const ed25519_CURVE = {
  p: 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffedn,
  n: 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3edn,
  h: 8n,
  a: 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffecn,
  d: 0x52036cee2b6ffe738cc740797779e89800700a4d4141d8ab75eb4dca135978a3n,
  Gx: 0x216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51an,
  Gy: 0x6666666666666666666666666666666666666666666666666666666666666658n,
};
const ed25519_Point = edwards(ed25519_CURVE);

import { ecdsa } from '@noble/curves/abstract/weierstrass.js';
import { sha256 } from '@noble/hashes/sha2.js';
const p192 = ecdsa(p192_Point, sha256);
const p192_sha224 = ecdsa(p192.Point, sha224);
const keys = p192.keygen();
const msg = new TextEncoder().encode('custom curve');
const sig = p192.sign(msg, keys.secretKey);
const isValid = p192.verify(sig, msg, keys.publicKey);
// const ed25519 = eddsa(ed25519_Point, { hash: sha512 });

import { secp256k1_hasher } from '@noble/curves/secp256k1.js';
import { p256_hasher, p384_hasher, p521_hasher } from '@noble/curves/nist.js';
import { ristretto255_hasher } from '@noble/curves/ed25519.js';
import { decaf448_hasher } from '@noble/curves/ed448.js';

import { bls12_381 } from '@noble/curves/bls12-381.js';
bls12_381.G1.hashToCurve(randomBytes(), { DST: 'another' });
bls12_381.G2.hashToCurve(randomBytes(), { DST: 'custom' });

import { expand_message_xmd, expand_message_xof, hash_to_field } from '@noble/curves/abstract/hash-to-curve.js';

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 { p256_oprf, p384_oprf, p521_oprf } from '@noble/curves/nist.js';
import { ristretto255_oprf } from '@noble/curves/ed25519.js';
import { decaf448_orpf } from '@noble/curves/ed448.js';

We provide OPRFs, conforming to RFC 9497.

OPRF allows to interactively create an Output = PRF(Input, serverSecretKey):

• Server cannot calculate Output by itself: it doesn't know Input
• Client cannot calculate Output by itself: it doesn't know server secretKey
• An attacker interception the communication can't restore Input/Output/serverSecretKey and can't link Input to some value.

Implements Poseidon ZK-friendly hash: permutation and sponge.

There are many poseidon variants with different constants. We don't provide them: you should construct them manually. Check out scure-starknet package for a proper example.

import { poseidon, poseidonSponge } from '@noble/curves/abstract/poseidon.js';

const rate = 2;
const capacity = 1;
const { mds, roundConstants } = poseidon.grainGenConstants({
  Fp,
  t: rate + capacity,
  roundsFull: 8,
  roundsPartial: 31,
});
const opts = {
  Fp,
  rate,
  capacity,
  sboxPower: 17,
  mds,
  roundConstants,
  roundsFull: 8,
  roundsPartial: 31,
};
const permutation = poseidon.poseidon(opts);
const sponge = poseidon.poseidonSponge(opts); // use carefully, not specced

Experimental implementation of NTT / FFT (Fast Fourier Transform) over finite fields. API may change at any time. The code has not been audited. Feature requests are welcome.

import * as fft from '@noble/curves/abstract/fft.js';

import * as utils from '@noble/curves/abstract/utils.js';

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:

• at version 1.6.0, in Sep 2024, by Cure53
  • PDFs: website, in-repo
  • Changes since audit
  • Scope: ed25519, ed448, their add-ons, bls12-381, bn254, hash-to-curve, low-level primitives bls, tower, edwards, montgomery.
  • The audit has been funded by OpenSats
• at version 1.2.0, in Sep 2023, by Kudelski Security
  • PDFs: in-repo
  • Changes since audit
  • Scope: scure-starknet and its related abstract modules of noble-curves: curve, modular, poseidon, weierstrass
  • The audit has been funded by Starkware
• at version 0.7.3, in Feb 2023, by Trail of Bits
  • PDFs: website, in-repo
  • Changes since audit
  • Scope: abstract modules curve, hash-to-curve, modular, poseidon, utils, weierstrass and top-level modules _shortw_utils and secp256k1
  • The audit has been funded by Ryan Shea

It is tested against property-based, cross-library and Wycheproof vectors, and is being fuzzed in the separate repo.

If you see anything unusual: investigate and report.

We're targetting algorithmic constant time. 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.

Use low-level languages instead of JS / WASM if your goal is absolute security.

The library mostly uses Uint8Arrays and bigints.

• Uint8Arrays have .fill(0) which instructs to fill content with zeroes but there are no guarantees in JS
• bigints are immutable and don't have a method to zeroize their content: a user needs to wait until the next garbage collection cycle
• hex strings are also immutable: there is no way to zeroize them
• await fn() will write all internal variables to memory. With async functions there are no guarantees when the code chunk would be executed. Which means attacker can have plenty of time to read data from memory.

This means some secrets could stay in memory longer than anticipated. However, if an attacker can read application memory, it's doomed anyway: there is no way to guarantee anything about zeroizing sensitive data without complex tests-suite which will dump process memory and verify that there is no sensitive data left. For JS it means testing all browsers (including mobile). And, of course, it will be useless without using the same test-suite in the actual application that consumes the library.

• Commits are signed with PGP keys, to prevent forgery. Make sure to verify commit signatures
• Releases are transparent and built on GitHub CI. Make sure to verify provenance logs
  • Use GitHub CLI to verify single-file builds: gh attestation verify --owner paulmillr noble-curves.js
• Rare releasing is followed to ensure less re-audit need for end-users
• Dependencies are minimized and locked-down: any dependency could get hacked and users will be downloading malware with every install.
  • We make sure to use as few dependencies as possible
  • Automatic dep updates are prevented by locking-down version ranges; diffs are checked with npm-diff
• Dev Dependencies are disabled for end-users; they are only used to develop / build the source code

For this package, there is 1 dependency; and a few dev dependencies:

• noble-hashes provides cryptographic hashing functionality
• micro-bmark, micro-should and jsbt are used for benchmarking / testing / build tooling and developed by the same author
• prettier, fast-check and typescript are used for code quality / test generation / ts compilation. It's hard to audit their source code thoroughly and fully because of their size

We'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.

Cryptographically relevant quantum computer, if built, will allow to break elliptic curve cryptography (both ECDSA / EdDSA & ECDH) using Shor's algorithm.

Consider switching to newer / hybrid algorithms, such as SPHINCS+. They are available in noble-post-quantum.

NIST prohibits classical cryptography (RSA, DSA, ECDSA, ECDH) after 2035. Australian ASD prohibits it after 2030.

npm run bench:install && npm run bench

noble-curves spends 10+ ms to generate 20MB+ of base point precomputes. This is done one-time per curve.

The generation is deferred until any method (pubkey, sign, verify) is called. User can force precompute generation by manually calling Point.BASE.precompute(windowSize, false). Check out the source code.

Benchmark results on Apple M4:

# secp256k1
init 10ms
getPublicKey x 9,099 ops/sec @ 109μs/op
sign x 7,182 ops/sec @ 139μs/op
verify x 1,188 ops/sec @ 841μs/op
getSharedSecret x 735 ops/sec @ 1ms/op
recoverPublicKey x 1,265 ops/sec @ 790μs/op
schnorr.sign x 957 ops/sec @ 1ms/op
schnorr.verify x 1,210 ops/sec @ 825μs/op

# ed25519
init 14ms
getPublicKey x 14,216 ops/sec @ 70μs/op
sign x 6,849 ops/sec @ 145μs/op
verify x 1,400 ops/sec @ 713μs/op

# ed448
init 37ms
getPublicKey x 5,273 ops/sec @ 189μs/op
sign x 2,494 ops/sec @ 400μs/op
verify x 476 ops/sec @ 2ms/op

# p256
init 17ms
getPublicKey x 8,977 ops/sec @ 111μs/op
sign x 7,236 ops/sec @ 138μs/op
verify x 877 ops/sec @ 1ms/op

# p384
init 42ms
getPublicKey x 4,084 ops/sec @ 244μs/op
sign x 3,247 ops/sec @ 307μs/op
verify x 331 ops/sec @ 3ms/op

# p521
init 83ms
getPublicKey x 2,049 ops/sec @ 487μs/op
sign x 1,748 ops/sec @ 571μs/op
verify x 170 ops/sec @ 5ms/op

# ristretto255
add x 931,966 ops/sec @ 1μs/op
multiply x 15,444 ops/sec @ 64μs/op
encode x 21,367 ops/sec @ 46μs/op
decode x 21,715 ops/sec @ 46μs/op

# decaf448
add x 478,011 ops/sec @ 2μs/op
multiply x 416 ops/sec @ 2ms/op
encode x 8,562 ops/sec @ 116μs/op
decode x 8,636 ops/sec @ 115μs/op

# ECDH
x25519 x 1,981 ops/sec @ 504μs/op
x448 x 743 ops/sec @ 1ms/op
secp256k1 x 728 ops/sec @ 1ms/op
p256 x 705 ops/sec @ 1ms/op
p384 x 268 ops/sec @ 3ms/op
p521 x 137 ops/sec @ 7ms/op

# hash-to-curve
hashToPrivateScalar x 1,754,385 ops/sec @ 570ns/op
hash_to_field x 135,703 ops/sec @ 7μs/op
hashToCurve secp256k1 x 3,194 ops/sec @ 313μs/op
hashToCurve p256 x 5,962 ops/sec @ 167μs/op
hashToCurve p384 x 2,230 ops/sec @ 448μs/op
hashToCurve p521 x 1,063 ops/sec @ 940μs/op
hashToCurve ed25519 x 4,047 ops/sec @ 247μs/op
hashToCurve ed448 x 1,691 ops/sec @ 591μs/op
hash_to_ristretto255 x 8,733 ops/sec @ 114μs/op
hash_to_decaf448 x 3,882 ops/sec @ 257μs/op

# modular over secp256k1 P field
invert a x 866,551 ops/sec @ 1μs/op
invert b x 693,962 ops/sec @ 1μs/op
sqrt p = 3 mod 4 x 25,738 ops/sec @ 38μs/op
sqrt tonneli-shanks x 847 ops/sec @ 1ms/op

# bls12-381
init 22ms
getPublicKey x 1,325 ops/sec @ 754μs/op
sign x 80 ops/sec @ 12ms/op
verify x 62 ops/sec @ 15ms/op
pairing x 166 ops/sec @ 6ms/op
pairing10 x 54 ops/sec @ 18ms/op ± 23.48% (15ms..36ms)
MSM 4096 scalars x points 3286ms
aggregatePublicKeys/8 x 173 ops/sec @ 5ms/op
aggregatePublicKeys/32 x 46 ops/sec @ 21ms/op
aggregatePublicKeys/128 x 11 ops/sec @ 84ms/op
aggregatePublicKeys/512 x 2 ops/sec @ 335ms/op
aggregatePublicKeys/2048 x 0 ops/sec @ 1346ms/op
aggregateSignatures/8 x 82 ops/sec @ 12ms/op
aggregateSignatures/32 x 21 ops/sec @ 45ms/op
aggregateSignatures/128 x 5 ops/sec @ 178ms/op
aggregateSignatures/512 x 1 ops/sec @ 705ms/op
aggregateSignatures/2048 x 0 ops/sec @ 2823ms/op

Supported node.js versions:

• v2: v20.19+ (ESM-only)
• v1: v14.21+ (ESM & CJS)

WIP. Changelog of v2, when upgrading from curves v1.

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.

• getPublicKey
  • now produce 33-byte compressed signatures by default
  • to use old behavior, which produced 65-byte uncompressed keys, set argument isCompressed to false: getPublicKey(priv, false)
• sign
  • is now sync
  • now returns Signature instance with { r, s, recovery } properties
  • canonical option was renamed to lowS
  • recovered option has been removed because recovery bit is always returned now
  • der option has been removed. There are 2 options:
    1. Use compact encoding: fromCompact, toCompactRawBytes, toCompactHex. Compact encoding is simply a concatenation of 32-byte r and 32-byte s.
    2. If you must use DER encoding, switch to noble-curves (see above).
• verify
  • is now sync
  • strict option was renamed to lowS
• getSharedSecret
  • now produce 33-byte compressed signatures by default
  • to use old behavior, which produced 65-byte uncompressed keys, set argument 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 instead
• Point (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:

• Methods are now sync by default
• bigint is no longer allowed in getPublicKey, sign, verify. Reason: ed25519 is LE, can lead to bugs
• Point (2d xy) has been changed to ExtendedPoint (xyzt)
• Signature was removed: just use raw bytes or hex now
• utils were split into utils (same api as in noble-curves) and etc (sha512Sync and others)
• getSharedSecret was moved to x25519 module
• toX25519 has been moved to edwardsToMontgomeryPub and edwardsToMontgomeryPriv 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

• npm install && npm run build && npm test will build the code and run tests.
• npm run lint / npm run format will run linter / fix linter issues.
• npm run bench will run benchmarks, which may need their deps first (npm run bench:install)
• npm run build:release will build single file

Check out github.com/paulmillr/guidelines for general coding practices and rules.

See paulmillr.com/noble for useful resources, articles, documentation and demos related to the library.

MuSig2 signature scheme and BIP324 ElligatorSwift mapping for secp256k1 are available in a separate package.

The MIT License (MIT)

Copyright (c) 2022 Paul Miller (https://paulmillr.com)

See LICENSE file.