@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.
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.
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 } from '@noble/curves/ed25519.js';
import { ed448, ed448ph, ed448ctx, x448 } 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 } from '@noble/curves/misc.js';
import { bytesToHex, hexToBytes, concatBytes, utf8ToBytes } from '@noble/curves/abstract/utils.js';
import { secp256k1 } from '@noble/curves/secp256k1.js';
// import { p256 } from '@noble/curves/nist.js'; // 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);
// public key recovery
// 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
The same code would work for NIST P256 (secp256r1), P384 (secp384r1) & P521 (secp521r1).
const noisySignature = secp256k1.sign(msg, priv, { extraEntropy: true });
const ent = new Uint8Array(32).fill(3); // set custom entropy
const noisySignature2 = 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 spec draft.
const someonesPub = secp256k1.getPublicKey(secp256k1.utils.randomPrivateKey());
const shared = secp256k1.getSharedSecret(priv, someonesPub);
// NOTE:
// - `shared` includes parity byte: strip it using shared.slice(1)
// - `shared` is not hashed: more secure way is sha256(shared) or hkdf(shared)
import { schnorr } from '@noble/curves/secp256k1.js';
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.js';
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 }); // SBS / e-voting / RFC8032 / FIPS 186-5
// Variants from RFC8032: with context, prehashed
import { ed25519ctx, ed25519ph } from '@noble/curves/ed25519.js';
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).
// X25519 aka ECDH on Curve25519 from [RFC7748](https://www.rfc-editor.org/rfc/rfc7748)
import { x25519 } from '@noble/curves/ed25519.js';
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.js';
edwardsToMontgomeryPub(ed25519.getPublicKey(ed25519.utils.randomPrivateKey()));
edwardsToMontgomeryPriv(ed25519.utils.randomPrivateKey());
import { sha512 } from '@noble/hashes/sha2.js';
import {
hashToCurve,
encodeToCurve,
RistrettoPoint,
hashToRistretto255,
} from '@noble/curves/ed25519.js';
const msg = new TextEncoder().encode('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_' });
Check out RFC9496 more info on ristretto255.
import { ed448 } from '@noble/curves/ed448.js';
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.js';
// X448 aka ECDH on Curve448 from [RFC7748](https://www.rfc-editor.org/rfc/rfc7748)
import { x448 } from '@noble/curves/ed448.js';
x448.getSharedSecret(priv, pub) === x448.scalarMult(priv, pub); // aliases
x448.getPublicKey(priv) === x448.scalarMultBase(priv);
// ed448 => x448 conversion
import { edwardsToMontgomeryPub } from '@noble/curves/ed448.js';
edwardsToMontgomeryPub(ed448.getPublicKey(ed448.utils.randomPrivateKey()));
// decaf448 from [RFC9496](https://www.rfc-editor.org/rfc/rfc9496)
import { shake256 } from '@noble/hashes/sha3.js';
import { hashToCurve, encodeToCurve, DecafPoint, hashToDecaf448 } from '@noble/curves/ed448.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).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_' });
Check out RFC9496 more info on decaf448.
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.
import { bn254 } from '@noble/curves/bn254.js';
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.
We don't implement Point methods toHex / toRawBytes. 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:
For example usage, check out the implementation of bn254 EVM precompiles.
import { jubjub, babyjubjub } from '@noble/curves/misc.js';
Miscellaneous, rarely used curves are contained in the module. Jubjub curves have Fp over scalar fields of other curves. They are friendly to ZK proofs. jubjub Fp = bls n. babyjubjub Fp = bn254 n.
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.
Implementations use noble-hashes.
It's always possible to use different hashing library.
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);
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.
// # weierstrass Point methods
// projective (homogeneous) coordinates: (x, y, z) ∋ (x=x/z, y=y/z)
// const p = new Point(x, y, z);
const p = Point.BASE;
// arithmetics
p.add(p).equals(p.double());
p.subtract(p).equals(Point.ZERO);
p.negate();
p.multiply(31415n);
// decoding, encoding
const b = p.toBytes();
const p2 = Point.fromBytes(b);
// affine conversion
const { x, y } = p.toAffine();
const p3 = Point.fromAffine({ x, y });
// Multi-scalar-multiplication (MSM) is basically `(Pa + Qb + Rc + ...)`.
// It's 10-30x faster vs naive addition for large amount of points.
// Pippenger algorithm is used underneath.
const points = [Point.BASE, Point.BASE.multiply(2n), Point.BASE.multiply(4n), Point.BASE.multiply(8n)];
Point.msm(points, [3n, 5n, 7n, 11n]).equals(Point.BASE.multiply(129n)); // 129*G
import { ecdsa } from '@noble/curves/abstract/weierstrass.js';
import { sha256 } from '@noble/hashes/sha2.js';
const p192 = ecdsa(p192_Point, sha256);
const priv = p192.utils.randomPrivateKey();
const pub = p192.getPublicKey(priv);
const msg = sha256(new TextEncoder().encode('custom curve'));
const sig = p192.sign(msg);
const isValid = p192.verify(sig, msg, pub);
ECDSA signatures:
Signature instances with r, s and optional recovery propertiesrecoverPublicKey(), toBytes() with optional format: 'compact' | 'der'sign(msgHash, privKey) (default, prehash: false) - you did hashing beforesign(msg, privKey, {prehash: true}) - curves will do hashing for youimport { 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);
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.
const Point = ed25519_Point;
// extended coordinates: (x, y, z, t) ∋ (x=x/z, y=y/z)
// const p = new Point(x, y, z, t);
const p = Point.BASE;
// arithmetics
p.add(p).equals(p.double());
p.subtract(p).equals(Point.ZERO);
p.negate();
p.multiply(31415n);
// decoding, encoding
const b = p.toBytes();
const p2 = Point.fromBytes(b);
// on-curve test
p.assertValidity();
// affine conversion
const { x, y } = p.toAffine();
const p3 = Point.fromAffine({ x, y });
// misc
const pcl = p.clearCofactor();
console.log(p.isTorsionFree(), p.isSmallOrder());
const ed25519 = eddsa(ed25519_Point, { hash: sha512 });
// ed25519.getPublicKey();
// ed25519.sign();
// ed25519.verify();
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 ruleszip215: false switches verification criteria to strict
RFC8032 / FIPS 186-5
and additionally provides non-repudiation with SBS,
which is useful for:
The module contains methods for x-only ECDH on Curve25519 / Curve448 from RFC7748. Proper Elliptic Curve Points are not implemented yet.
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.js';
import { randomBytes } from '@noble/hashes/utils.js';
hashToCurve('0102abcd');
console.log(hashToCurve(randomBytes()));
console.log(encodeToCurve(randomBytes()));
import { bls12_381 } from '@noble/curves/bls12-381.js';
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: 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
import * as mod from '@noble/curves/abstract/modular.js';
// 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.
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';
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/nist.js';
import { sha256 } from '@noble/hashes/sha2.js';
import { hkdf } from '@noble/hashes/hkdf.js';
import * as mod from '@noble/curves/abstract/modular.js';
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.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]));
test/unreleased-xeddsa.ts contains implementation of XEd25519, defined by Signaltest/misc/endomorphism.js contains tool for generation of endomorphism params for Koblitz curvesThe 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 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.
.fill(0) which instructs to fill content with zeroes
but there are no guarantees in JSawait 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.
gh attestation verify --owner paulmillr noble-curves.jsnpm-diffFor this package, there is 1 dependency; and a few dev dependencies:
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:
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
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 && 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 fileCheck 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.
FAQs
Audited & minimal JS implementation of elliptic curve cryptography
The npm package @noble/curves receives a total of 5,077,217 weekly downloads. As such, @noble/curves popularity was classified as popular.
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