noble-secp256k1

Fastest 4KB JS implementation of secp256k1 signatures & ECDH.

• ✍️ ECDSA signatures compliant with RFC6979
• 🤝 Elliptic Curve Diffie-Hellman ECDH
• 🔒 Supports hedged signatures guarding against fault attacks
• 🪶 4KB gzipped, 530 lines of pure ESM, bundler-less code

The module is a sister project of noble-curves, focusing on smaller attack surface & better auditability. Curves are drop-in replacement and have more features: Common.js, Schnorr signatures, DER encoding or support for different hash functions. To upgrade from v1 to v2, see Upgrading.

This library belongs to noble cryptography

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 with provenance
• Check out homepage & all libraries: ciphers, curves, hashes, post-quantum, 4kb secp256k1 / ed25519

Usage

npm install @noble/secp256k1

deno add jsr:@noble/secp256k1

deno doc jsr:@noble/secp256k1 # command-line documentation

We support all major platforms and runtimes. For node.js <= 18 and React Native, additional polyfills are needed: see below.

import * as secp from '@noble/secp256k1';
// import * as secp from "https://unpkg.com/@noble/secp256k1"; // Unpkg
(async () => {
  // Uint8Arrays or hex strings are accepted:
  // Uint8Array.from([0xde, 0xad, 0xbe, 0xef]) is equal to 'deadbeef'
  const privKey = secp.utils.randomPrivateKey(); // Secure random private key
  // sha256 of 'hello world'
  const msgHash = 'b94d27b9934d3e08a52e52d7da7dabfac484efe37a5380ee9088f7ace2efcde9';
  const pubKey = secp.getPublicKey(privKey);
  const signature = await secp.signAsync(msgHash, privKey); // Sync methods below
  const isValid = secp.verify(signature, msgHash, pubKey);

  const alicesPub = secp.getPublicKey(secp.utils.randomPrivateKey());
  const shared = secp.getSharedSecret(privKey, alicesPub); // Diffie-Hellman
  const pub2 = signature.recoverPublicKey(msgHash); // Public key recovery
})();

Enabling synchronous methods

Only async methods are available by default, to keep the library dependency-free. To enable sync methods:

import { hmac } from '@noble/hashes/hmac';
import { sha256 } from '@noble/hashes/sha256';
secp.etc.hmacSha256Sync = (k, ...m) => hmac(sha256, k, secp.etc.concatBytes(...m));

React Native: polyfill getRandomValues and sha512

import 'react-native-get-random-values';
import { hmac } from '@noble/hashes/hmac';
import { sha256 } from '@noble/hashes/sha256';
secp.etc.hmacSha256Sync = (k, ...m) => hmac(sha256, k, secp.etc.concatBytes(...m));
secp.etc.hmacSha256Async = (k, ...m) => Promise.resolve(secp.etc.hmacSha256Sync(k, ...m));

nodejs v18 and older: polyfill webcrypto

import { webcrypto } from 'node:crypto';
// @ts-ignore
if (!globalThis.crypto) globalThis.crypto = webcrypto;

API

There are 3 main methods:

• getPublicKey(privateKey)
• sign(messageHash, privateKey) and signAsync(messageHash, privateKey)
• verify(signature, messageHash, publicKey)

Functions generally accept Uint8Array. There are optional utilities which convert hex strings, utf8 strings or bigints to u8a.

getPublicKey

import { getPublicKey, utils, ProjectivePoint } from '@noble/secp256k1';
const privKey = utils.randomPrivateKey();
const pubKey33b = getPublicKey(privKey);

// Variants
const pubKey65b = getPublicKey(privKey, false);
const pubKeyPoint = ProjectivePoint.fromPrivateKey(privKey);
const samePoint = ProjectivePoint.fromHex(pubKeyPoint.toHex());

Generates 33-byte compressed (default) or 65-byte public key from 32-byte private key.

sign

import * as secp from '@noble/secp256k1';
import { sha256 } from '@noble/hashes/sha256';
import { utf8ToBytes } from '@noble/hashes/utils';
const msg = 'noble cryptography';
const msgHash = sha256(utf8ToBytes(msg));
const priv = secp.utils.randomPrivateKey();

const sigA = secp.sign(msgHash, priv);

// Variants
const sigB = await secp.signAsync(msgHash, priv);
const sigC = secp.sign(msgHash, priv, { extraEntropy: true }); // hedged sig
const sigC2 = secp.sign(msgHash, priv, { extraEntropy: Uint8Array.from([0xca, 0xfe]) });
const sigD = secp.sign(msgHash, priv, { lowS: false }); // malleable sig

Generates low-s deterministic-k RFC6979 ECDSA signature. Requries hash of message, which means you'll need to do something like sha256(message) before signing.

extraEntropy: true enables hedged signatures. They incorporate extra randomness into RFC6979 (described in section 3.6), to provide additional protection against fault attacks. Check out blog post Deterministic signatures are not your friends. Even if their RNG is broken, they will fall back to determinism.

Default behavior lowS: true prohibits signatures which have (sig.s >= CURVE.n/2n) and is compatible with BTC/ETH. Setting lowS: false allows to create malleable signatures, which is default openssl behavior. Non-malleable signatures can still be successfully verified in openssl.

verify

import * as secp from '@noble/secp256k1';
const hex = secp.etc.hexToBytes;
const sig = hex(
  'ddc633c5b48a1a6725c31201892715dda3058350f7b444e89d32c33c90d9c9e218d7eaf02c2254e88c3b33d755394b08bcc7efd13df02338510b750b64572983'
);
const msgHash = hex('736403f76264eccc1b77ba58dc8fc690e76b2b1532ba82c736a60f3862082db3');
// const priv = 'd60937c2a1ece169888d4c48717dfcc0e1a7af915505823148cca11859210e9c';
const pubKey = hex('020b6d70b68873ff8fd729adf5cf4bf45021b34236f991768249cba06b11136ec6');

// verify
const isValid = secp.verify(sig, msgHash, pubKey);
const isValidLoose = secp.verify(sig, msgHash, pubKey, { lowS: false });

Verifies ECDSA signature. Default behavior lowS: true prohibits malleable signatures which have (sig.s >= CURVE.n/2n) and is compatible with BTC / ETH. Setting lowS: false allows to create signatures, which is default openssl behavior.

getSharedSecret

import * as secp from '@noble/secp256k1';
const bobsPriv = secp.utils.randomPrivateKey();
const alicesPub = secp.getPublicKey(secp.utils.randomPrivateKey());

// ECDH between Alice and Bob
const shared33b = secp.getSharedSecret(bobsPriv, alicesPub);
const shared65b = secp.getSharedSecret(bobsPriv, alicesPub, false);
const sharedPoint = secp.ProjectivePoint.fromHex(alicesPub).multiply(bobsPriv);

Computes ECDH (Elliptic Curve Diffie-Hellman) shared secret between key A and different key B.

recoverPublicKey

import * as secp from '@noble/secp256k1';

import { sha256 } from '@noble/hashes/sha256';
import { utf8ToBytes } from '@noble/hashes/utils';
const msg = 'noble cryptography';
const msgHash = sha256(utf8ToBytes(msg));
const priv = secp.utils.randomPrivateKey();
const pub1 = secp.getPubkicKey(priv);
const sig = secp.sign(msgHash, priv);

const pub2 = sig.recoverPublicKey(msgHash);

Recover public key from Signature instance with recovery bit set.

utils

A bunch of useful utilities are also exposed:

type Bytes = Uint8Array;
const etc: {
  hexToBytes: (hex: string) => Bytes;
  bytesToHex: (b: Bytes) => string;
  concatBytes: (...arrs: Bytes[]) => Bytes;
  bytesToNumberBE: (b: Bytes) => bigint;
  numberToBytesBE: (num: bigint) => Bytes;
  mod: (a: bigint, b?: bigint) => bigint;
  invert: (num: bigint, md?: bigint) => bigint;
  hmacSha256Async: (key: Bytes, ...msgs: Bytes[]) => Promise<Bytes>;
  hmacSha256Sync: HmacFnSync;
  hashToPrivateKey: (hash: Hex) => Bytes;
  randomBytes: (len: number) => Bytes;
};
const utils: {
  normPrivateKeyToScalar: (p: PrivKey) => bigint;
  randomPrivateKey: () => Bytes; // Uses CSPRNG https://developer.mozilla.org/en-US/docs/Web/API/Crypto/getRandomValues
  isValidPrivateKey: (key: Hex) => boolean;
  precompute(p: ProjectivePoint, windowSize?: number): ProjectivePoint;
};
class ProjectivePoint {
  constructor(px: bigint, py: bigint, pz: bigint);
  static readonly BASE: ProjectivePoint;
  static readonly ZERO: ProjectivePoint;
  static fromAffine(point: AffinePoint): ProjectivePoint;
  static fromHex(hex: Hex): ProjectivePoint;
  static fromPrivateKey(n: PrivKey): ProjectivePoint;
  get x(): bigint;
  get y(): bigint;
  add(other: ProjectivePoint): ProjectivePoint;
  assertValidity(): void;
  equals(other: ProjectivePoint): boolean;
  multiply(n: bigint): ProjectivePoint;
  negate(): ProjectivePoint;
  subtract(other: ProjectivePoint): ProjectivePoint;
  toAffine(): AffinePoint;
  toHex(isCompressed?: boolean): string;
  toRawBytes(isCompressed?: boolean): Bytes;
}
class Signature {
  constructor(r: bigint, s: bigint, recovery?: number | undefined);
  static fromCompact(hex: Hex): Signature;
  readonly r: bigint;
  readonly s: bigint;
  readonly recovery?: number | undefined;
  ok(): Signature;
  hasHighS(): boolean;
  normalizeS(): Signature;
  recoverPublicKey(msgh: Hex): Point;
  toCompactRawBytes(): Bytes;
  toCompactHex(): string;
}
CURVE; // curve prime; order; equation params, generator coordinates

Security

The module is production-ready.

We cross-test against sister project noble-curves, which was audited and provides improved security.

• The current version has not been independently audited. It is a rewrite of v1, which has been audited by cure53 in Apr 2021: PDF (funded by Umbra.cash & community).
• It's being fuzzed in a separate repository

Constant-timeness

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.

Supply chain security

• 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-secp256k1.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 are 0 dependencies; 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

Randomness

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.

Quantum computers

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.

Speed

Use noble-curves if you need even higher performance.

Benchmarks measured with Apple M2 on MacOS 13 with node.js 20.

getPublicKey(utils.randomPrivateKey()) x 6,430 ops/sec @ 155μs/op
sign x 3,367 ops/sec @ 296μs/op
verify x 600 ops/sec @ 1ms/op
getSharedSecret x 505 ops/sec @ 1ms/op
recoverPublicKey x 612 ops/sec @ 1ms/op
Point.fromHex (decompression) x 9,185 ops/sec @ 108μs/op

Compare to other libraries on M1 (openssl uses native bindings, not JS):

elliptic#getPublicKey x 1,940 ops/sec
sjcl#getPublicKey x 211 ops/sec

elliptic#sign x 1,808 ops/sec
sjcl#sign x 199 ops/sec
openssl#sign x 4,243 ops/sec
ecdsa#sign x 116 ops/sec

elliptic#verify x 812 ops/sec
sjcl#verify x 166 ops/sec
openssl#verify x 4,452 ops/sec
ecdsa#verify x 80 ops/sec

elliptic#ecdh x 971 ops/sec

Upgrading

noble-secp256k1 v2 features improved security and smaller attack surface. The goal of v2 is to provide minimum possible JS library which is safe and fast.

That means the library was reduced 4x, to just over 400 lines. In order to achieve the goal, some features were moved to noble-curves, which is even safer and faster drop-in replacement library with same API. Switch to curves if you intend to keep using these features:

• DER encoding: toDERHex, toDERRawBytes, signing / verification of DER sigs
• Schnorr signatures
• Using utils.precompute() for non-base point
• Support for environments which don't support bigint literals
• Common.js support
• Support for node.js 18 and older without shim

Other changes for upgrading from @noble/secp256k1 1.7 to 2.0:

• 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; use signAsync for async version
  • 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
  • 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)

Contributing & testing

• npm install && npm run build && npm test will build the code and run tests.
• npm run bench will run benchmarks, which may need their deps first (npm run bench:install)
• npm run loc will count total output size, important to be less than 4KB

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.

License

MIT (c) Paul Miller (https://paulmillr.com), see LICENSE file.