noble-secp256k1

Fastest 4KB JS implementation of secp256k1 signatures & ECDH.

• ✍️ Deterministic ECDSA signatures compliant with RFC6979
• 🤝 Elliptic Curve Diffie-Hellman ECDH
• 📦 Pure ESM, can be imported without transpilers
• 🪶 4KB gzipped, 450 lines of code

Use larger drop-in replacement noble-curves instead, if you need additional features such as 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

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://deno.land/x/secp256k1/mod.ts"; // Deno
// import * as secp from "https://unpkg.com/@noble/secp256k1"; // Unpkg
(async () => {
  // keys, messages & other inputs can be Uint8Arrays or hex strings
  // Uint8Array.from([0xde, 0xad, 0xbe, 0xef]) === '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 alicesPubkey = secp.getPublicKey(secp.utils.randomPrivateKey());
  secp.getSharedSecret(privKey, alicesPubkey); // Elliptic curve diffie-hellman
  signature.recoverPublicKey(msgHash); // Public key recovery
})();

Additional polyfills for some environments:

// 1. Enable synchronous methods.
// Only async methods are available by default, to keep the library dependency-free.
import { hmac } from '@noble/hashes/hmac';
import { sha256 } from '@noble/hashes/sha256';
secp.etc.hmacSha256Sync = (k, ...m) => hmac(sha256, k, secp.etc.concatBytes(...m))
// Sync methods can be used now:
// secp.sign(msgHash, privKey);

// 2. node.js 18 and older, requires polyfilling globalThis.crypto
import { webcrypto } from 'node:crypto';
// @ts-ignore
if (!globalThis.crypto) globalThis.crypto = webcrypto;

// 3. React Native needs crypto.getRandomValues polyfill 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));

API

There are 3 main methods: getPublicKey(privateKey), sign(messageHash, privateKey) and verify(signature, messageHash, publicKey). We accept Hex type everywhere:

type Hex = Uint8Array | string

getPublicKey

function getPublicKey(privateKey: Hex, isCompressed?: boolean): Uint8Array;

Generates 33-byte compressed public key from 32-byte private key.

• If you need uncompressed 65-byte public key, set second argument to false.
• Use ProjectivePoint.fromPrivateKey(privateKey) for Point instance.
• Use ProjectivePoint.fromHex(publicKey) to convert Hex / Uint8Array into Point.

sign

function sign(
  messageHash: Hex, // message hash (not message) which would be signed
  privateKey: Hex, // private key which will sign the hash
  opts?: { lowS: boolean, extraEntropy: boolean | Hex } // optional params
): Signature;
function signAsync(
  messageHash: Hex,
  privateKey: Hex,
  opts?: { lowS: boolean; extraEntropy: boolean | Hex }
): Promise;

sign(msgHash, privKey, { lowS: false }); // Malleable signature
sign(msgHash, privKey, { extraEntropy: true }); // Improved security

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

1. lowS: false allows to create malleable signatures, for compatibility with openssl. Default lowS: true prohibits signatures which have (sig.s >= CURVE.n/2n) and is compatible with BTC/ETH.
2. extraEntropy: true improves security by adding entropy, follows section 3.6 of RFC6979:
   • No disadvantage: if an entropy generator is broken, sigs would be the same as they are without the option
   • It would help a lot in case there is an error somewhere in k gen. Exposing k could leak private keys
   • Sigs with extra entropy would have different r / s, which means they would still be valid, but may break some test vectors if you're cross-testing against other libs

verify

function verify(
  signature: Hex | Signature, // returned by the `sign` function
  messageHash: Hex, // message hash (not message) that must be verified
  publicKey: Hex, // public (not private) key
  opts?: { lowS: boolean } // optional params; { lowS: true } by default
): boolean;

Verifies ECDSA signature and ensures it has lowS (compatible with BTC/ETH). lowS: false turns off malleability check, but makes it OpenSSL-compatible.

getSharedSecret

function getSharedSecret(
  privateKeyA: Uint8Array | string, // Alices's private key
  publicKeyB: Uint8Array | string, // Bob's public key
  isCompressed = true // optional arg. (default) true=33b key, false=65b.
): Uint8Array;

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

Use ProjectivePoint.fromHex(publicKeyB).multiply(privateKeyA) for Point instance

recoverPublicKey

signature.recoverPublicKey(
  msgHash: Uint8Array | string
): Uint8Array | undefined;

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;
  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. It is cross-tested against noble-curves, and has similar security.

1. The current version is rewrite of v1, which has been audited by cure53: PDF (funded by Umbra.cash & community).
2. It's being fuzzed by Guido Vranken's cryptofuzz: run the fuzzer by yourself to check.

Our EC multiplication is hardened to be algorithmically constant time. We're using built-in JS BigInt, which is potentially vulnerable to timing attacks as per MDN. But, JIT-compiler and Garbage Collector make "constant time" extremely hard to achieve in a scripting language. Which means any other JS library doesn't use constant-time bigints. Including bn.js or anything else. 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.

We consider infrastructure attacks like rogue NPM modules very important; that's why it's crucial to minimize the amount of 3rd-party dependencies & native bindings. If your app uses 500 dependencies, any dep could get hacked and you'll be downloading malware with every npm install. Our goal is to minimize this attack vector.

As for key generation, we're deferring to built-in crypto.getRandomValues which is considered cryptographically secure (CSPRNG).

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

Contributing

1. Clone the repository.
2. npm install to install build dependencies like TypeScript
3. npm run build to compile TypeScript code
4. npm test to run jest on test/index.ts

Special thanks to Roman Koblov, who have helped to improve scalar multiplication speed.

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)

License

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