noble-secp256k1

Fastest JS implementation of secp256k1, an elliptic curve that could be used for asymmetric encryption, ECDH key agreement protocol and signature schemes. Supports deterministic ECDSA from RFC6979 and Schnorr signatures from BIP0340.

Audited by an independent security firm. Check out the online demo and blog post: Learning fast elliptic-curve cryptography in JS

This library belongs to noble crypto

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

• No dependencies, one small file
• Easily auditable TypeScript/JS code
• Supported in all major browsers and stable node.js versions
• All releases are signed with PGP keys
• Check out homepage & all libraries: secp256k1, ed25519, bls12-381, hashes

Usage

Use NPM in node.js / browser, or include single file from GitHub's releases page:

npm install @noble/secp256k1

// Common.js and ECMAScript Modules (ESM)
import * as secp from '@noble/secp256k1';
// If you're using single file, use global variable instead: `window.nobleSecp256k1`

// Supports both async and sync methods, see docs
(async () => {
  // keys, messages & other inputs can be Uint8Arrays or hex strings
  // Uint8Array.from([0xde, 0xad, 0xbe, 0xef]) === 'deadbeef'
  const privKey = secp.utils.randomPrivateKey();
  const pubKey = secp.getPublicKey(privKey);
  const msgHash = await secp.utils.sha256('hello world');
  const signature = await secp.sign(msgHash, privKey);
  const isValid = secp.verify(signature, msgHash, pubKey);

  // Schnorr signatures
  const rpub = secp.schnorr.getPublicKey(privKey);
  const rsignature = await secp.schnorr.sign(message, privKey);
  const risValid = await secp.schnorr.verify(rsignature, message, rpub);
})();

To use the module with Deno, you will need import map:

• deno run --import-map=imports.json app.ts
• app.ts: import * as secp from "https://deno.land/x/secp256k1/mod.ts";
• imports.json: {"imports": {"crypto": "https://deno.land/std@0.153.0/node/crypto.ts"}}

API

• getPublicKey(privateKey)
• sign(msgHash, privateKey)
• verify(signature, msgHash, publicKey)
• getSharedSecret(privateKeyA, publicKeyB)
• recoverPublicKey(hash, signature, recovery)
• schnorr.getPublicKey(privateKey)
• schnorr.sign(message, privateKey)
• schnorr.verify(signature, message, publicKey)
• Utilities

getPublicKey(privateKey)

function getPublicKey(privateKey: Uint8Array | string | bigint, isCompressed = false): Uint8Array;

Creates public key for the corresponding private key. The default is full 65-byte key.

• isCompressed = false determines whether to return compact (33-byte), or full (65-byte) key.

Internally, it does Point.BASE.multiply(privateKey). If you need actual Point instead of Uint8Array, use Point.fromPrivateKey(privateKey).

sign(msgHash, privateKey)

function sign(
  msgHash: Uint8Array | string,
  privateKey: Uint8Array | string,
  opts?: Options
): Promise<Uint8Array>;
function sign(
  msgHash: Uint8Array | string,
  privateKey: Uint8Array | string,
  opts?: Options
): Promise<[Uint8Array, number]>;

Generates low-s deterministic ECDSA signature as per RFC6979.

• msgHash: Uint8Array | string - 32-byte message hash which would be signed
• privateKey: Uint8Array | string | bigint - private key which will sign the hash
• options?: Options - optional object related to signature value and format with following keys:
  • recovered: boolean = false - whether the recovered bit should be included in the result. In this case, the result would be an array of two items.
  • canonical: boolean = true - whether a signature s should be no more than 1/2 prime order. true (default) makes signatures compatible with libsecp256k1, false makes signatures compatible with openssl
  • der: boolean = true - whether the returned signature should be in DER format. If false, it would be in Compact format (32-byte r + 32-byte s)
  • extraEntropy: Uint8Array | string | true - additional entropy k' for deterministic signature, follows section 3.6 of RFC6979. When true, it would automatically be filled with 32 bytes of cryptographically secure entropy. Strongly recommended to pass true to improve security:
    • Schnorr signatures are doing it every time
    • It would help a lot in case there is an error somewhere in k generation. Exposing k could leak private keys
    • If the entropy generator is broken, signatures would be the same as they are without the option
    • Signatures 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

The function is asynchronous because we're utilizing built-in HMAC API to not rely on dependencies.

(async () => {
  // Signatures with improved security
  const signatureE = await secp.sign(msgHash, privKey, { extraEntropy: true });
  // Malleable signatures, but compatible with openssl
  const signatureM = await secp.sign(msgHash, privKey, { canonical: false });
})();

function signSync(
  msgHash: Uint8Array | string,
  privateKey: Uint8Array | string,
  opts?: Options
): Uint8Array | [Uint8Array, number];

signSync counterpart could also be used, you need to set utils.hmacSha256Sync to a function with signature key: Uint8Array, ...messages: Uint8Array[]) => Uint8Array. Example with noble-hashes package:

import { hmac } from '@noble/hashes/hmac';
import { sha256 } from '@noble/hashes/sha256';
secp256k1.utils.hmacSha256Sync = (key, ...msgs) => hmac(sha256, key, secp256k1.utils.concatBytes(...msgs))
secp256k1.utils.sha256Sync = (...msgs) => sha256(secp256k1.utils.concatBytes(...msgs))
// Can be used now
secp256k1.signSync(msgHash, privateKey);
schnorr.signSync(message, privateKey)

verify(signature, msgHash, publicKey)

function verify(
  signature: Uint8Array | string,
  msgHash: Uint8Array | string,
  publicKey: Uint8Array | string
): boolean;
function verify(signature: Signature, msgHash: Uint8Array | string, publicKey: Point): boolean;

• signature: Uint8Array | string | { r: bigint, s: bigint } - object returned by the sign function
• msgHash: Uint8Array | string - message hash that needs to be verified
• publicKey: Uint8Array | string | Point - e.g. that was generated from privateKey by getPublicKey
• options?: Options - optional object related to signature value and format
  • strict: boolean = true - whether a signature s should be no more than 1/2 prime order. true (default) makes signatures compatible with libsecp256k1, false makes signatures compatible with openssl
• Returns boolean: true if signature == hash; otherwise false

getSharedSecret(privateKeyA, publicKeyB)

function getSharedSecret(
  privateKeyA: Uint8Array | string | bigint,
  publicKeyB: Uint8Array | string | Point,
  isCompressed = false
): Uint8Array;

Computes ECDH (Elliptic Curve Diffie-Hellman) shared secret between a private key and a different public key.

• To get Point instance, use Point.fromHex(publicKeyB).multiply(privateKeyA)

• isCompressed = false determines whether to return compact (33-byte), or full (65-byte) key

• If you have one public key you'll be creating lots of secrets against, consider massive speed-up by using precomputations:

  const pub = secp.utils.precompute(8, publicKeyB);
  // Use pub everywhere instead of publicKeyB
  getSharedSecret(privKey, pub); // Now 12x faster

recoverPublicKey(hash, signature, recovery)

function recoverPublicKey(
  msgHash: Uint8Array | string,
  signature: Uint8Array | string,
  recovery: number,
  isCompressed = false
): Uint8Array | undefined;

Recovers public key from message hash, signature & recovery bit. The default is full 65-byte key.

• msgHash: Uint8Array | string - message hash which would be signed
• signature: Uint8Array | string | { r: bigint, s: bigint } - object returned by the sign function
• recovery: number - recovery bit returned by sign with recovered option
• isCompressed = false determines whether to return compact (33-byte), or full (65-byte) key

Public key is generated by doing scalar multiplication of a base Point(x, y) by a fixed integer. The result is another Point(x, y) which we will by default encode to hex Uint8Array. If signature is invalid - function will return undefined as result. To get Point instance, use Point.fromSignature(hash, signature, recovery).

schnorr.getPublicKey(privateKey)

function schnorrGetPublicKey(privateKey: Uint8Array | string): Uint8Array;

Calculates 32-byte public key from a private key.

Warning: it is incompatible with non-schnorr pubkey. Specifically, its y coordinate may be flipped. See BIP340 for clarification.

schnorr.sign(message, privateKey)

function schnorrSign(
  message: Uint8Array | string,
  privateKey: Uint8Array | string,
  auxilaryRandom?: Uint8Array
): Promise<Uint8Array>;

Generates Schnorr signature as per BIP0340. Asynchronous, so use await.

• message: Uint8Array | string - message (not hash) which would be signed
• privateKey: Uint8Array | string | bigint - private key which will sign the hash
• auxilaryRandom?: Uint8Array — optional 32 random bytes. By default, the method gathers cryptogarphically secure entropy
• Returns Schnorr signature in Hex format.

schnorr.verify(signature, message, publicKey)

function schnorrVerify(
  signature: Uint8Array | string,
  message: Uint8Array | string,
  publicKey: Uint8Array | string
): boolean;

• signature: Uint8Array | string | { r: bigint, s: bigint } - object returned by the sign function
• message: Uint8Array | string - message (not hash) that needs to be verified
• publicKey: Uint8Array | string | Point - e.g. that was generated from privateKey by getPublicKey
• Returns boolean: true if signature == hash; otherwise false

Utilities

secp256k1 exposes a few internal utilities for improved developer experience.

// Default output is Uint8Array. If you need hex string as an output:
console.log(secp.utils.bytesToHex(pubKey));

const utils: {
  // Can take 40 or more bytes of uniform input e.g. from CSPRNG or KDF
  // and convert them into private key, with the modulo bias being neglible.
  // As per FIPS 186 B.1.1.
  hashToPrivateKey: (hash: Hex) => Uint8Array;
  // Returns `Uint8Array` of 32 cryptographically secure random bytes that can be used as private key
  randomPrivateKey: () => Uint8Array;
  // Checks private key for validity
  isValidPrivateKey(privateKey: PrivKey): boolean;

  // Returns `Uint8Array` of x cryptographically secure random bytes.
  randomBytes: (bytesLength?: number) => Uint8Array;
  // Converts Uint8Array to hex string
  bytesToHex(uint8a: Uint8Array): string;
  hexToBytes(hex: string): Uint8Array;
  concatBytes(...arrays: Uint8Array[]): Uint8Array;
  // Modular division over curve prime
  mod: (number: number | bigint, modulo = CURVE.P): bigint;
  // Modular inversion
  invert(number: bigint, modulo?: bigint): bigint;

  sha256: (message: Uint8Array) => Promise<Uint8Array>;
  hmacSha256: (key: Uint8Array, ...messages: Uint8Array[]) => Promise<Uint8Array>;

  // You can set up your synchronous methods for `signSync`/`signSchnorrSync` to work.
  // The argument order is identical to async methods from above
  sha256Sync: undefined;
  hmacSha256Sync: undefined;

  // BIP0340-style tagged hashes
  taggedHash: (tag: string, ...messages: Uint8Array[]) => Promise<Uint8Array>;
  taggedHashSync: (tag: string, ...messages: Uint8Array[]) => Uint8Array;

  // 1. Returns cached point which you can use to pass to `getSharedSecret` or to `#multiply` by it.
  // 2. Precomputes point multiplication table. Is done by default on first `getPublicKey()` call.
  // If you want your first getPublicKey to take 0.16ms instead of 20ms, make sure to call
  // utils.precompute() somewhere without arguments first.
  precompute(windowSize?: number, point?: Point): Point;
};

secp256k1.CURVE.P // Field, 2 ** 256 - 2 ** 32 - 977
secp256k1.CURVE.n // Order, 2 ** 256 - 432420386565659656852420866394968145599
secp256k1.Point.BASE // new secp256k1.Point(Gx, Gy) where
// Gx = 55066263022277343669578718895168534326250603453777594175500187360389116729240n
// Gy = 32670510020758816978083085130507043184471273380659243275938904335757337482424n;

// Elliptic curve point in Affine (x, y) coordinates.
secp256k1.Point {
  constructor(x: bigint, y: bigint);
  // Supports compressed and non-compressed hex
  static fromHex(hex: Uint8Array | string);
  static fromPrivateKey(privateKey: Uint8Array | string | number | bigint);
  static fromSignature(
    msgHash: Hex,
    signature: Signature,
    recovery: number | bigint
  ): Point | undefined {
  toRawBytes(isCompressed = false): Uint8Array;
  toHex(isCompressed = false): string;
  equals(other: Point): boolean;
  negate(): Point;
  add(other: Point): Point;
  subtract(other: Point): Point;
  // Constant-time scalar multiplication.
  multiply(scalar: bigint | Uint8Array): Point;
}
secp256k1.Signature {
  constructor(r: bigint, s: bigint);
  // DER encoded ECDSA signature
  static fromDER(hex: Uint8Array | string);
  // R, S 32-byte each
  static fromCompact(hex: Uint8Array | string);
  assertValidity(): void;
  hasHighS(): boolean; // high-S sigs cannot be produced using { canonical: true }
  toDERRawBytes(): Uint8Array;
  toDERHex(): string;
  toCompactRawBytes(): Uint8Array;
  toCompactHex(): string;
}

Security

Noble is production-ready.

1. The library has been audited by an independent security firm cure53: PDF. See changes since audit.
   • The audit has been crowdfunded by community with help of Umbra.cash.
2. The library has also been fuzzed by Guido Vranken's cryptofuzz. You can run the fuzzer by yourself to check it.

We're using built-in JS BigInt, which is potentially vulnerable to timing attacks as per official spec. 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. Nonetheless we've hardened implementation of ec curve multiplication to be algorithmically constant time.

We however 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.

Speed

Benchmarks measured with Apple M2 on MacOS 12 with node.js 18.8.

getPublicKey(utils.randomPrivateKey()) x 7,035 ops/sec @ 142μs/op
sign x 5,452 ops/sec @ 183μs/op
signSync (@noble/hashes) x 5,082 ops/sec @ 196μs/op
verify x 1,042 ops/sec @ 959μs/op
recoverPublicKey x 955 ops/sec @ 1ms/op
getSharedSecret aka ecdh x 624 ops/sec @ 1ms/op
getSharedSecret (precomputed) x 7,357 ops/sec @ 135μs/op
Point.fromHex (decompression) x 13,725 ops/sec @ 72μs/op
schnorr.sign x 770 ops/sec @ 1ms/op
schnorr.verify x 1,093 ops/sec @ 914μs/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
bip-schnorr#sign x 60 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
bip-schnorr#verify x 56 ops/sec

elliptic#ecdh x 971 ops/sec

Contributing

Check out a blog post about this library: Learning fast elliptic-curve cryptography in JS.

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.

License

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