noble-ed25519

Fastest JS implementation of ed25519, an elliptic curve that could be used for EDDSA signature scheme and X25519 ECDH key agreement.

Conforms to RFC7748, RFC8032 and ZIP215. Includes support for ristretto255 (spec): a technique for constructing prime order elliptic curve groups with non-malleable encodings. Check out the online demo.

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/ed25519

// Common.js and ECMAScript Modules (ESM)
import * as ed from '@noble/ed25519';
// If you're using single file, use global variable: nobleEd25519

const privateKey = ed.utils.randomPrivateKey(); // 32-byte Uint8Array or string.
const message = 'deadbeefdeadbeefdeadbeefdeadbeefdeadbeefdeadbeefdeadbeefdeadbeef';
(async () => {
  const publicKey = await ed.getPublicKey(privateKey);
  const signature = await ed.sign(message, privateKey);
  const isSigned = await ed.verify(signature, message, publicKey);
})();

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

• deno run --import-map=imports.json app.ts

• app.ts

  import * as ed from "https://deno.land/x/ed25519/mod.ts";
  const publicKey = await ed.getPublicKey(ed.utils.randomPrivateKey());
  console.log(publicKey);

• imports.json

  {"imports": {"crypto": "https://deno.land/std@0.119.0/node/crypto.ts"}}

API

• getPublicKey(privateKey)
• sign(message, privateKey)
• verify(signature, message, publicKey)
• getSharedSecret(privateKey, publicKey)
• X25519 and curve25519
• ristretto255
• Utilities

getPublicKey(privateKey)

function getPublicKey(privateKey: Uint8Array | string | bigint): Promise<Uint8Array>;

• privateKey: Uint8Array | string | bigint will be used to generate public key. If you want to pass bigints, ensure they are Big-Endian.
• Returns Promise<Uint8Array>. Uses promises, because ed25519 uses SHA internally; and we're using built-in browser window.crypto, which returns Promise.

To generate ed25519 public key:

1. private key is hashed with sha512, then first 32 bytes are taken from the hash
2. 3 least significant bits of the first byte are cleared

• Use Point.fromPrivateKey(privateKey) if you want Point instance instead
• Use Point.fromHex(publicKey) if you want to convert hex / bytes into Point. It will use decompression algorithm 5.1.3 of RFC 8032.
• Use utils.getExtendedPublicKey if you need full SHA512 hash of seed

sign(message, privateKey)

function sign(message: Uint8Array | string, privateKey: Uint8Array | string): Promise<Uint8Array>;

• message: Uint8Array | string - message which would be signed
• privateKey: Uint8Array | string - private key which will sign the hash
• Returns EdDSA signature. You can consume it with Signature.fromHex() method:
  • Signature.fromHex(ed25519.sign(hash, privateKey))

verify(signature, message, publicKey)

function verify(
  signature: Uint8Array | string | Signature,
  message: Uint8Array | string,
  publicKey: Uint8Array | string | Point
): Promise<boolean>

• signature: Uint8Array | string | Signature - returned by the sign function
• message: Uint8Array | string - message that needs to be verified
• publicKey: Uint8Array | string | Point - e.g. that was generated from privateKey by getPublicKey
• Returns Promise<boolean>

Verifies signature. Compatible with ZIP215: allows sigs/public keys bigger than curve prime, but less than 2^256.

For additional info about verification strictness, check out It’s 255:19AM.

getSharedSecret(privateKey, publicKey)

function getSharedSecret(privateKey: Uint8Array | string | bigint, publicKey: Uint8Array | string): Promise<Uint8Array>;

Converts ed25519 private / public keys to Curve25519 and calculates Elliptic Curve Diffie Hellman (ECDH) with X25519. Conforms to RFC7748.

X25519 and curve25519

const pub = ed25519.curve25519.scalarMultBase(privateKey);
const shared = ed25519.curve25519.scalarMult(privateKeyA, publicKeyB);

The library includes namespace curve25519 that you could use to calculate Curve25519 keys. It uses Montgomery Ladder specified in RFC7748.

You cannot use ed25519 keys, because they are hashed with sha512. However, you can use Point#toX25519() method on ed25519 public keys. See implementation of ed25519.getSharedSecret for details.

Ristretto255

Each Point in ed25519 has 8 different equivalent points. No matter which one of these 8 equivalent points you give the Ristretto algorithm, it will give you exactly the same one. The other 7 points are no longer representable. Two caveats:

1. Always use RistrettoPoint.fromHex() and RistrettoPoint#toHex()
2. Never mix ExtendedPoint & RistrettoPoint: ristretto is not a subgroup of ed25519. ExtendedPoint you are mixing with, may not be the representative for the set of possible points.

(taken from the comment)

import { RistrettoPoint } from '@noble/ed25519';

// Decode a byte-string representing a compressed Ristretto point.
// Not compatible with Point.toHex()
RistrettoPoint.fromHex(hex: Uint8Array | string): RistrettoPoint;

// Encode a Ristretto point represented by the point (X:Y:Z:T) to Uint8Array
RistrettoPoint#toHex(): Uint8Array;

// Takes uniform output of 64-bit hash function like sha512 and converts it to RistrettoPoint
// **Note:** this is one-way map, there is no conversion from point to hash.
RistrettoPoint.hashToCurve(hash: Uint8Array | string): RistrettoPoint;

It extends Mike Hamburg's Decaf approach to cofactor elimination to support cofactor-8 curves such as Curve25519.

In particular, this allows an existing Curve25519 library to implement a prime-order group with only a thin abstraction layer, and makes it possible for systems using Ed25519 signatures to be safely extended with zero-knowledge protocols, with no additional cryptographic assumptions and minimal code changes.

For more information on the topic, check out:

• Ristretto website
• irtf-cfrg-ristretto255-decaf448 standard draft
• Exploiting Low Order Generators in One-Time Ring Signatures
• Details of ristretto internals
• Rust implementation with lots of comments

Utilities

We provide a bunch of useful utils and expose some internal classes.

// Returns cryptographically secure random `Uint8Array` that could be used as private key
utils.randomPrivateKey();

// Native sha512 calculation
utils.sha512(message: Uint8Array): Promise<Uint8Array>;

// Modular division
utils.mod(number: bigint, modulo = CURVE.P): bigint;

// Convert Uint8Array to hex string
utils.bytesToHex(bytes: Uint8Array): string;

// returns { head, prefix, scalar, point, pointBytes }
utils.getExtendedPublicKey(privateKey);

// Call it without arguments if you want your first calculation of public key to take normal time instead of ~20ms
utils.precompute(W = 8, point = Point.BASE)

// Elliptic curve point in Affine (x, y) coordinates.
class Point {
  constructor(x: bigint, y: bigint);
  static fromHex(hash: string);
  static fromPrivateKey(privateKey: string | Uint8Array);
  toX25519(): Uint8Array; // Converts to Curve25519 u coordinate in LE form
  toRawBytes(): Uint8Array;
  toHex(): string; // Compact representation of a Point
  isTorsionFree(): boolean; // Multiplies the point by curve order
  equals(other: Point): boolean;
  negate(): Point;
  add(other: Point): Point;
  subtract(other: Point): Point;
  multiply(scalar: bigint): Point;
}
// Elliptic curve point in Extended (x, y, z, t) coordinates.
class ExtendedPoint {
  constructor(x: bigint, y: bigint, z: bigint, t: bigint);
  static fromAffine(point: Point): ExtendedPoint;
  toAffine(): Point;
}
// Also (x, y, z, t)
class RistrettoPoint {
  static hashToCurve(hex: Hex): RistrettoPoint;
  static fromHex(hex: Hex): RistrettoPoint;
  toRawBytes(): Uint8Array;
  toHex(): string;
  equals(other: RistrettoPoint): boolean;
  add(other: RistrettoPoint): RistrettoPoint;
  subtract(other: RistrettoPoint): RistrettoPoint;
  multiply(scalar: number | bigint): RistrettoPoint;
}
class Signature {
  constructor(r: bigint, s: bigint);
  static fromHex(hex: Hex): Signature;
  toRawBytes(): Uint8Array;
  toHex(): string;
}

// Curve params
ed25519.CURVE.P // 2 ** 255 - 19
ed25519.CURVE.l // 2 ** 252 + 27742317777372353535851937790883648493
ed25519.Point.BASE // new ed25519.Point(Gx, Gy) where
// Gx = 15112221349535400772501151409588531511454012693041857206046113283949847762202n
// Gy = 46316835694926478169428394003475163141307993866256225615783033603165251855960n;

ed25519.utils.TORSION_SUBGROUP; // The 8-torsion subgroup ℰ8.

Security

Noble is production-ready.

1. No public audits have been done yet. Our goal is to crowdfund the audit.
2. It was developed in a very similar fashion to noble-secp256k1, which was audited by a third-party firm.
3. It was fuzzed by Guido Vranken's cryptofuzz, no serious issues have been found. You can run the fuzzer by yourself to check it.

We're using built-in JS BigInt, which is "unsuitable for use in cryptography" as per official spec. This means that the lib is potentially vulnerable to timing attacks. 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 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 done with Apple M1.

getPublicKey(utils.randomPrivateKey()) x 6,835 ops/sec @ 146μs/op
sign x 3,474 ops/sec @ 287μs/op
verify x 726 ops/sec @ 1ms/op
verifyBatch x 888 ops/sec @ 1ms/op
Point.fromHex decompression x 11,783 ops/sec @ 84μs/op
ristretto255#fromHash x 5,482 ops/sec @ 182μs/op
ristretto255 round x 5,621 ops/sec @ 177μs/op
curve25519.scalarMultBase x 1,113 ops/sec @ 898μs/op
ed25519.getSharedSecret x 844 ops/sec @ 1ms/op

Compare to alternative implementations:

# tweetnacl-fast@1.0.3
getPublicKey x 920 ops/sec @ 1ms/op # aka scalarMultBase
sign x 519 ops/sec @ 2ms/op

# ristretto255@0.1.1
getPublicKey x 877 ops/sec @ 1ms/op # aka scalarMultBase

# sodium-native@3.2.1, native bindings to libsodium, node.js-only
sodium-native#sign x 58,661 ops/sec @ 17μs/op

Contributing

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

License

MIT (c) 2019 Paul Miller (https://paulmillr.com), see LICENSE file.