Module
Fastest JS implementation of ed25519, x25519 & ristretto255. Independently audited, high-security, 0-dependency EDDSA sigs & ECDH key agreement
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// https://ed25519.cr.yp.to// https://tools.ietf.org/html/rfc8032// https://en.wikipedia.org/wiki/EdDSA// Thanks DJB!
export const CURVE_PARAMS = { // Params: a, b a: -1n, // Equal to -121665/121666 over finite field. // Negative number is P - number, and division is modInverse(number, P) d: 37095705934669439343138083508754565189542113879843219016388785533085940283555n, // Finite field 𝔽p over which we'll do calculations P: 2n ** 255n - 19n, // Subgroup order aka prime_order n: 2n ** 252n + 27742317777372353535851937790883648493n, // Cofactor h: 8n, // Base point (x, y) aka generator point Gx: 15112221349535400772501151409588531511454012693041857206046113283949847762202n, Gy: 46316835694926478169428394003475163141307993866256225615783033603165251855960n};
type PrivKey = Uint8Array | string | bigint | number;type PubKey = Uint8Array | string | Point;type Hex = Uint8Array | string;type Signature = Uint8Array | string | SignResult;
const ENCODING_LENGTH = 32;const P = CURVE_PARAMS.P;const PRIME_ORDER = CURVE_PARAMS.n;const I = powMod(2n, (P - 1n) / 4n, P);
// Default Point works in default aka affine coordinates: (x, y)// Extended Point works in extended coordinates: (x, y, z, t) ∋ (x=x/z, y=y/z, t=xy)// https://en.wikipedia.org/wiki/Twisted_Edwards_curve#Extended_coordinatesclass ExtendedPoint { static ZERO_POINT = new ExtendedPoint(0n, 1n, 1n, 0n); static fromPoint(p: Point): ExtendedPoint { if (p.equals(Point.ZERO_POINT)) return ExtendedPoint.ZERO_POINT; return new ExtendedPoint(p.x, p.y, 1n, mod(p.x * p.y)); }
constructor(public x: bigint, public y: bigint, public z: bigint, public t: bigint) {}
// Takes a bunch of Jacobian Points but executes only one // modInverse on all of them. modInverse is very slow operation, // so this improves performance massively. static batchAffine(points: ExtendedPoint[]): Point[] { const toInv = batchInverse(points.map(p => p.z)); return points.map((p, i) => p.toAffine(toInv[i])); }
// Compare one point to another. equals(other: ExtendedPoint): boolean { const a = this; const b = other; const [T1, T2, Z1, Z2] = [a.t, b.t, a.z, b.z]; return mod(T1 * Z2) === mod(T2 * Z1); }
// Inverses point to one corresponding to (x, -y) in Affine coordinates. negate(): ExtendedPoint { return new ExtendedPoint(mod(-this.x), this.y, this.z, mod(-this.t)); }
// Fast algo for doubling Extended Point when curve's a=-1. // http://hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#doubling-dbl-2008-hwcd // Cost: 3M + 4S + 1*a + 7add + 1*2. double(): ExtendedPoint { const _a = this; const X1 = _a.x, Y1 = _a.y, Z1 = _a.z; const { a } = CURVE_PARAMS; const A = mod(X1 ** 2n); const B = mod(Y1 ** 2n); const C = mod(2n * Z1 ** 2n); const D = mod(a * A); const E = mod((X1 + Y1) ** 2n - A - B); const G = mod(D + B); const F = mod(G - C); const H = mod(D - B); const X3 = mod(E * F); const Y3 = mod(G * H); const T3 = mod(E * H); const Z3 = mod(F * G); return new ExtendedPoint(X3, Y3, Z3, T3); }
// Fast algo for adding 2 Extended Points when curve's a=-1. // http://hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#addition-add-2008-hwcd-4 // Cost: 8M + 8add + 2*2. add(other: ExtendedPoint): ExtendedPoint { const X1 = this.x; const Y1 = this.y; const Z1 = this.z; const T1 = this.t; const X2 = other.x; const Y2 = other.y; const Z2 = other.z; const T2 = other.t; const A = mod((Y1 - X1) * (Y2 + X2)); const B = mod((Y1 + X1) * (Y2 - X2)); const F = mod(B - A); if (F === 0n) { // Same point. return this.double(); } const C = mod(Z1 * 2n * T2); const D = mod(T1 * 2n * Z2); const E = mod(D + C); const G = mod(B + A); const H = mod(D - C); const X3 = mod(E * F); const Y3 = mod(G * H); const T3 = mod(E * H); const Z3 = mod(F * G); return new ExtendedPoint(X3, Y3, Z3, T3); }
// Non-constant-time multiplication. Uses double-and-add algorithm. // It's faster, but should only be used when you don't care about // an exposed private key e.g. sig verification. multiplyUnsafe(scalar: bigint): ExtendedPoint { if (typeof scalar !== 'number' && typeof scalar !== 'bigint') { throw new TypeError('Point#multiply: expected number or bigint'); } let n = mod(BigInt(scalar), PRIME_ORDER); if (n <= 0) { throw new Error('Point#multiply: invalid scalar, expected positive integer'); } let p = ExtendedPoint.ZERO_POINT; let d: ExtendedPoint = this; while (n > 0n) { if (n & 1n) p = p.add(d); d = d.double(); n >>= 1n; } return p; }
// Converts Extended point to default (x, y) coordinates. // Can accept precomputed Z^-1 - for example, from batchInverse. toAffine(invZ: bigint = modInverse(this.z)): Point { const x = mod(this.x * invZ); const y = mod(this.y * invZ); return new Point(x, y); }}
// Default Point works in default aka affine coordinates: (x, y)export class Point { // Base point aka generator // public_key = base_point * private_key static BASE_POINT: Point = new Point(CURVE_PARAMS.Gx, CURVE_PARAMS.Gy); // Identity point aka point at infinity // point = point + zero_point static ZERO_POINT: Point = new Point(0n, 1n); // We calculate precomputes for elliptic curve point multiplication // using windowed method. This specifies window size and // stores precomputed values. Usually only base point would be precomputed. private WINDOW_SIZE?: number; private PRECOMPUTES?: ExtendedPoint[];
constructor(public x: bigint, public y: bigint) {}
// "Private method", don't use it directly. _setWindowSize(windowSize: number) { this.WINDOW_SIZE = windowSize; this.PRECOMPUTES = undefined; } // Converts hash string or Uint8Array to Point. // Uses algo from RFC8032 5.1.3. static fromHex(hash: Hex) { const { d } = CURVE_PARAMS; const bytes = hash instanceof Uint8Array ? hash : hexToArray(hash); const len = bytes.length - 1; const normedLast = bytes[len] & ~0x80; const isLastByteOdd = (bytes[len] & 0x80) !== 0; const normed = Uint8Array.from(Array.from(bytes.slice(0, len)).concat(normedLast)); const y = arrayToNumberLE(normed); if (y >= P) { throw new Error('Point#fromHex expects hex <= Fp'); } const sqrY = y * y; const sqrX = mod((sqrY - 1n) * modInverse(d * sqrY + 1n), P); let x = powMod(sqrX, (P + 3n) / 8n, P); if (mod(x * x - sqrX) !== 0n) { x = mod(x * I); } const isXOdd = (x & 1n) === 1n; if (isLastByteOdd !== isXOdd) { x = mod(-x); } return new Point(x, y); }
/** * Converts point to compressed representation of its Y. * ECDSA uses `04${x}${y}` to represent long form and * `02${x}` / `03${x}` to represent short form, * where leading bit signifies positive or negative Y. * EDDSA (ed25519) uses short form. */ toRawBytes(): Uint8Array { const hex = numberToHex(this.y); const u8 = new Uint8Array(ENCODING_LENGTH); for (let i = hex.length - 2, j = 0; j < ENCODING_LENGTH && i >= 0; i -= 2, j++) { u8[j] = parseInt(hex[i] + hex[i + 1], 16); } const mask = this.x & 1n ? 0x80 : 0; u8[ENCODING_LENGTH - 1] |= mask; return u8; }
// Same as toRawBytes, but returns string. toHex(): string { return arrayToHex(this.toRawBytes()); }
// Converts to Montgomery; aka x coordinate of curve25519. // We don't have fromX25519, because we don't know sign! toX25519() { // curve25519 is birationally equivalent to ed25519 // x, y: ed25519 coordinates // u, v: x25519 coordinates // u = (1 + y) / (1 - y) // See https://blog.filippo.io/using-ed25519-keys-for-encryption return mod((1n + this.y) * modInverse(1n - this.y)); }
equals(other: Point): boolean { return this.x === other.x && this.y === other.y; }
negate(): Point { return new Point(this.x, mod(-this.y)); }
// Adds point to itself. http://hyperelliptic.org/EFD/g1p/auto-twisted.html add(other: Point): Point { if (!(other instanceof Point)) { throw new TypeError('Point#add: expected Point'); } const { d } = CURVE_PARAMS; const X1 = this.x; const Y1 = this.y; const X2 = other.x; const Y2 = other.y; const X3 = (X1 * Y2 + Y1 * X2) * modInverse(1n + d * X1 * X2 * Y1 * Y2); const Y3 = (Y1 * Y2 + X1 * X2) * modInverse(1n - d * X1 * X2 * Y1 * Y2); return new Point(mod(X3), mod(Y3)); }
subtract(other: Point) { return this.add(other.negate()); }
private precomputeWindow(W: number): ExtendedPoint[] { if (this.PRECOMPUTES) return this.PRECOMPUTES; const points: ExtendedPoint[] = new Array(2 ** W * W); let currPoint: ExtendedPoint = ExtendedPoint.fromPoint(this); const winSize = 2 ** W; for (let currWin = 0; currWin < 256 / W; currWin++) { let offset = currWin * winSize; let point: ExtendedPoint = ExtendedPoint.ZERO_POINT; for (let i = 0; i < winSize; i++) { points[offset + i] = point; point = point.add(currPoint); } currPoint = point; } let res = points; if (W !== 1) { res = ExtendedPoint.batchAffine(points).map(p => ExtendedPoint.fromPoint(p)); this.PRECOMPUTES = res; } return res; }
// Constant time multiplication. // Uses window method to generate 2^W precomputed points. multiply(scalar: bigint, isAffine: false): ExtendedPoint; multiply(scalar: bigint, isAffine?: true): Point; multiply(scalar: bigint, isAffine = true): Point | ExtendedPoint { if (typeof scalar !== 'number' && typeof scalar !== 'bigint') { throw new TypeError('Point#multiply: expected number or bigint'); } let n = mod(BigInt(scalar), PRIME_ORDER); if (n <= 0) { throw new Error('Point#multiply: invalid scalar, expected positive integer'); } const W = this.WINDOW_SIZE || 1; if (256 % W) { throw new Error('Point#multiply: Invalid precomputation window, must be power of 2'); } const precomputes = this.precomputeWindow(W); const winSize = 2 ** W; let p = ExtendedPoint.ZERO_POINT; for (let byteIdx = 0; byteIdx < 256 / W; byteIdx++) { const offset = winSize * byteIdx; const masked = Number(n & BigInt(winSize - 1)); p = p.add(precomputes[offset + masked]); n >>= BigInt(W); } return isAffine ? p.toAffine() : p; }}const { BASE_POINT } = Point;
export class SignResult { constructor(public r: Point, public s: bigint) {}
static fromHex(hex: Hex) { hex = ensureArray(hex); const r = Point.fromHex(hex.slice(0, 32)); const s = arrayToNumberLE(hex.slice(32)); return new SignResult(r, s); }
toRawBytes() { const numberBytes = hexToArray(numberToHex(this.s)).reverse(); const sBytes = new Uint8Array(ENCODING_LENGTH); sBytes.set(numberBytes); const res = new Uint8Array(64); res.set(this.r.toRawBytes()); res.set(sBytes, 32); return res; // return concatTypedArrays(this.r.toRawBytes(), sBytes); }
toHex() { return arrayToHex(this.toRawBytes()); }}
// SHA512 implementation.let sha512: (message: Uint8Array) => Promise<Uint8Array>;let generateRandomPrivateKey = (bytesLength: number = 32) => new Uint8Array(0);
if (typeof window == 'object' && 'crypto' in window) { sha512 = async (message: Uint8Array) => { const buffer = await window.crypto.subtle.digest('SHA-512', message.buffer); return new Uint8Array(buffer); }; generateRandomPrivateKey = (bytesLength: number = 32): Uint8Array => { return window.crypto.getRandomValues(new Uint8Array(bytesLength)); };} else if (typeof process === 'object' && 'node' in process.versions) { const req = require; const { createHash, randomBytes } = req('crypto'); sha512 = async (message: Uint8Array) => { const hash = createHash('sha512'); hash.update(message); return Uint8Array.from(hash.digest()); }; generateRandomPrivateKey = (bytesLength: number = 32): Uint8Array => { return new Uint8Array(randomBytes(bytesLength).buffer); };} else { throw new Error("The environment doesn't have sha512 function");}
function concatTypedArrays(...arrays: Uint8Array[]): Uint8Array { if (arrays.length === 1) return arrays[0]; const length = arrays.reduce((a, arr) => a + arr.length, 0); const result = new Uint8Array(length); for (let i = 0, pad = 0; i < arrays.length; i++) { const arr = arrays[i]; result.set(arr, pad); pad += arr.length; } return result;}
// Convert between types// ---------------------function arrayToHex(uint8a: Uint8Array): string { // pre-caching chars could speed this up 6x. let hex = ''; for (let i = 0; i < uint8a.length; i++) { hex += uint8a[i].toString(16).padStart(2, '0'); } return hex;}
function pad64(num: number | bigint): string { return num.toString(16).padStart(64, '0');}
function numberToHex(num: number | bigint): string { const hex = num.toString(16); return hex.length & 1 ? `0${hex}` : hex;}
function hexToArray(hex: string): Uint8Array { hex = hex.length & 1 ? `0${hex}` : hex; const array = new Uint8Array(hex.length / 2); for (let i = 0; i < array.length; i++) { let j = i * 2; array[i] = Number.parseInt(hex.slice(j, j + 2), 16); } return array;}
// Little Endianfunction arrayToNumberLE(uint8a: Uint8Array): bigint { let value = 0n; for (let i = 0; i < uint8a.length; i++) { value += BigInt(uint8a[i]) << (8n * BigInt(i)); } return value;}// -------------------------
function mod(a: bigint, b: bigint = P) { const res = a % b; return res >= 0n ? res : b + res;}
function powMod(x: bigint, power: bigint, order: bigint) { let res = 1n; while (power > 0) { if (power & 1n) { res = mod(res * x, order); } power >>= 1n; x = mod(x * x, order); } return res;}
// Eucledian GCD// https://brilliant.org/wiki/extended-euclidean-algorithm/function egcd(a: bigint, b: bigint) { let [x, y, u, v] = [0n, 1n, 1n, 0n]; while (a !== 0n) { let q = b / a; let r = b % a; let m = x - u * q; let n = y - v * q; [b, a] = [a, r]; [x, y] = [u, v]; [u, v] = [m, n]; } let gcd = b; return [gcd, x, y];}
function modInverse(number: bigint, modulo: bigint = P) { if (number === 0n || modulo <= 0n) { console.log(number); throw new Error('modInverse: expected positive integers'); } let [gcd, x] = egcd(mod(number, modulo), modulo); if (gcd !== 1n) { throw new Error('modInverse: does not exist'); } return mod(x, modulo);}
function batchInverse(nums: bigint[], n: bigint = P): bigint[] { const len = nums.length; const scratch = new Array(len); let acc = 1n; for (let i = 0; i < len; i++) { if (nums[i] === 0n) continue; scratch[i] = acc; acc = mod(acc * nums[i], n); } acc = modInverse(acc, n); for (let i = len - 1; i >= 0; i--) { if (nums[i] === 0n) continue; let tmp = mod(acc * nums[i], n); nums[i] = mod(acc * scratch[i], n); acc = tmp; } return nums;}
async function sha512ToNumberLE(...args: Uint8Array[]): Promise<bigint> { const messageArray = concatTypedArrays(...args); const hash = await sha512(messageArray); const value = arrayToNumberLE(hash); return mod(value, PRIME_ORDER);}
function keyPrefix(privateBytes: Uint8Array) { return privateBytes.slice(ENCODING_LENGTH);}
function encodePrivate(privateBytes: Uint8Array): bigint { const last = ENCODING_LENGTH - 1; const head = privateBytes.slice(0, ENCODING_LENGTH); head[0] &= 248; head[last] &= 127; head[last] |= 64;
return arrayToNumberLE(head);}
function ensureArray(hash: Hex): Uint8Array { return hash instanceof Uint8Array ? hash : hexToArray(hash);}
function ensurePrivInputArray(privateKey: PrivKey): Uint8Array { if (privateKey instanceof Uint8Array) return privateKey; if (typeof privateKey === 'string') return hexToArray(privateKey.padStart(64, '0')); return hexToArray(pad64(BigInt(privateKey)));}
export function getPublicKey(privateKey: Uint8Array): Promise<Uint8Array>;export function getPublicKey(privateKey: string): Promise<string>;export function getPublicKey(privateKey: bigint | number): Promise<Uint8Array>;export async function getPublicKey(privateKey: PrivKey) { const privBytes = await sha512(ensurePrivInputArray(privateKey)); const publicKey = BASE_POINT.multiply(encodePrivate(privBytes)); return typeof privateKey === 'string' ? publicKey.toHex() : publicKey.toRawBytes();}
export function sign(hash: Uint8Array, privateKey: Hex): Promise<Uint8Array>;export function sign(hash: string, privateKey: Hex): Promise<string>;export async function sign(hash: Hex, privateKey: Hex) { const privBytes = await sha512(ensurePrivInputArray(privateKey)); const p = encodePrivate(privBytes); const P = BASE_POINT.multiply(p); const msg = ensureArray(hash); const r = await sha512ToNumberLE(keyPrefix(privBytes), msg); const R = BASE_POINT.multiply(r); const h = await sha512ToNumberLE(R.toRawBytes(), P.toRawBytes(), msg); const S = mod(r + h * p, PRIME_ORDER); const sig = new SignResult(R, S); return typeof hash === 'string' ? sig.toHex() : sig.toRawBytes();}
export async function verify(signature: Signature, hash: Hex, publicKey: PubKey) { hash = ensureArray(hash); if (!(publicKey instanceof Point)) publicKey = Point.fromHex(publicKey); if (!(signature instanceof SignResult)) signature = SignResult.fromHex(signature); const h = await sha512ToNumberLE(signature.r.toRawBytes(), publicKey.toRawBytes(), hash); const Ph = ExtendedPoint.fromPoint(publicKey).multiplyUnsafe(h); const Gs = BASE_POINT.multiply(signature.s, false); const RPh = ExtendedPoint.fromPoint(signature.r).add(Ph); return Gs.equals(RPh);}
// Enable precomputes. Slows down first publicKey computation by 20ms.BASE_POINT._setWindowSize(4);
export const utils = { generateRandomPrivateKey,
precompute(windowSize = 4, point = BASE_POINT): Point { const cached = point.equals(BASE_POINT) ? point : new Point(point.x, point.y); cached._setWindowSize(windowSize); cached.multiply(1n); return cached; }};