Module
Fastest JS implementation of ed25519, x25519 & ristretto255. Independently audited, high-security, 0-dependency EDDSA signatures and ECDH key agreement
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// Uses built-in crypto module from node.js to generate randomness / hmac-sha256.// In browser the line is automatically removed during build time: uses crypto.subtle instead.import nodeCrypto from 'crypto';
// Be friendly to bad ECMAScript parsers by not using bigint literals like 123nconst _0n = BigInt(0);const _1n = BigInt(1);const _2n = BigInt(2);const _255n = BigInt(255);
/** * ed25519 is Twisted Edwards curve with equation of * ``` * −x² + y² = 1 − (121665/121666) * x² * y² * ``` */const CURVE = { // Params: a, b a: BigInt(-1), // Equal to -121665/121666 over finite field. // Negative number is P - number, and division is invert(number, P) d: BigInt('37095705934669439343138083508754565189542113879843219016388785533085940283555'), // Finite field 𝔽p over which we'll do calculations P: _2n ** _255n - BigInt(19), // Subgroup order aka C n: _2n ** BigInt(252) + BigInt('27742317777372353535851937790883648493'), // Cofactor h: BigInt(8), // Base point (x, y) aka generator point Gx: BigInt('15112221349535400772501151409588531511454012693041857206046113283949847762202'), Gy: BigInt('46316835694926478169428394003475163141307993866256225615783033603165251855960'),};
// Cleaner output this way.export { CURVE };
type Hex = Uint8Array | string;type PrivKey = Hex | bigint | number;type PubKey = Hex | Point;type SigType = Hex | Signature;
// √(-1) aka √(a) aka 2^((p-1)/4)const SQRT_M1 = BigInt( '19681161376707505956807079304988542015446066515923890162744021073123829784752');// √d aka sqrt(-486664)const SQRT_D = BigInt( '6853475219497561581579357271197624642482790079785650197046958215289687604742');// √(ad - 1)const SQRT_AD_MINUS_ONE = BigInt( '25063068953384623474111414158702152701244531502492656460079210482610430750235');// 1 / √(a-d)const INVSQRT_A_MINUS_D = BigInt( '54469307008909316920995813868745141605393597292927456921205312896311721017578');// 1-d²const ONE_MINUS_D_SQ = BigInt( '1159843021668779879193775521855586647937357759715417654439879720876111806838');// (d-1)²const D_MINUS_ONE_SQ = BigInt( '40440834346308536858101042469323190826248399146238708352240133220865137265952');
/** * Extended Point works in extended coordinates: (x, y, z, t) ∋ (x=x/z, y=y/z, t=xy). * Default Point works in affine coordinates: (x, y) * https://en.wikipedia.org/wiki/Twisted_Edwards_curve#Extended_coordinates */class ExtendedPoint { constructor(readonly x: bigint, readonly y: bigint, readonly z: bigint, readonly t: bigint) {}
static BASE = new ExtendedPoint(CURVE.Gx, CURVE.Gy, _1n, mod(CURVE.Gx * CURVE.Gy)); static ZERO = new ExtendedPoint(_0n, _1n, _1n, _0n); static fromAffine(p: Point): ExtendedPoint { if (!(p instanceof Point)) { throw new TypeError('ExtendedPoint#fromAffine: expected Point'); } if (p.equals(Point.ZERO)) return ExtendedPoint.ZERO; return new ExtendedPoint(p.x, p.y, _1n, mod(p.x * p.y)); } // Takes a bunch of Jacobian Points but executes only one // invert on all of them. invert is very slow operation, // so this improves performance massively. static toAffineBatch(points: ExtendedPoint[]): Point[] { const toInv = invertBatch(points.map((p) => p.z)); return points.map((p, i) => p.toAffine(toInv[i])); }
static normalizeZ(points: ExtendedPoint[]): ExtendedPoint[] { return this.toAffineBatch(points).map(this.fromAffine); }
// Ristretto-related methods.
// The hash-to-group operation applies Elligator twice and adds the results. // https://ristretto.group/formulas/elligator.html static fromRistrettoHash(hash: Uint8Array): ExtendedPoint { hash = ensureBytes(hash); assertLen(64, hash); const r1 = bytes255ToNumberLE(hash.slice(0, 32)); const R1 = this.calcElligatorRistrettoMap(r1); const r2 = bytes255ToNumberLE(hash.slice(32, 64)); const R2 = this.calcElligatorRistrettoMap(r2); return R1.add(R2); }
// Computes Elligator map for Ristretto // https://ristretto.group/formulas/elligator.html private static calcElligatorRistrettoMap(r0: bigint) { const { d } = CURVE; const r = mod(SQRT_M1 * r0 * r0); // 1 const Ns = mod((r + _1n) * ONE_MINUS_D_SQ); // 2 let c = BigInt(-1); // 3 const D = mod((c - d * r) * mod(r + d)); // 4 let { isValid: Ns_D_is_sq, value: s } = uvRatio(Ns, D); // 5 let s_ = mod(s * r0); // 6 if (!edIsNegative(s_)) s_ = mod(-s_); if (!Ns_D_is_sq) s = s_; // 7 if (!Ns_D_is_sq) c = r; // 8 const Nt = mod(c * (r - _1n) * D_MINUS_ONE_SQ - D); // 9 const s2 = s * s; const W0 = mod((s + s) * D); // 10 const W1 = mod(Nt * SQRT_AD_MINUS_ONE); // 11 const W2 = mod(_1n - s2); // 12 const W3 = mod(_1n + s2); // 13 return new ExtendedPoint(mod(W0 * W3), mod(W2 * W1), mod(W1 * W3), mod(W0 * W2)); }
// Ristretto: Decoding to Extended Coordinates // https://ristretto.group/formulas/decoding.html static fromRistrettoBytes(bytes: Hex): ExtendedPoint { bytes = ensureBytes(bytes); assertLen(32, bytes); const { a, d } = CURVE; const emsg = 'ExtendedPoint.fromRistrettoBytes: Cannot convert bytes to Ristretto Point'; const s = bytes255ToNumberLE(bytes); // 1. Check that s_bytes is the canonical encoding of a field element, or else abort. // 3. Check that s is non-negative, or else abort if (!equalBytes(numberToBytesLEPadded(s, 32), bytes) || edIsNegative(s)) throw new Error(emsg); const s2 = mod(s * s); const u1 = mod(_1n + a * s2); // 4 (a is -1) const u2 = mod(_1n - a * s2); // 5 const u1_2 = mod(u1 * u1); const u2_2 = mod(u2 * u2); const v = mod(a * d * u1_2 - u2_2); // 6 const { isValid, value: I } = invertSqrt(mod(v * u2_2)); // 7 const Dx = mod(I * u2); // 8 const Dy = mod(I * Dx * v); // 9 let x = mod((s + s) * Dx); // 10 if (edIsNegative(x)) x = mod(-x); // 10 const y = mod(u1 * Dy); // 11 const t = mod(x * y); // 12 if (!isValid || edIsNegative(t) || y === _0n) throw new Error(emsg); return new ExtendedPoint(x, y, _1n, t); }
// Ristretto: Encoding from Extended Coordinates // https://ristretto.group/formulas/encoding.html toRistrettoBytes(): Uint8Array { let { x, y, z, t } = this; const u1 = mod(mod(z + y) * mod(z - y)); // 1 const u2 = mod(x * y); // 2 // Square root always exists const { value: invsqrt } = invertSqrt(mod(u1 * u2 ** _2n)); // 3 const D1 = mod(invsqrt * u1); // 4 const D2 = mod(invsqrt * u2); // 5 const zInv = mod(D1 * D2 * t); // 6 let D: bigint; // 7 if (edIsNegative(t * zInv)) { let _x = mod(y * SQRT_M1); let _y = mod(x * SQRT_M1); x = _x; y = _y; D = mod(D1 * INVSQRT_A_MINUS_D); } else { D = D2; // 8 } if (edIsNegative(x * zInv)) y = mod(-y); // 9 let s = mod((z - y) * D); // 10 (check footer's note, no sqrt(-a)) if (edIsNegative(s)) s = mod(-s); return numberToBytesLEPadded(s, 32); // 11 } // Ristretto methods end.
// Compare one point to another. equals(other: ExtendedPoint): boolean { const a = this; const b = other; return mod(a.t * b.z) === mod(b.t * a.z); }
// 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 X1 = this.x; const Y1 = this.y; const Z1 = this.z; const { a } = CURVE; 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); }
subtract(other: ExtendedPoint): ExtendedPoint { return this.add(other.negate()); }
// 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: number | bigint): ExtendedPoint { let n = normalizeScalar(scalar); const P0 = ExtendedPoint.ZERO; if (this.equals(P0) || n === _1n) return this; let p = P0; let d: ExtendedPoint = this; while (n > _0n) { if (n & _1n) p = p.add(d); d = d.double(); n >>= _1n; } return p; }
private precomputeWindow(W: number): ExtendedPoint[] { const windows = 256 / W + 1; let points: ExtendedPoint[] = []; let p: ExtendedPoint = this; let base = p; for (let window = 0; window < windows; window++) { base = p; points.push(base); for (let i = 1; i < 2 ** (W - 1); i++) { base = base.add(p); points.push(base); } p = base.double(); } return points; }
private wNAF(n: bigint, affinePoint?: Point): [ExtendedPoint, ExtendedPoint] { if (!affinePoint && this.equals(ExtendedPoint.BASE)) affinePoint = Point.BASE; const W = (affinePoint && affinePoint._WINDOW_SIZE) || 1; if (256 % W) { throw new Error('Point#wNAF: Invalid precomputation window, must be power of 2'); }
let precomputes = affinePoint && pointPrecomputes.get(affinePoint); if (!precomputes) { precomputes = this.precomputeWindow(W); if (affinePoint && W !== 1) { precomputes = ExtendedPoint.normalizeZ(precomputes); pointPrecomputes.set(affinePoint, precomputes); } }
let p = ExtendedPoint.ZERO; let f = ExtendedPoint.ZERO;
const windows = 256 / W + 1; const windowSize = 2 ** (W - 1); const mask = BigInt(2 ** W - 1); // Create mask with W ones: 0b1111 for W=4 etc. const maxNumber = 2 ** W; const shiftBy = BigInt(W);
for (let window = 0; window < windows; window++) { const offset = window * windowSize; // Extract W bits. let wbits = Number(n & mask);
// Shift number by W bits. n >>= shiftBy;
// If the bits are bigger than max size, we'll split those. // +224 => 256 - 32 if (wbits > windowSize) { wbits -= maxNumber; n += _1n; }
// Check if we're onto Zero point. // Add random point inside current window to f. if (wbits === 0) { let pr = precomputes[offset]; if (window % 2) pr = pr.negate(); f = f.add(pr); } else { let cached = precomputes[offset + Math.abs(wbits) - 1]; if (wbits < 0) cached = cached.negate(); p = p.add(cached); } } return [p, f]; }
// Constant time multiplication. // Uses wNAF method. Windowed method may be 10% faster, // but takes 2x longer to generate and consumes 2x memory. multiply(scalar: number | bigint, affinePoint?: Point): ExtendedPoint { const n = normalizeScalar(scalar); return ExtendedPoint.normalizeZ(this.wNAF(n, affinePoint))[0]; }
// Converts Extended point to default (x, y) coordinates. // Can accept precomputed Z^-1 - for example, from invertBatch. toAffine(invZ: bigint = invert(this.z)): Point { const x = mod(this.x * invZ); const y = mod(this.y * invZ); return new Point(x, y); }}
// Stores precomputed values for points.const pointPrecomputes = new WeakMap<Point, ExtendedPoint[]>();
/** * Default Point works in affine coordinates: (x, y) */class Point { // Base point aka generator // public_key = Point.BASE * private_key static BASE: Point = new Point(CURVE.Gx, CURVE.Gy); // Identity point aka point at infinity // point = point + zero_point static ZERO: 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. _WINDOW_SIZE?: number;
constructor(readonly x: bigint, readonly y: bigint) {}
// "Private method", don't use it directly. _setWindowSize(windowSize: number) { this._WINDOW_SIZE = windowSize; pointPrecomputes.delete(this); }
// Converts hash string or Uint8Array to Point. // Uses algo from RFC8032 5.1.3. static fromHex(hex: Hex) { const { d, P } = CURVE; const bytes = ensureBytes(hex); assertLen(32, bytes); // 1. First, interpret the string as an integer in little-endian // representation. Bit 255 of this number is the least significant // bit of the x-coordinate and denote this value x_0. The // y-coordinate is recovered simply by clearing this bit. If the // resulting value is >= p, decoding fails. const normed = bytes.slice(); normed[31] = bytes[31] & ~0x80; const y = bytesToNumberLE(normed);
if (y >= P) throw new Error('Point.fromHex expects hex <= Fp');
// 2. To recover the x-coordinate, the curve equation implies // x² = (y² - 1) / (d y² + 1) (mod p). The denominator is always // non-zero mod p. Let u = y² - 1 and v = d y² + 1. const y2 = mod(y * y); const u = mod(y2 - _1n); const v = mod(d * y2 + _1n); let { isValid, value: x } = uvRatio(u, v); if (!isValid) throw new Error('Point.fromHex: invalid y coordinate');
// 4. Finally, use the x_0 bit to select the right square root. If // x = 0, and x_0 = 1, decoding fails. Otherwise, if x_0 != x mod // 2, set x <-- p - x. Return the decoded point (x,y). const isXOdd = (x & _1n) === _1n; const isLastByteOdd = (bytes[31] & 0x80) !== 0; if (isLastByteOdd !== isXOdd) { x = mod(-x); } return new Point(x, y); }
static async fromPrivateKey(privateKey: PrivKey) { return (await getExtendedPublicKey(privateKey)).point; }
// There can always be only two x values (x, -x) for any y // When compressing point, it's enough to only store its y coordinate // and use the last byte to encode sign of x. toRawBytes(): Uint8Array { const bytes = numberToBytesLEPadded(this.y, 32); bytes[31] |= this.x & _1n ? 0x80 : 0; return bytes; }
// Same as toRawBytes, but returns string. toHex(): string { return bytesToHex(this.toRawBytes()); }
/** * Converts to Montgomery; aka x coordinate of curve25519. * We don't have fromX25519, because we don't know sign. * * ``` * u, v: curve25519 coordinates * x, y: ed25519 coordinates * (u, v) = ((1+y)/(1-y), sqrt(-486664)*u/x) * (x, y) = (sqrt(-486664)*u/v, (u-1)/(u+1)) * ``` * https://blog.filippo.io/using-ed25519-keys-for-encryption * @returns u coordinate of curve25519 point */ toX25519() { const { y } = this; return mod((_1n + y) * invert(_1n - y)); }
equals(other: Point): boolean { return this.x === other.x && this.y === other.y; }
negate() { return new Point(mod(-this.x), this.y); }
add(other: Point) { return ExtendedPoint.fromAffine(this).add(ExtendedPoint.fromAffine(other)).toAffine(); }
subtract(other: Point) { return this.add(other.negate()); }
/** * Constant time multiplication. * @param scalar Big-Endian number * @returns new point */ multiply(scalar: number | bigint): Point { return ExtendedPoint.fromAffine(this).multiply(scalar, this).toAffine(); }}
/** * EDDSA signature. */class Signature { readonly s: bigint; constructor(readonly r: Point, s: bigint) { if (!(r instanceof Point)) throw new Error('Expected Point instance'); this.s = normalizeScalar(s); }
static fromHex(hex: Hex) { const bytes = ensureBytes(hex); assertLen(64, bytes); const r = Point.fromHex(bytes.slice(0, 32)); const s = bytesToNumberLE(bytes.slice(32, 64)); return new Signature(r, s); }
toRawBytes() { const u8 = new Uint8Array(64); u8.set(this.r.toRawBytes()); u8.set(numberToBytesLEPadded(this.s, 32), 32); return u8; }
toHex() { return bytesToHex(this.toRawBytes()); }}
export { ExtendedPoint, Point, Signature };
function concatBytes(...arrays: Uint8Array[]): Uint8Array { if (!arrays.every((a) => a instanceof Uint8Array)) throw new Error('Expected Uint8Array list'); 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// ---------------------const hexes = Array.from({ length: 256 }, (v, i) => i.toString(16).padStart(2, '0'));function bytesToHex(uint8a: Uint8Array): string { // pre-caching improves the speed 6x let hex = ''; for (let i = 0; i < uint8a.length; i++) { hex += hexes[uint8a[i]]; } return hex;}
// Caching slows it down 2-3xfunction hexToBytes(hex: string): Uint8Array { if (typeof hex !== 'string') { throw new TypeError('hexToBytes: expected string, got ' + typeof hex); } if (hex.length % 2) throw new Error('hexToBytes: received invalid unpadded hex'); const array = new Uint8Array(hex.length / 2); for (let i = 0; i < array.length; i++) { const j = i * 2; const hexByte = hex.slice(j, j + 2); const byte = Number.parseInt(hexByte, 16); if (Number.isNaN(byte)) throw new Error('Invalid byte sequence'); array[i] = byte; } return array;}
function numberToBytesBEPadded(num: bigint, length: number) { const hex = num.toString(16).padStart(length * 2, '0'); return hexToBytes(hex);}
function numberToBytesLEPadded(num: bigint, length: number) { return numberToBytesBEPadded(num, length).reverse();}
// Little-endian check for first LE bit (last BE bit);function edIsNegative(num: bigint) { return (mod(num) & _1n) === _1n;}
// Little Endianfunction bytesToNumberLE(uint8a: Uint8Array): bigint { if (!(uint8a instanceof Uint8Array)) throw new Error(`bytesToNumberLE: expected Uint8Array, got ${uint8a}`); let value = _0n; const _8n = BigInt(8); for (let i = 0; i < uint8a.length; i++) { value += BigInt(uint8a[i]) << (_8n * BigInt(i)); } return value;}
function bytes255ToNumberLE(bytes: Uint8Array): bigint { return mod(bytesToNumberLE(bytes) & (_2n ** _255n - _1n));}// -------------------------
function mod(a: bigint, b: bigint = CURVE.P) { const res = a % b; return res >= _0n ? res : b + res;}
// Note: this egcd-based invert is 50% faster than powMod-based one.// Inverses number over modulofunction invert(number: bigint, modulo: bigint = CURVE.P): bigint { if (number === _0n || modulo <= _0n) { throw new Error(`invert: expected positive integers, got n=${number} mod=${modulo}`); } // Eucledian GCD https://brilliant.org/wiki/extended-euclidean-algorithm/ let a = mod(number, modulo); let b = modulo; // prettier-ignore let x = _0n, y = _1n, u = _1n, v = _0n; while (a !== _0n) { const q = b / a; const r = b % a; const m = x - u * q; const n = y - v * q; // prettier-ignore b = a, a = r, x = u, y = v, u = m, v = n; } const gcd = b; if (gcd !== _1n) throw new Error('invert: does not exist'); return mod(x, modulo);}
// Takes a bunch of numbers, inverses all of themfunction invertBatch(nums: bigint[], modulo: bigint = CURVE.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], modulo); } acc = invert(acc, modulo); for (let i = len - 1; i >= 0; i--) { if (nums[i] === _0n) continue; let tmp = mod(acc * nums[i], modulo); nums[i] = mod(acc * scratch[i], modulo); acc = tmp; } return nums;}
// Does x ^ (2 ^ power) mod p. pow2(30, 4) == 30 ^ (2 ^ 4)function pow2(x: bigint, power: bigint): bigint { const { P } = CURVE; let res = x; while (power-- > _0n) { res *= res; res %= P; } return res;}
// Power to (p-5)/8 aka x^(2^252-3)// Used to calculate y - the square root of y².// Exponentiates it to very big number.// We are unwrapping the loop because it's 2x faster.// (2n**252n-3n).toString(2) would produce bits [250x 1, 0, 1]// We are multiplying it bit-by-bitfunction pow_2_252_3(x: bigint) { const { P } = CURVE; const _5n = BigInt(5); const _10n = BigInt(10); const _20n = BigInt(20); const _40n = BigInt(40); const _80n = BigInt(80); const x2 = (x * x) % P; const b2 = (x2 * x) % P; // x^3, 11 const b4 = (pow2(b2, _2n) * b2) % P; // x^15, 1111 const b5 = (pow2(b4, _1n) * x) % P; // x^31 const b10 = (pow2(b5, _5n) * b5) % P; const b20 = (pow2(b10, _10n) * b10) % P; const b40 = (pow2(b20, _20n) * b20) % P; const b80 = (pow2(b40, _40n) * b40) % P; const b160 = (pow2(b80, _80n) * b80) % P; const b240 = (pow2(b160, _80n) * b80) % P; const b250 = (pow2(b240, _10n) * b10) % P; const pow_p_5_8 = (pow2(b250, _2n) * x) % P; // ^ To pow to (p+3)/8, multiply it by x. return { pow_p_5_8, b2 };}
// Ratio of u to v. Allows us to combine inversion and square root. Uses algo from RFC8032 5.1.3.// Constant-time// prettier-ignorefunction uvRatio(u: bigint, v: bigint): { isValid: boolean, value: bigint } { const v3 = mod(v * v * v); // v³ const v7 = mod(v3 * v3 * v); // v⁷ const pow = pow_2_252_3(u * v7).pow_p_5_8; let x = mod(u * v3 * pow); // (uv³)(uv⁷)^(p-5)/8 const vx2 = mod(v * x * x); // vx² const root1 = x; // First root candidate const root2 = mod(x * SQRT_M1); // Second root candidate const useRoot1 = vx2 === u; // If vx² = u (mod p), x is a square root const useRoot2 = vx2 === mod(-u); // If vx² = -u, set x <-- x * 2^((p-1)/4) const noRoot = vx2 === mod(-u * SQRT_M1); // There is no valid root, vx² = -u√(-1) if (useRoot1) x = root1; if (useRoot2 || noRoot) x = root2; // We return root2 anyway, for const-time if (edIsNegative(x)) x = mod(-x); return { isValid: useRoot1 || useRoot2, value: x };}
// Calculates 1/√(number)function invertSqrt(number: bigint) { return uvRatio(_1n, number);}// Math end
// Little-endian SHA512 with modulo nasync function sha512ModnLE(...args: Uint8Array[]): Promise<bigint> { const messageArray = concatBytes(...args); const hash = await utils.sha512(messageArray); const value = bytesToNumberLE(hash); return mod(value, CURVE.n);}
function equalBytes(b1: Uint8Array, b2: Uint8Array) { // We don't care about timing attacks here if (b1.length !== b2.length) { return false; } for (let i = 0; i < b1.length; i++) { if (b1[i] !== b2[i]) { return false; } } return true;}
function ensureBytes(hash: Hex): Uint8Array { // Uint8Array.from() instead of hash.slice() because node.js Buffer // is instance of Uint8Array, and its slice() creates **mutable** copy return hash instanceof Uint8Array ? Uint8Array.from(hash) : hexToBytes(hash);}
function assertLen(len: number, bytes: Uint8Array): void { if (bytes.length !== len) throw new Error(`Expected ${len} bytes`);}
function normalizeScalar(num: number | bigint, max = CURVE.n): bigint { if (typeof num === 'number' && num > 0 && Number.isSafeInteger(num)) return BigInt(num); if (typeof num === 'bigint' && _0n < num && num < max) return num; throw new TypeError('Expected valid scalar: 0 < scalar < max');}
function normalizePrivateKey(key: PrivKey): Uint8Array { const bytes = typeof key === 'bigint' || typeof key === 'number' ? numberToBytesBEPadded(normalizeScalar(key, _2n ** BigInt(256)), 32) : ensureBytes(key); assertLen(32, bytes); return bytes;}
function decodeScalar25519(n: Hex): bigint { n = ensureBytes(n); assertLen(32, n); // Section 5: For X25519, in order to decode 32 random bytes as an integer scalar, // set the three least significant bits of the first byte n[0] &= 248; // 0b1111_1000 // and the most significant bit of the last to zero, n[31] &= 127; // 0b0111_1111 // set the second most significant bit of the last byte to 1 n[31] |= 64; // 0b0100_0000 // and, finally, decode as little-endian. // This means that the resulting integer is of the form 2 ^ 254 plus eight times a value between 0 and 2 ^ 251 - 1(inclusive). return bytesToNumberLE(n);}
// Private convenience method// RFC8032 5.1.5async function getExtendedPublicKey(key: PrivKey) { // hash to produce 64 bytes const hashed = await utils.sha512(normalizePrivateKey(key)); // Takes first 32 bytes of 64b uniformingly random input, // clears 3 bits of it to produce a random field element. const head = hashed.slice(0, 32); // Second 32 bytes is called key prefix (5.1.6) const prefix = hashed.slice(32, 64); const scalar = mod(decodeScalar25519(head), CURVE.n); const point = Point.BASE.multiply(scalar); const pubBytes = point.toRawBytes(); return { head, prefix, scalar, point, pubBytes };}
///** * Calculates 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 * RFC8032 5.1.5 */export async function getPublicKey(privateKey: PrivKey): Promise<Uint8Array> { return (await getExtendedPublicKey(privateKey)).pubBytes;}
/** * Signs message with privateKey. * RFC8032 5.1.6 */export async function sign(message: Hex, privateKey: Hex): Promise<Uint8Array> { const msg = ensureBytes(message); const { prefix, scalar: p, pubBytes } = await getExtendedPublicKey(privateKey); const r = await sha512ModnLE(prefix, msg); // r = hash(prefix + msg) const R = Point.BASE.multiply(r); // R = rG const k = await sha512ModnLE(R.toRawBytes(), pubBytes, msg); // k = hash(R + P + msg) const S = mod(r + k * p, CURVE.n); // S = r + kp return new Signature(R, S).toRawBytes();}
/** * Verifies ed25519 signature against message and public key. * An extended group equation is checked. * RFC8032 5.1.7 */export async function verify(sig: SigType, message: Hex, publicKey: PubKey): Promise<boolean> { message = ensureBytes(message); if (!(publicKey instanceof Point)) publicKey = Point.fromHex(publicKey); if (!(sig instanceof Signature)) sig = Signature.fromHex(sig); const SB = ExtendedPoint.BASE.multiply(sig.s); const k = await sha512ModnLE(sig.r.toRawBytes(), publicKey.toRawBytes(), message); const kA = ExtendedPoint.fromAffine(publicKey).multiplyUnsafe(k); const RkA = ExtendedPoint.fromAffine(sig.r).add(kA); // [8][S]B = [8]R + [8][k]A' return RkA.subtract(SB).multiplyUnsafe(CURVE.h).equals(ExtendedPoint.ZERO);}
/** * Calculates X25519 DH shared secret from ed25519 private & public keys. * @param privateKey ed25519 private key * @param publicKey ed25519 public key * @returns X25519 shared key */export async function getSharedSecret(privateKey: PrivKey, publicKey: Hex): Promise<Uint8Array> { const { scalar: p } = await getExtendedPublicKey(privateKey); const u = Point.fromHex(publicKey).toX25519(); return montgomeryLadderChecked(p, u);}
// Enable precomputes. Slows down first publicKey computation by 20ms.Point.BASE._setWindowSize(8);
// curve25519-related code// Curve equation: v^2 = u^3 + A*u^2 + u// https://datatracker.ietf.org/doc/html/rfc7748
// cswap from RFC7748function cswap(swap: bigint, x_2: bigint, x_3: bigint): [bigint, bigint] { const dummy = mod(swap * (x_2 - x_3)); x_2 = mod(x_2 - dummy); x_3 = mod(x_3 + dummy); return [x_2, x_3];}
// x25519 from 4/** * * @param pointU u coordinate (x) on Montgomery Curve 25519 * @param scalar by which the point would be multiplied * @returns new Point on Montgomery curve */function montgomeryLadder(pointU: bigint, scalar: bigint): bigint { const { P, n } = CURVE; const u = normalizeScalar(pointU, P); // Section 5: Implementations MUST accept non-canonical values and process them as // if they had been reduced modulo the field prime. const k = normalizeScalar(scalar, P); // The constant a24 is (486662 - 2) / 4 = 121665 for curve25519/X25519 const a24 = BigInt(121665); const x_1 = u; let x_2 = _1n; let z_2 = _0n; let x_3 = u; let z_3 = _1n; let swap = _0n; let sw: [bigint, bigint]; for (let t = BigInt(255 - 1); t >= _0n; t--) { const k_t = (k >> t) & _1n; swap ^= k_t; sw = cswap(swap, x_2, x_3); x_2 = sw[0]; x_3 = sw[1]; sw = cswap(swap, z_2, z_3); z_2 = sw[0]; z_3 = sw[1]; swap = k_t;
const A = mod(x_2 + z_2); const AA = mod(A * A); const B = mod(x_2 - z_2); const BB = mod(B * B); const E = mod(AA - BB); const C = mod(x_3 + z_3); const D = mod(x_3 - z_3); const DA = mod(D * A); const CB = mod(C * B); x_3 = mod(mod(DA + CB) ** _2n); z_3 = mod(x_1 * mod(DA - CB) ** _2n); x_2 = mod(AA * BB); z_2 = mod(E * (AA + mod(a24 * E))); } sw = cswap(swap, x_2, x_3); x_2 = sw[0]; x_3 = sw[1]; sw = cswap(swap, z_2, z_3); z_2 = sw[0]; z_3 = sw[1]; const { pow_p_5_8, b2 } = pow_2_252_3(z_2); // x^(p-2) aka x^(2^255-21) const xp2 = mod(pow2(pow_p_5_8, BigInt(3)) * b2); return mod(x_2 * xp2);}
function encodeUCoordinate(u: bigint): Uint8Array { return numberToBytesLEPadded(mod(u, CURVE.P), 32);}
function montgomeryLadderChecked(u: bigint, p: bigint): Uint8Array { const pu = montgomeryLadder(u, p); if (pu === _0n) throw new Error('Invalid private or public key received'); return encodeUCoordinate(pu);}
function decodeUCoordinate(uEnc: Hex): bigint { const u = ensureBytes(uEnc); assertLen(32, u); // Section 5: When receiving such an array, implementations of X25519 // MUST mask the most significant bit in the final byte. u[31] &= 127; // 0b0111_1111 return bytesToNumberLE(u);}
export const curve25519 = { BASE_POINT_U: '0900000000000000000000000000000000000000000000000000000000000000',
// crypto_scalarmult aka getSharedSecret scalarMult(privateKey: Hex, publicKey: Hex): Uint8Array { const u = decodeUCoordinate(publicKey); const p = decodeScalar25519(privateKey); return montgomeryLadderChecked(u, p); },
// crypto_scalarmult_base aka getPublicKey scalarMultBase(privateKey: Hex): Uint8Array { return curve25519.scalarMult(privateKey, curve25519.BASE_POINT_U); },};
// Global symbol available in browsers only. Ensure we do not depend on @types/domdeclare const self: Record<string, any> | undefined;const crypto: { node?: any; web?: any } = { node: nodeCrypto, web: typeof self === 'object' && 'crypto' in self ? self.crypto : undefined,};
export const utils = { // The 8-torsion subgroup ℰ8. // Those are "buggy" points, if you multiply them by 8, you'll receive Point.ZERO. // Ported from curve25519-dalek. TORSION_SUBGROUP: [ '0100000000000000000000000000000000000000000000000000000000000000', 'c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac037a', '0000000000000000000000000000000000000000000000000000000000000080', '26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc05', 'ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f', '26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc85', '0000000000000000000000000000000000000000000000000000000000000000', 'c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa', ], bytesToHex, getExtendedPublicKey, randomBytes: (bytesLength: number = 32): Uint8Array => { if (crypto.web) { return crypto.web.getRandomValues(new Uint8Array(bytesLength)); } else if (crypto.node) { const { randomBytes } = crypto.node; return new Uint8Array(randomBytes(bytesLength).buffer); } else { throw new Error("The environment doesn't have randomBytes function"); } }, // Note: ed25519 private keys are uniform 32-bit strings. We do not need // to check for modulo bias like we do in noble-secp256k1 randomPrivateKey() randomPrivateKey: (): Uint8Array => { return utils.randomBytes(32); }, sha512: async (message: Uint8Array): Promise<Uint8Array> => { if (crypto.web) { const buffer = await crypto.web.subtle.digest('SHA-512', message.buffer); return new Uint8Array(buffer); } else if (crypto.node) { return Uint8Array.from(crypto.node.createHash('sha512').update(message).digest()); } else { throw new Error("The environment doesn't have sha512 function"); } }, precompute(windowSize = 8, point = Point.BASE): Point { const cached = point.equals(Point.BASE) ? point : new Point(point.x, point.y); cached._setWindowSize(windowSize); cached.multiply(_1n); return cached; },};