mozilla-central/testing/web-platform/tests/fledge/tentative/third_party/noble-ed25519/noble-ed25519.js (file symbol)

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/*! noble-ed25519 - MIT License (c) 2019 Paul Miller (paulmillr.com) */
/**
* 4KB JS implementation of ed25519 EDDSA signatures compliant with RFC8032, FIPS 186-5 & ZIP215.
* @module
*/
const P = 2n ** 255n - 19n; // ed25519 is twisted edwards curve
const N = 2n ** 252n + 27742317777372353535851937790883648493n; // curve's (group) order
const Gx = 0x216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51an; // base point x
const Gy = 0x6666666666666666666666666666666666666666666666666666666666666658n; // base point y
const _d = 37095705934669439343138083508754565189542113879843219016388785533085940283555n;
/**
* ed25519 curve parameters. Equation is −x² + y² = -a + dx²y².
* Gx and Gy are generator coordinates. p is field order, n is group order.
* h is cofactor.
*/
const CURVE = {
a: -1n, // -1 mod p
d: _d, // -(121665/121666) mod p
p: P, n: N, h: 8, Gx: Gx, Gy: Gy // field prime, curve (group) order, cofactor
};
const err = (m = '') => { throw new Error(m); }; // error helper, messes-up stack trace
const isS = (s) => typeof s === 'string'; // is string
const isu8 = (a) => (a instanceof Uint8Array || (ArrayBuffer.isView(a) && a.constructor.name === 'Uint8Array'));
const au8 = (a, l) => // is Uint8Array (of specific length)
!isu8(a) || (typeof l === 'number' && l > 0 && a.length !== l) ?
err('Uint8Array of valid length expected') : a;
const u8n = (data) => new Uint8Array(data); // creates Uint8Array
const toU8 = (a, len) => au8(isS(a) ? h2b(a) : u8n(au8(a)), len); // norm(hex/u8a) to u8a
const M = (a, b = P) => { let r = a % b; return r >= 0n ? r : b + r; }; // mod division
const isPoint = (p) => (p instanceof Point ? p : err('Point expected')); // is xyzt point
/** Point in xyzt extended coordinates. */
class Point {
constructor(ex, ey, ez, et) {
this.ex = ex;
this.ey = ey;
this.ez = ez;
this.et = et;
}
static fromAffine(p) { return new Point(p.x, p.y, 1n, M(p.x * p.y)); }
/** RFC8032 5.1.3: hex / Uint8Array to Point. */
static fromHex(hex, zip215 = false) {
const { d } = CURVE;
hex = toU8(hex, 32);
const normed = hex.slice(); // copy the array to not mess it up
const lastByte = hex[31];
normed[31] = lastByte & ~0x80; // adjust first LE byte = last BE byte
const y = b2n_LE(normed); // decode as little-endian, convert to num
if (zip215 && !(0n <= y && y < 2n ** 256n))
err('bad y coord 1'); // zip215=true [1..2^256-1]
if (!zip215 && !(0n <= y && y < P))
err('bad y coord 2'); // zip215=false [1..P-1]
const y2 = M(y * y); // y²
const u = M(y2 - 1n); // u=y²-1
const v = M(d * y2 + 1n); // v=dy²+1
let { isValid, value: x } = uvRatio(u, v); // (uv³)(uv⁷)^(p-5)/8; square root
if (!isValid)
err('bad y coordinate 3'); // not square root: bad point
const isXOdd = (x & 1n) === 1n; // adjust sign of x coordinate
const isLastByteOdd = (lastByte & 0x80) !== 0; // x_0, last bit
if (!zip215 && x === 0n && isLastByteOdd)
err('bad y coord 3'); // x=0 and x_0 = 1
if (isLastByteOdd !== isXOdd)
x = M(-x);
return new Point(x, y, 1n, M(x * y)); // Z=1, T=xy
}
get x() { return this.toAffine().x; } // .x, .y will call expensive toAffine.
get y() { return this.toAffine().y; } // Should be used with care.
equals(other) {
const { ex: X1, ey: Y1, ez: Z1 } = this;
const { ex: X2, ey: Y2, ez: Z2 } = isPoint(other); // isPoint() checks class equality
const X1Z2 = M(X1 * Z2), X2Z1 = M(X2 * Z1);
const Y1Z2 = M(Y1 * Z2), Y2Z1 = M(Y2 * Z1);
return X1Z2 === X2Z1 && Y1Z2 === Y2Z1;
}
is0() { return this.equals(I); }
negate() {
return new Point(M(-this.ex), this.ey, this.ez, M(-this.et));
}
/** Point doubling. Complete formula. */
double() {
const { ex: X1, ey: Y1, ez: Z1 } = this; // Cost: 4M + 4S + 1*a + 6add + 1*2
const A = M(X1 * X1);
const B = M(Y1 * Y1);
const C = M(2n * M(Z1 * Z1));
const D = M(a * A);
const x1y1 = X1 + Y1;
const E = M(M(x1y1 * x1y1) - A - B);
const G = D + B;
const F = G - C;
const H = D - B;
const X3 = M(E * F);
const Y3 = M(G * H);
const T3 = M(E * H);
const Z3 = M(F * G);
return new Point(X3, Y3, Z3, T3);
}
/** Point addition. Complete formula. */
add(other) {
const { ex: X1, ey: Y1, ez: Z1, et: T1 } = this; // Cost: 8M + 1*k + 8add + 1*2.
const { ex: X2, ey: Y2, ez: Z2, et: T2 } = isPoint(other); // doesn't check if other on-curve
const A = M(X1 * X2);
const B = M(Y1 * Y2);
const C = M(T1 * d * T2);
const D = M(Z1 * Z2);
const E = M((X1 + Y1) * (X2 + Y2) - A - B);
const F = M(D - C);
const G = M(D + C);
const H = M(B - a * A);
const X3 = M(E * F);
const Y3 = M(G * H);
const T3 = M(E * H);
const Z3 = M(F * G);
return new Point(X3, Y3, Z3, T3);
}
mul(n, safe = true) {
if (n === 0n)
return safe === true ? err('cannot multiply by 0') : I;
if (!(typeof n === 'bigint' && 0n < n && n < N))
err('invalid scalar, must be < L');
if (!safe && this.is0() || n === 1n)
return this; // safe=true bans 0. safe=false allows 0.
if (this.equals(G))
return wNAF(n).p; // use wNAF precomputes for base points
let p = I, f = G; // init result point & fake point
for (let d = this; n > 0n; d = d.double(), n >>= 1n) { // double-and-add ladder
if (n & 1n)
p = p.add(d); // if bit is present, add to point
else if (safe)
f = f.add(d); // if not, add to fake for timing safety
}
return p;
}
multiply(scalar) { return this.mul(scalar); } // Aliases for compatibilty
clearCofactor() { return this.mul(BigInt(CURVE.h), false); } // multiply by cofactor
isSmallOrder() { return this.clearCofactor().is0(); } // check if P is small order
isTorsionFree() {
let p = this.mul(N / 2n, false).double(); // ensures the point is not "bad".
if (N % 2n)
p = p.add(this); // P^(N+1) // P*N == (P*(N/2))*2+P
return p.is0();
}
/** converts point to 2d xy affine point. (x, y, z, t) ∋ (x=x/z, y=y/z, t=xy). */
toAffine() {
const { ex: x, ey: y, ez: z } = this;
if (this.equals(I))
return { x: 0n, y: 1n }; // fast-path for zero point
const iz = invert(z, P); // z^-1: invert z
if (M(z * iz) !== 1n)
err('invalid inverse'); // (z * z^-1) must be 1, otherwise bad math
return { x: M(x * iz), y: M(y * iz) }; // x = x*z^-1; y = y*z^-1
}
toRawBytes() {
const { x, y } = this.toAffine(); // convert to affine 2d point
const b = n2b_32LE(y); // encode number to 32 bytes
b[31] |= x & 1n ? 0x80 : 0; // store sign in first LE byte
return b;
}
toHex() { return b2h(this.toRawBytes()); } // encode to hex string
}
/** Generator / Base point */
Point.BASE = new Point(Gx, Gy, 1n, M(Gx * Gy));
/** Identity / Zero point */
Point.ZERO = new Point(0n, 1n, 1n, 0n);
const { BASE: G, ZERO: I } = Point; // Generator, identity points
const padh = (num, pad) => num.toString(16).padStart(pad, '0');
const b2h = (b) => Array.from(au8(b)).map(e => padh(e, 2)).join(''); // bytes to hex
const C = { _0: 48, _9: 57, A: 65, F: 70, a: 97, f: 102 }; // ASCII characters
const _ch = (ch) => {
if (ch >= C._0 && ch <= C._9)
return ch - C._0; // '2' => 50-48
if (ch >= C.A && ch <= C.F)
return ch - (C.A - 10); // 'B' => 66-(65-10)
if (ch >= C.a && ch <= C.f)
return ch - (C.a - 10); // 'b' => 98-(97-10)
return;
};
const h2b = (hex) => {
const e = 'hex invalid';
if (!isS(hex))
return err(e);
const hl = hex.length, al = hl / 2;
if (hl % 2)
return err(e);
const array = u8n(al);
for (let ai = 0, hi = 0; ai < al; ai++, hi += 2) { // treat each char as ASCII
const n1 = _ch(hex.charCodeAt(hi)); // parse first char, multiply it by 16
const n2 = _ch(hex.charCodeAt(hi + 1)); // parse second char
if (n1 === undefined || n2 === undefined)
return err(e);
array[ai] = n1 * 16 + n2; // example: 'A9' => 10*16 + 9
}
return array;
};
const n2b_32LE = (num) => h2b(padh(num, 32 * 2)).reverse(); // number to bytes LE
const b2n_LE = (b) => BigInt('0x' + b2h(u8n(au8(b)).reverse())); // bytes LE to num
const concatB = (...arrs) => {
const r = u8n(arrs.reduce((sum, a) => sum + au8(a).length, 0)); // create u8a of summed length
let pad = 0; // walk through each array,
arrs.forEach(a => { r.set(a, pad); pad += a.length; }); // ensure they have proper type
return r;
};
const invert = (num, md) => {
if (num === 0n || md <= 0n)
err('no inverse n=' + num + ' mod=' + md); // no neg exponent for now
let a = M(num, md), b = md, x = 0n, y = 1n, u = 1n, v = 0n;
while (a !== 0n) { // uses euclidean gcd algorithm
const q = b / a, r = b % a; // not constant-time
const m = x - u * q, n = y - v * q;
b = a, a = r, x = u, y = v, u = m, v = n;
}
return b === 1n ? M(x, md) : err('no inverse'); // b is gcd at this point
};
const pow2 = (x, power) => {
let r = x;
while (power-- > 0n) {
r *= r;
r %= P;
}
return r;
};
const pow_2_252_3 = (x) => {
const x2 = (x * x) % P; // x^2, bits 1
const b2 = (x2 * x) % P; // x^3, bits 11
const b4 = (pow2(b2, 2n) * b2) % P; // x^(2^4-1), bits 1111
const b5 = (pow2(b4, 1n) * x) % P; // x^(2^5-1), bits 11111
const b10 = (pow2(b5, 5n) * b5) % P; // x^(2^10)
const b20 = (pow2(b10, 10n) * b10) % P; // x^(2^20)
const b40 = (pow2(b20, 20n) * b20) % P; // x^(2^40)
const b80 = (pow2(b40, 40n) * b40) % P; // x^(2^80)
const b160 = (pow2(b80, 80n) * b80) % P; // x^(2^160)
const b240 = (pow2(b160, 80n) * b80) % P; // x^(2^240)
const b250 = (pow2(b240, 10n) * b10) % P; // x^(2^250)
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 };
};
const RM1 = 19681161376707505956807079304988542015446066515923890162744021073123829784752n; // √-1
const uvRatio = (u, v) => {
const v3 = M(v * v * v); // v³
const v7 = M(v3 * v3 * v); // v⁷
const pow = pow_2_252_3(u * v7).pow_p_5_8; // (uv⁷)^(p-5)/8
let x = M(u * v3 * pow); // (uv³)(uv⁷)^(p-5)/8
const vx2 = M(v * x * x); // vx²
const root1 = x; // First root candidate
const root2 = M(x * RM1); // Second root candidate; RM1 is √-1
const useRoot1 = vx2 === u; // If vx² = u (mod p), x is a square root
const useRoot2 = vx2 === M(-u); // If vx² = -u, set x <-- x * 2^((p-1)/4)
const noRoot = vx2 === M(-u * RM1); // 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 ((M(x) & 1n) === 1n)
x = M(-x); // edIsNegative
return { isValid: useRoot1 || useRoot2, value: x };
};
const modL_LE = (hash) => M(b2n_LE(hash), N); // modulo L; but little-endian
let _shaS;
const sha512a = (...m) => etc.sha512Async(...m); // Async SHA512
const sha512s = (...m) => // Sync SHA512, not set by default
typeof _shaS === 'function' ? _shaS(...m) : err('etc.sha512Sync not set');
const hash2extK = (hashed) => {
const head = hashed.slice(0, 32); // slice creates a copy, unlike subarray
head[0] &= 248; // Clamp bits: 0b1111_1000,
head[31] &= 127; // 0b0111_1111,
head[31] |= 64; // 0b0100_0000
const prefix = hashed.slice(32, 64); // private key "prefix"
const scalar = modL_LE(head); // modular division over curve order
const point = G.mul(scalar); // public key point
const pointBytes = point.toRawBytes(); // point serialized to Uint8Array
return { head, prefix, scalar, point, pointBytes };
};
// RFC8032 5.1.5; getPublicKey async, sync. Hash priv key and extract point.
const getExtendedPublicKeyAsync = (priv) => sha512a(toU8(priv, 32)).then(hash2extK);
const getExtendedPublicKey = (priv) => hash2extK(sha512s(toU8(priv, 32)));
/** Creates 32-byte ed25519 public key from 32-byte private key. Async. */
const getPublicKeyAsync = (priv) => getExtendedPublicKeyAsync(priv).then(p => p.pointBytes);
/** Creates 32-byte ed25519 public key from 32-byte private key. To use, set `etc.sha512Sync` first. */
const getPublicKey = (priv) => getExtendedPublicKey(priv).pointBytes;
function hashFinish(asynchronous, res) {
if (asynchronous)
return sha512a(res.hashable).then(res.finish);
return res.finish(sha512s(res.hashable));
}
const _sign = (e, rBytes, msg) => {
const { pointBytes: P, scalar: s } = e;
const r = modL_LE(rBytes); // r was created outside, reduce it modulo L
const R = G.mul(r).toRawBytes(); // R = [r]B
const hashable = concatB(R, P, msg); // dom2(F, C) || R || A || PH(M)
const finish = (hashed) => {
const S = M(r + modL_LE(hashed) * s, N); // S = (r + k * s) mod L; 0 <= s < l
return au8(concatB(R, n2b_32LE(S)), 64); // 64-byte sig: 32b R.x + 32b LE(S)
};
return { hashable, finish };
};
/** Signs message (NOT message hash) using private key. Async. */
const signAsync = async (msg, privKey) => {
const m = toU8(msg); // RFC8032 5.1.6: sign msg with key async
const e = await getExtendedPublicKeyAsync(privKey); // pub,prfx
const rBytes = await sha512a(e.prefix, m); // r = SHA512(dom2(F, C) || prefix || PH(M))
return hashFinish(true, _sign(e, rBytes, m)); // gen R, k, S, then 64-byte signature
};
/** Signs message (NOT message hash) using private key. To use, set `etc.sha512Sync` first. */
const sign = (msg, privKey) => {
const m = toU8(msg); // RFC8032 5.1.6: sign msg with key sync
const e = getExtendedPublicKey(privKey); // pub,prfx
const rBytes = sha512s(e.prefix, m); // r = SHA512(dom2(F, C) || prefix || PH(M))
return hashFinish(false, _sign(e, rBytes, m)); // gen R, k, S, then 64-byte signature
};
const dvo = { zip215: true };
const _verify = (sig, msg, pub, opts = dvo) => {
sig = toU8(sig, 64); // Signature hex str/Bytes, must be 64 bytes
msg = toU8(msg); // Message hex str/Bytes
pub = toU8(pub, 32);
const { zip215 } = opts; // switch between zip215 and rfc8032 verif
let A, R, s, SB, hashable = new Uint8Array();
try {
A = Point.fromHex(pub, zip215); // public key A decoded
R = Point.fromHex(sig.slice(0, 32), zip215); // 0 <= R < 2^256: ZIP215 R can be >= P
s = b2n_LE(sig.slice(32, 64)); // Decode second half as an integer S
SB = G.mul(s, false); // in the range 0 <= s < L
hashable = concatB(R.toRawBytes(), A.toRawBytes(), msg); // dom2(F, C) || R || A || PH(M)
}
catch (error) { }
const finish = (hashed) => {
if (SB == null)
return false; // false if try-catch catched an error
if (!zip215 && A.isSmallOrder())
return false; // false for SBS: Strongly Binding Signature
const k = modL_LE(hashed); // decode in little-endian, modulo L
const RkA = R.add(A.mul(k, false)); // [8]R + [8][k]A'
return RkA.add(SB.negate()).clearCofactor().is0(); // [8][S]B = [8]R + [8][k]A'
};
return { hashable, finish };
};
// RFC8032 5.1.7: verification async, sync
/** Verifies signature on message and public key. Async. */
const verifyAsync = async (s, m, p, opts = dvo) => hashFinish(true, _verify(s, m, p, opts));
/** Verifies signature on message and public key. To use, set `etc.sha512Sync` first. */
const verify = (s, m, p, opts = dvo) => hashFinish(false, _verify(s, m, p, opts));
const cr = () => // We support: 1) browsers 2) node.js 19+
typeof globalThis === 'object' && 'crypto' in globalThis ? globalThis.crypto : undefined;
/** Math, hex, byte helpers. Not in `utils` because utils share API with noble-curves. */
const etc = {
bytesToHex: b2h,
hexToBytes: h2b,
concatBytes: concatB,
mod: M,
invert: invert,
randomBytes: (len = 32) => {
const c = cr(); // Can be shimmed in node.js <= 18 to prevent error:
// import { webcrypto } from 'node:crypto';
// if (!globalThis.crypto) globalThis.crypto = webcrypto;
if (!c || !c.getRandomValues)
err('crypto.getRandomValues must be defined');
return c.getRandomValues(u8n(len));
},
sha512Async: async (...messages) => {
const c = cr();
const s = c && c.subtle;
if (!s)
err('etc.sha512Async or crypto.subtle must be defined');
const m = concatB(...messages);
return u8n(await s.digest('SHA-512', m.buffer));
},
sha512Sync: undefined, // Actual logic below
};
Object.defineProperties(etc, { sha512Sync: {
configurable: false, get() { return _shaS; }, set(f) { if (!_shaS)
_shaS = f; },
} });
/** ed25519-specific key utilities. */
const utils = {
getExtendedPublicKeyAsync: getExtendedPublicKeyAsync,
getExtendedPublicKey: getExtendedPublicKey,
randomPrivateKey: () => etc.randomBytes(32),
precompute: (w = 8, p = G) => { p.multiply(3n); w; return p; }, // no-op
};
const W = 8; // Precomputes-related code. W = window size
const precompute = () => {
const points = []; // 10x sign(), 2x verify(). To achieve this,
const windows = 256 / W + 1; // app needs to spend 40ms+ to calculate
let p = G, b = p; // a lot of points related to base point G.
for (let w = 0; w < windows; w++) { // Points are stored in array and used
b = p; // any time Gx multiplication is done.
points.push(b); // They consume 16-32 MiB of RAM.
for (let i = 1; i < 2 ** (W - 1); i++) {
b = b.add(p);
points.push(b);
}
p = b.double(); // Precomputes don't speed-up getSharedKey,
} // which multiplies user point by scalar,
return points; // when precomputes are using base point
};
let Gpows = undefined; // precomputes for base point G
const wNAF = (n) => {
// Compared to other point mult methods,
const comp = Gpows || (Gpows = precompute()); // stores 2x less points using subtraction
const neg = (cnd, p) => { let n = p.negate(); return cnd ? n : p; }; // negate
let p = I, f = G; // f must be G, or could become I in the end
const windows = 1 + 256 / W; // W=8 17 windows
const wsize = 2 ** (W - 1); // W=8 128 window size
const mask = BigInt(2 ** W - 1); // W=8 will create mask 0b11111111
const maxNum = 2 ** W; // W=8 256
const shiftBy = BigInt(W); // W=8 8
for (let w = 0; w < windows; w++) {
const off = w * wsize;
let wbits = Number(n & mask); // extract W bits.
n >>= shiftBy; // shift number by W bits.
if (wbits > wsize) {
wbits -= maxNum;
n += 1n;
} // split if bits > max: +224 => 256-32
const off1 = off, off2 = off + Math.abs(wbits) - 1; // offsets, evaluate both
const cnd1 = w % 2 !== 0, cnd2 = wbits < 0; // conditions, evaluate both
if (wbits === 0) {
f = f.add(neg(cnd1, comp[off1])); // bits are 0: add garbage to fake point
}
else { // ^ can't add off2, off2 = I
p = p.add(neg(cnd2, comp[off2])); // bits are 1: add to result point
}
}
return { p, f }; // return both real and fake points for JIT
}; // !! you can disable precomputes by commenting-out call of the wNAF() inside Point#mul()
export { getPublicKey, getPublicKeyAsync, sign, verify, // Remove the export to easily use in REPL
signAsync, verifyAsync, CURVE, etc, utils, Point as ExtendedPoint }; // envs like browser console