/*! 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
* @example
* ```js
import * as ed from '@noble/ed25519';
(async () => {
const privKey = ed.utils.randomPrivateKey();
const message = Uint8Array.from([0xab, 0xbc, 0xcd, 0xde]);
const pubKey = await ed.getPublicKeyAsync(privKey); // Sync methods are also present
const signature = await ed.signAsync(message, privKey);
const isValid = await ed.verifyAsync(signature, message, pubKey);
})();
```
*/
/**
* Curve params. ed25519 is twisted edwards curve. Equation is −x² + y² = -a + dx²y².
* * P = `2n**255n - 19n` // field over which calculations are done
* * N = `2n**252n + 27742317777372353535851937790883648493n` // group order, amount of curve points
* * h = 8 // cofactor
* * a = `Fp.create(BigInt(-1))` // equation param
* * d = -121665/121666 a.k.a. `Fp.neg(121665 * Fp.inv(121666))` // equation param
* * Gx, Gy are coordinates of Generator / base point
*/
const ed25519_CURVE = {
p: 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffedn,
n: 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3edn,
h: 8n,
a: 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffecn,
d: 0x52036cee2b6ffe738cc740797779e89800700a4d4141d8ab75eb4dca135978a3n,
Gx: 0x216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51an,
Gy: 0x6666666666666666666666666666666666666666666666666666666666666658n,
};
const { p: P, n: N, Gx, Gy, a: _a, d: _d } = ed25519_CURVE;
const h = 8n; // cofactor
const L = 32; // field / group byte length
const L2 = 64;
// Helpers and Precomputes sections are reused between libraries
// ## Helpers
// ----------
// error helper, messes-up stack trace
const err = (m = '') => {
throw new Error(m);
};
const isBig = (n) => typeof n === 'bigint'; // is big integer
const isStr = (s) => typeof s === 'string'; // is string
const isBytes = (a) => a instanceof Uint8Array || (ArrayBuffer.isView(a) && a.constructor.name === 'Uint8Array');
/** assert is Uint8Array (of specific length) */
const abytes = (a, l) => !isBytes(a) || (typeof l === 'number' && l > 0 && a.length !== l)
? err('Uint8Array expected')
: a;
/** create Uint8Array */
const u8n = (len) => new Uint8Array(len);
const u8fr = (buf) => Uint8Array.from(buf);
const padh = (n, pad) => n.toString(16).padStart(pad, '0');
const bytesToHex = (b) => Array.from(abytes(b))
.map((e) => padh(e, 2))
.join('');
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 hexToBytes = (hex) => {
const e = 'hex invalid';
if (!isStr(hex))
return err(e);
const hl = hex.length;
const 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;
};
/** normalize hex or ui8a to ui8a */
const toU8 = (a, len) => abytes(isStr(a) ? hexToBytes(a) : u8fr(abytes(a)), len);
const cr = () => globalThis?.crypto; // WebCrypto is available in all modern environments
const subtle = () => cr()?.subtle ?? err('crypto.subtle must be defined');
// prettier-ignore
const concatBytes = (...arrs) => {
const r = u8n(arrs.reduce((sum, a) => sum + abytes(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;
};
/** WebCrypto OS-level CSPRNG (random number generator). Will throw when not available. */
const randomBytes = (len = L) => {
const c = cr();
return c.getRandomValues(u8n(len));
};
const big = BigInt;
const arange = (n, min, max, msg = 'bad number: out of range') => isBig(n) && min <= n && n < max ? n : err(msg);
/** modular division */
const M = (a, b = P) => {
const r = a % b;
return r >= 0n ? r : b + r;
};
const modN = (a) => M(a, N);
/** Modular inversion using eucledian GCD (non-CT). No negative exponent for now. */
// prettier-ignore
const invert = (num, md) => {
if (num === 0n || md <= 0n)
err('no inverse n=' + num + ' mod=' + md);
let a = M(num, md), b = md, x = 0n, y = 1n, u = 1n, v = 0n;
while (a !== 0n) {
const q = b / a, r = b % a;
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 callHash = (name) => {
// @ts-ignore
const fn = etc[name];
if (typeof fn !== 'function')
err('hashes.' + name + ' not set');
return fn;
};
const apoint = (p) => (p instanceof Point ? p : err('Point expected'));
// ## End of Helpers
// -----------------
const B256 = 2n ** 256n;
/** Point in XYZT extended coordinates. */
class Point {
static BASE;
static ZERO;
ex;
ey;
ez;
et;
constructor(ex, ey, ez, et) {
const max = B256;
this.ex = arange(ex, 0n, max);
this.ey = arange(ey, 0n, max);
this.ez = arange(ez, 1n, max);
this.et = arange(et, 0n, max);
Object.freeze(this);
}
static fromAffine(p) {
return new Point(p.x, p.y, 1n, M(p.x * p.y));
}
/** RFC8032 5.1.3: Uint8Array to Point. */
static fromBytes(hex, zip215 = false) {
const d = _d;
// Copy array to not mess it up.
const normed = u8fr(abytes(hex, L));
// adjust first LE byte = last BE byte
const lastByte = hex[31];
normed[31] = lastByte & ~0x80;
const y = bytesToNumLE(normed);
// zip215=true: 0 <= y < 2^256
// zip215=false, RFC8032: 0 <= y < 2^255-19
const max = zip215 ? B256 : P;
arange(y, 0n, max);
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 point: y not sqrt'); // 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 point: x==0, isLastByteOdd'); // x=0, x_0=1
if (isLastByteOdd !== isXOdd)
x = M(-x);
return new Point(x, y, 1n, M(x * y)); // Z=1, T=xy
}
/** Checks if the point is valid and on-curve. */
assertValidity() {
const a = _a;
const d = _d;
const p = this;
if (p.is0())
throw new Error('bad point: ZERO'); // TODO: optimize, with vars below?
// Equation in affine coordinates: ax² + y² = 1 + dx²y²
// Equation in projective coordinates (X/Z, Y/Z, Z): (aX² + Y²)Z² = Z⁴ + dX²Y²
const { ex: X, ey: Y, ez: Z, et: T } = p;
const X2 = M(X * X); // X²
const Y2 = M(Y * Y); // Y²
const Z2 = M(Z * Z); // Z²
const Z4 = M(Z2 * Z2); // Z⁴
const aX2 = M(X2 * a); // aX²
const left = M(Z2 * M(aX2 + Y2)); // (aX² + Y²)Z²
const right = M(Z4 + M(d * M(X2 * Y2))); // Z⁴ + dX²Y²
if (left !== right)
throw new Error('bad point: equation left != right (1)');
// In Extended coordinates we also have T, which is x*y=T/Z: check X*Y == Z*T
const XY = M(X * Y);
const ZT = M(Z * T);
if (XY !== ZT)
throw new Error('bad point: equation left != right (2)');
return this;
}
/** Equality check: compare points P&Q. */
equals(other) {
const { ex: X1, ey: Y1, ez: Z1 } = this;
const { ex: X2, ey: Y2, ez: Z2 } = apoint(other); // checks class equality
const X1Z2 = M(X1 * Z2);
const X2Z1 = M(X2 * Z1);
const Y1Z2 = M(Y1 * Z2);
const Y2Z1 = M(Y2 * Z1);
return X1Z2 === X2Z1 && Y1Z2 === Y2Z1;
}
is0() {
return this.equals(I);
}
/** Flip point over y coordinate. */
negate() {
return new Point(M(-this.ex), this.ey, this.ez, M(-this.et));
}
/** Point doubling. Complete formula. Cost: `4M + 4S + 1*a + 6add + 1*2`. */
double() {
const { ex: X1, ey: Y1, ez: Z1 } = this;
const a = _a;
// https://hyperelliptic.org/EFD/g1p/auto-twisted-extended.html#doubling-dbl-2008-hwcd
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. Cost: `8M + 1*k + 8add + 1*2`. */
add(other) {
const { ex: X1, ey: Y1, ez: Z1, et: T1 } = this;
const { ex: X2, ey: Y2, ez: Z2, et: T2 } = apoint(other); // doesn't check if other on-curve
const a = _a;
const d = _d;
// https://hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#addition-add-2008-hwcd-3
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);
}
/**
* Point-by-scalar multiplication. Scalar must be in range 1 <= n < CURVE.n.
* Uses {@link wNAF} for base point.
* Uses fake point to mitigate side-channel leakage.
* @param n scalar by which point is multiplied
* @param safe safe mode guards against timing attacks; unsafe mode is faster
*/
multiply(n, safe = true) {
if (!safe && (n === 0n || this.is0()))
return I;
arange(n, 1n, N);
if (n === 1n)
return this;
if (this.equals(G))
return wNAF(n).p;
// init result point & fake point
let p = I;
let f = G;
for (let d = this; n > 0n; d = d.double(), n >>= 1n) {
// if bit is present, add to point
// if not present, add to fake, for timing safety
if (n & 1n)
p = p.add(d);
else if (safe)
f = f.add(d);
}
return p;
}
/** Convert point to 2d xy affine point. (X, Y, Z) ∋ (x=X/Z, y=Y/Z) */
toAffine() {
const { ex: x, ey: y, ez: z } = this;
// fast-paths for ZERO point OR Z=1
if (this.equals(I))
return { x: 0n, y: 1n };
const iz = invert(z, P);
// (Z * Z^-1) must be 1, otherwise bad math
if (M(z * iz) !== 1n)
err('invalid inverse');
// x = X*Z^-1; y = Y*Z^-1
return { x: M(x * iz), y: M(y * iz) };
}
toBytes() {
const { x, y } = this.assertValidity().toAffine();
const b = numTo32bLE(y);
// store sign in first LE byte
b[31] |= x & 1n ? 0x80 : 0;
return b;
}
toHex() {
return bytesToHex(this.toBytes());
} // encode to hex string
clearCofactor() {
return this.multiply(big(h), false);
}
isSmallOrder() {
return this.clearCofactor().is0();
}
isTorsionFree() {
// multiply by big number CURVE.n
let p = this.multiply(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();
}
static fromHex(hex, zip215) {
return Point.fromBytes(toU8(hex), zip215);
}
get x() {
return this.toAffine().x;
}
get y() {
return this.toAffine().y;
}
toRawBytes() {
return this.toBytes();
}
}
/** Generator / base point */
const G = new Point(Gx, Gy, 1n, M(Gx * Gy));
/** Identity / zero point */
const I = new Point(0n, 1n, 1n, 0n);
// Static aliases
Point.BASE = G;
Point.ZERO = I;
const numTo32bLE = (num) => hexToBytes(padh(arange(num, 0n, B256), L2)).reverse();
const bytesToNumLE = (b) => big('0x' + bytesToHex(u8fr(abytes(b)).reverse()));
const pow2 = (x, power) => {
// pow2(x, 4) == x^(2^4)
let r = x;
while (power-- > 0n) {
r *= r;
r %= P;
}
return r;
};
// prettier-ignore
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 = 0x2b8324804fc1df0b2b4d00993dfbd7a72f431806ad2fe478c4ee1b274a0ea0b0n; // √-1
// for sqrt comp
// prettier-ignore
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 };
};
// N == L, just weird naming
const modL_LE = (hash) => modN(bytesToNumLE(hash)); // modulo L; but little-endian
const sha512a = (...m) => etc.sha512Async(...m); // Async SHA512
const sha512s = (...m) => callHash('sha512Sync')(...m);
// RFC8032 5.1.5
const hash2extK = (hashed) => {
// slice creates a copy, unlike subarray
const head = hashed.slice(0, L);
head[0] &= 248; // Clamp bits: 0b1111_1000
head[31] &= 127; // 0b0111_1111
head[31] |= 64; // 0b0100_0000
const prefix = hashed.slice(L, L2); // private key "prefix"
const scalar = modL_LE(head); // modular division over curve order
const point = G.multiply(scalar); // public key point
const pointBytes = point.toBytes(); // 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, L)).then(hash2extK);
const getExtendedPublicKey = (priv) => hash2extK(sha512s(toU8(priv, L)));
/** 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;
const hashFinishA = (res) => sha512a(res.hashable).then(res.finish);
const hashFinishS = (res) => res.finish(sha512s(res.hashable));
const _sign = (e, rBytes, msg) => {
// sign() shared code
const { pointBytes: P, scalar: s } = e;
const r = modL_LE(rBytes); // r was created outside, reduce it modulo L
const R = G.multiply(r).toBytes(); // R = [r]B
const hashable = concatBytes(R, P, msg); // dom2(F, C) || R || A || PH(M)
const finish = (hashed) => {
// k = SHA512(dom2(F, C) || R || A || PH(M))
const S = modN(r + modL_LE(hashed) * s); // S = (r + k * s) mod L; 0 <= s < l
return abytes(concatBytes(R, numTo32bLE(S)), L2); // 64-byte sig: 32b R.x + 32b LE(S)
};
return { hashable, finish };
};
/**
* Signs message (NOT message hash) using private key. Async.
* Follows RFC8032 5.1.6.
*/
const signAsync = async (msg, privKey) => {
const m = toU8(msg);
const e = await getExtendedPublicKeyAsync(privKey);
const rBytes = await sha512a(e.prefix, m); // r = SHA512(dom2(F, C) || prefix || PH(M))
return hashFinishA(_sign(e, rBytes, m)); // gen R, k, S, then 64-byte signature
};
/**
* Signs message (NOT message hash) using private key. To use, set `hashes.sha512` first.
* Follows RFC8032 5.1.6.
*/
const sign = (msg, privKey) => {
const m = toU8(msg);
const e = getExtendedPublicKey(privKey);
const rBytes = sha512s(e.prefix, m); // r = SHA512(dom2(F, C) || prefix || PH(M))
return hashFinishS(_sign(e, rBytes, m)); // gen R, k, S, then 64-byte signature
};
const veriOpts = { zip215: true };
const _verify = (sig, msg, pub, opts = veriOpts) => {
sig = toU8(sig, L2); // Signature hex str/Bytes, must be 64 bytes
msg = toU8(msg); // Message hex str/Bytes
pub = toU8(pub, L);
const { zip215 } = opts; // switch between zip215 and rfc8032 verif
let A;
let R;
let s;
let SB;
let hashable = Uint8Array.of();
try {
A = Point.fromHex(pub, zip215); // public key A decoded
R = Point.fromHex(sig.slice(0, L), zip215); // 0 <= R < 2^256: ZIP215 R can be >= P
s = bytesToNumLE(sig.slice(L, L2)); // Decode second half as an integer S
SB = G.multiply(s, false); // in the range 0 <= s < L
hashable = concatBytes(R.toBytes(), A.toBytes(), msg); // dom2(F, C) || R || A || PH(M)
}
catch (error) { }
const finish = (hashed) => {
// k = SHA512(dom2(F, C) || R || A || PH(M))
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.multiply(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 };
};
/** Verifies signature on message and public key. Async. Follows RFC8032 5.1.7. */
const verifyAsync = async (s, m, p, opts = veriOpts) => hashFinishA(_verify(s, m, p, opts));
/** Verifies signature on message and public key. To use, set `hashes.sha512` first. Follows RFC8032 5.1.7. */
const verify = (s, m, p, opts = veriOpts) => hashFinishS(_verify(s, m, p, opts));
/** Math, hex, byte helpers. Not in `utils` because utils share API with noble-curves. */
const etc = {
sha512Async: async (...messages) => {
const s = subtle();
const m = concatBytes(...messages);
return u8n(await s.digest('SHA-512', m.buffer));
},
sha512Sync: undefined,
bytesToHex: bytesToHex,
hexToBytes: hexToBytes,
concatBytes: concatBytes,
mod: M,
invert: invert,
randomBytes: randomBytes,
};
/** ed25519-specific key utilities. */
const utils = {
getExtendedPublicKeyAsync: getExtendedPublicKeyAsync,
getExtendedPublicKey: getExtendedPublicKey,
randomPrivateKey: () => randomBytes(L),
precompute: (w = 8, p = G) => {
p.multiply(3n);
w;
return p;
}, // no-op
};
// ## Precomputes
// --------------
const W = 8; // W is window size
const scalarBits = 256;
const pwindows = Math.ceil(scalarBits / W) + 1; // 33 for W=8
const pwindowSize = 2 ** (W - 1); // 128 for W=8
const precompute = () => {
const points = [];
let p = G;
let b = p;
for (let w = 0; w < pwindows; w++) {
b = p;
points.push(b);
for (let i = 1; i < pwindowSize; i++) {
b = b.add(p);
points.push(b);
} // i=1, bc we skip 0
p = b.double();
}
return points;
};
let Gpows = undefined; // precomputes for base point G
// const-time negate
const ctneg = (cnd, p) => {
const n = p.negate();
return cnd ? n : p;
};
/**
* Precomputes give 12x faster getPublicKey(), 10x sign(), 2x verify() by
* caching multiples of G (base point). Cache is stored in 32MB of RAM.
* Any time `G.multiply` is done, precomputes are used.
* Not used for getSharedSecret, which instead multiplies random pubkey `P.multiply`.
*
* w-ary non-adjacent form (wNAF) precomputation method is 10% slower than windowed method,
* but takes 2x less RAM. RAM reduction is possible by utilizing `.subtract`.
*
* !! Precomputes can be disabled by commenting-out call of the wNAF() inside Point#multiply().
*/
const wNAF = (n) => {
const comp = Gpows || (Gpows = precompute());
let p = I;
let f = G; // f must be G, or could become I in the end
const pow_2_w = 2 ** W; // 256 for W=8
const maxNum = pow_2_w; // 256 for W=8
const mask = big(pow_2_w - 1); // 255 for W=8 == mask 0b11111111
const shiftBy = big(W); // 8 for W=8
for (let w = 0; w < pwindows; w++) {
let wbits = Number(n & mask); // extract W bits.
n >>= shiftBy; // shift number by W bits.
if (wbits > pwindowSize) {
wbits -= maxNum;
n += 1n;
} // split if bits > max: +224 => 256-32
const off = w * pwindowSize;
const offF = off; // offsets, evaluate both
const offP = off + Math.abs(wbits) - 1;
const isEven = w % 2 !== 0; // conditions, evaluate both
const isNeg = wbits < 0;
if (wbits === 0) {
// off == I: can't add it. Adding random offF instead.
f = f.add(ctneg(isEven, comp[offF])); // bits are 0: add garbage to fake point
}
else {
p = p.add(ctneg(isNeg, comp[offP])); // bits are 1: add to result point
}
}
return { p, f }; // return both real and fake points for JIT
};
// !! Remove the export to easily use in REPL / browser console
export { ed25519_CURVE as CURVE, etc, Point as ExtendedPoint, getPublicKey, getPublicKeyAsync, Point, sign, signAsync, utils, verify, verifyAsync, };