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Текущая директория: /usr/lib/node_modules/bitgo/node_modules/@noble/curves/src
Просмотр файла: ed25519.ts
/**
* ed25519 Twisted Edwards curve with following addons:
* - X25519 ECDH
* - Ristretto cofactor elimination
* - Elligator hash-to-group / point indistinguishability
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { sha512 } from '@noble/hashes/sha2.js';
import { abytes, concatBytes, utf8ToBytes } from '@noble/hashes/utils.js';
import { pippenger, type AffinePoint } from './abstract/curve.ts';
import {
PrimeEdwardsPoint,
twistedEdwards,
type CurveFn,
type EdwardsOpts,
type EdwardsPoint,
} from './abstract/edwards.ts';
import {
_DST_scalar,
createHasher,
expand_message_xmd,
type H2CHasher,
type H2CHasherBase,
type H2CMethod,
type htfBasicOpts,
} from './abstract/hash-to-curve.ts';
import {
Field,
FpInvertBatch,
FpSqrtEven,
isNegativeLE,
mod,
pow2,
type IField,
} from './abstract/modular.ts';
import { montgomery, type MontgomeryECDH as XCurveFn } from './abstract/montgomery.ts';
import { bytesToNumberLE, ensureBytes, equalBytes, type Hex } from './utils.ts';
// prettier-ignore
const _0n = /* @__PURE__ */ BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);
// prettier-ignore
const _5n = BigInt(5), _8n = BigInt(8);
// P = 2n**255n-19n
const ed25519_CURVE_p = BigInt(
'0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed'
);
// N = 2n**252n + 27742317777372353535851937790883648493n
// a = Fp.create(BigInt(-1))
// d = -121665/121666 a.k.a. Fp.neg(121665 * Fp.inv(121666))
const ed25519_CURVE: EdwardsOpts = /* @__PURE__ */ (() => ({
p: ed25519_CURVE_p,
n: BigInt('0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed'),
h: _8n,
a: BigInt('0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec'),
d: BigInt('0x52036cee2b6ffe738cc740797779e89800700a4d4141d8ab75eb4dca135978a3'),
Gx: BigInt('0x216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51a'),
Gy: BigInt('0x6666666666666666666666666666666666666666666666666666666666666658'),
}))();
function ed25519_pow_2_252_3(x: bigint) {
// prettier-ignore
const _10n = BigInt(10), _20n = BigInt(20), _40n = BigInt(40), _80n = BigInt(80);
const P = ed25519_CURVE_p;
const x2 = (x * x) % P;
const b2 = (x2 * x) % P; // x^3, 11
const b4 = (pow2(b2, _2n, P) * b2) % P; // x^15, 1111
const b5 = (pow2(b4, _1n, P) * x) % P; // x^31
const b10 = (pow2(b5, _5n, P) * b5) % P;
const b20 = (pow2(b10, _10n, P) * b10) % P;
const b40 = (pow2(b20, _20n, P) * b20) % P;
const b80 = (pow2(b40, _40n, P) * b40) % P;
const b160 = (pow2(b80, _80n, P) * b80) % P;
const b240 = (pow2(b160, _80n, P) * b80) % P;
const b250 = (pow2(b240, _10n, P) * b10) % P;
const pow_p_5_8 = (pow2(b250, _2n, P) * x) % P;
// ^ To pow to (p+3)/8, multiply it by x.
return { pow_p_5_8, b2 };
}
function adjustScalarBytes(bytes: Uint8Array): Uint8Array {
// 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
bytes[0] &= 248; // 0b1111_1000
// and the most significant bit of the last to zero,
bytes[31] &= 127; // 0b0111_1111
// set the second most significant bit of the last byte to 1
bytes[31] |= 64; // 0b0100_0000
return bytes;
}
// √(-1) aka √(a) aka 2^((p-1)/4)
// Fp.sqrt(Fp.neg(1))
const ED25519_SQRT_M1 = /* @__PURE__ */ BigInt(
'19681161376707505956807079304988542015446066515923890162744021073123829784752'
);
// sqrt(u/v)
function uvRatio(u: bigint, v: bigint): { isValid: boolean; value: bigint } {
const P = ed25519_CURVE_p;
const v3 = mod(v * v * v, P); // v³
const v7 = mod(v3 * v3 * v, P); // v⁷
// (p+3)/8 and (p-5)/8
const pow = ed25519_pow_2_252_3(u * v7).pow_p_5_8;
let x = mod(u * v3 * pow, P); // (uv³)(uv⁷)^(p-5)/8
const vx2 = mod(v * x * x, P); // vx²
const root1 = x; // First root candidate
const root2 = mod(x * ED25519_SQRT_M1, P); // Second root candidate
const useRoot1 = vx2 === u; // If vx² = u (mod p), x is a square root
const useRoot2 = vx2 === mod(-u, P); // If vx² = -u, set x <-- x * 2^((p-1)/4)
const noRoot = vx2 === mod(-u * ED25519_SQRT_M1, P); // 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 (isNegativeLE(x, P)) x = mod(-x, P);
return { isValid: useRoot1 || useRoot2, value: x };
}
const Fp = /* @__PURE__ */ (() => Field(ed25519_CURVE.p, { isLE: true }))();
const Fn = /* @__PURE__ */ (() => Field(ed25519_CURVE.n, { isLE: true }))();
const ed25519Defaults = /* @__PURE__ */ (() => ({
...ed25519_CURVE,
Fp,
hash: sha512,
adjustScalarBytes,
// dom2
// Ratio of u to v. Allows us to combine inversion and square root. Uses algo from RFC8032 5.1.3.
// Constant-time, u/√v
uvRatio,
}))();
/**
* ed25519 curve with EdDSA signatures.
* @example
* import { ed25519 } from '@noble/curves/ed25519';
* const { secretKey, publicKey } = ed25519.keygen();
* const msg = new TextEncoder().encode('hello');
* const sig = ed25519.sign(msg, priv);
* ed25519.verify(sig, msg, pub); // Default mode: follows ZIP215
* ed25519.verify(sig, msg, pub, { zip215: false }); // RFC8032 / FIPS 186-5
*/
export const ed25519: CurveFn = /* @__PURE__ */ (() => twistedEdwards(ed25519Defaults))();
function ed25519_domain(data: Uint8Array, ctx: Uint8Array, phflag: boolean) {
if (ctx.length > 255) throw new Error('Context is too big');
return concatBytes(
utf8ToBytes('SigEd25519 no Ed25519 collisions'),
new Uint8Array([phflag ? 1 : 0, ctx.length]),
ctx,
data
);
}
/** Context of ed25519. Uses context for domain separation. */
export const ed25519ctx: CurveFn = /* @__PURE__ */ (() =>
twistedEdwards({
...ed25519Defaults,
domain: ed25519_domain,
}))();
/** Prehashed version of ed25519. Accepts already-hashed messages in sign() and verify(). */
export const ed25519ph: CurveFn = /* @__PURE__ */ (() =>
twistedEdwards(
Object.assign({}, ed25519Defaults, {
domain: ed25519_domain,
prehash: sha512,
})
))();
/**
* ECDH using curve25519 aka x25519.
* @example
* import { x25519 } from '@noble/curves/ed25519';
* const priv = 'a546e36bf0527c9d3b16154b82465edd62144c0ac1fc5a18506a2244ba449ac4';
* const pub = 'e6db6867583030db3594c1a424b15f7c726624ec26b3353b10a903a6d0ab1c4c';
* x25519.getSharedSecret(priv, pub) === x25519.scalarMult(priv, pub); // aliases
* x25519.getPublicKey(priv) === x25519.scalarMultBase(priv);
* x25519.getPublicKey(x25519.utils.randomSecretKey());
*/
export const x25519: XCurveFn = /* @__PURE__ */ (() => {
const P = Fp.ORDER;
return montgomery({
P,
type: 'x25519',
powPminus2: (x: bigint): bigint => {
// x^(p-2) aka x^(2^255-21)
const { pow_p_5_8, b2 } = ed25519_pow_2_252_3(x);
return mod(pow2(pow_p_5_8, _3n, P) * b2, P);
},
adjustScalarBytes,
});
})();
// Hash To Curve Elligator2 Map (NOTE: different from ristretto255 elligator)
// NOTE: very important part is usage of FpSqrtEven for ELL2_C1_EDWARDS, since
// SageMath returns different root first and everything falls apart
const ELL2_C1 = /* @__PURE__ */ (() => (ed25519_CURVE_p + _3n) / _8n)(); // 1. c1 = (q + 3) / 8 # Integer arithmetic
const ELL2_C2 = /* @__PURE__ */ (() => Fp.pow(_2n, ELL2_C1))(); // 2. c2 = 2^c1
const ELL2_C3 = /* @__PURE__ */ (() => Fp.sqrt(Fp.neg(Fp.ONE)))(); // 3. c3 = sqrt(-1)
// prettier-ignore
function map_to_curve_elligator2_curve25519(u: bigint) {
const ELL2_C4 = (ed25519_CURVE_p - _5n) / _8n; // 4. c4 = (q - 5) / 8 # Integer arithmetic
const ELL2_J = BigInt(486662);
let tv1 = Fp.sqr(u); // 1. tv1 = u^2
tv1 = Fp.mul(tv1, _2n); // 2. tv1 = 2 * tv1
let xd = Fp.add(tv1, Fp.ONE); // 3. xd = tv1 + 1 # Nonzero: -1 is square (mod p), tv1 is not
let x1n = Fp.neg(ELL2_J); // 4. x1n = -J # x1 = x1n / xd = -J / (1 + 2 * u^2)
let tv2 = Fp.sqr(xd); // 5. tv2 = xd^2
let gxd = Fp.mul(tv2, xd); // 6. gxd = tv2 * xd # gxd = xd^3
let gx1 = Fp.mul(tv1, ELL2_J);// 7. gx1 = J * tv1 # x1n + J * xd
gx1 = Fp.mul(gx1, x1n); // 8. gx1 = gx1 * x1n # x1n^2 + J * x1n * xd
gx1 = Fp.add(gx1, tv2); // 9. gx1 = gx1 + tv2 # x1n^2 + J * x1n * xd + xd^2
gx1 = Fp.mul(gx1, x1n); // 10. gx1 = gx1 * x1n # x1n^3 + J * x1n^2 * xd + x1n * xd^2
let tv3 = Fp.sqr(gxd); // 11. tv3 = gxd^2
tv2 = Fp.sqr(tv3); // 12. tv2 = tv3^2 # gxd^4
tv3 = Fp.mul(tv3, gxd); // 13. tv3 = tv3 * gxd # gxd^3
tv3 = Fp.mul(tv3, gx1); // 14. tv3 = tv3 * gx1 # gx1 * gxd^3
tv2 = Fp.mul(tv2, tv3); // 15. tv2 = tv2 * tv3 # gx1 * gxd^7
let y11 = Fp.pow(tv2, ELL2_C4); // 16. y11 = tv2^c4 # (gx1 * gxd^7)^((p - 5) / 8)
y11 = Fp.mul(y11, tv3); // 17. y11 = y11 * tv3 # gx1*gxd^3*(gx1*gxd^7)^((p-5)/8)
let y12 = Fp.mul(y11, ELL2_C3); // 18. y12 = y11 * c3
tv2 = Fp.sqr(y11); // 19. tv2 = y11^2
tv2 = Fp.mul(tv2, gxd); // 20. tv2 = tv2 * gxd
let e1 = Fp.eql(tv2, gx1); // 21. e1 = tv2 == gx1
let y1 = Fp.cmov(y12, y11, e1); // 22. y1 = CMOV(y12, y11, e1) # If g(x1) is square, this is its sqrt
let x2n = Fp.mul(x1n, tv1); // 23. x2n = x1n * tv1 # x2 = x2n / xd = 2 * u^2 * x1n / xd
let y21 = Fp.mul(y11, u); // 24. y21 = y11 * u
y21 = Fp.mul(y21, ELL2_C2); // 25. y21 = y21 * c2
let y22 = Fp.mul(y21, ELL2_C3); // 26. y22 = y21 * c3
let gx2 = Fp.mul(gx1, tv1); // 27. gx2 = gx1 * tv1 # g(x2) = gx2 / gxd = 2 * u^2 * g(x1)
tv2 = Fp.sqr(y21); // 28. tv2 = y21^2
tv2 = Fp.mul(tv2, gxd); // 29. tv2 = tv2 * gxd
let e2 = Fp.eql(tv2, gx2); // 30. e2 = tv2 == gx2
let y2 = Fp.cmov(y22, y21, e2); // 31. y2 = CMOV(y22, y21, e2) # If g(x2) is square, this is its sqrt
tv2 = Fp.sqr(y1); // 32. tv2 = y1^2
tv2 = Fp.mul(tv2, gxd); // 33. tv2 = tv2 * gxd
let e3 = Fp.eql(tv2, gx1); // 34. e3 = tv2 == gx1
let xn = Fp.cmov(x2n, x1n, e3); // 35. xn = CMOV(x2n, x1n, e3) # If e3, x = x1, else x = x2
let y = Fp.cmov(y2, y1, e3); // 36. y = CMOV(y2, y1, e3) # If e3, y = y1, else y = y2
let e4 = Fp.isOdd!(y); // 37. e4 = sgn0(y) == 1 # Fix sign of y
y = Fp.cmov(y, Fp.neg(y), e3 !== e4); // 38. y = CMOV(y, -y, e3 XOR e4)
return { xMn: xn, xMd: xd, yMn: y, yMd: _1n }; // 39. return (xn, xd, y, 1)
}
const ELL2_C1_EDWARDS = /* @__PURE__ */ (() => FpSqrtEven(Fp, Fp.neg(BigInt(486664))))(); // sgn0(c1) MUST equal 0
function map_to_curve_elligator2_edwards25519(u: bigint) {
const { xMn, xMd, yMn, yMd } = map_to_curve_elligator2_curve25519(u); // 1. (xMn, xMd, yMn, yMd) =
// map_to_curve_elligator2_curve25519(u)
let xn = Fp.mul(xMn, yMd); // 2. xn = xMn * yMd
xn = Fp.mul(xn, ELL2_C1_EDWARDS); // 3. xn = xn * c1
let xd = Fp.mul(xMd, yMn); // 4. xd = xMd * yMn # xn / xd = c1 * xM / yM
let yn = Fp.sub(xMn, xMd); // 5. yn = xMn - xMd
let yd = Fp.add(xMn, xMd); // 6. yd = xMn + xMd # (n / d - 1) / (n / d + 1) = (n - d) / (n + d)
let tv1 = Fp.mul(xd, yd); // 7. tv1 = xd * yd
let e = Fp.eql(tv1, Fp.ZERO); // 8. e = tv1 == 0
xn = Fp.cmov(xn, Fp.ZERO, e); // 9. xn = CMOV(xn, 0, e)
xd = Fp.cmov(xd, Fp.ONE, e); // 10. xd = CMOV(xd, 1, e)
yn = Fp.cmov(yn, Fp.ONE, e); // 11. yn = CMOV(yn, 1, e)
yd = Fp.cmov(yd, Fp.ONE, e); // 12. yd = CMOV(yd, 1, e)
const [xd_inv, yd_inv] = FpInvertBatch(Fp, [xd, yd], true); // batch division
return { x: Fp.mul(xn, xd_inv), y: Fp.mul(yn, yd_inv) }; // 13. return (xn, xd, yn, yd)
}
/** Hashing to ed25519 points / field. RFC 9380 methods. */
export const ed25519_hasher: H2CHasher<bigint> = /* @__PURE__ */ (() =>
createHasher(
ed25519.Point,
(scalars: bigint[]) => map_to_curve_elligator2_edwards25519(scalars[0]),
{
DST: 'edwards25519_XMD:SHA-512_ELL2_RO_',
encodeDST: 'edwards25519_XMD:SHA-512_ELL2_NU_',
p: ed25519_CURVE_p,
m: 1,
k: 128,
expand: 'xmd',
hash: sha512,
}
))();
// √(-1) aka √(a) aka 2^((p-1)/4)
const SQRT_M1 = ED25519_SQRT_M1;
// √(ad - 1)
const SQRT_AD_MINUS_ONE = /* @__PURE__ */ BigInt(
'25063068953384623474111414158702152701244531502492656460079210482610430750235'
);
// 1 / √(a-d)
const INVSQRT_A_MINUS_D = /* @__PURE__ */ BigInt(
'54469307008909316920995813868745141605393597292927456921205312896311721017578'
);
// 1-d²
const ONE_MINUS_D_SQ = /* @__PURE__ */ BigInt(
'1159843021668779879193775521855586647937357759715417654439879720876111806838'
);
// (d-1)²
const D_MINUS_ONE_SQ = /* @__PURE__ */ BigInt(
'40440834346308536858101042469323190826248399146238708352240133220865137265952'
);
// Calculates 1/√(number)
const invertSqrt = (number: bigint) => uvRatio(_1n, number);
const MAX_255B = /* @__PURE__ */ BigInt(
'0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff'
);
const bytes255ToNumberLE = (bytes: Uint8Array) =>
ed25519.Point.Fp.create(bytesToNumberLE(bytes) & MAX_255B);
type ExtendedPoint = EdwardsPoint;
/**
* Computes Elligator map for Ristretto255.
* Described in [RFC9380](https://www.rfc-editor.org/rfc/rfc9380#appendix-B) and on
* the [website](https://ristretto.group/formulas/elligator.html).
*/
function calcElligatorRistrettoMap(r0: bigint): ExtendedPoint {
const { d } = ed25519_CURVE;
const P = ed25519_CURVE_p;
const mod = (n: bigint) => Fp.create(n);
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 (!isNegativeLE(s_, P)) 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 ed25519.Point(mod(W0 * W3), mod(W2 * W1), mod(W1 * W3), mod(W0 * W2));
}
function ristretto255_map(bytes: Uint8Array): _RistrettoPoint {
abytes(bytes, 64);
const r1 = bytes255ToNumberLE(bytes.subarray(0, 32));
const R1 = calcElligatorRistrettoMap(r1);
const r2 = bytes255ToNumberLE(bytes.subarray(32, 64));
const R2 = calcElligatorRistrettoMap(r2);
return new _RistrettoPoint(R1.add(R2));
}
/**
* Wrapper over Edwards Point for ristretto255.
*
* Each ed25519/ExtendedPoint has 8 different equivalent points. This can be
* a source of bugs for protocols like ring signatures. Ristretto was created to solve this.
* Ristretto point operates in X:Y:Z:T extended coordinates like ExtendedPoint,
* but it should work in its own namespace: do not combine those two.
* See [RFC9496](https://www.rfc-editor.org/rfc/rfc9496).
*/
class _RistrettoPoint extends PrimeEdwardsPoint<_RistrettoPoint> {
// Do NOT change syntax: the following gymnastics is done,
// because typescript strips comments, which makes bundlers disable tree-shaking.
// prettier-ignore
static BASE: _RistrettoPoint =
/* @__PURE__ */ (() => new _RistrettoPoint(ed25519.Point.BASE))();
// prettier-ignore
static ZERO: _RistrettoPoint =
/* @__PURE__ */ (() => new _RistrettoPoint(ed25519.Point.ZERO))();
// prettier-ignore
static Fp: IField<bigint> =
/* @__PURE__ */ (() => Fp)();
// prettier-ignore
static Fn: IField<bigint> =
/* @__PURE__ */ (() => Fn)();
constructor(ep: ExtendedPoint) {
super(ep);
}
static fromAffine(ap: AffinePoint<bigint>): _RistrettoPoint {
return new _RistrettoPoint(ed25519.Point.fromAffine(ap));
}
protected assertSame(other: _RistrettoPoint): void {
if (!(other instanceof _RistrettoPoint)) throw new Error('RistrettoPoint expected');
}
protected init(ep: EdwardsPoint): _RistrettoPoint {
return new _RistrettoPoint(ep);
}
/** @deprecated use `import { ristretto255_hasher } from '@noble/curves/ed25519.js';` */
static hashToCurve(hex: Hex): _RistrettoPoint {
return ristretto255_map(ensureBytes('ristrettoHash', hex, 64));
}
static fromBytes(bytes: Uint8Array): _RistrettoPoint {
abytes(bytes, 32);
const { a, d } = ed25519_CURVE;
const P = ed25519_CURVE_p;
const mod = (n: bigint) => Fp.create(n);
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(Fp.toBytes(s), bytes) || isNegativeLE(s, P))
throw new Error('invalid ristretto255 encoding 1');
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 (isNegativeLE(x, P)) x = mod(-x); // 10
const y = mod(u1 * Dy); // 11
const t = mod(x * y); // 12
if (!isValid || isNegativeLE(t, P) || y === _0n)
throw new Error('invalid ristretto255 encoding 2');
return new _RistrettoPoint(new ed25519.Point(x, y, _1n, t));
}
/**
* Converts ristretto-encoded string to ristretto point.
* Described in [RFC9496](https://www.rfc-editor.org/rfc/rfc9496#name-decode).
* @param hex Ristretto-encoded 32 bytes. Not every 32-byte string is valid ristretto encoding
*/
static fromHex(hex: Hex): _RistrettoPoint {
return _RistrettoPoint.fromBytes(ensureBytes('ristrettoHex', hex, 32));
}
static msm(points: _RistrettoPoint[], scalars: bigint[]): _RistrettoPoint {
return pippenger(_RistrettoPoint, ed25519.Point.Fn, points, scalars);
}
/**
* Encodes ristretto point to Uint8Array.
* Described in [RFC9496](https://www.rfc-editor.org/rfc/rfc9496#name-encode).
*/
toBytes(): Uint8Array {
let { X, Y, Z, T } = this.ep;
const P = ed25519_CURVE_p;
const mod = (n: bigint) => Fp.create(n);
const u1 = mod(mod(Z + Y) * mod(Z - Y)); // 1
const u2 = mod(X * Y); // 2
// Square root always exists
const u2sq = mod(u2 * u2);
const { value: invsqrt } = invertSqrt(mod(u1 * u2sq)); // 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 (isNegativeLE(T * zInv, P)) {
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 (isNegativeLE(X * zInv, P)) Y = mod(-Y); // 9
let s = mod((Z - Y) * D); // 10 (check footer's note, no sqrt(-a))
if (isNegativeLE(s, P)) s = mod(-s);
return Fp.toBytes(s); // 11
}
/**
* Compares two Ristretto points.
* Described in [RFC9496](https://www.rfc-editor.org/rfc/rfc9496#name-equals).
*/
equals(other: _RistrettoPoint): boolean {
this.assertSame(other);
const { X: X1, Y: Y1 } = this.ep;
const { X: X2, Y: Y2 } = other.ep;
const mod = (n: bigint) => Fp.create(n);
// (x1 * y2 == y1 * x2) | (y1 * y2 == x1 * x2)
const one = mod(X1 * Y2) === mod(Y1 * X2);
const two = mod(Y1 * Y2) === mod(X1 * X2);
return one || two;
}
is0(): boolean {
return this.equals(_RistrettoPoint.ZERO);
}
}
export const ristretto255: {
Point: typeof _RistrettoPoint;
} = { Point: _RistrettoPoint };
/** Hashing to ristretto255 points / field. RFC 9380 methods. */
export const ristretto255_hasher: H2CHasherBase<bigint> = {
hashToCurve(msg: Uint8Array, options?: htfBasicOpts): _RistrettoPoint {
const DST = options?.DST || 'ristretto255_XMD:SHA-512_R255MAP_RO_';
const xmd = expand_message_xmd(msg, DST, 64, sha512);
return ristretto255_map(xmd);
},
hashToScalar(msg: Uint8Array, options: htfBasicOpts = { DST: _DST_scalar }) {
const xmd = expand_message_xmd(msg, options.DST, 64, sha512);
return Fn.create(bytesToNumberLE(xmd));
},
};
// export const ristretto255_oprf: OPRF = createORPF({
// name: 'ristretto255-SHA512',
// Point: RistrettoPoint,
// hash: sha512,
// hashToGroup: ristretto255_hasher.hashToCurve,
// hashToScalar: ristretto255_hasher.hashToScalar,
// });
/**
* Weird / bogus points, useful for debugging.
* All 8 ed25519 points of 8-torsion subgroup can be generated from the point
* T = `26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc05`.
* ⟨T⟩ = { O, T, 2T, 3T, 4T, 5T, 6T, 7T }
*/
export const ED25519_TORSION_SUBGROUP: string[] = [
'0100000000000000000000000000000000000000000000000000000000000000',
'c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac037a',
'0000000000000000000000000000000000000000000000000000000000000080',
'26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc05',
'ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f',
'26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc85',
'0000000000000000000000000000000000000000000000000000000000000000',
'c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa',
];
/** @deprecated use `ed25519.utils.toMontgomery` */
export function edwardsToMontgomeryPub(edwardsPub: Hex): Uint8Array {
return ed25519.utils.toMontgomery(ensureBytes('pub', edwardsPub));
}
/** @deprecated use `ed25519.utils.toMontgomery` */
export const edwardsToMontgomery: typeof edwardsToMontgomeryPub = edwardsToMontgomeryPub;
/** @deprecated use `ed25519.utils.toMontgomerySecret` */
export function edwardsToMontgomeryPriv(edwardsPriv: Uint8Array): Uint8Array {
return ed25519.utils.toMontgomerySecret(ensureBytes('pub', edwardsPriv));
}
/** @deprecated use `ristretto255.Point` */
export const RistrettoPoint: typeof _RistrettoPoint = _RistrettoPoint;
/** @deprecated use `import { ed25519_hasher } from '@noble/curves/ed25519.js';` */
export const hashToCurve: H2CMethod<bigint> = /* @__PURE__ */ (() => ed25519_hasher.hashToCurve)();
/** @deprecated use `import { ed25519_hasher } from '@noble/curves/ed25519.js';` */
export const encodeToCurve: H2CMethod<bigint> = /* @__PURE__ */ (() =>
ed25519_hasher.encodeToCurve)();
type RistHasher = (msg: Uint8Array, options: htfBasicOpts) => _RistrettoPoint;
/** @deprecated use `import { ristretto255_hasher } from '@noble/curves/ed25519.js';` */
export const hashToRistretto255: RistHasher = /* @__PURE__ */ (() =>
ristretto255_hasher.hashToCurve as RistHasher)();
/** @deprecated use `import { ristretto255_hasher } from '@noble/curves/ed25519.js';` */
export const hash_to_ristretto255: RistHasher = /* @__PURE__ */ (() =>
ristretto255_hasher.hashToCurve as RistHasher)();
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Для локальной разработки. Не используйте в интернете!