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"use strict";
Object.defineProperty(exports, "__esModule", { value: true });
exports.hash_to_ristretto255 = exports.hashToRistretto255 = exports.RistrettoPoint = exports.encodeToCurve = exports.hashToCurve = exports.edwardsToMontgomery = exports.x25519 = exports.ed25519ph = exports.ed25519ctx = exports.ed25519 = exports.ED25519_TORSION_SUBGROUP = void 0;
exports.edwardsToMontgomeryPub = edwardsToMontgomeryPub;
exports.edwardsToMontgomeryPriv = edwardsToMontgomeryPriv;
/**
* 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) */
const sha512_1 = require("@noble/hashes/sha512");
const utils_1 = require("@noble/hashes/utils");
const curve_js_1 = require("./abstract/curve.js");
const edwards_js_1 = require("./abstract/edwards.js");
const hash_to_curve_js_1 = require("./abstract/hash-to-curve.js");
const modular_js_1 = require("./abstract/modular.js");
const montgomery_js_1 = require("./abstract/montgomery.js");
const utils_js_1 = require("./abstract/utils.js");
const ED25519_P = BigInt('57896044618658097711785492504343953926634992332820282019728792003956564819949');
// √(-1) aka √(a) aka 2^((p-1)/4)
const ED25519_SQRT_M1 = /* @__PURE__ */ BigInt('19681161376707505956807079304988542015446066515923890162744021073123829784752');
// prettier-ignore
const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);
// prettier-ignore
const _5n = BigInt(5), _8n = BigInt(8);
function ed25519_pow_2_252_3(x) {
// prettier-ignore
const _10n = BigInt(10), _20n = BigInt(20), _40n = BigInt(40), _80n = BigInt(80);
const P = ED25519_P;
const x2 = (x * x) % P;
const b2 = (x2 * x) % P; // x^3, 11
const b4 = ((0, modular_js_1.pow2)(b2, _2n, P) * b2) % P; // x^15, 1111
const b5 = ((0, modular_js_1.pow2)(b4, _1n, P) * x) % P; // x^31
const b10 = ((0, modular_js_1.pow2)(b5, _5n, P) * b5) % P;
const b20 = ((0, modular_js_1.pow2)(b10, _10n, P) * b10) % P;
const b40 = ((0, modular_js_1.pow2)(b20, _20n, P) * b20) % P;
const b80 = ((0, modular_js_1.pow2)(b40, _40n, P) * b40) % P;
const b160 = ((0, modular_js_1.pow2)(b80, _80n, P) * b80) % P;
const b240 = ((0, modular_js_1.pow2)(b160, _80n, P) * b80) % P;
const b250 = ((0, modular_js_1.pow2)(b240, _10n, P) * b10) % P;
const pow_p_5_8 = ((0, modular_js_1.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) {
// 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;
}
// sqrt(u/v)
function uvRatio(u, v) {
const P = ED25519_P;
const v3 = (0, modular_js_1.mod)(v * v * v, P); // v³
const v7 = (0, modular_js_1.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 = (0, modular_js_1.mod)(u * v3 * pow, P); // (uv³)(uv⁷)^(p-5)/8
const vx2 = (0, modular_js_1.mod)(v * x * x, P); // vx²
const root1 = x; // First root candidate
const root2 = (0, modular_js_1.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 === (0, modular_js_1.mod)(-u, P); // If vx² = -u, set x <-- x * 2^((p-1)/4)
const noRoot = vx2 === (0, modular_js_1.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 ((0, modular_js_1.isNegativeLE)(x, P))
x = (0, modular_js_1.mod)(-x, P);
return { isValid: useRoot1 || useRoot2, value: x };
}
// Just in case
exports.ED25519_TORSION_SUBGROUP = [
'0100000000000000000000000000000000000000000000000000000000000000',
'c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac037a',
'0000000000000000000000000000000000000000000000000000000000000080',
'26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc05',
'ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f',
'26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc85',
'0000000000000000000000000000000000000000000000000000000000000000',
'c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa',
];
const Fp = /* @__PURE__ */ (() => (0, modular_js_1.Field)(ED25519_P, undefined, true))();
const ed25519Defaults = /* @__PURE__ */ (() => ({
// Param: a
a: BigInt(-1), // Fp.create(-1) is proper; our way still works and is faster
// d is 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; 2n**255n - 19n
Fp,
// Subgroup order: how many points curve has
// 2n**252n + 27742317777372353535851937790883648493n;
n: BigInt('7237005577332262213973186563042994240857116359379907606001950938285454250989'),
// Cofactor
h: _8n,
// Base point (x, y) aka generator point
Gx: BigInt('15112221349535400772501151409588531511454012693041857206046113283949847762202'),
Gy: BigInt('46316835694926478169428394003475163141307993866256225615783033603165251855960'),
hash: sha512_1.sha512,
randomBytes: utils_1.randomBytes,
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 priv = ed25519.utils.randomPrivateKey();
* const pub = ed25519.getPublicKey(priv);
* 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
*/
exports.ed25519 = (() => (0, edwards_js_1.twistedEdwards)(ed25519Defaults))();
function ed25519_domain(data, ctx, phflag) {
if (ctx.length > 255)
throw new Error('Context is too big');
return (0, utils_1.concatBytes)((0, utils_1.utf8ToBytes)('SigEd25519 no Ed25519 collisions'), new Uint8Array([phflag ? 1 : 0, ctx.length]), ctx, data);
}
exports.ed25519ctx = (() => (0, edwards_js_1.twistedEdwards)({
...ed25519Defaults,
domain: ed25519_domain,
}))();
exports.ed25519ph = (() => (0, edwards_js_1.twistedEdwards)(Object.assign({}, ed25519Defaults, {
domain: ed25519_domain,
prehash: sha512_1.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.randomPrivateKey());
*/
exports.x25519 = (() => (0, montgomery_js_1.montgomery)({
P: ED25519_P,
a: BigInt(486662),
montgomeryBits: 255, // n is 253 bits
nByteLength: 32,
Gu: BigInt(9),
powPminus2: (x) => {
const P = ED25519_P;
// x^(p-2) aka x^(2^255-21)
const { pow_p_5_8, b2 } = ed25519_pow_2_252_3(x);
return (0, modular_js_1.mod)((0, modular_js_1.pow2)(pow_p_5_8, _3n, P) * b2, P);
},
adjustScalarBytes,
randomBytes: utils_1.randomBytes,
}))();
/**
* Converts ed25519 public key to x25519 public key. Uses formula:
* * `(u, v) = ((1+y)/(1-y), sqrt(-486664)*u/x)`
* * `(x, y) = (sqrt(-486664)*u/v, (u-1)/(u+1))`
* @example
* const someonesPub = ed25519.getPublicKey(ed25519.utils.randomPrivateKey());
* const aPriv = x25519.utils.randomPrivateKey();
* x25519.getSharedSecret(aPriv, edwardsToMontgomeryPub(someonesPub))
*/
function edwardsToMontgomeryPub(edwardsPub) {
const { y } = exports.ed25519.ExtendedPoint.fromHex(edwardsPub);
const _1n = BigInt(1);
return Fp.toBytes(Fp.create((_1n + y) * Fp.inv(_1n - y)));
}
exports.edwardsToMontgomery = edwardsToMontgomeryPub; // deprecated
/**
* Converts ed25519 secret key to x25519 secret key.
* @example
* const someonesPub = x25519.getPublicKey(x25519.utils.randomPrivateKey());
* const aPriv = ed25519.utils.randomPrivateKey();
* x25519.getSharedSecret(edwardsToMontgomeryPriv(aPriv), someonesPub)
*/
function edwardsToMontgomeryPriv(edwardsPriv) {
const hashed = ed25519Defaults.hash(edwardsPriv.subarray(0, 32));
return ed25519Defaults.adjustScalarBytes(hashed).subarray(0, 32);
}
// 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__ */ (() => (Fp.ORDER + _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) {
const ELL2_C4 = (Fp.ORDER - _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__ */ (() => (0, modular_js_1.FpSqrtEven)(Fp, Fp.neg(BigInt(486664))))(); // sgn0(c1) MUST equal 0
function map_to_curve_elligator2_edwards25519(u) {
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 inv = Fp.invertBatch([xd, yd]); // batch division
return { x: Fp.mul(xn, inv[0]), y: Fp.mul(yn, inv[1]) }; // 13. return (xn, xd, yn, yd)
}
const htf = /* @__PURE__ */ (() => (0, hash_to_curve_js_1.createHasher)(exports.ed25519.ExtendedPoint, (scalars) => map_to_curve_elligator2_edwards25519(scalars[0]), {
DST: 'edwards25519_XMD:SHA-512_ELL2_RO_',
encodeDST: 'edwards25519_XMD:SHA-512_ELL2_NU_',
p: Fp.ORDER,
m: 1,
k: 128,
expand: 'xmd',
hash: sha512_1.sha512,
}))();
exports.hashToCurve = (() => htf.hashToCurve)();
exports.encodeToCurve = (() => htf.encodeToCurve)();
function assertRstPoint(other) {
if (!(other instanceof RistPoint))
throw new Error('RistrettoPoint expected');
}
// √(-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) => uvRatio(_1n, number);
const MAX_255B = /* @__PURE__ */ BigInt('0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff');
const bytes255ToNumberLE = (bytes) => exports.ed25519.CURVE.Fp.create((0, utils_js_1.bytesToNumberLE)(bytes) & MAX_255B);
// Computes Elligator map for Ristretto
// https://ristretto.group/formulas/elligator.html
function calcElligatorRistrettoMap(r0) {
const { d } = exports.ed25519.CURVE;
const P = exports.ed25519.CURVE.Fp.ORDER;
const mod = exports.ed25519.CURVE.Fp.create;
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 (!(0, modular_js_1.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 exports.ed25519.ExtendedPoint(mod(W0 * W3), mod(W2 * W1), mod(W1 * W3), mod(W0 * W2));
}
/**
* 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.
* https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-ristretto255-decaf448
*/
class RistPoint {
// Private property to discourage combining ExtendedPoint + RistrettoPoint
// Always use Ristretto encoding/decoding instead.
constructor(ep) {
this.ep = ep;
}
static fromAffine(ap) {
return new RistPoint(exports.ed25519.ExtendedPoint.fromAffine(ap));
}
/**
* Takes uniform output of 64-byte hash function like sha512 and converts it to `RistrettoPoint`.
* The hash-to-group operation applies Elligator twice and adds the results.
* **Note:** this is one-way map, there is no conversion from point to hash.
* https://ristretto.group/formulas/elligator.html
* @param hex 64-byte output of a hash function
*/
static hashToCurve(hex) {
hex = (0, utils_js_1.ensureBytes)('ristrettoHash', hex, 64);
const r1 = bytes255ToNumberLE(hex.slice(0, 32));
const R1 = calcElligatorRistrettoMap(r1);
const r2 = bytes255ToNumberLE(hex.slice(32, 64));
const R2 = calcElligatorRistrettoMap(r2);
return new RistPoint(R1.add(R2));
}
/**
* Converts ristretto-encoded string to ristretto point.
* https://ristretto.group/formulas/decoding.html
* @param hex Ristretto-encoded 32 bytes. Not every 32-byte string is valid ristretto encoding
*/
static fromHex(hex) {
hex = (0, utils_js_1.ensureBytes)('ristrettoHex', hex, 32);
const { a, d } = exports.ed25519.CURVE;
const P = exports.ed25519.CURVE.Fp.ORDER;
const mod = exports.ed25519.CURVE.Fp.create;
const emsg = 'RistrettoPoint.fromHex: the hex is not valid encoding of RistrettoPoint';
const s = bytes255ToNumberLE(hex);
// 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 (!(0, utils_js_1.equalBytes)((0, utils_js_1.numberToBytesLE)(s, 32), hex) || (0, modular_js_1.isNegativeLE)(s, P))
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 ((0, modular_js_1.isNegativeLE)(x, P))
x = mod(-x); // 10
const y = mod(u1 * Dy); // 11
const t = mod(x * y); // 12
if (!isValid || (0, modular_js_1.isNegativeLE)(t, P) || y === _0n)
throw new Error(emsg);
return new RistPoint(new exports.ed25519.ExtendedPoint(x, y, _1n, t));
}
static msm(points, scalars) {
const Fn = (0, modular_js_1.Field)(exports.ed25519.CURVE.n, exports.ed25519.CURVE.nBitLength);
return (0, curve_js_1.pippenger)(RistPoint, Fn, points, scalars);
}
/**
* Encodes ristretto point to Uint8Array.
* https://ristretto.group/formulas/encoding.html
*/
toRawBytes() {
let { ex: x, ey: y, ez: z, et: t } = this.ep;
const P = exports.ed25519.CURVE.Fp.ORDER;
const mod = exports.ed25519.CURVE.Fp.create;
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; // 7
if ((0, modular_js_1.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 ((0, modular_js_1.isNegativeLE)(x * zInv, P))
y = mod(-y); // 9
let s = mod((z - y) * D); // 10 (check footer's note, no sqrt(-a))
if ((0, modular_js_1.isNegativeLE)(s, P))
s = mod(-s);
return (0, utils_js_1.numberToBytesLE)(s, 32); // 11
}
toHex() {
return (0, utils_js_1.bytesToHex)(this.toRawBytes());
}
toString() {
return this.toHex();
}
// Compare one point to another.
equals(other) {
assertRstPoint(other);
const { ex: X1, ey: Y1 } = this.ep;
const { ex: X2, ey: Y2 } = other.ep;
const mod = exports.ed25519.CURVE.Fp.create;
// (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;
}
add(other) {
assertRstPoint(other);
return new RistPoint(this.ep.add(other.ep));
}
subtract(other) {
assertRstPoint(other);
return new RistPoint(this.ep.subtract(other.ep));
}
multiply(scalar) {
return new RistPoint(this.ep.multiply(scalar));
}
multiplyUnsafe(scalar) {
return new RistPoint(this.ep.multiplyUnsafe(scalar));
}
double() {
return new RistPoint(this.ep.double());
}
negate() {
return new RistPoint(this.ep.negate());
}
}
exports.RistrettoPoint = (() => {
if (!RistPoint.BASE)
RistPoint.BASE = new RistPoint(exports.ed25519.ExtendedPoint.BASE);
if (!RistPoint.ZERO)
RistPoint.ZERO = new RistPoint(exports.ed25519.ExtendedPoint.ZERO);
return RistPoint;
})();
// Hashing to ristretto255. https://www.rfc-editor.org/rfc/rfc9380#appendix-B
const hashToRistretto255 = (msg, options) => {
const d = options.DST;
const DST = typeof d === 'string' ? (0, utils_1.utf8ToBytes)(d) : d;
const uniform_bytes = (0, hash_to_curve_js_1.expand_message_xmd)(msg, DST, 64, sha512_1.sha512);
const P = RistPoint.hashToCurve(uniform_bytes);
return P;
};
exports.hashToRistretto255 = hashToRistretto255;
exports.hash_to_ristretto255 = exports.hashToRistretto255; // legacy
//# sourceMappingURL=ed25519.js.mapВыполнить команду
Для локальной разработки. Не используйте в интернете!