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433 lines
20 KiB
433 lines
20 KiB
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */ |
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import { sha512 } from '@noble/hashes/sha512'; |
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import { concatBytes, randomBytes, utf8ToBytes } from '@noble/hashes/utils'; |
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import { twistedEdwards } from './abstract/edwards.js'; |
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import { montgomery } from './abstract/montgomery.js'; |
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import { Field, FpSqrtEven, isNegativeLE, mod, pow2 } from './abstract/modular.js'; |
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import { bytesToHex, bytesToNumberLE, ensureBytes, equalBytes, numberToBytesLE, } from './abstract/utils.js'; |
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import { createHasher, expand_message_xmd } from './abstract/hash-to-curve.js'; |
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/** |
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* ed25519 Twisted Edwards curve with following addons: |
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* - X25519 ECDH |
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* - Ristretto cofactor elimination |
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* - Elligator hash-to-group / point indistinguishability |
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*/ |
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const ED25519_P = BigInt('57896044618658097711785492504343953926634992332820282019728792003956564819949'); |
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// √(-1) aka √(a) aka 2^((p-1)/4) |
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const ED25519_SQRT_M1 = BigInt('19681161376707505956807079304988542015446066515923890162744021073123829784752'); |
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// prettier-ignore |
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const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _5n = BigInt(5); |
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// prettier-ignore |
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const _10n = BigInt(10), _20n = BigInt(20), _40n = BigInt(40), _80n = BigInt(80); |
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function ed25519_pow_2_252_3(x) { |
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const P = ED25519_P; |
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const x2 = (x * x) % P; |
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const b2 = (x2 * x) % P; // x^3, 11 |
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const b4 = (pow2(b2, _2n, P) * b2) % P; // x^15, 1111 |
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const b5 = (pow2(b4, _1n, P) * x) % P; // x^31 |
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const b10 = (pow2(b5, _5n, P) * b5) % P; |
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const b20 = (pow2(b10, _10n, P) * b10) % P; |
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const b40 = (pow2(b20, _20n, P) * b20) % P; |
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const b80 = (pow2(b40, _40n, P) * b40) % P; |
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const b160 = (pow2(b80, _80n, P) * b80) % P; |
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const b240 = (pow2(b160, _80n, P) * b80) % P; |
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const b250 = (pow2(b240, _10n, P) * b10) % P; |
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const pow_p_5_8 = (pow2(b250, _2n, P) * x) % P; |
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// ^ To pow to (p+3)/8, multiply it by x. |
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return { pow_p_5_8, b2 }; |
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} |
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function adjustScalarBytes(bytes) { |
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// Section 5: For X25519, in order to decode 32 random bytes as an integer scalar, |
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// set the three least significant bits of the first byte |
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bytes[0] &= 248; // 0b1111_1000 |
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// and the most significant bit of the last to zero, |
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bytes[31] &= 127; // 0b0111_1111 |
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// set the second most significant bit of the last byte to 1 |
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bytes[31] |= 64; // 0b0100_0000 |
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return bytes; |
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} |
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// sqrt(u/v) |
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function uvRatio(u, v) { |
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const P = ED25519_P; |
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const v3 = mod(v * v * v, P); // v³ |
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const v7 = mod(v3 * v3 * v, P); // v⁷ |
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// (p+3)/8 and (p-5)/8 |
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const pow = ed25519_pow_2_252_3(u * v7).pow_p_5_8; |
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let x = mod(u * v3 * pow, P); // (uv³)(uv⁷)^(p-5)/8 |
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const vx2 = mod(v * x * x, P); // vx² |
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const root1 = x; // First root candidate |
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const root2 = mod(x * ED25519_SQRT_M1, P); // Second root candidate |
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const useRoot1 = vx2 === u; // If vx² = u (mod p), x is a square root |
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const useRoot2 = vx2 === mod(-u, P); // If vx² = -u, set x <-- x * 2^((p-1)/4) |
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const noRoot = vx2 === mod(-u * ED25519_SQRT_M1, P); // There is no valid root, vx² = -u√(-1) |
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if (useRoot1) |
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x = root1; |
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if (useRoot2 || noRoot) |
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x = root2; // We return root2 anyway, for const-time |
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if (isNegativeLE(x, P)) |
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x = mod(-x, P); |
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return { isValid: useRoot1 || useRoot2, value: x }; |
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} |
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// Just in case |
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export const ED25519_TORSION_SUBGROUP = [ |
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'0100000000000000000000000000000000000000000000000000000000000000', |
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'c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac037a', |
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'0000000000000000000000000000000000000000000000000000000000000080', |
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'26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc05', |
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'ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f', |
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'26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc85', |
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'0000000000000000000000000000000000000000000000000000000000000000', |
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'c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa', |
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]; |
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const Fp = Field(ED25519_P, undefined, true); |
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const ed25519Defaults = { |
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// Param: a |
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a: BigInt(-1), |
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// d is equal to -121665/121666 over finite field. |
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// Negative number is P - number, and division is invert(number, P) |
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d: BigInt('37095705934669439343138083508754565189542113879843219016388785533085940283555'), |
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// Finite field 𝔽p over which we'll do calculations; 2n**255n - 19n |
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Fp, |
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// Subgroup order: how many points curve has |
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// 2n**252n + 27742317777372353535851937790883648493n; |
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n: BigInt('7237005577332262213973186563042994240857116359379907606001950938285454250989'), |
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// Cofactor |
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h: BigInt(8), |
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// Base point (x, y) aka generator point |
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Gx: BigInt('15112221349535400772501151409588531511454012693041857206046113283949847762202'), |
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Gy: BigInt('46316835694926478169428394003475163141307993866256225615783033603165251855960'), |
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hash: sha512, |
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randomBytes, |
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adjustScalarBytes, |
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// dom2 |
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// Ratio of u to v. Allows us to combine inversion and square root. Uses algo from RFC8032 5.1.3. |
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// Constant-time, u/√v |
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uvRatio, |
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}; |
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export const ed25519 = /* @__PURE__ */ twistedEdwards(ed25519Defaults); |
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function ed25519_domain(data, ctx, phflag) { |
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if (ctx.length > 255) |
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throw new Error('Context is too big'); |
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return concatBytes(utf8ToBytes('SigEd25519 no Ed25519 collisions'), new Uint8Array([phflag ? 1 : 0, ctx.length]), ctx, data); |
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} |
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export const ed25519ctx = /* @__PURE__ */ twistedEdwards({ |
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...ed25519Defaults, |
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domain: ed25519_domain, |
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}); |
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export const ed25519ph = /* @__PURE__ */ twistedEdwards({ |
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...ed25519Defaults, |
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domain: ed25519_domain, |
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prehash: sha512, |
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}); |
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export const x25519 = /* @__PURE__ */ (() => montgomery({ |
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P: ED25519_P, |
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a: BigInt(486662), |
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montgomeryBits: 255, |
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nByteLength: 32, |
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Gu: BigInt(9), |
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powPminus2: (x) => { |
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const P = ED25519_P; |
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// x^(p-2) aka x^(2^255-21) |
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const { pow_p_5_8, b2 } = ed25519_pow_2_252_3(x); |
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return mod(pow2(pow_p_5_8, BigInt(3), P) * b2, P); |
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}, |
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adjustScalarBytes, |
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randomBytes, |
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}))(); |
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/** |
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* Converts ed25519 public key to x25519 public key. Uses formula: |
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* * `(u, v) = ((1+y)/(1-y), sqrt(-486664)*u/x)` |
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* * `(x, y) = (sqrt(-486664)*u/v, (u-1)/(u+1))` |
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* @example |
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* const someonesPub = ed25519.getPublicKey(ed25519.utils.randomPrivateKey()); |
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* const aPriv = x25519.utils.randomPrivateKey(); |
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* x25519.getSharedSecret(aPriv, edwardsToMontgomeryPub(someonesPub)) |
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*/ |
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export function edwardsToMontgomeryPub(edwardsPub) { |
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const { y } = ed25519.ExtendedPoint.fromHex(edwardsPub); |
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const _1n = BigInt(1); |
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return Fp.toBytes(Fp.create((_1n + y) * Fp.inv(_1n - y))); |
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} |
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export const edwardsToMontgomery = edwardsToMontgomeryPub; // deprecated |
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/** |
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* Converts ed25519 secret key to x25519 secret key. |
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* @example |
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* const someonesPub = x25519.getPublicKey(x25519.utils.randomPrivateKey()); |
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* const aPriv = ed25519.utils.randomPrivateKey(); |
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* x25519.getSharedSecret(edwardsToMontgomeryPriv(aPriv), someonesPub) |
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*/ |
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export function edwardsToMontgomeryPriv(edwardsPriv) { |
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const hashed = ed25519Defaults.hash(edwardsPriv.subarray(0, 32)); |
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return ed25519Defaults.adjustScalarBytes(hashed).subarray(0, 32); |
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} |
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// Hash To Curve Elligator2 Map (NOTE: different from ristretto255 elligator) |
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// NOTE: very important part is usage of FpSqrtEven for ELL2_C1_EDWARDS, since |
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// SageMath returns different root first and everything falls apart |
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const ELL2_C1 = (Fp.ORDER + BigInt(3)) / BigInt(8); // 1. c1 = (q + 3) / 8 # Integer arithmetic |
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const ELL2_C2 = Fp.pow(_2n, ELL2_C1); // 2. c2 = 2^c1 |
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const ELL2_C3 = Fp.sqrt(Fp.neg(Fp.ONE)); // 3. c3 = sqrt(-1) |
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const ELL2_C4 = (Fp.ORDER - BigInt(5)) / BigInt(8); // 4. c4 = (q - 5) / 8 # Integer arithmetic |
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const ELL2_J = BigInt(486662); |
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// prettier-ignore |
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function map_to_curve_elligator2_curve25519(u) { |
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let tv1 = Fp.sqr(u); // 1. tv1 = u^2 |
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tv1 = Fp.mul(tv1, _2n); // 2. tv1 = 2 * tv1 |
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let xd = Fp.add(tv1, Fp.ONE); // 3. xd = tv1 + 1 # Nonzero: -1 is square (mod p), tv1 is not |
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let x1n = Fp.neg(ELL2_J); // 4. x1n = -J # x1 = x1n / xd = -J / (1 + 2 * u^2) |
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let tv2 = Fp.sqr(xd); // 5. tv2 = xd^2 |
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let gxd = Fp.mul(tv2, xd); // 6. gxd = tv2 * xd # gxd = xd^3 |
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let gx1 = Fp.mul(tv1, ELL2_J); // 7. gx1 = J * tv1 # x1n + J * xd |
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gx1 = Fp.mul(gx1, x1n); // 8. gx1 = gx1 * x1n # x1n^2 + J * x1n * xd |
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gx1 = Fp.add(gx1, tv2); // 9. gx1 = gx1 + tv2 # x1n^2 + J * x1n * xd + xd^2 |
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gx1 = Fp.mul(gx1, x1n); // 10. gx1 = gx1 * x1n # x1n^3 + J * x1n^2 * xd + x1n * xd^2 |
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let tv3 = Fp.sqr(gxd); // 11. tv3 = gxd^2 |
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tv2 = Fp.sqr(tv3); // 12. tv2 = tv3^2 # gxd^4 |
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tv3 = Fp.mul(tv3, gxd); // 13. tv3 = tv3 * gxd # gxd^3 |
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tv3 = Fp.mul(tv3, gx1); // 14. tv3 = tv3 * gx1 # gx1 * gxd^3 |
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tv2 = Fp.mul(tv2, tv3); // 15. tv2 = tv2 * tv3 # gx1 * gxd^7 |
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let y11 = Fp.pow(tv2, ELL2_C4); // 16. y11 = tv2^c4 # (gx1 * gxd^7)^((p - 5) / 8) |
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y11 = Fp.mul(y11, tv3); // 17. y11 = y11 * tv3 # gx1*gxd^3*(gx1*gxd^7)^((p-5)/8) |
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let y12 = Fp.mul(y11, ELL2_C3); // 18. y12 = y11 * c3 |
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tv2 = Fp.sqr(y11); // 19. tv2 = y11^2 |
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tv2 = Fp.mul(tv2, gxd); // 20. tv2 = tv2 * gxd |
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let e1 = Fp.eql(tv2, gx1); // 21. e1 = tv2 == gx1 |
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let y1 = Fp.cmov(y12, y11, e1); // 22. y1 = CMOV(y12, y11, e1) # If g(x1) is square, this is its sqrt |
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let x2n = Fp.mul(x1n, tv1); // 23. x2n = x1n * tv1 # x2 = x2n / xd = 2 * u^2 * x1n / xd |
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let y21 = Fp.mul(y11, u); // 24. y21 = y11 * u |
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y21 = Fp.mul(y21, ELL2_C2); // 25. y21 = y21 * c2 |
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let y22 = Fp.mul(y21, ELL2_C3); // 26. y22 = y21 * c3 |
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let gx2 = Fp.mul(gx1, tv1); // 27. gx2 = gx1 * tv1 # g(x2) = gx2 / gxd = 2 * u^2 * g(x1) |
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tv2 = Fp.sqr(y21); // 28. tv2 = y21^2 |
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tv2 = Fp.mul(tv2, gxd); // 29. tv2 = tv2 * gxd |
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let e2 = Fp.eql(tv2, gx2); // 30. e2 = tv2 == gx2 |
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let y2 = Fp.cmov(y22, y21, e2); // 31. y2 = CMOV(y22, y21, e2) # If g(x2) is square, this is its sqrt |
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tv2 = Fp.sqr(y1); // 32. tv2 = y1^2 |
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tv2 = Fp.mul(tv2, gxd); // 33. tv2 = tv2 * gxd |
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let e3 = Fp.eql(tv2, gx1); // 34. e3 = tv2 == gx1 |
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let xn = Fp.cmov(x2n, x1n, e3); // 35. xn = CMOV(x2n, x1n, e3) # If e3, x = x1, else x = x2 |
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let y = Fp.cmov(y2, y1, e3); // 36. y = CMOV(y2, y1, e3) # If e3, y = y1, else y = y2 |
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let e4 = Fp.isOdd(y); // 37. e4 = sgn0(y) == 1 # Fix sign of y |
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y = Fp.cmov(y, Fp.neg(y), e3 !== e4); // 38. y = CMOV(y, -y, e3 XOR e4) |
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return { xMn: xn, xMd: xd, yMn: y, yMd: _1n }; // 39. return (xn, xd, y, 1) |
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} |
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const ELL2_C1_EDWARDS = FpSqrtEven(Fp, Fp.neg(BigInt(486664))); // sgn0(c1) MUST equal 0 |
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function map_to_curve_elligator2_edwards25519(u) { |
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const { xMn, xMd, yMn, yMd } = map_to_curve_elligator2_curve25519(u); // 1. (xMn, xMd, yMn, yMd) = |
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// map_to_curve_elligator2_curve25519(u) |
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let xn = Fp.mul(xMn, yMd); // 2. xn = xMn * yMd |
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xn = Fp.mul(xn, ELL2_C1_EDWARDS); // 3. xn = xn * c1 |
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let xd = Fp.mul(xMd, yMn); // 4. xd = xMd * yMn # xn / xd = c1 * xM / yM |
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let yn = Fp.sub(xMn, xMd); // 5. yn = xMn - xMd |
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let yd = Fp.add(xMn, xMd); // 6. yd = xMn + xMd # (n / d - 1) / (n / d + 1) = (n - d) / (n + d) |
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let tv1 = Fp.mul(xd, yd); // 7. tv1 = xd * yd |
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let e = Fp.eql(tv1, Fp.ZERO); // 8. e = tv1 == 0 |
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xn = Fp.cmov(xn, Fp.ZERO, e); // 9. xn = CMOV(xn, 0, e) |
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xd = Fp.cmov(xd, Fp.ONE, e); // 10. xd = CMOV(xd, 1, e) |
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yn = Fp.cmov(yn, Fp.ONE, e); // 11. yn = CMOV(yn, 1, e) |
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yd = Fp.cmov(yd, Fp.ONE, e); // 12. yd = CMOV(yd, 1, e) |
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const inv = Fp.invertBatch([xd, yd]); // batch division |
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return { x: Fp.mul(xn, inv[0]), y: Fp.mul(yn, inv[1]) }; // 13. return (xn, xd, yn, yd) |
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} |
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const htf = /* @__PURE__ */ (() => createHasher(ed25519.ExtendedPoint, (scalars) => map_to_curve_elligator2_edwards25519(scalars[0]), { |
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DST: 'edwards25519_XMD:SHA-512_ELL2_RO_', |
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encodeDST: 'edwards25519_XMD:SHA-512_ELL2_NU_', |
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p: Fp.ORDER, |
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m: 1, |
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k: 128, |
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expand: 'xmd', |
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hash: sha512, |
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}))(); |
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export const hashToCurve = /* @__PURE__ */ (() => htf.hashToCurve)(); |
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export const encodeToCurve = /* @__PURE__ */ (() => htf.encodeToCurve)(); |
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function assertRstPoint(other) { |
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if (!(other instanceof RistPoint)) |
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throw new Error('RistrettoPoint expected'); |
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} |
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// √(-1) aka √(a) aka 2^((p-1)/4) |
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const SQRT_M1 = ED25519_SQRT_M1; |
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// √(ad - 1) |
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const SQRT_AD_MINUS_ONE = BigInt('25063068953384623474111414158702152701244531502492656460079210482610430750235'); |
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// 1 / √(a-d) |
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const INVSQRT_A_MINUS_D = BigInt('54469307008909316920995813868745141605393597292927456921205312896311721017578'); |
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// 1-d² |
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const ONE_MINUS_D_SQ = BigInt('1159843021668779879193775521855586647937357759715417654439879720876111806838'); |
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// (d-1)² |
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const D_MINUS_ONE_SQ = BigInt('40440834346308536858101042469323190826248399146238708352240133220865137265952'); |
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// Calculates 1/√(number) |
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const invertSqrt = (number) => uvRatio(_1n, number); |
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const MAX_255B = BigInt('0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff'); |
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const bytes255ToNumberLE = (bytes) => ed25519.CURVE.Fp.create(bytesToNumberLE(bytes) & MAX_255B); |
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// Computes Elligator map for Ristretto |
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// https://ristretto.group/formulas/elligator.html |
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function calcElligatorRistrettoMap(r0) { |
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const { d } = ed25519.CURVE; |
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const P = ed25519.CURVE.Fp.ORDER; |
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const mod = ed25519.CURVE.Fp.create; |
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const r = mod(SQRT_M1 * r0 * r0); // 1 |
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const Ns = mod((r + _1n) * ONE_MINUS_D_SQ); // 2 |
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let c = BigInt(-1); // 3 |
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const D = mod((c - d * r) * mod(r + d)); // 4 |
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let { isValid: Ns_D_is_sq, value: s } = uvRatio(Ns, D); // 5 |
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let s_ = mod(s * r0); // 6 |
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if (!isNegativeLE(s_, P)) |
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s_ = mod(-s_); |
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if (!Ns_D_is_sq) |
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s = s_; // 7 |
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if (!Ns_D_is_sq) |
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c = r; // 8 |
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const Nt = mod(c * (r - _1n) * D_MINUS_ONE_SQ - D); // 9 |
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const s2 = s * s; |
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const W0 = mod((s + s) * D); // 10 |
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const W1 = mod(Nt * SQRT_AD_MINUS_ONE); // 11 |
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const W2 = mod(_1n - s2); // 12 |
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const W3 = mod(_1n + s2); // 13 |
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return new ed25519.ExtendedPoint(mod(W0 * W3), mod(W2 * W1), mod(W1 * W3), mod(W0 * W2)); |
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} |
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/** |
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* Each ed25519/ExtendedPoint has 8 different equivalent points. This can be |
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* a source of bugs for protocols like ring signatures. Ristretto was created to solve this. |
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* Ristretto point operates in X:Y:Z:T extended coordinates like ExtendedPoint, |
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* but it should work in its own namespace: do not combine those two. |
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* https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-ristretto255-decaf448 |
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*/ |
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class RistPoint { |
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// Private property to discourage combining ExtendedPoint + RistrettoPoint |
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// Always use Ristretto encoding/decoding instead. |
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constructor(ep) { |
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this.ep = ep; |
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} |
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static fromAffine(ap) { |
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return new RistPoint(ed25519.ExtendedPoint.fromAffine(ap)); |
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} |
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/** |
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* Takes uniform output of 64-byte hash function like sha512 and converts it to `RistrettoPoint`. |
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* The hash-to-group operation applies Elligator twice and adds the results. |
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* **Note:** this is one-way map, there is no conversion from point to hash. |
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* https://ristretto.group/formulas/elligator.html |
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* @param hex 64-byte output of a hash function |
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*/ |
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static hashToCurve(hex) { |
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hex = ensureBytes('ristrettoHash', hex, 64); |
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const r1 = bytes255ToNumberLE(hex.slice(0, 32)); |
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const R1 = calcElligatorRistrettoMap(r1); |
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const r2 = bytes255ToNumberLE(hex.slice(32, 64)); |
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const R2 = calcElligatorRistrettoMap(r2); |
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return new RistPoint(R1.add(R2)); |
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} |
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/** |
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* Converts ristretto-encoded string to ristretto point. |
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* https://ristretto.group/formulas/decoding.html |
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* @param hex Ristretto-encoded 32 bytes. Not every 32-byte string is valid ristretto encoding |
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*/ |
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static fromHex(hex) { |
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hex = ensureBytes('ristrettoHex', hex, 32); |
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const { a, d } = ed25519.CURVE; |
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const P = ed25519.CURVE.Fp.ORDER; |
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const mod = ed25519.CURVE.Fp.create; |
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const emsg = 'RistrettoPoint.fromHex: the hex is not valid encoding of RistrettoPoint'; |
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const s = bytes255ToNumberLE(hex); |
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// 1. Check that s_bytes is the canonical encoding of a field element, or else abort. |
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// 3. Check that s is non-negative, or else abort |
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if (!equalBytes(numberToBytesLE(s, 32), hex) || isNegativeLE(s, P)) |
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throw new Error(emsg); |
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const s2 = mod(s * s); |
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const u1 = mod(_1n + a * s2); // 4 (a is -1) |
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const u2 = mod(_1n - a * s2); // 5 |
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const u1_2 = mod(u1 * u1); |
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const u2_2 = mod(u2 * u2); |
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const v = mod(a * d * u1_2 - u2_2); // 6 |
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const { isValid, value: I } = invertSqrt(mod(v * u2_2)); // 7 |
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const Dx = mod(I * u2); // 8 |
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const Dy = mod(I * Dx * v); // 9 |
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let x = mod((s + s) * Dx); // 10 |
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if (isNegativeLE(x, P)) |
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x = mod(-x); // 10 |
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const y = mod(u1 * Dy); // 11 |
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const t = mod(x * y); // 12 |
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if (!isValid || isNegativeLE(t, P) || y === _0n) |
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throw new Error(emsg); |
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return new RistPoint(new ed25519.ExtendedPoint(x, y, _1n, t)); |
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} |
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/** |
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* Encodes ristretto point to Uint8Array. |
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* https://ristretto.group/formulas/encoding.html |
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*/ |
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toRawBytes() { |
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let { ex: x, ey: y, ez: z, et: t } = this.ep; |
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const P = ed25519.CURVE.Fp.ORDER; |
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const mod = ed25519.CURVE.Fp.create; |
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const u1 = mod(mod(z + y) * mod(z - y)); // 1 |
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const u2 = mod(x * y); // 2 |
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// Square root always exists |
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const u2sq = mod(u2 * u2); |
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const { value: invsqrt } = invertSqrt(mod(u1 * u2sq)); // 3 |
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const D1 = mod(invsqrt * u1); // 4 |
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const D2 = mod(invsqrt * u2); // 5 |
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const zInv = mod(D1 * D2 * t); // 6 |
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let D; // 7 |
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if (isNegativeLE(t * zInv, P)) { |
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let _x = mod(y * SQRT_M1); |
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let _y = mod(x * SQRT_M1); |
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x = _x; |
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y = _y; |
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D = mod(D1 * INVSQRT_A_MINUS_D); |
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} |
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else { |
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D = D2; // 8 |
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} |
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if (isNegativeLE(x * zInv, P)) |
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y = mod(-y); // 9 |
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let s = mod((z - y) * D); // 10 (check footer's note, no sqrt(-a)) |
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if (isNegativeLE(s, P)) |
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s = mod(-s); |
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return numberToBytesLE(s, 32); // 11 |
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} |
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toHex() { |
|
return bytesToHex(this.toRawBytes()); |
|
} |
|
toString() { |
|
return this.toHex(); |
|
} |
|
// Compare one point to another. |
|
equals(other) { |
|
assertRstPoint(other); |
|
const { ex: X1, ey: Y1 } = this.ep; |
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const { ex: X2, ey: Y2 } = other.ep; |
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const mod = ed25519.CURVE.Fp.create; |
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// (x1 * y2 == y1 * x2) | (y1 * y2 == x1 * x2) |
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const one = mod(X1 * Y2) === mod(Y1 * X2); |
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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)); |
|
} |
|
} |
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export const RistrettoPoint = /* @__PURE__ */ (() => { |
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if (!RistPoint.BASE) |
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RistPoint.BASE = new RistPoint(ed25519.ExtendedPoint.BASE); |
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if (!RistPoint.ZERO) |
|
RistPoint.ZERO = new RistPoint(ed25519.ExtendedPoint.ZERO); |
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return RistPoint; |
|
})(); |
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// Hashing to ristretto255. https://www.rfc-editor.org/rfc/rfc9380#appendix-B |
|
export const hashToRistretto255 = (msg, options) => { |
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const d = options.DST; |
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const DST = typeof d === 'string' ? utf8ToBytes(d) : d; |
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const uniform_bytes = expand_message_xmd(msg, DST, 64, sha512); |
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const P = RistPoint.hashToCurve(uniform_bytes); |
|
return P; |
|
}; |
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export const hash_to_ristretto255 = hashToRistretto255; // legacy |
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//# sourceMappingURL=ed25519.js.map
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