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Implement hash-to-curve for weierstrass curves, add test vectors

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This commit is contained in:
Paul Miller 2022-12-28 05:31:41 +00:00
parent cae888d942
commit d837831d22
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42 changed files with 3318 additions and 404 deletions
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21
curve-definitions/benchmark/index.js
View File

@ -304,6 +304,17 @@ export const CURVES = {
old: () => old_bls.pairing(oldp1, oldp2), old: () => old_bls.pairing(oldp1, oldp2),
noble: () => bls.pairing(p1, p2), noble: () => bls.pairing(p1, p2),
}, },
'hashToCurve/G1': {
samples: 500,
old: () => old_bls.PointG1.hashToCurve('abcd'),
noble: () => bls.G1.Point.hashToCurve('abcd'),
},
'hashToCurve/G2': {
samples: 200,
old: () => old_bls.PointG2.hashToCurve('abcd'),
noble: () => bls.G2.Point.hashToCurve('abcd'),
},
// SLOW PART
// Requires points which we cannot init before (data fn same for all) // Requires points which we cannot init before (data fn same for all)
// await mark('sign/nc', 30, () => bls.sign(msgp, priv)); // await mark('sign/nc', 30, () => bls.sign(msgp, priv));
// await mark('verify/nc', 30, () => bls.verify(sigp, msgp, pubp)); // await mark('verify/nc', 30, () => bls.verify(sigp, msgp, pubp));
@ -357,16 +368,6 @@ export const CURVES = {
old: ({ sig2048 }) => old_bls.aggregateSignatures(sig2048.map(old_bls.PointG2.fromSignature)), old: ({ sig2048 }) => old_bls.aggregateSignatures(sig2048.map(old_bls.PointG2.fromSignature)),
noble: ({ sig2048 }) => bls.aggregateSignatures(sig2048.map(bls.Signature.decode)), noble: ({ sig2048 }) => bls.aggregateSignatures(sig2048.map(bls.Signature.decode)),
}, },
'hashToCurve/G1': {
samples: 500,
old: () => old_bls.PointG1.hashToCurve('abcd'),
noble: () => bls.G1.Point.hashToCurve('abcd'),
},
'hashToCurve/G2': {
samples: 200,
old: () => old_bls.PointG2.hashToCurve('abcd'),
noble: () => bls.G2.Point.hashToCurve('abcd'),
},
}, },
}; };

505
curve-definitions/src/bls12-381.ts
View File

@ -14,13 +14,20 @@ import {
bitMask, bitMask,
} from '@noble/curves/utils'; } from '@noble/curves/utils';
// Types // Types
import { PointType, ProjectivePointType, ProjectiveConstructor } from '@noble/curves/weierstrass'; import {
PointType,
ProjectivePointType,
ProjectiveConstructor,
mapToCurveSimpleSWU,
} from '@noble/curves/weierstrass';
import { isogenyMap } from '@noble/curves/hashToCurve';
// Differences from bls12-381: // Differences from bls12-381:
// - PointG1 -> G1.Point // - PointG1 -> G1.Point
// - PointG2 -> G2.Point // - PointG2 -> G2.Point
// - PointG2.fromSignature -> Signature.decode // - PointG2.fromSignature -> Signature.decode
// - PointG2.toSignature -> Signature.encode // - PointG2.toSignature -> Signature.encode
// - Fixed Fp2 ORDER
// Points now have only two coordinates // Points now have only two coordinates
// CURVE FIELDS // CURVE FIELDS
@ -73,10 +80,10 @@ type Fp2Utils = {
// where Fp2 is Fp[√−1]/(x2+1). #E2(Fp2 ) = h2q, where // where Fp2 is Fp[√−1]/(x2+1). #E2(Fp2 ) = h2q, where
// G² - 1 // G² - 1
// h2q // h2q
// NOTE: ORDER was wrong!
const FP2_ORDER = const FP2_ORDER =
0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaabn ** 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaabn **
2n - 2n;
1n;
const Fp2: mod.Field<Fp2> & Fp2Utils = { const Fp2: mod.Field<Fp2> & Fp2Utils = {
ORDER: FP2_ORDER, ORDER: FP2_ORDER,
@ -144,12 +151,24 @@ const Fp2: mod.Field<Fp2> & Fp2Utils = {
if (im1 > im2 || (im1 === im2 && re1 > re2)) return x1; if (im1 > im2 || (im1 === im2 && re1 > re2)) return x1;
return x2; return x2;
}, },
// Same as sgn0_fp2 in draft-irtf-cfrg-hash-to-curve-16
isOdd: (x: Fp2) => {
const { re: x0, im: x1 } = Fp2.reim(x);
const sign_0 = x0 % 2n;
const zero_0 = x0 === 0n;
const sign_1 = x1 % 2n;
return BigInt(sign_0 || (zero_0 && sign_1)) == 1n;
},
// Bytes util // Bytes util
fromBytes(b: Uint8Array): Fp2 { fromBytes(b: Uint8Array): Fp2 {
if (b.length !== Fp2.BYTES) throw new Error(`fromBytes wrong length=${b.length}`); if (b.length !== Fp2.BYTES) throw new Error(`fromBytes wrong length=${b.length}`);
return { c0: Fp.fromBytes(b.subarray(0, Fp.BYTES)), c1: Fp.fromBytes(b.subarray(Fp.BYTES)) }; return { c0: Fp.fromBytes(b.subarray(0, Fp.BYTES)), c1: Fp.fromBytes(b.subarray(Fp.BYTES)) };
}, },
toBytes: ({ c0, c1 }) => concatBytes(Fp.toBytes(c0), Fp.toBytes(c1)), toBytes: ({ c0, c1 }) => concatBytes(Fp.toBytes(c0), Fp.toBytes(c1)),
cmov: ({ c0, c1 }, { c0: r0, c1: r1 }, c) => ({
c0: Fp.cmov(c0, r0, c),
c1: Fp.cmov(c1, r1, c),
}),
// Specific utils // Specific utils
// toString() { // toString() {
// return `Fp2(${this.c0} + ${this.c1}×i)`; // return `Fp2(${this.c0} + ${this.c1}×i)`;
@ -331,7 +350,11 @@ const Fp6: mod.Field<Fp6> & Fp6Utils = {
}, },
toBytes: ({ c0, c1, c2 }): Uint8Array => toBytes: ({ c0, c1, c2 }): Uint8Array =>
concatBytes(Fp2.toBytes(c0), Fp2.toBytes(c1), Fp2.toBytes(c2)), concatBytes(Fp2.toBytes(c0), Fp2.toBytes(c1), Fp2.toBytes(c2)),
cmov: ({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6, c) => ({
c0: Fp2.cmov(c0, r0, c),
c1: Fp2.cmov(c1, r1, c),
c2: Fp2.cmov(c2, r2, c),
}),
// Utils // Utils
// fromTriple(triple: [Fp2, Fp2, Fp2]) { // fromTriple(triple: [Fp2, Fp2, Fp2]) {
// return new Fp6(...triple); // return new Fp6(...triple);
@ -530,7 +553,10 @@ const Fp12: mod.Field<Fp12> & Fp12Utils = {
}; };
}, },
toBytes: ({ c0, c1 }): Uint8Array => concatBytes(Fp6.toBytes(c0), Fp6.toBytes(c1)), toBytes: ({ c0, c1 }): Uint8Array => concatBytes(Fp6.toBytes(c0), Fp6.toBytes(c1)),
cmov: ({ c0, c1 }, { c0: r0, c1: r1 }, c) => ({
c0: Fp6.cmov(c0, r0, c),
c1: Fp6.cmov(c1, r1, c),
}),
// Utils // Utils
// toString() { // toString() {
// return `Fp12(${this.c0} + ${this.c1} * w)`; // return `Fp12(${this.c0} + ${this.c1} * w)`;
@ -676,309 +702,170 @@ const FP12_FROBENIUS_COEFFICIENTS = [
// END OF CURVE FIELDS // END OF CURVE FIELDS
// HashToCurve // HashToCurve
// TODO: try to move-out generic version
// Utilities for 3-isogeny map from E' to E.
const ISOGENY_COEFFICIENTS_G2: [Fp2[], Fp2[], Fp2[], Fp2[]] = [
// xNum
[
[
0x171d6541fa38ccfaed6dea691f5fb614cb14b4e7f4e810aa22d6108f142b85757098e38d0f671c7188e2aaaaaaaa5ed1n,
0x0n,
],
[
0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71en,
0x8ab05f8bdd54cde190937e76bc3e447cc27c3d6fbd7063fcd104635a790520c0a395554e5c6aaaa9354ffffffffe38dn,
],
[
0x0n,
0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71an,
],
[
0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97d6n,
0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97d6n,
],
],
// xDen
[
[0x0n, 0x0n],
[0x1n, 0x0n],
[
0xcn,
0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa9fn,
],
[
0x0n,
0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa63n,
],
],
// yNum
[
[
0x124c9ad43b6cf79bfbf7043de3811ad0761b0f37a1e26286b0e977c69aa274524e79097a56dc4bd9e1b371c71c718b10n,
0x0n,
],
[
0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71cn,
0x8ab05f8bdd54cde190937e76bc3e447cc27c3d6fbd7063fcd104635a790520c0a395554e5c6aaaa9354ffffffffe38fn,
],
[
0x0n,
0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97ben,
],
[
0x1530477c7ab4113b59a4c18b076d11930f7da5d4a07f649bf54439d87d27e500fc8c25ebf8c92f6812cfc71c71c6d706n,
0x1530477c7ab4113b59a4c18b076d11930f7da5d4a07f649bf54439d87d27e500fc8c25ebf8c92f6812cfc71c71c6d706n,
],
],
// yDen
[
[0x1n, 0x0n],
[
0x12n,
0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa99n,
],
[
0x0n,
0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa9d3n,
],
[
0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa8fbn,
0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa8fbn,
],
],
].map((i) => i.map((pair) => Fp2.fromBigTuple(pair))) as [Fp2[], Fp2[], Fp2[], Fp2[]];
const ISOGENY_COEFFICIENTS_G1: [Fp[], Fp[], Fp[], Fp[]] = [
// xNum
[
0x06e08c248e260e70bd1e962381edee3d31d79d7e22c837bc23c0bf1bc24c6b68c24b1b80b64d391fa9c8ba2e8ba2d229n,
0x10321da079ce07e272d8ec09d2565b0dfa7dccdde6787f96d50af36003b14866f69b771f8c285decca67df3f1605fb7bn,
0x169b1f8e1bcfa7c42e0c37515d138f22dd2ecb803a0c5c99676314baf4bb1b7fa3190b2edc0327797f241067be390c9en,
0x080d3cf1f9a78fc47b90b33563be990dc43b756ce79f5574a2c596c928c5d1de4fa295f296b74e956d71986a8497e317n,
0x17b81e7701abdbe2e8743884d1117e53356de5ab275b4db1a682c62ef0f2753339b7c8f8c8f475af9ccb5618e3f0c88en,
0x0d6ed6553fe44d296a3726c38ae652bfb11586264f0f8ce19008e218f9c86b2a8da25128c1052ecaddd7f225a139ed84n,
0x1630c3250d7313ff01d1201bf7a74ab5db3cb17dd952799b9ed3ab9097e68f90a0870d2dcae73d19cd13c1c66f652983n,
0x0e99726a3199f4436642b4b3e4118e5499db995a1257fb3f086eeb65982fac18985a286f301e77c451154ce9ac8895d9n,
0x1778e7166fcc6db74e0609d307e55412d7f5e4656a8dbf25f1b33289f1b330835336e25ce3107193c5b388641d9b6861n,
0x0d54005db97678ec1d1048c5d10a9a1bce032473295983e56878e501ec68e25c958c3e3d2a09729fe0179f9dac9edcb0n,
0x17294ed3e943ab2f0588bab22147a81c7c17e75b2f6a8417f565e33c70d1e86b4838f2a6f318c356e834eef1b3cb83bbn,
0x11a05f2b1e833340b809101dd99815856b303e88a2d7005ff2627b56cdb4e2c85610c2d5f2e62d6eaeac1662734649b7n,
],
// xDen
[
0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001n,
0x095fc13ab9e92ad4476d6e3eb3a56680f682b4ee96f7d03776df533978f31c1593174e4b4b7865002d6384d168ecdd0an,
0x0a10ecf6ada54f825e920b3dafc7a3cce07f8d1d7161366b74100da67f39883503826692abba43704776ec3a79a1d641n,
0x14a7ac2a9d64a8b230b3f5b074cf01996e7f63c21bca68a81996e1cdf9822c580fa5b9489d11e2d311f7d99bbdcc5a5en,
0x0772caacf16936190f3e0c63e0596721570f5799af53a1894e2e073062aede9cea73b3538f0de06cec2574496ee84a3an,
0x0e7355f8e4e667b955390f7f0506c6e9395735e9ce9cad4d0a43bcef24b8982f7400d24bc4228f11c02df9a29f6304a5n,
0x13a8e162022914a80a6f1d5f43e7a07dffdfc759a12062bb8d6b44e833b306da9bd29ba81f35781d539d395b3532a21en,
0x03425581a58ae2fec83aafef7c40eb545b08243f16b1655154cca8abc28d6fd04976d5243eecf5c4130de8938dc62cd8n,
0x0b2962fe57a3225e8137e629bff2991f6f89416f5a718cd1fca64e00b11aceacd6a3d0967c94fedcfcc239ba5cb83e19n,
0x12561a5deb559c4348b4711298e536367041e8ca0cf0800c0126c2588c48bf5713daa8846cb026e9e5c8276ec82b3bffn,
0x08ca8d548cff19ae18b2e62f4bd3fa6f01d5ef4ba35b48ba9c9588617fc8ac62b558d681be343df8993cf9fa40d21b1cn,
],
// yNum
[
0x15e6be4e990f03ce4ea50b3b42df2eb5cb181d8f84965a3957add4fa95af01b2b665027efec01c7704b456be69c8b604n,
0x05c129645e44cf1102a159f748c4a3fc5e673d81d7e86568d9ab0f5d396a7ce46ba1049b6579afb7866b1e715475224bn,
0x0245a394ad1eca9b72fc00ae7be315dc757b3b080d4c158013e6632d3c40659cc6cf90ad1c232a6442d9d3f5db980133n,
0x0b182cac101b9399d155096004f53f447aa7b12a3426b08ec02710e807b4633f06c851c1919211f20d4c04f00b971ef8n,
0x18b46a908f36f6deb918c143fed2edcc523559b8aaf0c2462e6bfe7f911f643249d9cdf41b44d606ce07c8a4d0074d8en,
0x19713e47937cd1be0dfd0b8f1d43fb93cd2fcbcb6caf493fd1183e416389e61031bf3a5cce3fbafce813711ad011c132n,
0x0e1bba7a1186bdb5223abde7ada14a23c42a0ca7915af6fe06985e7ed1e4d43b9b3f7055dd4eba6f2bafaaebca731c30n,
0x09fc4018bd96684be88c9e221e4da1bb8f3abd16679dc26c1e8b6e6a1f20cabe69d65201c78607a360370e577bdba587n,
0x0987c8d5333ab86fde9926bd2ca6c674170a05bfe3bdd81ffd038da6c26c842642f64550fedfe935a15e4ca31870fb29n,
0x04ab0b9bcfac1bbcb2c977d027796b3ce75bb8ca2be184cb5231413c4d634f3747a87ac2460f415ec961f8855fe9d6f2n,
0x16603fca40634b6a2211e11db8f0a6a074a7d0d4afadb7bd76505c3d3ad5544e203f6326c95a807299b23ab13633a5f0n,
0x08cc03fdefe0ff135caf4fe2a21529c4195536fbe3ce50b879833fd221351adc2ee7f8dc099040a841b6daecf2e8fedbn,
0x01f86376e8981c217898751ad8746757d42aa7b90eeb791c09e4a3ec03251cf9de405aba9ec61deca6355c77b0e5f4cbn,
0x00cc786baa966e66f4a384c86a3b49942552e2d658a31ce2c344be4b91400da7d26d521628b00523b8dfe240c72de1f6n,
0x134996a104ee5811d51036d776fb46831223e96c254f383d0f906343eb67ad34d6c56711962fa8bfe097e75a2e41c696n,
0x090d97c81ba24ee0259d1f094980dcfa11ad138e48a869522b52af6c956543d3cd0c7aee9b3ba3c2be9845719707bb33n,
],
// yDen
[
0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001n,
0x0e0fa1d816ddc03e6b24255e0d7819c171c40f65e273b853324efcd6356caa205ca2f570f13497804415473a1d634b8fn,
0x02660400eb2e4f3b628bdd0d53cd76f2bf565b94e72927c1cb748df27942480e420517bd8714cc80d1fadc1326ed06f7n,
0x0ad6b9514c767fe3c3613144b45f1496543346d98adf02267d5ceef9a00d9b8693000763e3b90ac11e99b138573345ccn,
0x0accbb67481d033ff5852c1e48c50c477f94ff8aefce42d28c0f9a88cea7913516f968986f7ebbea9684b529e2561092n,
0x04d2f259eea405bd48f010a01ad2911d9c6dd039bb61a6290e591b36e636a5c871a5c29f4f83060400f8b49cba8f6aa8n,
0x167a55cda70a6e1cea820597d94a84903216f763e13d87bb5308592e7ea7d4fbc7385ea3d529b35e346ef48bb8913f55n,
0x1866c8ed336c61231a1be54fd1d74cc4f9fb0ce4c6af5920abc5750c4bf39b4852cfe2f7bb9248836b233d9d55535d4an,
0x16a3ef08be3ea7ea03bcddfabba6ff6ee5a4375efa1f4fd7feb34fd206357132b920f5b00801dee460ee415a15812ed9n,
0x166007c08a99db2fc3ba8734ace9824b5eecfdfa8d0cf8ef5dd365bc400a0051d5fa9c01a58b1fb93d1a1399126a775cn,
0x08d9e5297186db2d9fb266eaac783182b70152c65550d881c5ecd87b6f0f5a6449f38db9dfa9cce202c6477faaf9b7acn,
0x0be0e079545f43e4b00cc912f8228ddcc6d19c9f0f69bbb0542eda0fc9dec916a20b15dc0fd2ededda39142311a5001dn,
0x16b7d288798e5395f20d23bf89edb4d1d115c5dbddbcd30e123da489e726af41727364f2c28297ada8d26d98445f5416n,
0x058df3306640da276faaae7d6e8eb15778c4855551ae7f310c35a5dd279cd2eca6757cd636f96f891e2538b53dbf67f2n,
0x1962d75c2381201e1a0cbd6c43c348b885c84ff731c4d59ca4a10356f453e01f78a4260763529e3532f6102c2e49a03dn,
0x16112c4c3a9c98b252181140fad0eae9601a6de578980be6eec3232b5be72e7a07f3688ef60c206d01479253b03663c1n,
],
];
// Looks like is_y_even for fp + fp2?
// For Fp2: if (sgn0_fp2(t) !== sgn0_fp2(y)) y = Fp2.negate(y);
// For Fp: const y = sgn0_m_eq_1(u) == sgn0_m_eq_1(yPos) ? yPos : yNeg;
function sgn0_fp2(x: Fp2) {
const { re: x0, im: x1 } = Fp2.reim(x);
const sign_0 = x0 % 2n;
const zero_0 = x0 === 0n;
const sign_1 = x1 % 2n;
return BigInt(sign_0 || (zero_0 && sign_1));
}
function sgn0_m_eq_1(x: Fp) {
return Boolean(x % 2n);
}
const P_MINUS_9_DIV_16 = (Fp.ORDER ** 2n - 9n) / 16n;
// Does not return a square root.
// Returns uv⁷ * (uv¹⁵)^((p² - 9) / 16) * root of unity
// if valid square root is found
function sqrt_div_fp2(u: Fp2, v: Fp2) {
const v7 = Fp2.pow(v, 7n);
const uv7 = Fp2.mul(u, v7);
const uv15 = Fp2.mul(uv7, Fp2.mul(v7, v));
// gamma = uv⁷ * (uv¹⁵)^((p² - 9) / 16)
const gamma = Fp2.mul(Fp2.pow(uv15, P_MINUS_9_DIV_16), uv7);
let success = false;
let result = gamma;
// Constant-time routine, so we do not early-return.
const positiveRootsOfUnity = FP2_ROOTS_OF_UNITY.slice(0, 4);
positiveRootsOfUnity.forEach((root) => {
// Valid if (root * gamma)² * v - u == 0
const candidate = Fp2.mul(root, gamma);
if (Fp2.isZero(Fp2.sub(Fp2.mul(Fp2.pow(candidate, 2n), v), u)) && !success) {
success = true;
result = candidate;
}
});
return { success, sqrtCandidateOrGamma: result };
}
// Optimized SWU Map - Fp2 to G2': y² = x³ + 240i * x + 1012 + 1012i
// Found in Section 4 of https://eprint.iacr.org/2019/403
// Note: it's constant-time
// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#appendix-G.2.3
function map_to_curve_simple_swu_9mod16(t: bigint[] | Fp2): [Fp2, Fp2] {
const iso_3_a = Fp2.create({ c0: Fp.create(0n), c1: Fp.create(240n) });
const iso_3_b = Fp2.create({ c0: Fp.create(1012n), c1: Fp.create(1012n) });
const iso_3_z = Fp2.create({ c0: Fp.create(-2n), c1: Fp.create(-1n) });
if (Array.isArray(t)) t = Fp2.fromBigTuple(t);
const t2 = Fp2.pow(t, 2n);
const iso_3_z_t2 = Fp2.mul(iso_3_z, t2);
const ztzt = Fp2.add(iso_3_z_t2, Fp2.pow(iso_3_z_t2, 2n)); // (Z * t² + Z² * t⁴)
let denominator = Fp2.negate(Fp2.mul(iso_3_a, ztzt)); // -a(Z * t² + Z² * t⁴)
let numerator = Fp2.mul(iso_3_b, Fp2.add(ztzt, Fp2.ONE)); // b(Z * t² + Z² * t⁴ + 1)
// Exceptional case
if (Fp2.isZero(denominator)) denominator = Fp2.mul(iso_3_z, iso_3_a);
// v = D³
let v = Fp2.pow(denominator, 3n);
// u = N³ + a * N * D² + b * D³
let u = Fp2.add(
Fp2.add(Fp2.pow(numerator, 3n), Fp2.mul(Fp2.mul(iso_3_a, numerator), Fp2.pow(denominator, 2n))),
Fp2.mul(iso_3_b, v)
);
// Attempt y = sqrt(u / v)
const { success, sqrtCandidateOrGamma } = sqrt_div_fp2(u, v);
let y;
if (success) y = sqrtCandidateOrGamma;
// Handle case where (u / v) is not square
// sqrt_candidate(x1) = sqrt_candidate(x0) * t³
const sqrtCandidateX1 = Fp2.mul(sqrtCandidateOrGamma, Fp2.pow(t, 3n));
// u(x1) = Z³ * t⁶ * u(x0)
u = Fp2.mul(Fp2.pow(iso_3_z_t2, 3n), u);
let success2 = false;
FP2_ETAs.forEach((eta) => {
// Valid solution if (eta * sqrt_candidate(x1))² * v - u == 0
const etaSqrtCandidate = Fp2.mul(eta, sqrtCandidateX1);
const temp = Fp2.sub(Fp2.mul(Fp2.pow(etaSqrtCandidate, 2n), v), u);
if (Fp2.isZero(temp) && !success && !success2) {
y = etaSqrtCandidate;
success2 = true;
}
});
if (!success && !success2) throw new Error('Hash to Curve - Optimized SWU failure');
if (success2) numerator = Fp2.mul(numerator, iso_3_z_t2);
y = y as Fp2;
if (sgn0_fp2(t) !== sgn0_fp2(y)) y = Fp2.negate(y);
return [Fp2.div(numerator, denominator), y];
}
// Optimized SWU Map - Fp to G1
// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#appendix-G.2.1
function map_to_curve_simple_swu_3mod4(u: Fp): [Fp, Fp] {
const A =
Fp.create(
0x144698a3b8e9433d693a02c96d4982b0ea985383ee66a8d8e8981aefd881ac98936f8da0e0f97f5cf428082d584c1dn
);
const B =
Fp.create(
0x12e2908d11688030018b12e8753eee3b2016c1f0f24f4070a0b9c14fcef35ef55a23215a316ceaa5d1cc48e98e172be0n
);
const Z = Fp.create(11n);
const c1 = (Fp.ORDER - 3n) / 4n; // (q - 3) / 4
// Static value so we can know that is there always root
const c2 = Fp.sqrt(Fp.pow(Fp.negate(Z), 3n)); // sqrt((-Z) ^ 3)
const tv1 = Fp.square(u); // u ** 2n;
const tv3 = Fp.mul(Z, tv1); //
let xDen = Fp.add(Fp.square(tv3), tv3);
// X
const xNum1 = Fp.mul(Fp.add(xDen, Fp.ONE), B); // (xd + 1) * B
const xNum2 = Fp.mul(tv3, xNum1); // x2 = x2n / xd = Z * u^2 * x1n / xd
xDen = Fp.mul(Fp.negate(A), xDen); // -A * xDen
if (Fp.isZero(xDen)) xDen = Fp.mul(A, Z);
let tv2 = Fp.square(xDen); // xDen ^ 2
const gxd = Fp.mul(tv2, xDen); // xDen ^ 3
tv2 = Fp.mul(A, tv2); // A * tv2
let gx1 = Fp.mul(Fp.add(Fp.square(xNum1), tv2), xNum1); // x1n^3 + A * x1n * xd^2
tv2 = Fp.mul(B, gxd); // B * gxd
gx1 = Fp.add(gx1, tv2); // x1n^3 + A * x1n * xd^2 + B * xd^3
tv2 = Fp.mul(gx1, gxd); // gx1 * gxd
const tv4 = Fp.mul(Fp.square(gxd), tv2); // gx1 * gxd^3
// Y
const y1 = Fp.mul(Fp.pow(tv4, c1), tv2); // gx1 * gxd * (gx1 * gxd^3)^((q - 3) / 4)
const y2 = Fp.mul(Fp.mul(Fp.mul(y1, c2), tv1), u); // y1 * c2 * tv1 * u
let xNum, yPos;
// y1^2 * gxd == gx1
if (Fp.equals(Fp.mul(Fp.square(y1), gxd), gx1)) {
xNum = xNum1;
yPos = y1;
} else {
xNum = xNum2;
yPos = y2;
}
const yNeg = Fp.negate(yPos);
const y = sgn0_m_eq_1(u) == sgn0_m_eq_1(yPos) ? yPos : yNeg;
// NOTE: we can batch inversion for hashToCurve, but it doesn't impact performance
return [Fp.div(xNum, xDen), y];
}
function isogenyMap<T, F extends mod.Field<T>>(
field: F,
COEFF: [T[], T[], T[], T[]],
x: T,
y: T
): [T, T] {
const [xNum, xDen, yNum, yDen] = COEFF.map((val) =>
val.reduce((acc, i) => field.add(field.mul(acc, x), i))
);
x = field.div(xNum, xDen); // xNum / xDen
y = field.mul(y, field.div(yNum, yDen)); // y * (yNum / yDev)
return [x, y];
}
// 3-isogeny map from E' to E // 3-isogeny map from E' to E
// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#appendix-E.3 // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#appendix-E.3
const isogenyMapG2 = (x: Fp2, y: Fp2) => isogenyMap(Fp2, ISOGENY_COEFFICIENTS_G2, x, y); const isogenyMapG2 = isogenyMap(
Fp2,
[
// xNum
[
[
'0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97d6',
'0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97d6',
],
[
'0x0',
'0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71a',
],
[
'0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71e',
'0x8ab05f8bdd54cde190937e76bc3e447cc27c3d6fbd7063fcd104635a790520c0a395554e5c6aaaa9354ffffffffe38d',
],
[
'0x171d6541fa38ccfaed6dea691f5fb614cb14b4e7f4e810aa22d6108f142b85757098e38d0f671c7188e2aaaaaaaa5ed1',
'0x0',
],
],
// xDen
[
[
'0x0',
'0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa63',
],
[
'0xc',
'0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa9f',
],
['0x1', '0x0'], // LAST 1
],
// yNum
[
[
'0x1530477c7ab4113b59a4c18b076d11930f7da5d4a07f649bf54439d87d27e500fc8c25ebf8c92f6812cfc71c71c6d706',
'0x1530477c7ab4113b59a4c18b076d11930f7da5d4a07f649bf54439d87d27e500fc8c25ebf8c92f6812cfc71c71c6d706',
],
[
'0x0',
'0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97be',
],
[
'0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71c',
'0x8ab05f8bdd54cde190937e76bc3e447cc27c3d6fbd7063fcd104635a790520c0a395554e5c6aaaa9354ffffffffe38f',
],
[
'0x124c9ad43b6cf79bfbf7043de3811ad0761b0f37a1e26286b0e977c69aa274524e79097a56dc4bd9e1b371c71c718b10',
'0x0',
],
],
// yDen
[
[
'0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa8fb',
'0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa8fb',
],
[
'0x0',
'0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa9d3',
],
[
'0x12',
'0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa99',
],
['0x1', '0x0'], // LAST 1
],
].map((i) => i.map((pair) => Fp2.fromBigTuple(pair.map(BigInt)))) as [Fp2[], Fp2[], Fp2[], Fp2[]]
);
// 11-isogeny map from E' to E // 11-isogeny map from E' to E
const isogenyMapG1 = (x: Fp, y: Fp) => isogenyMap(Fp, ISOGENY_COEFFICIENTS_G1, x, y); const isogenyMapG1 = isogenyMap(
Fp,
[
// xNum
[
'0x11a05f2b1e833340b809101dd99815856b303e88a2d7005ff2627b56cdb4e2c85610c2d5f2e62d6eaeac1662734649b7',
'0x17294ed3e943ab2f0588bab22147a81c7c17e75b2f6a8417f565e33c70d1e86b4838f2a6f318c356e834eef1b3cb83bb',
'0xd54005db97678ec1d1048c5d10a9a1bce032473295983e56878e501ec68e25c958c3e3d2a09729fe0179f9dac9edcb0',
'0x1778e7166fcc6db74e0609d307e55412d7f5e4656a8dbf25f1b33289f1b330835336e25ce3107193c5b388641d9b6861',
'0xe99726a3199f4436642b4b3e4118e5499db995a1257fb3f086eeb65982fac18985a286f301e77c451154ce9ac8895d9',
'0x1630c3250d7313ff01d1201bf7a74ab5db3cb17dd952799b9ed3ab9097e68f90a0870d2dcae73d19cd13c1c66f652983',
'0xd6ed6553fe44d296a3726c38ae652bfb11586264f0f8ce19008e218f9c86b2a8da25128c1052ecaddd7f225a139ed84',
'0x17b81e7701abdbe2e8743884d1117e53356de5ab275b4db1a682c62ef0f2753339b7c8f8c8f475af9ccb5618e3f0c88e',
'0x80d3cf1f9a78fc47b90b33563be990dc43b756ce79f5574a2c596c928c5d1de4fa295f296b74e956d71986a8497e317',
'0x169b1f8e1bcfa7c42e0c37515d138f22dd2ecb803a0c5c99676314baf4bb1b7fa3190b2edc0327797f241067be390c9e',
'0x10321da079ce07e272d8ec09d2565b0dfa7dccdde6787f96d50af36003b14866f69b771f8c285decca67df3f1605fb7b',
'0x6e08c248e260e70bd1e962381edee3d31d79d7e22c837bc23c0bf1bc24c6b68c24b1b80b64d391fa9c8ba2e8ba2d229',
],
// xDen
[
'0x8ca8d548cff19ae18b2e62f4bd3fa6f01d5ef4ba35b48ba9c9588617fc8ac62b558d681be343df8993cf9fa40d21b1c',
'0x12561a5deb559c4348b4711298e536367041e8ca0cf0800c0126c2588c48bf5713daa8846cb026e9e5c8276ec82b3bff',
'0xb2962fe57a3225e8137e629bff2991f6f89416f5a718cd1fca64e00b11aceacd6a3d0967c94fedcfcc239ba5cb83e19',
'0x3425581a58ae2fec83aafef7c40eb545b08243f16b1655154cca8abc28d6fd04976d5243eecf5c4130de8938dc62cd8',
'0x13a8e162022914a80a6f1d5f43e7a07dffdfc759a12062bb8d6b44e833b306da9bd29ba81f35781d539d395b3532a21e',
'0xe7355f8e4e667b955390f7f0506c6e9395735e9ce9cad4d0a43bcef24b8982f7400d24bc4228f11c02df9a29f6304a5',
'0x772caacf16936190f3e0c63e0596721570f5799af53a1894e2e073062aede9cea73b3538f0de06cec2574496ee84a3a',
'0x14a7ac2a9d64a8b230b3f5b074cf01996e7f63c21bca68a81996e1cdf9822c580fa5b9489d11e2d311f7d99bbdcc5a5e',
'0xa10ecf6ada54f825e920b3dafc7a3cce07f8d1d7161366b74100da67f39883503826692abba43704776ec3a79a1d641',
'0x95fc13ab9e92ad4476d6e3eb3a56680f682b4ee96f7d03776df533978f31c1593174e4b4b7865002d6384d168ecdd0a',
'0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001', // LAST 1
],
// yNum
[
'0x90d97c81ba24ee0259d1f094980dcfa11ad138e48a869522b52af6c956543d3cd0c7aee9b3ba3c2be9845719707bb33',
'0x134996a104ee5811d51036d776fb46831223e96c254f383d0f906343eb67ad34d6c56711962fa8bfe097e75a2e41c696',
'0xcc786baa966e66f4a384c86a3b49942552e2d658a31ce2c344be4b91400da7d26d521628b00523b8dfe240c72de1f6',
'0x1f86376e8981c217898751ad8746757d42aa7b90eeb791c09e4a3ec03251cf9de405aba9ec61deca6355c77b0e5f4cb',
'0x8cc03fdefe0ff135caf4fe2a21529c4195536fbe3ce50b879833fd221351adc2ee7f8dc099040a841b6daecf2e8fedb',
'0x16603fca40634b6a2211e11db8f0a6a074a7d0d4afadb7bd76505c3d3ad5544e203f6326c95a807299b23ab13633a5f0',
'0x4ab0b9bcfac1bbcb2c977d027796b3ce75bb8ca2be184cb5231413c4d634f3747a87ac2460f415ec961f8855fe9d6f2',
'0x987c8d5333ab86fde9926bd2ca6c674170a05bfe3bdd81ffd038da6c26c842642f64550fedfe935a15e4ca31870fb29',
'0x9fc4018bd96684be88c9e221e4da1bb8f3abd16679dc26c1e8b6e6a1f20cabe69d65201c78607a360370e577bdba587',
'0xe1bba7a1186bdb5223abde7ada14a23c42a0ca7915af6fe06985e7ed1e4d43b9b3f7055dd4eba6f2bafaaebca731c30',
'0x19713e47937cd1be0dfd0b8f1d43fb93cd2fcbcb6caf493fd1183e416389e61031bf3a5cce3fbafce813711ad011c132',
'0x18b46a908f36f6deb918c143fed2edcc523559b8aaf0c2462e6bfe7f911f643249d9cdf41b44d606ce07c8a4d0074d8e',
'0xb182cac101b9399d155096004f53f447aa7b12a3426b08ec02710e807b4633f06c851c1919211f20d4c04f00b971ef8',
'0x245a394ad1eca9b72fc00ae7be315dc757b3b080d4c158013e6632d3c40659cc6cf90ad1c232a6442d9d3f5db980133',
'0x5c129645e44cf1102a159f748c4a3fc5e673d81d7e86568d9ab0f5d396a7ce46ba1049b6579afb7866b1e715475224b',
'0x15e6be4e990f03ce4ea50b3b42df2eb5cb181d8f84965a3957add4fa95af01b2b665027efec01c7704b456be69c8b604',
],
// yDen
[
'0x16112c4c3a9c98b252181140fad0eae9601a6de578980be6eec3232b5be72e7a07f3688ef60c206d01479253b03663c1',
'0x1962d75c2381201e1a0cbd6c43c348b885c84ff731c4d59ca4a10356f453e01f78a4260763529e3532f6102c2e49a03d',
'0x58df3306640da276faaae7d6e8eb15778c4855551ae7f310c35a5dd279cd2eca6757cd636f96f891e2538b53dbf67f2',
'0x16b7d288798e5395f20d23bf89edb4d1d115c5dbddbcd30e123da489e726af41727364f2c28297ada8d26d98445f5416',
'0xbe0e079545f43e4b00cc912f8228ddcc6d19c9f0f69bbb0542eda0fc9dec916a20b15dc0fd2ededda39142311a5001d',
'0x8d9e5297186db2d9fb266eaac783182b70152c65550d881c5ecd87b6f0f5a6449f38db9dfa9cce202c6477faaf9b7ac',
'0x166007c08a99db2fc3ba8734ace9824b5eecfdfa8d0cf8ef5dd365bc400a0051d5fa9c01a58b1fb93d1a1399126a775c',
'0x16a3ef08be3ea7ea03bcddfabba6ff6ee5a4375efa1f4fd7feb34fd206357132b920f5b00801dee460ee415a15812ed9',
'0x1866c8ed336c61231a1be54fd1d74cc4f9fb0ce4c6af5920abc5750c4bf39b4852cfe2f7bb9248836b233d9d55535d4a',
'0x167a55cda70a6e1cea820597d94a84903216f763e13d87bb5308592e7ea7d4fbc7385ea3d529b35e346ef48bb8913f55',
'0x4d2f259eea405bd48f010a01ad2911d9c6dd039bb61a6290e591b36e636a5c871a5c29f4f83060400f8b49cba8f6aa8',
'0xaccbb67481d033ff5852c1e48c50c477f94ff8aefce42d28c0f9a88cea7913516f968986f7ebbea9684b529e2561092',
'0xad6b9514c767fe3c3613144b45f1496543346d98adf02267d5ceef9a00d9b8693000763e3b90ac11e99b138573345cc',
'0x2660400eb2e4f3b628bdd0d53cd76f2bf565b94e72927c1cb748df27942480e420517bd8714cc80d1fadc1326ed06f7',
'0xe0fa1d816ddc03e6b24255e0d7819c171c40f65e273b853324efcd6356caa205ca2f570f13497804415473a1d634b8f',
'0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001', // LAST 1
],
].map((i) => i.map((j) => BigInt(j))) as [Fp[], Fp[], Fp[], Fp[]]
);
// SWU Map - Fp2 to G2': y² = x³ + 240i * x + 1012 + 1012i
const G2_SWU = mapToCurveSimpleSWU(Fp2, {
A: Fp2.create({ c0: Fp.create(0n), c1: Fp.create(240n) }), // A' = 240 * I
B: Fp2.create({ c0: Fp.create(1012n), c1: Fp.create(1012n) }), // B' = 1012 * (1 + I)
Z: Fp2.create({ c0: Fp.create(-2n), c1: Fp.create(-1n) }), // Z: -(2 + I)
});
// Optimized SWU Map - Fp to G1
const G1_SWU = mapToCurveSimpleSWU(Fp, {
A: Fp.create(
0x144698a3b8e9433d693a02c96d4982b0ea985383ee66a8d8e8981aefd881ac98936f8da0e0f97f5cf428082d584c1dn
),
B: Fp.create(
0x12e2908d11688030018b12e8753eee3b2016c1f0f24f4070a0b9c14fcef35ef55a23215a316ceaa5d1cc48e98e172be0n
),
Z: Fp.create(11n),
});
// Endomorphisms (for fast cofactor clearing) // Endomorphisms (for fast cofactor clearing)
// Ψ(P) endomorphism // Ψ(P) endomorphism
@ -1122,9 +1009,8 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
return point.multiplyUnsafe(bls12_381.CURVE.x).add(point); // x*P + P return point.multiplyUnsafe(bls12_381.CURVE.x).add(point); // x*P + P
}, },
mapToCurve: (scalars: bigint[]) => { mapToCurve: (scalars: bigint[]) => {
const [x0, y0] = map_to_curve_simple_swu_3mod4(Fp.create(scalars[0])); const { x, y } = G1_SWU(Fp.create(scalars[0]));
const [x, y] = isogenyMapG1(x0, y0); return isogenyMapG1(x, y);
return { x, y };
}, },
fromBytes: (bytes: Uint8Array): { x: Fp; y: Fp } => { fromBytes: (bytes: Uint8Array): { x: Fp; y: Fp } => {
if (bytes.length === 48) { if (bytes.length === 48) {
@ -1197,9 +1083,8 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
wrapPrivateKey: true, wrapPrivateKey: true,
allowInfinityPoint: true, allowInfinityPoint: true,
mapToCurve: (scalars: bigint[]) => { mapToCurve: (scalars: bigint[]) => {
const [x0, y0] = map_to_curve_simple_swu_9mod16(Fp2.fromBigTuple(scalars)); const { x, y } = G2_SWU(Fp2.fromBigTuple(scalars));
const [x, y] = isogenyMapG2(x0, y0); return isogenyMapG2(x, y);
return { x, y };
}, },
// Checks is the point resides in prime-order subgroup. // Checks is the point resides in prime-order subgroup.
// point.isTorsionFree() should return true for valid points // point.isTorsionFree() should return true for valid points

54
curve-definitions/src/ed25519.ts
View File

@ -3,7 +3,7 @@ import { sha512 } from '@noble/hashes/sha512';
import { concatBytes, randomBytes, utf8ToBytes } from '@noble/hashes/utils'; import { concatBytes, randomBytes, utf8ToBytes } from '@noble/hashes/utils';
import { twistedEdwards, ExtendedPointType } from '@noble/curves/edwards'; import { twistedEdwards, ExtendedPointType } from '@noble/curves/edwards';
import { montgomery } from '@noble/curves/montgomery'; import { montgomery } from '@noble/curves/montgomery';
import { mod, pow2, isNegativeLE, Fp } from '@noble/curves/modular'; import { mod, pow2, isNegativeLE, Fp as Field } from '@noble/curves/modular';
import { import {
ensureBytes, ensureBytes,
equalBytes, equalBytes,
@ -91,6 +91,8 @@ export const ED25519_TORSION_SUBGROUP = [
'c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa', 'c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa',
]; ];
const Fp = Field(ED25519_P);
const ED25519_DEF = { const ED25519_DEF = {
// Param: a // Param: a
a: BigInt(-1), a: BigInt(-1),
@ -98,7 +100,7 @@ const ED25519_DEF = {
// Negative number is P - number, and division is invert(number, P) // Negative number is P - number, and division is invert(number, P)
d: BigInt('37095705934669439343138083508754565189542113879843219016388785533085940283555'), d: BigInt('37095705934669439343138083508754565189542113879843219016388785533085940283555'),
// Finite field 𝔽p over which we'll do calculations; 2n ** 255n - 19n // Finite field 𝔽p over which we'll do calculations; 2n ** 255n - 19n
Fp: Fp(ED25519_P), Fp,
// Subgroup order: how many points ed25519 has // Subgroup order: how many points ed25519 has
// 2n ** 252n + 27742317777372353535851937790883648493n; // 2n ** 252n + 27742317777372353535851937790883648493n;
n: BigInt('7237005577332262213973186563042994240857116359379907606001950938285454250989'), n: BigInt('7237005577332262213973186563042994240857116359379907606001950938285454250989'),
@ -114,6 +116,19 @@ const ED25519_DEF = {
// Ratio of u to v. Allows us to combine inversion and square root. Uses algo from RFC8032 5.1.3. // Ratio of u to v. Allows us to combine inversion and square root. Uses algo from RFC8032 5.1.3.
// Constant-time, u/√v // Constant-time, u/√v
uvRatio, uvRatio,
htfDefaults: {
DST: 'edwards25519_XMD:SHA-512_ELL2_RO_',
p: Fp.ORDER,
m: 1,
k: 128,
expand: true,
hash: sha512,
},
mapToCurve: (scalars: bigint[]): { x: bigint; y: bigint } => {
throw new Error('Not supported yet');
// const { x, y } = calcElligatorRistrettoMap(scalars[0]).toAffine();
// return { x, y };
},
} as const; } as const;
export const ed25519 = twistedEdwards(ED25519_DEF); export const ed25519 = twistedEdwards(ED25519_DEF);
@ -180,24 +195,9 @@ const bytes255ToNumberLE = (bytes: Uint8Array) =>
type ExtendedPoint = ExtendedPointType; type ExtendedPoint = ExtendedPointType;
/**
* 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
*/
export class RistrettoPoint {
static BASE = new RistrettoPoint(ed25519.ExtendedPoint.BASE);
static ZERO = new RistrettoPoint(ed25519.ExtendedPoint.ZERO);
// Private property to discourage combining ExtendedPoint + RistrettoPoint
// Always use Ristretto encoding/decoding instead.
constructor(private readonly ep: ExtendedPoint) {}
// Computes Elligator map for Ristretto // Computes Elligator map for Ristretto
// https://ristretto.group/formulas/elligator.html // https://ristretto.group/formulas/elligator.html
private static calcElligatorRistrettoMap(r0: bigint): ExtendedPoint { function calcElligatorRistrettoMap(r0: bigint): ExtendedPoint {
const { d } = ed25519.CURVE; const { d } = ed25519.CURVE;
const P = ed25519.CURVE.Fp.ORDER; const P = ed25519.CURVE.Fp.ORDER;
const { mod } = ed25519.utils; const { mod } = ed25519.utils;
@ -219,6 +219,20 @@ export class RistrettoPoint {
return new ed25519.ExtendedPoint(mod(W0 * W3), mod(W2 * W1), mod(W1 * W3), mod(W0 * W2)); return new 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
*/
export class RistrettoPoint {
static BASE = new RistrettoPoint(ed25519.ExtendedPoint.BASE);
static ZERO = new RistrettoPoint(ed25519.ExtendedPoint.ZERO);
// Private property to discourage combining ExtendedPoint + RistrettoPoint
// Always use Ristretto encoding/decoding instead.
constructor(private readonly ep: ExtendedPoint) {}
/** /**
* Takes uniform output of 64-bit hash function like sha512 and converts it to `RistrettoPoint`. * Takes uniform output of 64-bit hash function like sha512 and converts it to `RistrettoPoint`.
* The hash-to-group operation applies Elligator twice and adds the results. * The hash-to-group operation applies Elligator twice and adds the results.
@ -229,9 +243,9 @@ export class RistrettoPoint {
static hashToCurve(hex: Hex): RistrettoPoint { static hashToCurve(hex: Hex): RistrettoPoint {
hex = ensureBytes(hex, 64); hex = ensureBytes(hex, 64);
const r1 = bytes255ToNumberLE(hex.slice(0, 32)); const r1 = bytes255ToNumberLE(hex.slice(0, 32));
const R1 = this.calcElligatorRistrettoMap(r1); const R1 = calcElligatorRistrettoMap(r1);
const r2 = bytes255ToNumberLE(hex.slice(32, 64)); const r2 = bytes255ToNumberLE(hex.slice(32, 64));
const R2 = this.calcElligatorRistrettoMap(r2); const R2 = calcElligatorRistrettoMap(r2);
return new RistrettoPoint(R1.add(R2)); return new RistrettoPoint(R1.add(R2));
} }

31
curve-definitions/src/p256.ts
View File

@ -1,17 +1,29 @@
/*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */ /*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { createCurve } from './_shortw_utils.js'; import { createCurve } from './_shortw_utils.js';
import { sha256 } from '@noble/hashes/sha256'; import { sha256 } from '@noble/hashes/sha256';
import { Fp } from '@noble/curves/modular'; import { Fp as Field } from '@noble/curves/modular';
import { mapToCurveSimpleSWU } from '@noble/curves/weierstrass';
// NIST secp256r1 aka P256 // NIST secp256r1 aka P256
// https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-256 // https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-256
// Field over which we'll do calculations; 2n**224n * (2n**32n-1n) + 2n**192n + 2n**96n-1n
const Fp = Field(BigInt('0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff'));
const CURVE_A = Fp.create(BigInt('-3'));
const CURVE_B = BigInt('0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b');
const mapSWU = mapToCurveSimpleSWU(Fp, {
A: CURVE_A,
B: CURVE_B,
Z: Fp.create(BigInt('-10')),
});
export const P256 = createCurve( export const P256 = createCurve(
{ {
// Params: a, b // Params: a, b
a: BigInt('0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc'), a: CURVE_A,
b: BigInt('0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b'), b: CURVE_B,
// Field over which we'll do calculations; 2n**224n * (2n**32n-1n) + 2n**192n + 2n**96n-1n Fp,
Fp: Fp(BigInt('0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff')),
// Curve order, total count of valid points in the field // Curve order, total count of valid points in the field
n: BigInt('0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551'), n: BigInt('0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551'),
// Base point (x, y) aka generator point // Base point (x, y) aka generator point
@ -19,6 +31,15 @@ export const P256 = createCurve(
Gy: BigInt('0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5'), Gy: BigInt('0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5'),
h: BigInt(1), h: BigInt(1),
lowS: false, lowS: false,
mapToCurve: (scalars: bigint[]) => mapSWU(scalars[0]),
htfDefaults: {
DST: 'P256_XMD:SHA-256_SSWU_RO_',
p: Fp.ORDER,
m: 1,
k: 128,
expand: true,
hash: sha256,
},
} as const, } as const,
sha256 sha256
); );

37
curve-definitions/src/p384.ts
View File

@ -1,17 +1,33 @@
/*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */ /*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { createCurve } from './_shortw_utils.js'; import { createCurve } from './_shortw_utils.js';
import { sha384 } from '@noble/hashes/sha512'; import { sha384 } from '@noble/hashes/sha512';
import { Fp } from '@noble/curves/modular'; import { Fp as Field } from '@noble/curves/modular';
import { mapToCurveSimpleSWU } from '@noble/curves/weierstrass';
// NIST secp384r1 aka P384 // NIST secp384r1 aka P384
// https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-384 // https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-384
// Field over which we'll do calculations. 2n**384n - 2n**128n - 2n**96n + 2n**32n - 1n
// prettier-ignore
const P = BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff');
const Fp = Field(P);
const CURVE_A = Fp.create(BigInt('-3'));
// prettier-ignore
const CURVE_B = BigInt('0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef');
const mapSWU = mapToCurveSimpleSWU(Fp, {
A: CURVE_A,
B: CURVE_B,
Z: Fp.create(BigInt('-12')),
});
// prettier-ignore // prettier-ignore
export const P384 = createCurve({ export const P384 = createCurve({
// Params: a, b // Params: a, b
a: BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc'), a: CURVE_A,
b: BigInt('0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef'), b: CURVE_B,
// Field over which we'll do calculations. 2n**384n - 2n**128n - 2n**96n + 2n**32n - 1n // Field over which we'll do calculations. 2n**384n - 2n**128n - 2n**96n + 2n**32n - 1n
Fp: Fp(BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff')), Fp,
// Curve order, total count of valid points in the field. // Curve order, total count of valid points in the field.
n: BigInt('0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973'), n: BigInt('0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973'),
// Base point (x, y) aka generator point // Base point (x, y) aka generator point
@ -19,5 +35,16 @@ export const P384 = createCurve({
Gy: BigInt('0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f'), Gy: BigInt('0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f'),
h: BigInt(1), h: BigInt(1),
lowS: false, lowS: false,
} as const, sha384); mapToCurve: (scalars: bigint[]) => mapSWU(scalars[0]),
htfDefaults: {
DST: 'P384_XMD:SHA-384_SSWU_RO_',
p: Fp.ORDER,
m: 1,
k: 192,
expand: true,
hash: sha384,
},
} as const,
sha384
);
export const secp384r1 = P384; export const secp384r1 = P384;

37
curve-definitions/src/p521.ts
View File

@ -1,19 +1,35 @@
/*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */ /*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { createCurve } from './_shortw_utils.js'; import { createCurve } from './_shortw_utils.js';
import { Fp } from '@noble/curves/modular';
import { sha512 } from '@noble/hashes/sha512'; import { sha512 } from '@noble/hashes/sha512';
import { bytesToHex, PrivKey } from '@noble/curves/utils'; import { bytesToHex, PrivKey } from '@noble/curves/utils';
import { Fp as Field } from '@noble/curves/modular';
import { mapToCurveSimpleSWU } from '@noble/curves/weierstrass';
// NIST secp521r1 aka P521 // NIST secp521r1 aka P521
// Note that it's 521, which differs from 512 of its hash function. // Note that it's 521, which differs from 512 of its hash function.
// https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-521 // https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-521
// Field over which we'll do calculations; 2n**521n - 1n
// prettier-ignore
const P = BigInt('0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff');
const Fp = Field(P);
const CURVE_A = Fp.create(BigInt('-3'));
// prettier-ignore
const CURVE_B = BigInt('0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00');
const mapSWU = mapToCurveSimpleSWU(Fp, {
A: CURVE_A,
B: CURVE_B,
Z: Fp.create(BigInt('-4')),
});
// prettier-ignore // prettier-ignore
export const P521 = createCurve({ export const P521 = createCurve({
// Params: a, b // Params: a, b
a: BigInt('0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc'), a: CURVE_A,
b: BigInt('0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00'), b: CURVE_B,
// Field over which we'll do calculations; 2n**521n - 1n Fp,
Fp: Fp(BigInt('0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff')),
// Curve order, total count of valid points in the field // Curve order, total count of valid points in the field
n: BigInt('0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409'), n: BigInt('0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409'),
// Base point (x, y) aka generator point // Base point (x, y) aka generator point
@ -31,6 +47,15 @@ export const P521 = createCurve({
throw new Error('Invalid key'); throw new Error('Invalid key');
} }
return key.padStart(66 * 2, '0'); return key.padStart(66 * 2, '0');
} },
mapToCurve: (scalars: bigint[]) => mapSWU(scalars[0]),
htfDefaults: {
DST: 'P521_XMD:SHA-512_SSWU_RO_',
p: Fp.ORDER,
m: 1,
k: 256,
expand: true,
hash: sha512,
},
} as const, sha512); } as const, sha512);
export const secp521r1 = P521; export const secp521r1 = P521;

61
curve-definitions/src/secp256k1.ts
View File

@ -1,8 +1,8 @@
/*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */ /*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { sha256 } from '@noble/hashes/sha256'; import { sha256 } from '@noble/hashes/sha256';
import { Fp, mod, pow2 } from '@noble/curves/modular'; import { Fp as Field, mod, pow2 } from '@noble/curves/modular';
import { createCurve } from './_shortw_utils.js'; import { createCurve } from './_shortw_utils.js';
import { PointType } from '@noble/curves/weierstrass'; import { PointType, mapToCurveSimpleSWU } from '@noble/curves/weierstrass';
import { import {
ensureBytes, ensureBytes,
concatBytes, concatBytes,
@ -12,6 +12,7 @@ import {
PrivKey, PrivKey,
} from '@noble/curves/utils'; } from '@noble/curves/utils';
import { randomBytes } from '@noble/hashes/utils'; import { randomBytes } from '@noble/hashes/utils';
import { isogenyMap } from '@noble/curves/hashToCurve';
/** /**
* secp256k1 belongs to Koblitz curves: it has * secp256k1 belongs to Koblitz curves: it has
@ -58,7 +59,47 @@ function sqrtMod(y: bigint): bigint {
return pow2(t2, _2n, P); return pow2(t2, _2n, P);
} }
const fp = Fp(secp256k1P, undefined, undefined, { sqrt: sqrtMod }); const Fp = Field(secp256k1P, undefined, undefined, { sqrt: sqrtMod });
type Fp = bigint;
const isoMap = isogenyMap(
Fp,
[
// xNum
[
'0x8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa8c7',
'0x7d3d4c80bc321d5b9f315cea7fd44c5d595d2fc0bf63b92dfff1044f17c6581',
'0x534c328d23f234e6e2a413deca25caece4506144037c40314ecbd0b53d9dd262',
'0x8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa88c',
],
// xDen
[
'0xd35771193d94918a9ca34ccbb7b640dd86cd409542f8487d9fe6b745781eb49b',
'0xedadc6f64383dc1df7c4b2d51b54225406d36b641f5e41bbc52a56612a8c6d14',
'0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1
],
// yNum
[
'0x4bda12f684bda12f684bda12f684bda12f684bda12f684bda12f684b8e38e23c',
'0xc75e0c32d5cb7c0fa9d0a54b12a0a6d5647ab046d686da6fdffc90fc201d71a3',
'0x29a6194691f91a73715209ef6512e576722830a201be2018a765e85a9ecee931',
'0x2f684bda12f684bda12f684bda12f684bda12f684bda12f684bda12f38e38d84',
],
// yDen
[
'0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffff93b',
'0x7a06534bb8bdb49fd5e9e6632722c2989467c1bfc8e8d978dfb425d2685c2573',
'0x6484aa716545ca2cf3a70c3fa8fe337e0a3d21162f0d6299a7bf8192bfd2a76f',
'0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1
],
].map((i) => i.map((j) => BigInt(j))) as [Fp[], Fp[], Fp[], Fp[]]
);
const mapSWU = mapToCurveSimpleSWU(Fp, {
A: BigInt('0x3f8731abdd661adca08a5558f0f5d272e953d363cb6f0e5d405447c01a444533'),
B: BigInt('1771'),
Z: Fp.create(BigInt('-11')),
});
export const secp256k1 = createCurve( export const secp256k1 = createCurve(
{ {
@ -68,7 +109,7 @@ export const secp256k1 = createCurve(
b: BigInt(7), b: BigInt(7),
// Field over which we'll do calculations; // Field over which we'll do calculations;
// 2n**256n - 2n**32n - 2n**9n - 2n**8n - 2n**7n - 2n**6n - 2n**4n - 1n // 2n**256n - 2n**32n - 2n**9n - 2n**8n - 2n**7n - 2n**6n - 2n**4n - 1n
Fp: fp, Fp,
// Curve order, total count of valid points in the field // Curve order, total count of valid points in the field
n: secp256k1N, n: secp256k1N,
// Base point (x, y) aka generator point // Base point (x, y) aka generator point
@ -102,6 +143,18 @@ export const secp256k1 = createCurve(
return { k1neg, k1, k2neg, k2 }; return { k1neg, k1, k2neg, k2 };
}, },
}, },
mapToCurve: (scalars: bigint[]) => {
const { x, y } = mapSWU(Fp.create(scalars[0]));
return isoMap(x, y);
},
htfDefaults: {
DST: 'secp256k1_XMD:SHA-256_SSWU_RO_',
p: Fp.ORDER,
m: 1,
k: 128,
expand: true,
hash: sha256,
},
}, },
sha256 sha256
); );

15
curve-definitions/test/bls12-381.test.js
View File

@ -336,10 +336,7 @@ const getPubKey = (priv) => bls.getPublicKey(priv);
const a = Fp2.fromBigTuple([num1[0], num1[1]]); const a = Fp2.fromBigTuple([num1[0], num1[1]]);
const b = Fp2.fromBigTuple([num2[0], num2[1]]); const b = Fp2.fromBigTuple([num2[0], num2[1]]);
const c = Fp2.fromBigTuple([num3[0], num3[1]]); const c = Fp2.fromBigTuple([num3[0], num3[1]]);
deepStrictEqual( deepStrictEqual(Fp2.mul(a, Fp2.add(b, c)), Fp2.add(Fp2.mul(b, a), Fp2.mul(c, a)));
Fp2.mul(a, Fp2.add(b, c)),
Fp2.add(Fp2.mul(b, a), Fp2.mul(c, a))
);
}) })
); );
}); });
@ -577,10 +574,7 @@ const getPubKey = (priv) => bls.getPublicKey(priv);
const a = Fp12.fromBigTwelve(num1); const a = Fp12.fromBigTwelve(num1);
const b = Fp12.fromBigTwelve(num2); const b = Fp12.fromBigTwelve(num2);
const c = Fp12.fromBigTwelve(num3); const c = Fp12.fromBigTwelve(num3);
deepStrictEqual( deepStrictEqual(Fp12.mul(a, Fp12.mul(b, c)), Fp12.mul(Fp12.mul(a, b), c));
Fp12.mul(a, Fp12.mul(b, c)),
Fp12.mul(Fp12.mul(a, b), c)
);
}) })
); );
}); });
@ -590,10 +584,7 @@ const getPubKey = (priv) => bls.getPublicKey(priv);
const a = Fp12.fromBigTwelve(num1); const a = Fp12.fromBigTwelve(num1);
const b = Fp12.fromBigTwelve(num2); const b = Fp12.fromBigTwelve(num2);
const c = Fp12.fromBigTwelve(num3); const c = Fp12.fromBigTwelve(num3);
deepStrictEqual( deepStrictEqual(Fp12.mul(a, Fp12.add(b, c)), Fp12.add(Fp12.mul(b, a), Fp12.mul(c, a)));
Fp12.mul(a, Fp12.add(b, c)),
Fp12.add(Fp12.mul(b, a), Fp12.mul(c, a))
);
}) })
); );
}); });

12
curve-definitions/test/fixtures/rfc6979.json vendored
View File

@ -28,16 +28,16 @@
"Uy": "EEAB6F3DEBE455E3DBF85416F7030CBD94F34F2D6F232C69F3C1385A", "Uy": "EEAB6F3DEBE455E3DBF85416F7030CBD94F34F2D6F232C69F3C1385A",
"cases": [ "cases": [
{ {
"k": "AD3029E0278F80643DE33917CE6908C70A8FF50A411F06E41DEDFCDC", "k": "C1D1F2F10881088301880506805FEB4825FE09ACB6816C36991AA06D",
"message": "sample", "message": "sample",
"r": "61AA3DA010E8E8406C656BC477A7A7189895E7E840CDFE8FF42307BA", "r": "1CDFE6662DDE1E4A1EC4CDEDF6A1F5A2FB7FBD9145C12113E6ABFD3E",
"s": "BC814050DAB5D23770879494F9E0A680DC1AF7161991BDE692B10101" "s": "A6694FD7718A21053F225D3F46197CA699D45006C06F871808F43EBC"
}, },
{ {
"k": "FF86F57924DA248D6E44E8154EB69F0AE2AEBAEE9931D0B5A969F904", "k": "DF8B38D40DCA3E077D0AC520BF56B6D565134D9B5F2EAE0D34900524",
"message": "test", "message": "test",
"r": "AD04DDE87B84747A243A631EA47A1BA6D1FAA059149AD2440DE6FBA6", "r": "C441CE8E261DED634E4CF84910E4C5D1D22C5CF3B732BB204DBEF019",
"s": "178D49B1AE90E3D8B629BE3DB5683915F4E8C99FDF6E666CF37ADCFD" "s": "902F42847A63BDC5F6046ADA114953120F99442D76510150F372A3F4"
} }
] ]
}, },

109
curve-definitions/test/hashToCurve.test.js Normal file
View File

@ -0,0 +1,109 @@
import { deepStrictEqual } from 'assert';
import { should } from 'micro-should';
import { bytesToHex } from '@noble/hashes/utils';
// Generic tests for all curves in package
import { sha256 } from '@noble/hashes/sha256';
import { sha512 } from '@noble/hashes/sha512';
import { secp256r1 } from '../lib/p256.js';
import { secp384r1 } from '../lib/p384.js';
import { secp521r1 } from '../lib/p521.js';
import { secp256k1 } from '../lib/secp256k1.js';
import { bls12_381 } from '../lib/bls12-381.js';
import { ed25519 } from '../lib/ed25519.js';
import { ed448 } from '../lib/ed448.js';
import { stringToBytes, expand_message_xmd } from '@noble/curves/hashToCurve';
import { default as xmd_sha256_38 } from './hashToCurve/expand_message_xmd_SHA256_38.json' assert { type: 'json' };
import { default as xmd_sha256_256 } from './hashToCurve/expand_message_xmd_SHA256_256.json' assert { type: 'json' };
import { default as xmd_sha512_38 } from './hashToCurve/expand_message_xmd_SHA512_38.json' assert { type: 'json' };
// P256
import { default as p256_ro } from './hashToCurve/P256_XMD:SHA-256_SSWU_RO_.json' assert { type: 'json' };
import { default as p256_nu } from './hashToCurve/P256_XMD:SHA-256_SSWU_NU_.json' assert { type: 'json' };
// P384
import { default as p384_ro } from './hashToCurve/P384_XMD:SHA-384_SSWU_RO_.json' assert { type: 'json' };
import { default as p384_nu } from './hashToCurve/P384_XMD:SHA-384_SSWU_NU_.json' assert { type: 'json' };
// P521
import { default as p521_ro } from './hashToCurve/P521_XMD:SHA-512_SSWU_RO_.json' assert { type: 'json' };
import { default as p521_nu } from './hashToCurve/P521_XMD:SHA-512_SSWU_NU_.json' assert { type: 'json' };
// secp256k1
import { default as secp256k1_ro } from './hashToCurve/secp256k1_XMD:SHA-256_SSWU_RO_.json' assert { type: 'json' };
import { default as secp256k1_nu } from './hashToCurve/secp256k1_XMD:SHA-256_SSWU_NU_.json' assert { type: 'json' };
// bls-G1
import { default as g1_ro } from './hashToCurve/BLS12381G1_XMD:SHA-256_SSWU_RO_.json' assert { type: 'json' };
import { default as g1_nu } from './hashToCurve/BLS12381G1_XMD:SHA-256_SSWU_NU_.json' assert { type: 'json' };
// bls-G2
import { default as g2_ro } from './hashToCurve/BLS12381G2_XMD:SHA-256_SSWU_RO_.json' assert { type: 'json' };
import { default as g2_nu } from './hashToCurve/BLS12381G2_XMD:SHA-256_SSWU_NU_.json' assert { type: 'json' };
// ed25519
import { default as ed25519_ro } from './hashToCurve/edwards25519_XMD:SHA-512_ELL2_RO_.json' assert { type: 'json' };
import { default as ed25519_nu } from './hashToCurve/edwards25519_XMD:SHA-512_ELL2_NU_.json' assert { type: 'json' };
// ed448
import { default as ed448_ro } from './hashToCurve/edwards448_XOF:SHAKE256_ELL2_RO_.json' assert { type: 'json' };
import { default as ed448_nu } from './hashToCurve/edwards448_XOF:SHAKE256_ELL2_NU_.json' assert { type: 'json' };
function testExpandXMD(hash, vectors) {
for (let i = 0; i < vectors.tests.length; i++) {
const t = vectors.tests[i];
should(`expand_message_xmd/${vectors.hash}/${vectors.DST.length}/${i}`, () => {
const p = expand_message_xmd(
stringToBytes(t.msg),
stringToBytes(vectors.DST),
t.len_in_bytes,
hash
);
deepStrictEqual(bytesToHex(p), t.uniform_bytes);
});
}
}
testExpandXMD(sha256, xmd_sha256_38);
testExpandXMD(sha256, xmd_sha256_256);
testExpandXMD(sha512, xmd_sha512_38);
function stringToFp(s) {
// bls-G2 support
if (s.includes(',')) {
const [c0, c1] = s.split(',').map(BigInt);
return { c0, c1 };
}
return BigInt(s);
}
function testCurve(curve, ro, nu) {
for (let i = 0; i < ro.vectors.length; i++) {
const t = ro.vectors[i];
should(`${ro.curve}/${ro.ciphersuite}(${i})`, () => {
const p = curve.Point.hashToCurve(stringToBytes(t.msg), {
DST: ro.dst,
});
deepStrictEqual(p.x, stringToFp(t.P.x), 'Px');
deepStrictEqual(p.y, stringToFp(t.P.y), 'Py');
});
}
for (let i = 0; i < nu.vectors.length; i++) {
const t = nu.vectors[i];
should(`${nu.curve}/${nu.ciphersuite}(${i})`, () => {
const p = curve.Point.encodeToCurve(stringToBytes(t.msg), {
DST: nu.dst,
});
deepStrictEqual(p.x, stringToFp(t.P.x), 'Px');
deepStrictEqual(p.y, stringToFp(t.P.y), 'Py');
});
}
}
testCurve(secp256r1, p256_ro, p256_nu);
testCurve(secp384r1, p384_ro, p384_nu);
testCurve(secp521r1, p521_ro, p521_nu);
// TODO: remove same tests from bls12
testCurve(bls12_381.G1, g1_ro, g1_nu);
testCurve(bls12_381.G2, g2_ro, g2_nu);
testCurve(secp256k1, secp256k1_ro, secp256k1_nu);
//testCurve(ed25519, ed25519_ro, ed25519_nu);
//testCurve(ed448, ed448_ro, ed448_nu);
// ESM is broken.
import url from 'url';
if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
should.run();
}

90
curve-definitions/test/hashToCurve/BLS12381G1_XMD:SHA-256_SSWU_NU_.json Normal file
View File

@ -0,0 +1,90 @@
{
"L": "0x40",
"Z": "0xb",
"ciphersuite": "BLS12381G1_XMD:SHA-256_SSWU_NU_",
"curve": "BLS12-381 G1",
"dst": "QUUX-V01-CS02-with-BLS12381G1_XMD:SHA-256_SSWU_NU_",
"expand": "XMD",
"field": {
"m": "0x1",
"p": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab"
},
"hash": "sha256",
"k": "0x80",
"map": {
"name": "SSWU"
},
"randomOracle": false,
"vectors": [
{
"P": {
"x": "0x184bb665c37ff561a89ec2122dd343f20e0f4cbcaec84e3c3052ea81d1834e192c426074b02ed3dca4e7676ce4ce48ba",
"y": "0x04407b8d35af4dacc809927071fc0405218f1401a6d15af775810e4e460064bcc9468beeba82fdc751be70476c888bf3"
},
"Q": {
"x": "0x11398d3b324810a1b093f8e35aa8571cced95858207e7f49c4fd74656096d61d8a2f9a23cdb18a4dd11cd1d66f41f709",
"y": "0x19316b6fb2ba7717355d5d66a361899057e1e84a6823039efc7beccefe09d023fb2713b1c415fcf278eb0c39a89b4f72"
},
"msg": "",
"u": [
"0x156c8a6a2c184569d69a76be144b5cdc5141d2d2ca4fe341f011e25e3969c55ad9e9b9ce2eb833c81a908e5fa4ac5f03"
]
},
{
"P": {
"x": "0x009769f3ab59bfd551d53a5f846b9984c59b97d6842b20a2c565baa167945e3d026a3755b6345df8ec7e6acb6868ae6d",
"y": "0x1532c00cf61aa3d0ce3e5aa20c3b531a2abd2c770a790a2613818303c6b830ffc0ecf6c357af3317b9575c567f11cd2c"
},
"Q": {
"x": "0x1998321bc27ff6d71df3051b5aec12ff47363d81a5e9d2dff55f444f6ca7e7d6af45c56fd029c58237c266ef5cda5254",
"y": "0x034d274476c6307ae584f951c82e7ea85b84f72d28f4d6471732356121af8d62a49bc263e8eb913a6cf6f125995514ee"
},
"msg": "abc",
"u": [
"0x147e1ed29f06e4c5079b9d14fc89d2820d32419b990c1c7bb7dbea2a36a045124b31ffbde7c99329c05c559af1c6cc82"
]
},
{
"P": {
"x": "0x1974dbb8e6b5d20b84df7e625e2fbfecb2cdb5f77d5eae5fb2955e5ce7313cae8364bc2fff520a6c25619739c6bdcb6a",
"y": "0x15f9897e11c6441eaa676de141c8d83c37aab8667173cbe1dfd6de74d11861b961dccebcd9d289ac633455dfcc7013a3"
},
"Q": {
"x": "0x17d502fa43bd6a4cad2859049a0c3ecefd60240d129be65da271a4c03a9c38fa78163b9d2a919d2beb57df7d609b4919",
"y": "0x109019902ae93a8732abecf2ff7fecd2e4e305eb91f41c9c3267f16b6c19de138c7272947f25512745da6c466cdfd1ac"
},
"msg": "abcdef0123456789",
"u": [
"0x04090815ad598a06897dd89bcda860f25837d54e897298ce31e6947378134d3761dc59a572154963e8c954919ecfa82d"
]
},
{
"P": {
"x": "0x0a7a047c4a8397b3446450642c2ac64d7239b61872c9ae7a59707a8f4f950f101e766afe58223b3bff3a19a7f754027c",
"y": "0x1383aebba1e4327ccff7cf9912bda0dbc77de048b71ef8c8a81111d71dc33c5e3aa6edee9cf6f5fe525d50cc50b77cc9"
},
"Q": {
"x": "0x112eb92dd2b3aa9cd38b08de4bef603f2f9fb0ca226030626a9a2e47ad1e9847fe0a5ed13766c339e38f514bba143b21",
"y": "0x17542ce2f8d0a54f2c5ba8c4b14e10b22d5bcd7bae2af3c965c8c872b571058c720eac448276c99967ded2bf124490e1"
},
"msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
"u": [
"0x08dccd088ca55b8bfbc96fb50bb25c592faa867a8bb78d4e94a8cc2c92306190244532e91feba2b7fed977e3c3bb5a1f"
]
},
{
"P": {
"x": "0x0e7a16a975904f131682edbb03d9560d3e48214c9986bd50417a77108d13dc957500edf96462a3d01e62dc6cd468ef11",
"y": "0x0ae89e677711d05c30a48d6d75e76ca9fb70fe06c6dd6ff988683d89ccde29ac7d46c53bb97a59b1901abf1db66052db"
},
"Q": {
"x": "0x1775d400a1bacc1c39c355da7e96d2d1c97baa9430c4a3476881f8521c09a01f921f592607961efc99c4cd46bd78ca19",
"y": "0x1109b5d59f65964315de65a7a143e86eabc053104ed289cf480949317a5685fad7254ff8e7fe6d24d3104e5d55ad6370"
},
"msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"u": [
"0x0dd824886d2123a96447f6c56e3a3fa992fbfefdba17b6673f9f630ff19e4d326529db37e1c1be43f905bf9202e0278d"
]
}
]
}

115
curve-definitions/test/hashToCurve/BLS12381G1_XMD:SHA-256_SSWU_RO_.json Normal file
View File

@ -0,0 +1,115 @@
{
"L": "0x40",
"Z": "0xb",
"ciphersuite": "BLS12381G1_XMD:SHA-256_SSWU_RO_",
"curve": "BLS12-381 G1",
"dst": "QUUX-V01-CS02-with-BLS12381G1_XMD:SHA-256_SSWU_RO_",
"expand": "XMD",
"field": {
"m": "0x1",
"p": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab"
},
"hash": "sha256",
"k": "0x80",
"map": {
"name": "SSWU"
},
"randomOracle": true,
"vectors": [
{
"P": {
"x": "0x052926add2207b76ca4fa57a8734416c8dc95e24501772c814278700eed6d1e4e8cf62d9c09db0fac349612b759e79a1",
"y": "0x08ba738453bfed09cb546dbb0783dbb3a5f1f566ed67bb6be0e8c67e2e81a4cc68ee29813bb7994998f3eae0c9c6a265"
},
"Q0": {
"x": "0x11a3cce7e1d90975990066b2f2643b9540fa40d6137780df4e753a8054d07580db3b7f1f03396333d4a359d1fe3766fe",
"y": "0x0eeaf6d794e479e270da10fdaf768db4c96b650a74518fc67b04b03927754bac66f3ac720404f339ecdcc028afa091b7"
},
"Q1": {
"x": "0x160003aaf1632b13396dbad518effa00fff532f604de1a7fc2082ff4cb0afa2d63b2c32da1bef2bf6c5ca62dc6b72f9c",
"y": "0x0d8bb2d14e20cf9f6036152ed386d79189415b6d015a20133acb4e019139b94e9c146aaad5817f866c95d609a361735e"
},
"msg": "",
"u": [
"0x0ba14bd907ad64a016293ee7c2d276b8eae71f25a4b941eece7b0d89f17f75cb3ae5438a614fb61d6835ad59f29c564f",
"0x019b9bd7979f12657976de2884c7cce192b82c177c80e0ec604436a7f538d231552f0d96d9f7babe5fa3b19b3ff25ac9"
]
},
{
"P": {
"x": "0x03567bc5ef9c690c2ab2ecdf6a96ef1c139cc0b2f284dca0a9a7943388a49a3aee664ba5379a7655d3c68900be2f6903",
"y": "0x0b9c15f3fe6e5cf4211f346271d7b01c8f3b28be689c8429c85b67af215533311f0b8dfaaa154fa6b88176c229f2885d"
},
"Q0": {
"x": "0x125435adce8e1cbd1c803e7123f45392dc6e326d292499c2c45c5865985fd74fe8f042ecdeeec5ecac80680d04317d80",
"y": "0x0e8828948c989126595ee30e4f7c931cbd6f4570735624fd25aef2fa41d3f79cfb4b4ee7b7e55a8ce013af2a5ba20bf2"
},
"Q1": {
"x": "0x11def93719829ecda3b46aa8c31fc3ac9c34b428982b898369608e4f042babee6c77ab9218aad5c87ba785481eff8ae4",
"y": "0x0007c9cef122ccf2efd233d6eb9bfc680aa276652b0661f4f820a653cec1db7ff69899f8e52b8e92b025a12c822a6ce6"
},
"msg": "abc",
"u": [
"0x0d921c33f2bad966478a03ca35d05719bdf92d347557ea166e5bba579eea9b83e9afa5c088573c2281410369fbd32951",
"0x003574a00b109ada2f26a37a91f9d1e740dffd8d69ec0c35e1e9f4652c7dba61123e9dd2e76c655d956e2b3462611139"
]
},
{
"P": {
"x": "0x11e0b079dea29a68f0383ee94fed1b940995272407e3bb916bbf268c263ddd57a6a27200a784cbc248e84f357ce82d98",
"y": "0x03a87ae2caf14e8ee52e51fa2ed8eefe80f02457004ba4d486d6aa1f517c0889501dc7413753f9599b099ebcbbd2d709"
},
"Q0": {
"x": "0x08834484878c217682f6d09a4b51444802fdba3d7f2df9903a0ddadb92130ebbfa807fffa0eabf257d7b48272410afff",
"y": "0x0b318f7ecf77f45a0f038e62d7098221d2dbbca2a394164e2e3fe953dc714ac2cde412d8f2d7f0c03b259e6795a2508e"
},
"Q1": {
"x": "0x158418ed6b27e2549f05531a8281b5822b31c3bf3144277fbb977f8d6e2694fedceb7011b3c2b192f23e2a44b2bd106e",
"y": "0x1879074f344471fac5f839e2b4920789643c075792bec5af4282c73f7941cda5aa77b00085eb10e206171b9787c4169f"
},
"msg": "abcdef0123456789",
"u": [
"0x062d1865eb80ebfa73dcfc45db1ad4266b9f3a93219976a3790ab8d52d3e5f1e62f3b01795e36834b17b70e7b76246d4",
"0x0cdc3e2f271f29c4ff75020857ce6c5d36008c9b48385ea2f2bf6f96f428a3deb798aa033cd482d1cdc8b30178b08e3a"
]
},
{
"P": {
"x": "0x15f68eaa693b95ccb85215dc65fa81038d69629f70aeee0d0f677cf22285e7bf58d7cb86eefe8f2e9bc3f8cb84fac488",
"y": "0x1807a1d50c29f430b8cafc4f8638dfeeadf51211e1602a5f184443076715f91bb90a48ba1e370edce6ae1062f5e6dd38"
},
"Q0": {
"x": "0x0cbd7f84ad2c99643fea7a7ac8f52d63d66cefa06d9a56148e58b984b3dd25e1f41ff47154543343949c64f88d48a710",
"y": "0x052c00e4ed52d000d94881a5638ae9274d3efc8bc77bc0e5c650de04a000b2c334a9e80b85282a00f3148dfdface0865"
},
"Q1": {
"x": "0x06493fb68f0d513af08be0372f849436a787e7b701ae31cb964d968021d6ba6bd7d26a38aaa5a68e8c21a6b17dc8b579",
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}

90
curve-definitions/test/hashToCurve/BLS12381G2_XMD:SHA-256_SSWU_NU_.json Normal file
View File

@ -0,0 +1,90 @@
{
"L": "0x40",
"Z": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaa9,0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa",
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"curve": "BLS12-381 G2",
"dst": "QUUX-V01-CS02-with-BLS12381G2_XMD:SHA-256_SSWU_NU_",
"expand": "XMD",
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},
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},
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]
}

115
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View File

@ -0,0 +1,115 @@
{
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"ciphersuite": "BLS12381G2_XMD:SHA-256_SSWU_RO_",
"curve": "BLS12-381 G2",
"dst": "QUUX-V01-CS02-with-BLS12381G2_XMD:SHA-256_SSWU_RO_",
"expand": "XMD",
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},
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},
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]
}
]
}

90
curve-definitions/test/hashToCurve/P256_XMD:SHA-256_SSWU_NU_.json Normal file
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@ -0,0 +1,90 @@
{
"L": "0x30",
"Z": "0xffffffff00000001000000000000000000000000fffffffffffffffffffffff5",
"ciphersuite": "P256_XMD:SHA-256_SSWU_NU_",
"curve": "NIST P-256",
"dst": "QUUX-V01-CS02-with-P256_XMD:SHA-256_SSWU_NU_",
"expand": "XMD",
"field": {
"m": "0x1",
"p": "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff"
},
"hash": "sha256",
"k": "0x80",
"map": {
"name": "SSWU"
},
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{
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}
]
}

115
curve-definitions/test/hashToCurve/P256_XMD:SHA-256_SSWU_RO_.json Normal file
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@ -0,0 +1,115 @@
{
"L": "0x30",
"Z": "0xffffffff00000001000000000000000000000000fffffffffffffffffffffff5",
"ciphersuite": "P256_XMD:SHA-256_SSWU_RO_",
"curve": "NIST P-256",
"dst": "QUUX-V01-CS02-with-P256_XMD:SHA-256_SSWU_RO_",
"expand": "XMD",
"field": {
"m": "0x1",
"p": "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff"
},
"hash": "sha256",
"k": "0x80",
"map": {
"name": "SSWU"
},
"randomOracle": true,
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{
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"y": "0xb45d1a36d00ad90e5ec7840a60a4de411917fbe7c82c3949a6e699e5a1b66aac"
},
"msg": "",
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{
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"y": "0x589a62d2b22357fed5449bc38065b760095ebe6aeac84b01156ee4252715446e"
},
"msg": "abc",
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"msg": "abcdef0123456789",
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]
}
]
}

90
curve-definitions/test/hashToCurve/P384_XMD:SHA-384_SSWU_NU_.json Normal file
View File

@ -0,0 +1,90 @@
{
"L": "0x48",
"Z": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffff3",
"ciphersuite": "P384_XMD:SHA-384_SSWU_NU_",
"curve": "NIST P-384",
"dst": "QUUX-V01-CS02-with-P384_XMD:SHA-384_SSWU_NU_",
"expand": "XMD",
"field": {
"m": "0x1",
"p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff"
},
"hash": "sha384",
"k": "0xc0",
"map": {
"name": "SSWU"
},
"randomOracle": false,
"vectors": [
{
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"msg": "",
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},
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}

115
curve-definitions/test/hashToCurve/P384_XMD:SHA-384_SSWU_RO_.json Normal file
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@ -0,0 +1,115 @@
{
"L": "0x48",
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},
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},
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}

90
curve-definitions/test/hashToCurve/P521_XMD:SHA-512_SSWU_NU_.json Normal file
View File

@ -0,0 +1,90 @@
{
"L": "0x62",
"Z": "0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffb",
"ciphersuite": "P521_XMD:SHA-512_SSWU_NU_",
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},
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}

115
curve-definitions/test/hashToCurve/P521_XMD:SHA-512_SSWU_RO_.json Normal file
View File

@ -0,0 +1,115 @@
{
"L": "0x62",
"Z": "0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffb",
"ciphersuite": "P521_XMD:SHA-512_SSWU_RO_",
"curve": "NIST P-521",
"dst": "QUUX-V01-CS02-with-P521_XMD:SHA-512_SSWU_RO_",
"expand": "XMD",
"field": {
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"p": "0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
},
"hash": "sha512",
"k": "0x100",
"map": {
"name": "SSWU"
},
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}

90
curve-definitions/test/hashToCurve/curve25519_XMD:SHA-512_ELL2_NU_.json Normal file
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@ -0,0 +1,90 @@
{
"L": "0x30",
"Z": "0x2",
"ciphersuite": "curve25519_XMD:SHA-512_ELL2_NU_",
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"dst": "QUUX-V01-CS02-with-curve25519_XMD:SHA-512_ELL2_NU_",
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},
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115
curve-definitions/test/hashToCurve/curve25519_XMD:SHA-512_ELL2_RO_.json Normal file
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@ -0,0 +1,115 @@
{
"L": "0x30",
"Z": "0x2",
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},
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}

90
curve-definitions/test/hashToCurve/curve448_XOF:SHAKE256_ELL2_NU_.json Normal file
View File

@ -0,0 +1,90 @@
{
"L": "0x54",
"Z": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffffffffffffffffffffffffffffffffffffffffffffffffffffe",
"ciphersuite": "curve448_XOF:SHAKE256_ELL2_NU_",
"curve": "curve448",
"dst": "QUUX-V01-CS02-with-curve448_XOF:SHAKE256_ELL2_NU_",
"expand": "XOF",
"field": {
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"p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
},
"hash": "shake_256",
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},
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115
curve-definitions/test/hashToCurve/curve448_XOF:SHAKE256_ELL2_RO_.json Normal file
View File

@ -0,0 +1,115 @@
{
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}

90
curve-definitions/test/hashToCurve/edwards25519_XMD:SHA-512_ELL2_NU_.json Normal file
View File

@ -0,0 +1,90 @@
{
"L": "0x30",
"Z": "0x2",
"ciphersuite": "edwards25519_XMD:SHA-512_ELL2_NU_",
"curve": "edwards25519",
"dst": "QUUX-V01-CS02-with-edwards25519_XMD:SHA-512_ELL2_NU_",
"expand": "XMD",
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},
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},
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115
curve-definitions/test/hashToCurve/edwards25519_XMD:SHA-512_ELL2_RO_.json Normal file
View File

@ -0,0 +1,115 @@
{
"L": "0x30",
"Z": "0x2",
"ciphersuite": "edwards25519_XMD:SHA-512_ELL2_RO_",
"curve": "edwards25519",
"dst": "QUUX-V01-CS02-with-edwards25519_XMD:SHA-512_ELL2_RO_",
"expand": "XMD",
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"p": "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed"
},
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},
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90
curve-definitions/test/hashToCurve/edwards448_XOF:SHAKE256_ELL2_NU_.json Normal file
View File

@ -0,0 +1,90 @@
{
"L": "0x54",
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115
curve-definitions/test/hashToCurve/edwards448_XOF:SHAKE256_ELL2_RO_.json Normal file
View File

@ -0,0 +1,115 @@
{
"L": "0x54",
"Z": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffffffffffffffffffffffffffffffffffffffffffffffffffffe",
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}

78
curve-definitions/test/hashToCurve/expand_message_xmd_SHA256_256.json Normal file
View File

@ -0,0 +1,78 @@
{
"DST": "QUUX-V01-CS02-with-expander-SHA256-128-long-DST-1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111",
"hash": "SHA256",
"k": 128,
"name": "expand_message_xmd",
"tests": [
{
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"len_in_bytes": "0x20",
"msg": "",
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{
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{
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{
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}

78
curve-definitions/test/hashToCurve/expand_message_xmd_SHA256_38.json Normal file
View File

@ -0,0 +1,78 @@
{
"DST": "QUUX-V01-CS02-with-expander-SHA256-128",
"hash": "SHA256",
"k": 128,
"name": "expand_message_xmd",
"tests": [
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413235362d31323826",
"len_in_bytes": "0x20",
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"uniform_bytes": "68a985b87eb6b46952128911f2a4412bbc302a9d759667f87f7a21d803f07235"
},
{
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"uniform_bytes": "d8ccab23b5985ccea865c6c97b6e5b8350e794e603b4b97902f53a8a0d605615"
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{
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{
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}
]
}

78
curve-definitions/test/hashToCurve/expand_message_xmd_SHA512_38.json Normal file
View File

@ -0,0 +1,78 @@
{
"DST": "QUUX-V01-CS02-with-expander-SHA512-256",
"hash": "SHA512",
"k": 256,
"name": "expand_message_xmd",
"tests": [
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
"len_in_bytes": "0x20",
"msg": "",
"msg_prime": "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002000515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
"uniform_bytes": "6b9a7312411d92f921c6f68ca0b6380730a1a4d982c507211a90964c394179ba"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348413531322d32353626",
"len_in_bytes": "0x20",
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{
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}

78
curve-definitions/test/hashToCurve/expand_message_xof_SHAKE128_256.json Normal file
View File

@ -0,0 +1,78 @@
{
"DST": "QUUX-V01-CS02-with-expander-SHAKE128-long-DST-111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111",
"hash": "SHAKE128",
"k": 128,
"name": "expand_message_xof",
"tests": [
{
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"len_in_bytes": "0x20",
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"uniform_bytes": "827c6216330a122352312bccc0c8d6e7a146c5257a776dbd9ad9d75cd880fc53"
},
{
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"uniform_bytes": "690c8d82c7213b4282c6cb41c00e31ea1d3e2005f93ad19bbf6da40f15790c5c"
},
{
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},
{
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}
]
}

78
curve-definitions/test/hashToCurve/expand_message_xof_SHAKE128_36.json Normal file
View File

@ -0,0 +1,78 @@
{
"DST": "QUUX-V01-CS02-with-expander-SHAKE128",
"hash": "SHAKE128",
"k": 128,
"name": "expand_message_xof",
"tests": [
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
"len_in_bytes": "0x20",
"msg": "",
"msg_prime": "0020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
"uniform_bytes": "86518c9cd86581486e9485aa74ab35ba150d1c75c88e26b7043e44e2acd735a2"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
"len_in_bytes": "0x20",
"msg": "abc",
"msg_prime": "6162630020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
"uniform_bytes": "8696af52a4d862417c0763556073f47bc9b9ba43c99b505305cb1ec04a9ab468"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
"len_in_bytes": "0x20",
"msg": "abcdef0123456789",
"msg_prime": "616263646566303132333435363738390020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
"uniform_bytes": "912c58deac4821c3509dbefa094df54b34b8f5d01a191d1d3108a2c89077acca"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
"len_in_bytes": "0x20",
"msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
"msg_prime": "713132385f71717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171710020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
"uniform_bytes": "1adbcc448aef2a0cebc71dac9f756b22e51839d348e031e63b33ebb50faeaf3f"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
"len_in_bytes": "0x20",
"msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"msg_prime": "613531325f61616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161610020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
"uniform_bytes": "df3447cc5f3e9a77da10f819218ddf31342c310778e0e4ef72bbaecee786a4fe"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
"len_in_bytes": "0x80",
"msg": "",
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"uniform_bytes": "7314ff1a155a2fb99a0171dc71b89ab6e3b2b7d59e38e64419b8b6294d03ffee42491f11370261f436220ef787f8f76f5b26bdcd850071920ce023f3ac46847744f4612b8714db8f5db83205b2e625d95afd7d7b4d3094d3bdde815f52850bb41ead9822e08f22cf41d615a303b0d9dde73263c049a7b9898208003a739a2e57"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
"len_in_bytes": "0x80",
"msg": "abc",
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"uniform_bytes": "c952f0c8e529ca8824acc6a4cab0e782fc3648c563ddb00da7399f2ae35654f4860ec671db2356ba7baa55a34a9d7f79197b60ddae6e64768a37d699a78323496db3878c8d64d909d0f8a7de4927dcab0d3dbbc26cb20a49eceb0530b431cdf47bc8c0fa3e0d88f53b318b6739fbed7d7634974f1b5c386d6230c76260d5337a"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
"len_in_bytes": "0x80",
"msg": "abcdef0123456789",
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"uniform_bytes": "19b65ee7afec6ac06a144f2d6134f08eeec185f1a890fe34e68f0e377b7d0312883c048d9b8a1d6ecc3b541cb4987c26f45e0c82691ea299b5e6889bbfe589153016d8131717ba26f07c3c14ffbef1f3eff9752e5b6183f43871a78219a75e7000fbac6a7072e2b83c790a3a5aecd9d14be79f9fd4fb180960a3772e08680495"
},
{
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"len_in_bytes": "0x80",
"msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
"msg_prime": "713132385f71717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171710080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
"uniform_bytes": "ca1b56861482b16eae0f4a26212112362fcc2d76dcc80c93c4182ed66c5113fe41733ed68be2942a3487394317f3379856f4822a611735e50528a60e7ade8ec8c71670fec6661e2c59a09ed36386513221688b35dc47e3c3111ee8c67ff49579089d661caa29db1ef10eb6eace575bf3dc9806e7c4016bd50f3c0e2a6481ee6d"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4531323824",
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"uniform_bytes": "9d763a5ce58f65c91531b4100c7266d479a5d9777ba761693d052acd37d149e7ac91c796a10b919cd74a591a1e38719fb91b7203e2af31eac3bff7ead2c195af7d88b8bc0a8adf3d1e90ab9bed6ddc2b7f655dd86c730bdeaea884e73741097142c92f0e3fc1811b699ba593c7fbd81da288a29d423df831652e3a01a9374999"
}
]
}

78
curve-definitions/test/hashToCurve/expand_message_xof_SHAKE256_36.json Normal file
View File

@ -0,0 +1,78 @@
{
"DST": "QUUX-V01-CS02-with-expander-SHAKE256",
"hash": "SHAKE256",
"k": 256,
"name": "expand_message_xof",
"tests": [
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
"len_in_bytes": "0x20",
"msg": "",
"msg_prime": "0020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
"uniform_bytes": "2ffc05c48ed32b95d72e807f6eab9f7530dd1c2f013914c8fed38c5ccc15ad76"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
"len_in_bytes": "0x20",
"msg": "abc",
"msg_prime": "6162630020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
"uniform_bytes": "b39e493867e2767216792abce1f2676c197c0692aed061560ead251821808e07"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
"len_in_bytes": "0x20",
"msg": "abcdef0123456789",
"msg_prime": "616263646566303132333435363738390020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
"uniform_bytes": "245389cf44a13f0e70af8665fe5337ec2dcd138890bb7901c4ad9cfceb054b65"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
"len_in_bytes": "0x20",
"msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
"msg_prime": "713132385f71717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171710020515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
"uniform_bytes": "719b3911821e6428a5ed9b8e600f2866bcf23c8f0515e52d6c6c019a03f16f0e"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
"len_in_bytes": "0x20",
"msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
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"uniform_bytes": "9181ead5220b1963f1b5951f35547a5ea86a820562287d6ca4723633d17ccbbc"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
"len_in_bytes": "0x80",
"msg": "",
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"uniform_bytes": "7a1361d2d7d82d79e035b8880c5a3c86c5afa719478c007d96e6c88737a3f631dd74a2c88df79a4cb5e5d9f7504957c70d669ec6bfedc31e01e2bacc4ff3fdf9b6a00b17cc18d9d72ace7d6b81c2e481b4f73f34f9a7505dccbe8f5485f3d20c5409b0310093d5d6492dea4e18aa6979c23c8ea5de01582e9689612afbb353df"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
"len_in_bytes": "0x80",
"msg": "abc",
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"uniform_bytes": "a54303e6b172909783353ab05ef08dd435a558c3197db0c132134649708e0b9b4e34fb99b92a9e9e28fc1f1d8860d85897a8e021e6382f3eea10577f968ff6df6c45fe624ce65ca25932f679a42a404bc3681efe03fcd45ef73bb3a8f79ba784f80f55ea8a3c367408f30381299617f50c8cf8fbb21d0f1e1d70b0131a7b6fbe"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
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"msg": "abcdef0123456789",
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"uniform_bytes": "e42e4d9538a189316e3154b821c1bafb390f78b2f010ea404e6ac063deb8c0852fcd412e098e231e43427bd2be1330bb47b4039ad57b30ae1fc94e34993b162ff4d695e42d59d9777ea18d3848d9d336c25d2acb93adcad009bcfb9cde12286df267ada283063de0bb1505565b2eb6c90e31c48798ecdc71a71756a9110ff373"
},
{
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"len_in_bytes": "0x80",
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"msg_prime": "713132385f71717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171717171710080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
"uniform_bytes": "4ac054dda0a38a65d0ecf7afd3c2812300027c8789655e47aecf1ecc1a2426b17444c7482c99e5907afd9c25b991990490bb9c686f43e79b4471a23a703d4b02f23c669737a886a7ec28bddb92c3a98de63ebf878aa363a501a60055c048bea11840c4717beae7eee28c3cfa42857b3d130188571943a7bd747de831bd6444e0"
},
{
"DST_prime": "515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
"len_in_bytes": "0x80",
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"msg_prime": "613531325f61616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161610080515555582d5630312d435330322d776974682d657870616e6465722d5348414b4532353624",
"uniform_bytes": "09afc76d51c2cccbc129c2315df66c2be7295a231203b8ab2dd7f95c2772c68e500bc72e20c602abc9964663b7a03a389be128c56971ce81001a0b875e7fd17822db9d69792ddf6a23a151bf470079c518279aef3e75611f8f828994a9988f4a8a256ddb8bae161e658d5a2a09bcfe839c6396dc06ee5c8ff3c22d3b1f9deb7e"
}
]
}

90
curve-definitions/test/hashToCurve/secp256k1_XMD:SHA-256_SSWU_NU_.json Normal file
View File

@ -0,0 +1,90 @@
{
"L": "0x30",
"Z": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc24",
"ciphersuite": "secp256k1_XMD:SHA-256_SSWU_NU_",
"curve": "secp256k1",
"dst": "QUUX-V01-CS02-with-secp256k1_XMD:SHA-256_SSWU_NU_",
"expand": "XMD",
"field": {
"m": "0x1",
"p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f"
},
"hash": "sha256",
"k": "0x80",
"map": {
"name": "SSWU"
},
"randomOracle": false,
"vectors": [
{
"P": {
"x": "0xa4792346075feae77ac3b30026f99c1441b4ecf666ded19b7522cf65c4c55c5b",
"y": "0x62c59e2a6aeed1b23be5883e833912b08ba06be7f57c0e9cdc663f31639ff3a7"
},
"Q": {
"x": "0xa4792346075feae77ac3b30026f99c1441b4ecf666ded19b7522cf65c4c55c5b",
"y": "0x62c59e2a6aeed1b23be5883e833912b08ba06be7f57c0e9cdc663f31639ff3a7"
},
"msg": "",
"u": [
"0x0137fcd23bc3da962e8808f97474d097a6c8aa2881fceef4514173635872cf3b"
]
},
{
"P": {
"x": "0x3f3b5842033fff837d504bb4ce2a372bfeadbdbd84a1d2b678b6e1d7ee426b9d",
"y": "0x902910d1fef15d8ae2006fc84f2a5a7bda0e0407dc913062c3a493c4f5d876a5"
},
"Q": {
"x": "0x3f3b5842033fff837d504bb4ce2a372bfeadbdbd84a1d2b678b6e1d7ee426b9d",
"y": "0x902910d1fef15d8ae2006fc84f2a5a7bda0e0407dc913062c3a493c4f5d876a5"
},
"msg": "abc",
"u": [
"0xe03f894b4d7caf1a50d6aa45cac27412c8867a25489e32c5ddeb503229f63a2e"
]
},
{
"P": {
"x": "0x07644fa6281c694709f53bdd21bed94dab995671e4a8cd1904ec4aa50c59bfdf",
"y": "0xc79f8d1dad79b6540426922f7fbc9579c3018dafeffcd4552b1626b506c21e7b"
},
"Q": {
"x": "0x07644fa6281c694709f53bdd21bed94dab995671e4a8cd1904ec4aa50c59bfdf",
"y": "0xc79f8d1dad79b6540426922f7fbc9579c3018dafeffcd4552b1626b506c21e7b"
},
"msg": "abcdef0123456789",
"u": [
"0xe7a6525ae7069ff43498f7f508b41c57f80563c1fe4283510b322446f32af41b"
]
},
{
"P": {
"x": "0xb734f05e9b9709ab631d960fa26d669c4aeaea64ae62004b9d34f483aa9acc33",
"y": "0x03fc8a4a5a78632e2eb4d8460d69ff33c1d72574b79a35e402e801f2d0b1d6ee"
},
"Q": {
"x": "0xb734f05e9b9709ab631d960fa26d669c4aeaea64ae62004b9d34f483aa9acc33",
"y": "0x03fc8a4a5a78632e2eb4d8460d69ff33c1d72574b79a35e402e801f2d0b1d6ee"
},
"msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
"u": [
"0xd97cf3d176a2f26b9614a704d7d434739d194226a706c886c5c3c39806bc323c"
]
},
{
"P": {
"x": "0x17d22b867658977b5002dbe8d0ee70a8cfddec3eec50fb93f36136070fd9fa6c",
"y": "0xe9178ff02f4dab73480f8dd590328aea99856a7b6cc8e5a6cdf289ecc2a51718"
},
"Q": {
"x": "0x17d22b867658977b5002dbe8d0ee70a8cfddec3eec50fb93f36136070fd9fa6c",
"y": "0xe9178ff02f4dab73480f8dd590328aea99856a7b6cc8e5a6cdf289ecc2a51718"
},
"msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"u": [
"0xa9ffbeee1d6e41ac33c248fb3364612ff591b502386c1bf6ac4aaf1ea51f8c3b"
]
}
]
}

115
curve-definitions/test/hashToCurve/secp256k1_XMD:SHA-256_SSWU_RO_.json Normal file
View File

@ -0,0 +1,115 @@
{
"L": "0x30",
"Z": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc24",
"ciphersuite": "secp256k1_XMD:SHA-256_SSWU_RO_",
"curve": "secp256k1",
"dst": "QUUX-V01-CS02-with-secp256k1_XMD:SHA-256_SSWU_RO_",
"expand": "XMD",
"field": {
"m": "0x1",
"p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f"
},
"hash": "sha256",
"k": "0x80",
"map": {
"name": "SSWU"
},
"randomOracle": true,
"vectors": [
{
"P": {
"x": "0xc1cae290e291aee617ebaef1be6d73861479c48b841eaba9b7b5852ddfeb1346",
"y": "0x64fa678e07ae116126f08b022a94af6de15985c996c3a91b64c406a960e51067"
},
"Q0": {
"x": "0x74519ef88b32b425a095e4ebcc84d81b64e9e2c2675340a720bb1a1857b99f1e",
"y": "0xc174fa322ab7c192e11748beed45b508e9fdb1ce046dee9c2cd3a2a86b410936"
},
"Q1": {
"x": "0x44548adb1b399263ded3510554d28b4bead34b8cf9a37b4bd0bd2ba4db87ae63",
"y": "0x96eb8e2faf05e368efe5957c6167001760233e6dd2487516b46ae725c4cce0c6"
},
"msg": "",
"u": [
"0x6b0f9910dd2ba71c78f2ee9f04d73b5f4c5f7fc773a701abea1e573cab002fb3",
"0x1ae6c212e08fe1a5937f6202f929a2cc8ef4ee5b9782db68b0d5799fd8f09e16"
]
},
{
"P": {
"x": "0x3377e01eab42db296b512293120c6cee72b6ecf9f9205760bd9ff11fb3cb2c4b",
"y": "0x7f95890f33efebd1044d382a01b1bee0900fb6116f94688d487c6c7b9c8371f6"
},
"Q0": {
"x": "0x07dd9432d426845fb19857d1b3a91722436604ccbbbadad8523b8fc38a5322d7",
"y": "0x604588ef5138cffe3277bbd590b8550bcbe0e523bbaf1bed4014a467122eb33f"
},
"Q1": {
"x": "0xe9ef9794d15d4e77dde751e06c182782046b8dac05f8491eb88764fc65321f78",
"y": "0xcb07ce53670d5314bf236ee2c871455c562dd76314aa41f012919fe8e7f717b3"
},
"msg": "abc",
"u": [
"0x128aab5d3679a1f7601e3bdf94ced1f43e491f544767e18a4873f397b08a2b61",
"0x5897b65da3b595a813d0fdcc75c895dc531be76a03518b044daaa0f2e4689e00"
]
},
{
"P": {
"x": "0xbac54083f293f1fe08e4a70137260aa90783a5cb84d3f35848b324d0674b0e3a",
"y": "0x4436476085d4c3c4508b60fcf4389c40176adce756b398bdee27bca19758d828"
},
"Q0": {
"x": "0x576d43ab0260275adf11af990d130a5752704f79478628761720808862544b5d",
"y": "0x643c4a7fb68ae6cff55edd66b809087434bbaff0c07f3f9ec4d49bb3c16623c3"
},
"Q1": {
"x": "0xf89d6d261a5e00fe5cf45e827b507643e67c2a947a20fd9ad71039f8b0e29ff8",
"y": "0xb33855e0cc34a9176ead91c6c3acb1aacb1ce936d563bc1cee1dcffc806caf57"
},
"msg": "abcdef0123456789",
"u": [
"0xea67a7c02f2cd5d8b87715c169d055a22520f74daeb080e6180958380e2f98b9",
"0x7434d0d1a500d38380d1f9615c021857ac8d546925f5f2355319d823a478da18"
]
},
{
"P": {
"x": "0xe2167bc785333a37aa562f021f1e881defb853839babf52a7f72b102e41890e9",
"y": "0xf2401dd95cc35867ffed4f367cd564763719fbc6a53e969fb8496a1e6685d873"
},
"Q0": {
"x": "0x9c91513ccfe9520c9c645588dff5f9b4e92eaf6ad4ab6f1cd720d192eb58247a",
"y": "0xc7371dcd0134412f221e386f8d68f49e7fa36f9037676e163d4a063fbf8a1fb8"
},
"Q1": {
"x": "0x10fee3284d7be6bd5912503b972fc52bf4761f47141a0015f1c6ae36848d869b",
"y": "0x0b163d9b4bf21887364332be3eff3c870fa053cf508732900fc69a6eb0e1b672"
},
"msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
"u": [
"0xeda89a5024fac0a8207a87e8cc4e85aa3bce10745d501a30deb87341b05bcdf5",
"0xdfe78cd116818fc2c16f3837fedbe2639fab012c407eac9dfe9245bf650ac51d"
]
},
{
"P": {
"x": "0xe3c8d35aaaf0b9b647e88a0a0a7ee5d5bed5ad38238152e4e6fd8c1f8cb7c998",
"y": "0x8446eeb6181bf12f56a9d24e262221cc2f0c4725c7e3803024b5888ee5823aa6"
},
"Q0": {
"x": "0xb32b0ab55977b936f1e93fdc68cec775e13245e161dbfe556bbb1f72799b4181",
"y": "0x2f5317098360b722f132d7156a94822641b615c91f8663be69169870a12af9e8"
},
"Q1": {
"x": "0x148f98780f19388b9fa93e7dc567b5a673e5fca7079cd9cdafd71982ec4c5e12",
"y": "0x3989645d83a433bc0c001f3dac29af861f33a6fd1e04f4b36873f5bff497298a"
},
"msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
"u": [
"0x8d862e7e7e23d7843fe16d811d46d7e6480127a6b78838c277bca17df6900e9f",
"0x68071d2530f040f081ba818d3c7188a94c900586761e9115efa47ae9bd847938"
]
}
]
}

1
curve-definitions/test/index.test.js
View File

@ -9,5 +9,6 @@ import './secp256k1.test.js';
import './stark/stark.test.js'; import './stark/stark.test.js';
import './jubjub.test.js'; import './jubjub.test.js';
import './bls12-381.test.js'; import './bls12-381.test.js';
import './hashToCurve.test.js';
should.run(); should.run();

4
curve-definitions/test/secp256k1.test.js
View File

@ -529,4 +529,8 @@ should('secp256k1.wychenproof vectors', () => {
} }
}); });
// ESM is broken.
import url from 'url';
if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
should.run(); should.run();
}

48
src/edwards.ts
View File

@ -23,6 +23,7 @@ import {
PrivKey, PrivKey,
} from './utils.js'; // TODO: import * as u from './utils.js'? } from './utils.js'; // TODO: import * as u from './utils.js'?
import { Group, GroupConstructor, wNAF } from './group.js'; import { Group, GroupConstructor, wNAF } from './group.js';
import { hash_to_field, htfOpts, validateHTFOpts } from './hashToCurve.js';
// Be friendly to bad ECMAScript parsers by not using bigint literals like 123n // Be friendly to bad ECMAScript parsers by not using bigint literals like 123n
const _0n = BigInt(0); const _0n = BigInt(0);
@ -48,6 +49,10 @@ export type CurveType = BasicCurve<bigint> & {
domain?: (data: Uint8Array, ctx: Uint8Array, phflag: boolean) => Uint8Array; domain?: (data: Uint8Array, ctx: Uint8Array, phflag: boolean) => Uint8Array;
uvRatio?: (u: bigint, v: bigint) => { isValid: boolean; value: bigint }; uvRatio?: (u: bigint, v: bigint) => { isValid: boolean; value: bigint };
preHash?: CHash; preHash?: CHash;
clearCofactor?: (c: ExtendedPointConstructor, point: ExtendedPointType) => ExtendedPointType;
// Hash to field opts
htfDefaults?: htfOpts;
mapToCurve?: (scalar: bigint[]) => { x: bigint; y: bigint };
}; };
// Should be separate from overrides, since overrides can use information about curve (for example nBits) // Should be separate from overrides, since overrides can use information about curve (for example nBits)
@ -62,10 +67,17 @@ function validateOpts(curve: CurveType) {
for (const fn of ['randomBytes'] as const) { for (const fn of ['randomBytes'] as const) {
if (typeof opts[fn] !== 'function') throw new Error(`Invalid ${fn} function`); if (typeof opts[fn] !== 'function') throw new Error(`Invalid ${fn} function`);
} }
for (const fn of ['adjustScalarBytes', 'domain', 'uvRatio'] as const) { for (const fn of [
'adjustScalarBytes',
'domain',
'uvRatio',
'mapToCurve',
'clearCofactor',
] as const) {
if (opts[fn] === undefined) continue; // Optional if (opts[fn] === undefined) continue; // Optional
if (typeof opts[fn] !== 'function') throw new Error(`Invalid ${fn} function`); if (typeof opts[fn] !== 'function') throw new Error(`Invalid ${fn} function`);
} }
if (opts.htfDefaults !== undefined) validateHTFOpts(opts.htfDefaults);
// Set defaults // Set defaults
return Object.freeze({ ...opts } as const); return Object.freeze({ ...opts } as const);
} }
@ -95,6 +107,7 @@ export interface ExtendedPointType extends Group<ExtendedPointType> {
isSmallOrder(): boolean; isSmallOrder(): boolean;
isTorsionFree(): boolean; isTorsionFree(): boolean;
toAffine(invZ?: bigint): PointType; toAffine(invZ?: bigint): PointType;
clearCofactor(): ExtendedPointType;
} }
// Static methods // Static methods
export interface ExtendedPointConstructor extends GroupConstructor<ExtendedPointType> { export interface ExtendedPointConstructor extends GroupConstructor<ExtendedPointType> {
@ -112,12 +125,15 @@ export interface PointType extends Group<PointType> {
toRawBytes(isCompressed?: boolean): Uint8Array; toRawBytes(isCompressed?: boolean): Uint8Array;
toHex(isCompressed?: boolean): string; toHex(isCompressed?: boolean): string;
isTorsionFree(): boolean; isTorsionFree(): boolean;
clearCofactor(): PointType;
} }
// Static methods // Static methods
export interface PointConstructor extends GroupConstructor<PointType> { export interface PointConstructor extends GroupConstructor<PointType> {
new (x: bigint, y: bigint): PointType; new (x: bigint, y: bigint): PointType;
fromHex(hex: Hex): PointType; fromHex(hex: Hex): PointType;
fromPrivateKey(privateKey: PrivKey): PointType; fromPrivateKey(privateKey: PrivKey): PointType;
hashToCurve(msg: Hex, options?: Partial<htfOpts>): PointType;
encodeToCurve(msg: Hex, options?: Partial<htfOpts>): PointType;
} }
export type PubKey = Hex | PointType; export type PubKey = Hex | PointType;
@ -354,6 +370,13 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
if (zz !== _1n) throw new Error('invZ was invalid'); if (zz !== _1n) throw new Error('invZ was invalid');
return new Point(ax, ay); return new Point(ax, ay);
} }
clearCofactor(): ExtendedPoint {
if (CURVE.h === _1n) return this; // Fast-path
// clear_cofactor(P) := h_eff * P
// hEff = h for ed25519/ed448. Maybe worth moving to params?
if (CURVE.clearCofactor) return CURVE.clearCofactor(ExtendedPoint, this) as ExtendedPoint;
return this.multiplyUnsafe(CURVE.h);
}
} }
const wnaf = wNAF(ExtendedPoint, groupLen * 8); const wnaf = wNAF(ExtendedPoint, groupLen * 8);
@ -479,6 +502,29 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
multiply(scalar: number | bigint): Point { multiply(scalar: number | bigint): Point {
return ExtendedPoint.fromAffine(this).multiply(scalar, this).toAffine(); return ExtendedPoint.fromAffine(this).multiply(scalar, this).toAffine();
} }
clearCofactor() {
return ExtendedPoint.fromAffine(this).clearCofactor().toAffine();
}
// Encodes byte string to elliptic curve
// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-3
static hashToCurve(msg: Hex, options?: Partial<htfOpts>) {
if (!CURVE.mapToCurve) throw new Error('No mapToCurve defined for curve');
msg = ensureBytes(msg);
const u = hash_to_field(msg, 2, { ...CURVE.htfDefaults, ...options } as htfOpts);
const { x: x0, y: y0 } = CURVE.mapToCurve(u[0]);
const { x: x1, y: y1 } = CURVE.mapToCurve(u[1]);
const p = new Point(x0, y0).add(new Point(x1, y1)).clearCofactor();
return p;
}
// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16#section-3
static encodeToCurve(msg: Hex, options?: Partial<htfOpts>) {
if (!CURVE.mapToCurve) throw new Error('No mapToCurve defined for curve');
msg = ensureBytes(msg);
const u = hash_to_field(msg, 1, { ...CURVE.htfDefaults, ...options } as htfOpts);
const { x, y } = CURVE.mapToCurve(u[0]);
return new Point(x, y).clearCofactor();
}
} }
/** /**

16
src/hashToCurve.ts
View File

@ -35,6 +35,7 @@ export function validateHTFOpts(opts: htfOpts) {
} }
// UTF8 to ui8a // UTF8 to ui8a
// TODO: looks broken, ASCII only, why not TextEncoder/TextDecoder? it is in hashes anyway
export function stringToBytes(str: string) { export function stringToBytes(str: string) {
const bytes = new Uint8Array(str.length); const bytes = new Uint8Array(str.length);
for (let i = 0; i < str.length; i++) bytes[i] = str.charCodeAt(i); for (let i = 0; i < str.length; i++) bytes[i] = str.charCodeAt(i);
@ -83,7 +84,7 @@ export function expand_message_xmd(
// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16#section-5.3.3 // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16#section-5.3.3
if (DST.length > 255) DST = H(concatBytes(stringToBytes('H2C-OVERSIZE-DST-'), DST)); if (DST.length > 255) DST = H(concatBytes(stringToBytes('H2C-OVERSIZE-DST-'), DST));
const b_in_bytes = H.outputLen; const b_in_bytes = H.outputLen;
const r_in_bytes = b_in_bytes * 2; const r_in_bytes = H.blockLen;
const ell = Math.ceil(lenInBytes / b_in_bytes); const ell = Math.ceil(lenInBytes / b_in_bytes);
if (ell > 255) throw new Error('Invalid xmd length'); if (ell > 255) throw new Error('Invalid xmd length');
const DST_prime = concatBytes(DST, i2osp(DST.length, 1)); const DST_prime = concatBytes(DST, i2osp(DST.length, 1));
@ -130,3 +131,16 @@ export function hash_to_field(msg: Uint8Array, count: number, options: htfOpts):
} }
return u; return u;
} }
export function isogenyMap<T, F extends mod.Field<T>>(field: F, map: [T[], T[], T[], T[]]) {
// Make same order as in spec
const COEFF = map.map((i) => Array.from(i).reverse());
return (x: T, y: T) => {
const [xNum, xDen, yNum, yDen] = COEFF.map((val) =>
val.reduce((acc, i) => field.add(field.mul(acc, x), i))
);
x = field.div(xNum, xDen); // xNum / xDen
y = field.mul(y, field.div(yNum, yDen)); // y * (yNum / yDev)
return { x, y };
};
}

99
src/modular.ts
View File

@ -1,9 +1,12 @@
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */ /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import * as utils from './utils.js'; import * as utils from './utils.js';
// Utilities for modular arithmetics and finite fields // Utilities for modular arithmetics and finite fields
const _0n = BigInt(0); // prettier-ignore
const _1n = BigInt(1); const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);
const _2n = BigInt(2); // prettier-ignore
const _4n = BigInt(4), _5n = BigInt(5), _7n = BigInt(7), _8n = BigInt(8);
// prettier-ignore
const _9n = BigInt(9), _16n = BigInt(16);
// Calculates a modulo b // Calculates a modulo b
export function mod(a: bigint, b: bigint): bigint { export function mod(a: bigint, b: bigint): bigint {
@ -80,7 +83,6 @@ export function legendre(num: bigint, fieldPrime: bigint): bigint {
// TODO: rewrite as generic Fp function && remove bls versions // TODO: rewrite as generic Fp function && remove bls versions
export function sqrt(number: bigint, modulo: bigint): bigint { export function sqrt(number: bigint, modulo: bigint): bigint {
// prettier-ignore // prettier-ignore
const _3n = BigInt(3), _4n = BigInt(4), _5n = BigInt(5), _8n = BigInt(8);
const n = number; const n = number;
const P = modulo; const P = modulo;
const p1div4 = (P + _1n) / _4n; const p1div4 = (P + _1n) / _4n;
@ -143,6 +145,7 @@ export const isNegativeLE = (num: bigint, modulo: bigint) => (mod(num, modulo) &
// - readable: add, mul, sqr, sqrt, inv, div, pow, eq, sub // - readable: add, mul, sqr, sqrt, inv, div, pow, eq, sub
// - unreadable mess: addition, multiply, square, squareRoot, inversion, divide, power, equals, subtract // - unreadable mess: addition, multiply, square, squareRoot, inversion, divide, power, equals, subtract
// Field is not always over prime, Fp2 for example has ORDER(q)=p^m
export interface Field<T> { export interface Field<T> {
ORDER: bigint; ORDER: bigint;
BYTES: number; BYTES: number;
@ -172,12 +175,15 @@ export interface Field<T> {
squareN(num: T): T; squareN(num: T): T;
// Optional // Optional
// Should be same as sgn0 function in https://datatracker.ietf.org/doc/draft-irtf-cfrg-hash-to-curve/
isOdd?(num: T): boolean; // Odd instead of even since we have it for Fp2 isOdd?(num: T): boolean; // Odd instead of even since we have it for Fp2
legendre?(num: T): T; legendre?(num: T): T;
pow(lhs: T, power: bigint): T; pow(lhs: T, power: bigint): T;
invertBatch: (lst: T[]) => T[]; invertBatch: (lst: T[]) => T[];
toBytes(num: T): Uint8Array; toBytes(num: T): Uint8Array;
fromBytes(bytes: Uint8Array): T; fromBytes(bytes: Uint8Array): T;
// If c is False, CMOV returns a, otherwise it returns b.
cmov(a: T, b: T, c: boolean): T;
} }
// prettier-ignore // prettier-ignore
const FIELD_FIELDS = [ const FIELD_FIELDS = [
@ -288,7 +294,9 @@ export function Fp(
invert: (num) => invert(num, ORDER), invert: (num) => invert(num, ORDER),
sqrt: redef.sqrt || sqrtP, sqrt: redef.sqrt || sqrtP,
invertBatch: (lst) => FpInvertBatch(f, lst), invertBatch: (lst) => FpInvertBatch(f, lst),
// TODO: do we really need constant cmov?
// We don't have const-time bigints anyway, so probably will be not very useful
cmov: (a, b, c) => (c ? b : a),
toBytes: (num) => toBytes: (num) =>
isLE ? utils.numberToBytesLE(num, BYTES) : utils.numberToBytesBE(num, BYTES), isLE ? utils.numberToBytesLE(num, BYTES) : utils.numberToBytesBE(num, BYTES),
@ -300,3 +308,84 @@ export function Fp(
} as Field<bigint>); } as Field<bigint>);
return Object.freeze(f); return Object.freeze(f);
} }
// TODO: re-use in bls/generic sqrt for field/etc?
// Something like sqrtUnsafe which always returns value, but sqrt throws exception if non-square
// From draft-irtf-cfrg-hash-to-curve-16
export function FpSqrt<T>(Fp: Field<T>) {
// NOTE: it requires another sqrt for constant precomputes, but no need for roots of unity,
// probably we can simply bls code using it
const q = Fp.ORDER;
const squareConst = (q - _1n) / _2n;
// is_square(x) := { True, if x^((q - 1) / 2) is 0 or 1 in F;
// { False, otherwise.
let isSquare: (x: T) => boolean = (x) => {
const p = Fp.pow(x, squareConst);
return Fp.equals(p, Fp.ZERO) || Fp.equals(p, Fp.ONE);
};
// Constant-time Tonelli-Shanks algorithm
let l = _0n;
for (let o = q - _1n; o % _2n === _0n; o /= _2n) l += _1n;
const c1 = l; // 1. c1, the largest integer such that 2^c1 divides q - 1.
const c2 = (q - _1n) / _2n ** c1; // 2. c2 = (q - 1) / (2^c1) # Integer arithmetic
const c3 = (c2 - _1n) / _2n; // 3. c3 = (c2 - 1) / 2 # Integer arithmetic
// 4. c4, a non-square value in F
// 5. c5 = c4^c2 in F
let c4 = Fp.ONE;
while (isSquare(c4)) c4 = Fp.add(c4, Fp.ONE);
const c5 = Fp.pow(c4, c2);
let sqrt: (x: T) => T = (x) => {
let z = Fp.pow(x, c3); // 1. z = x^c3
let t = Fp.square(z); // 2. t = z * z
t = Fp.mul(t, x); // 3. t = t * x
z = Fp.mul(z, x); // 4. z = z * x
let b = t; // 5. b = t
let c = c5; // 6. c = c5
// 7. for i in (c1, c1 - 1, ..., 2):
for (let i = c1; i > 1; i--) {
// 8. for j in (1, 2, ..., i - 2):
// 9. b = b * b
for (let j = _1n; j < i - _1n; i++) b = Fp.square(b);
const e = Fp.equals(b, Fp.ONE); // 10. e = b == 1
const zt = Fp.mul(z, c); // 11. zt = z * c
z = Fp.cmov(zt, z, e); // 12. z = CMOV(zt, z, e)
c = Fp.square(c); // 13. c = c * c
let tt = Fp.mul(t, c); // 14. tt = t * c
t = Fp.cmov(tt, t, e); // 15. t = CMOV(tt, t, e)
b = t; // 16. b = t
}
return z; // 17. return z
};
if (q % _4n === _3n) {
const c1 = (q + _1n) / _4n; // 1. c1 = (q + 1) / 4 # Integer arithmetic
sqrt = (x) => Fp.pow(x, c1);
} else if (q % _8n === _5n) {
const c1 = Fp.sqrt(Fp.negate(Fp.ONE)); // 1. c1 = sqrt(-1) in F, i.e., (c1^2) == -1 in F
const c2 = (q + _3n) / _8n; // 2. c2 = (q + 3) / 8 # Integer arithmetic
sqrt = (x) => {
let tv1 = Fp.pow(x, c2); // 1. tv1 = x^c2
let tv2 = Fp.mul(tv1, c1); // 2. tv2 = tv1 * c1
let e = Fp.equals(Fp.square(tv1), x); // 3. e = (tv1^2) == x
return Fp.cmov(tv2, tv1, e); // 4. z = CMOV(tv2, tv1, e)
};
} else if (Fp.ORDER % _16n === _9n) {
const c1 = Fp.sqrt(Fp.negate(Fp.ONE)); // 1. c1 = sqrt(-1) in F, i.e., (c1^2) == -1 in F
const c2 = Fp.sqrt(c1); // 2. c2 = sqrt(c1) in F, i.e., (c2^2) == c1 in F
const c3 = Fp.sqrt(Fp.negate(c1)); // 3. c3 = sqrt(-c1) in F, i.e., (c3^2) == -c1 in F
const c4 = (Fp.ORDER + _7n) / _16n; // 4. c4 = (q + 7) / 16 # Integer arithmetic
sqrt = (x) => {
let tv1 = Fp.pow(x, c4); // 1. tv1 = x^c4
let tv2 = Fp.mul(c1, tv1); // 2. tv2 = c1 * tv1
const tv3 = Fp.mul(c2, tv1); // 3. tv3 = c2 * tv1
let tv4 = Fp.mul(c3, tv1); // 4. tv4 = c3 * tv1
const e1 = Fp.equals(Fp.square(tv2), x); // 5. e1 = (tv2^2) == x
const e2 = Fp.equals(Fp.square(tv3), x); // 6. e2 = (tv3^2) == x
tv1 = Fp.cmov(tv1, tv2, e1); // 7. tv1 = CMOV(tv1, tv2, e1) # Select tv2 if (tv2^2) == x
tv2 = Fp.cmov(tv4, tv3, e2); // 8. tv2 = CMOV(tv4, tv3, e2) # Select tv3 if (tv3^2) == x
const e3 = Fp.equals(Fp.square(tv2), x); // 9. e3 = (tv2^2) == x
return Fp.cmov(tv1, tv2, e3); // 10. z = CMOV(tv1, tv2, e3) # Select the sqrt from tv1 and tv2
};
}
return { sqrt, isSquare };
}

116
src/weierstrass.ts
View File

@ -1272,3 +1272,119 @@ export function weierstrass(curveDef: CurveType): CurveFn {
utils, utils,
}; };
} }
// Implementation of the Shallue and van de Woestijne method for any Weierstrass curve
// TODO: check if there is a way to merge this with uvRation in Edwards && move to modular?
// b = True and y = sqrt(u / v) if (u / v) is square in F, and
// b = False and y = sqrt(Z * (u / v)) otherwise.
export function SWUFpSqrtRatio<T>(Fp: mod.Field<T>, Z: T) {
// Generic implementation
const q = Fp.ORDER;
let l = 0n;
for (let o = q - 1n; o % 2n === 0n; o /= 2n) l += 1n;
const c1 = l; // 1. c1, the largest integer such that 2^c1 divides q - 1.
const c2 = (q - 1n) / 2n ** c1; // 2. c2 = (q - 1) / (2^c1) # Integer arithmetic
const c3 = (c2 - 1n) / 2n; // 3. c3 = (c2 - 1) / 2 # Integer arithmetic
const c4 = 2n ** c1 - 1n; // 4. c4 = 2^c1 - 1 # Integer arithmetic
const c5 = 2n ** (c1 - 1n); // 5. c5 = 2^(c1 - 1) # Integer arithmetic
const c6 = Fp.pow(Z, c2); // 6. c6 = Z^c2
const c7 = Fp.pow(Z, (c2 + 1n) / 2n); // 7. c7 = Z^((c2 + 1) / 2)
let sqrtRatio = (u: T, v: T): { isValid: boolean; value: T } => {
let tv1 = c6; // 1. tv1 = c6
let tv2 = Fp.pow(v, c4); // 2. tv2 = v^c4
let tv3 = Fp.square(tv2); // 3. tv3 = tv2^2
tv3 = Fp.mul(tv3, v); // 4. tv3 = tv3 * v
let tv5 = Fp.mul(u, tv3); // 5. tv5 = u * tv3
tv5 = Fp.pow(tv5, c3); // 6. tv5 = tv5^c3
tv5 = Fp.mul(tv5, tv2); // 7. tv5 = tv5 * tv2
tv2 = Fp.mul(tv5, v); // 8. tv2 = tv5 * v
tv3 = Fp.mul(tv5, u); // 9. tv3 = tv5 * u
let tv4 = Fp.mul(tv3, tv2); // 10. tv4 = tv3 * tv2
tv5 = Fp.pow(tv4, c5); // 11. tv5 = tv4^c5
let isQR = Fp.equals(tv5, Fp.ONE); // 12. isQR = tv5 == 1
tv2 = Fp.mul(tv3, c7); // 13. tv2 = tv3 * c7
tv5 = Fp.mul(tv4, tv1); // 14. tv5 = tv4 * tv1
tv3 = Fp.cmov(tv2, tv3, isQR); // 15. tv3 = CMOV(tv2, tv3, isQR)
tv4 = Fp.cmov(tv5, tv4, isQR); // 16. tv4 = CMOV(tv5, tv4, isQR)
// 17. for i in (c1, c1 - 1, ..., 2):
for (let i = c1; i > 1; i--) {
let tv5 = 2n ** (i - 2n); // 18. tv5 = i - 2; 19. tv5 = 2^tv5
let tvv5 = Fp.pow(tv4, tv5); // 20. tv5 = tv4^tv5
const e1 = Fp.equals(tvv5, Fp.ONE); // 21. e1 = tv5 == 1
tv2 = Fp.mul(tv3, tv1); // 22. tv2 = tv3 * tv1
tv1 = Fp.mul(tv1, tv1); // 23. tv1 = tv1 * tv1
tvv5 = Fp.mul(tv4, tv1); // 24. tv5 = tv4 * tv1
tv3 = Fp.cmov(tv2, tv3, e1); // 25. tv3 = CMOV(tv2, tv3, e1)
tv4 = Fp.cmov(tvv5, tv4, e1); // 26. tv4 = CMOV(tv5, tv4, e1)
}
return { isValid: isQR, value: tv3 };
};
if (Fp.ORDER % 4n === 3n) {
// sqrt_ratio_3mod4(u, v)
const c1 = (Fp.ORDER - 3n) / 4n; // 1. c1 = (q - 3) / 4 # Integer arithmetic
const c2 = Fp.sqrt(Fp.negate(Z)); // 2. c2 = sqrt(-Z)
sqrtRatio = (u: T, v: T) => {
let tv1 = Fp.square(v); // 1. tv1 = v^2
const tv2 = Fp.mul(u, v); // 2. tv2 = u * v
tv1 = Fp.mul(tv1, tv2); // 3. tv1 = tv1 * tv2
let y1 = Fp.pow(tv1, c1); // 4. y1 = tv1^c1
y1 = Fp.mul(y1, tv2); // 5. y1 = y1 * tv2
const y2 = Fp.mul(y1, c2); // 6. y2 = y1 * c2
const tv3 = Fp.mul(Fp.square(y1), v); // 7. tv3 = y1^2; 8. tv3 = tv3 * v
const isQR = Fp.equals(tv3, u); // 9. isQR = tv3 == u
let y = Fp.cmov(y2, y1, isQR); // 10. y = CMOV(y2, y1, isQR)
return { isValid: isQR, value: y }; // 11. return (isQR, y) isQR ? y : y*c2
};
}
// No curves uses that
// if (Fp.ORDER % 8n === 5n) // sqrt_ratio_5mod8
return sqrtRatio;
}
// From draft-irtf-cfrg-hash-to-curve-16
export function mapToCurveSimpleSWU<T>(
Fp: mod.Field<T>,
opts: {
A: T;
B: T;
Z: T;
}
) {
mod.validateField(Fp);
if (!Fp.isValid(opts.A) || !Fp.isValid(opts.B) || !Fp.isValid(opts.Z))
throw new Error('mapToCurveSimpleSWU: invalid opts');
const sqrtRatio = SWUFpSqrtRatio(Fp, opts.Z);
if (!Fp.isOdd) throw new Error('Fp.isOdd is not implemented!');
// Input: u, an element of F.
// Output: (x, y), a point on E.
return (u: T): { x: T; y: T } => {
// prettier-ignore
let tv1, tv2, tv3, tv4, tv5, tv6, x, y;
tv1 = Fp.square(u); // 1. tv1 = u^2
tv1 = Fp.mul(tv1, opts.Z); // 2. tv1 = Z * tv1
tv2 = Fp.square(tv1); // 3. tv2 = tv1^2
tv2 = Fp.add(tv2, tv1); // 4. tv2 = tv2 + tv1
tv3 = Fp.add(tv2, Fp.ONE); // 5. tv3 = tv2 + 1
tv3 = Fp.mul(tv3, opts.B); // 6. tv3 = B * tv3
tv4 = Fp.cmov(opts.Z, Fp.negate(tv2), !Fp.equals(tv2, Fp.ZERO)); // 7. tv4 = CMOV(Z, -tv2, tv2 != 0)
tv4 = Fp.mul(tv4, opts.A); // 8. tv4 = A * tv4
tv2 = Fp.square(tv3); // 9. tv2 = tv3^2
tv6 = Fp.square(tv4); // 10. tv6 = tv4^2
tv5 = Fp.mul(tv6, opts.A); // 11. tv5 = A * tv6
tv2 = Fp.add(tv2, tv5); // 12. tv2 = tv2 + tv5
tv2 = Fp.mul(tv2, tv3); // 13. tv2 = tv2 * tv3
tv6 = Fp.mul(tv6, tv4); // 14. tv6 = tv6 * tv4
tv5 = Fp.mul(tv6, opts.B); // 15. tv5 = B * tv6
tv2 = Fp.add(tv2, tv5); // 16. tv2 = tv2 + tv5
x = Fp.mul(tv1, tv3); // 17. x = tv1 * tv3
const { isValid, value } = sqrtRatio(tv2, tv6); // 18. (is_gx1_square, y1) = sqrt_ratio(tv2, tv6)
y = Fp.mul(tv1, u); // 19. y = tv1 * u -> Z * u^3 * y1
y = Fp.mul(y, value); // 20. y = y * y1
x = Fp.cmov(x, tv3, isValid); // 21. x = CMOV(x, tv3, is_gx1_square)
y = Fp.cmov(y, value, isValid); // 22. y = CMOV(y, y1, is_gx1_square)
const e1 = Fp.isOdd!(u) === Fp.isOdd!(y); // 23. e1 = sgn0(u) == sgn0(y)
y = Fp.cmov(Fp.negate(y), y, e1); // 24. y = CMOV(-y, y, e1)
x = Fp.div(x, tv4); // 25. x = x / tv4
return { x, y };
};
}