diff --git a/src/secp256k1.ts b/src/secp256k1.ts index 7119222..10fbb9b 100644 --- a/src/secp256k1.ts +++ b/src/secp256k1.ts @@ -1,7 +1,7 @@ /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */ import { sha256 } from '@noble/hashes/sha256'; import { randomBytes } from '@noble/hashes/utils'; -import { Field, mod, pow2 } from './abstract/modular.js'; +import { Field, mod, pow2, FpIsSquare } from './abstract/modular.js'; import { ProjPointType as PointType, mapToCurveSimpleSWU } from './abstract/weierstrass.js'; import type { Hex, PrivKey } from './abstract/utils.js'; import { bytesToNumberBE, concatBytes, ensureBytes, numberToBytesBE } from './abstract/utils.js'; @@ -272,3 +272,124 @@ const htf = /* @__PURE__ */ (() => ))(); export const hashToCurve = /* @__PURE__ */ (() => htf.hashToCurve)(); export const encodeToCurve = /* @__PURE__ */ (() => htf.encodeToCurve)(); + +// ElligatorSwift: Schnorr-like x-only ECDH with public keys indistinguishable +// from uniformly random bytes. +// https://github.com/bitcoin/bips/blob/master/bip-0324.mediawiki, +// https://github.com/bitcoin/bitcoin/blob/master/src/secp256k1/doc/ellswift.md +// SwiftEC: Shallue-van de Woestijne Indifferentiable Function to Elliptic Curves. +// https://eprint.iacr.org/2022/759.pdf +// +// Curve25519 & P-521 are incompatible with SwiftEC. Differences from SwiftEC: +// - undefined inputs are remapped +// - y-parity is encoded in u/t values +const MINUS_3_SQRT = Fp.sqrt(Fp.create(BigInt(-3))); +const _3n = BigInt(3); +const _4n = BigInt(4); +const _7n = BigInt(7); +const isSquare = FpIsSquare(Fp); +const isValidX = (x: bigint) => isSquare(Fp.add(Fp.mul(Fp.mul(x, x), x), _7n)); +const trySqrt = (x: bigint): bigint | void => { + try { + return Fp.sqrt(x); + } catch (_e) {} +}; + +export const elligatorSwift = /* @__PURE__ */ { + // (internal stuff, exported for tests only): decode(u, _inv(x, u)) = x + _inv: (x: bigint, u: bigint, ellCase: number): bigint | void => { + if (!Number.isSafeInteger(ellCase) || ellCase < 0 || ellCase > 7) + throw new Error(`elligatorSwift._inv: wrong case=${ellCase}`); + let v: bigint, s: bigint; + // Most rejections happens in 3 condition (in comments, ~33% each) + const u2 = Fp.mul(u, u); // u**2 + const u3 = Fp.mul(u2, u); // u**3 + if ((ellCase & 2) === 0) { + if (isValidX(Fp.sub(Fp.neg(x), u))) return; // [1 condition] + v = x; + s = Fp.div(Fp.neg(Fp.add(u3, _7n)), Fp.add(Fp.add(u2, Fp.mul(u, v)), Fp.mul(v, v))); // = -(u**3 + 7) / (u**2 + u*v + v**2) + } else { + s = Fp.sub(x, u); // x - u + if (Fp.is0(s)) return; + const t0 = Fp.add(u3, _7n); // (u**3 + 7) + const t1 = Fp.mul(Fp.mul(_3n, s), u2); // 3 * s * u**2 + // r = (-s * (4 * (u**3 + 7) + 3 * s * u**2)).sqrt() + const r = trySqrt(Fp.mul(Fp.neg(s), Fp.add(Fp.mul(_4n, t0), t1))); + if (r === undefined) return; // [2 condition] + if (ellCase & 1 && Fp.is0(r)) return; + v = Fp.div(Fp.add(Fp.neg(u), Fp.div(r, s)), _2n); // v = (-u + r / s) / 2 + } + const w = trySqrt(s); + if (w === undefined) return; // [3 condition] + const last = ellCase & 5; // ellCase = 0..8, last = 0,1,4,5 + const t0 = last & 1 ? Fp.add(_1n, MINUS_3_SQRT) : Fp.sub(_1n, MINUS_3_SQRT); + const w0 = last === 0 || last === 5 ? Fp.neg(w) : w; // -w | w + // w0 * (u * t0 / 2 + v) + return Fp.mul(w0, Fp.add(Fp.div(Fp.mul(u, t0), _2n), v)); + }, + // Encode public key (point or x coordinate bigint) into 64-byte pseudorandom encoding + encode: (x: bigint | PointType): Uint8Array => { + if (x instanceof secp256k1.ProjectivePoint) x = x.x; + if (typeof x !== 'bigint') { + throw new Error( + 'elligatorSwift.encode: wrong public key. Should be Projective point or x coordinate (bigint)' + ); + } + // 200k test cycles per keygen: avg=4 max=48 + // seems too much, but same as for reference implementation + while (true) { + // random scalar 1..Fp.ORDER + const u = Fp.create(Fp.fromBytes(secp256k1.utils.randomPrivateKey())); + const ellCase = randomBytes(1)[0] & 7; // [0..8) + const t = elligatorSwift._inv(x, u, ellCase); + if (!t) continue; + return concatBytes(numberToBytesBE(u, 32), numberToBytesBE(t, 32)); + } + }, + // Decode elligatorSwift point to xonly + decode: (data: Hex): Uint8Array => { + const _data = ensureBytes('data', data, 64); + let u = Fp.create(Fp.fromBytes(_data.subarray(0, 32))); + let t = Fp.create(Fp.fromBytes(_data.subarray(32, 64))); + if (Fp.is0(u)) u = Fp.create(_1n); + if (Fp.is0(t)) t = Fp.create(_1n); + const u3 = Fp.mul(Fp.mul(u, u), u); // u**3 + const u3plus7 = Fp.add(u3, _7n); + // u**3 + t**2 + 7 == 0 -> t = 2 * t + if (Fp.is0(Fp.add(u3plus7, Fp.mul(t, t)))) t = Fp.add(t, t); + // X = (u**3 + 7 - t**2) / (2 * t) + const x = Fp.div(Fp.sub(u3plus7, Fp.mul(t, t)), Fp.add(t, t)); + // Y = (X + t) / (MINUS_3_SQRT * u); + const y = Fp.div(Fp.add(x, t), Fp.mul(MINUS_3_SQRT, u)); + // try different cases + let res = Fp.add(u, Fp.mul(Fp.mul(y, y), _4n)); // u + 4 * Y ** 2, + if (isValidX(res)) return numberToBytesBE(res, 32); + res = Fp.div(Fp.sub(Fp.div(Fp.neg(x), y), u), _2n); // (-X / Y - u) / 2 + if (isValidX(res)) return numberToBytesBE(res, 32); + res = Fp.div(Fp.sub(Fp.div(x, y), u), _2n); // (X / Y - u) / 2 + if (isValidX(res)) return numberToBytesBE(res, 32); + throw new Error('elligatorSwift: cannot decode public key'); + }, + // Generate pair (public key, secret key) + keygen: () => { + const privateKey = secp256k1.utils.randomPrivateKey(); + const publicKey = elligatorSwift.encode(Point.fromPrivateKey(privateKey)); + return { privateKey, publicKey }; + }, + // Generates shared secret between a pub key and a priv key + getSharedSecret: (privateKeyA: Hex, publicKeyB: Hex) => { + const pub = elligatorSwift.decode(publicKeyB); + const priv = ensureBytes('privKey', privateKeyA, 32); + const point = lift_x(Fp.fromBytes(pub)); + const d = bytesToNumberBE(priv); + return numberToBytesBE(point.multiply(d).x, 32); + }, + // BIP324 shared secret + getSharedSecretBip324: (privateKeyOurs: Hex, publicKeyTheirs: Hex, publicKeyOurs: Hex, initiating: boolean) => { + const ours = ensureBytes('publicKeyOurs', publicKeyOurs); + const theirs = ensureBytes('publicKeyTheirs', publicKeyTheirs); + const ecdhPoint = elligatorSwift.getSharedSecret(privateKeyOurs, theirs); + const pubs = initiating ? [ours, theirs] : [theirs, ours]; + return taggedHash('bip324_ellswift_xonly_ecdh', ...pubs, ecdhPoint); + }, +}; diff --git a/test/index.test.js b/test/index.test.js index 6c127d9..903a703 100644 --- a/test/index.test.js +++ b/test/index.test.js @@ -9,6 +9,7 @@ import './ed25519.test.js'; import './ed25519-addons.test.js'; import './secp256k1.test.js'; import './secp256k1-schnorr.test.js'; +import './secp256k1-bip-0324.test.js'; import './jubjub.test.js'; import './hash-to-curve.test.js'; import './poseidon.test.js'; diff --git a/test/secp256k1-bip-0324.test.js b/test/secp256k1-bip-0324.test.js new file mode 100644 index 0000000..7e412d6 --- /dev/null +++ b/test/secp256k1-bip-0324.test.js @@ -0,0 +1,122 @@ +import { deepStrictEqual } from 'assert'; +import { should, describe } from 'micro-should'; +import * as fs from 'fs'; +import { + hexToBytes, + hexToNumber, + concatBytes, + bytesToHex as toHex, +} from '../esm/abstract/utils.js'; +// Generic tests for all curves in package +import { secp256k1, elligatorSwift } from '../esm/secp256k1.js'; +// ESM is broken. +import { dirname } from 'path'; +import { fileURLToPath } from 'url'; +export const __dirname = dirname(fileURLToPath(import.meta.url)); + +// https://eprint.iacr.org/2022/759 + +const parseCSV = (path) => { + const data = fs.readFileSync(`${__dirname}/vectors/secp256k1/${path}`, 'utf8'); + const lines = data.split('\n').filter((i) => !!i); + const rows = lines.map((i) => i.trim().split(',')); + const lengths = new Set(rows.map((i) => i.length)); + if (lengths.size !== 1) throw new Error('wrong dimensions'); + if (rows.length < 2) throw new Error('wrong rows length'); + const [head, ...rest] = rows; + return rest.map((row) => Object.fromEntries(row.map((cell, j) => [head[j], cell]))); +}; + +describe('ElligatorSwift', () => { + should('packet_encoding_test_vectors', () => { + for (const t of parseCSV('bip-0324/packet_encoding_test_vectors.csv')) { + const inPriv = hexToNumber(t['in_priv_ours']); + const pubX = secp256k1.ProjectivePoint.BASE.multiply(inPriv) + .x.toString(16) + .padStart(2 * 32, '0'); + deepStrictEqual(pubX, t['mid_x_ours']); + + const bytesOurs = hexToBytes(t['in_ellswift_ours']); + const decoded = elligatorSwift.decode(bytesOurs); + deepStrictEqual(toHex(decoded), t['mid_x_ours']); + + const bytesTheirs = hexToBytes(t['in_ellswift_theirs']); + deepStrictEqual(toHex(elligatorSwift.decode(bytesTheirs)), t['mid_x_theirs']); + + const xShared = elligatorSwift.getSharedSecret(t['in_priv_ours'], bytesTheirs); + deepStrictEqual(toHex(xShared), t['mid_x_shared']); + + const sharedSecret = elligatorSwift.getSharedSecretBip324( + t['in_priv_ours'], + t['in_ellswift_theirs'], + t['in_ellswift_ours'], + t['in_initiating'] === '1' + ); + deepStrictEqual(toHex(sharedSecret), t['mid_shared_secret']); + } + }); + + should('xswiftec_inv_test_vectors', () => { + for (const t of parseCSV('bip-0324/xswiftec_inv_test_vectors.csv')) { + const Fp = secp256k1.CURVE.Fp; + const u = Fp.create(Fp.fromBytes(hexToBytes(t['u']))); + const x = Fp.create(Fp.fromBytes(hexToBytes(t['x']))); + for (let c = 0; c < 8; c++) { + const name = `case${c}_t`; + const ret = elligatorSwift._inv(x, u, c); + if (!ret) deepStrictEqual(t[name], '', 'empty case'); + else { + deepStrictEqual(toHex(Fp.toBytes(ret)), t[name], 'real case'); + deepStrictEqual( + elligatorSwift.decode(concatBytes(Fp.toBytes(u), Fp.toBytes(ret))), + Fp.toBytes(x) + ); + } + } + } + }); + + should('ellswift_decode_test_vectors', () => { + for (const t of parseCSV('bip-0324/ellswift_decode_test_vectors.csv')) { + deepStrictEqual(toHex(elligatorSwift.decode(t['ellswift'])), t['x']); + } + }); + should('Example', () => { + // random, so test more. + for (let i = 0; i < 100; i++) { + const alice = elligatorSwift.keygen(); + const bob = elligatorSwift.keygen(); + // ECDH + const sharedAlice = elligatorSwift.getSharedSecret(alice.privateKey, bob.publicKey); + const sharedBob = elligatorSwift.getSharedSecret(bob.privateKey, alice.publicKey); + deepStrictEqual(sharedAlice, sharedBob); + // ECDH BIP324 + const sharedAlice2 = elligatorSwift.getSharedSecretBip324( + alice.privateKey, + bob.publicKey, + alice.publicKey, + true + ); + const sharedBob2 = elligatorSwift.getSharedSecretBip324( + bob.privateKey, + alice.publicKey, + bob.publicKey, + false + ); + deepStrictEqual(sharedAlice2, sharedBob2); + // pubKey decoding + for (const k of [alice, bob]) { + deepStrictEqual( + toHex(elligatorSwift.decode(k.publicKey)), + toHex(secp256k1.getPublicKey(k.privateKey, true).subarray(1)) + ); + } + } + }); +}); + +// ESM is broken. +import url from 'url'; +if (import.meta.url === url.pathToFileURL(process.argv[1]).href) { + should.run(); +} diff --git a/test/vectors/secp256k1/bip-0324/ellswift_decode_test_vectors.csv b/test/vectors/secp256k1/bip-0324/ellswift_decode_test_vectors.csv new file mode 100644 index 0000000..1bab96b --- /dev/null +++ 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b/test/vectors/secp256k1/bip-0324/packet_encoding_test_vectors.csv new file mode 100644 index 0000000..4f70b92 --- /dev/null +++ b/test/vectors/secp256k1/bip-0324/packet_encoding_test_vectors.csv @@ -0,0 +1,8 @@ +in_idx,in_priv_ours,in_ellswift_ours,in_ellswift_theirs,in_initiating,in_contents,in_multiply,in_aad,in_ignore,mid_x_ours,mid_x_theirs,mid_x_shared,mid_shared_secret,mid_initiator_l,mid_initiator_p,mid_responder_l,mid_responder_p,mid_send_garbage_terminator,mid_recv_garbage_terminator,out_session_id,out_ciphertext,out_ciphertext_endswith 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diff --git a/test/vectors/secp256k1/bip-0324/xswiftec_inv_test_vectors.csv b/test/vectors/secp256k1/bip-0324/xswiftec_inv_test_vectors.csv new file mode 100644 index 0000000..138c4cf --- /dev/null +++ b/test/vectors/secp256k1/bip-0324/xswiftec_inv_test_vectors.csv @@ -0,0 +1,33 @@ +u,x,case0_t,case1_t,case2_t,case3_t,case4_t,case5_t,case6_t,case7_t,comment +05ff6bdad900fc3261bc7fe34e2fb0f569f06e091ae437d3a52e9da0cbfb9590,80cdf63774ec7022c89a5a8558e373a279170285e0ab27412dbce510bdfe23fc,,,45654798ece071ba79286d04f7f3eb1c3f1d17dd883610f2ad2efd82a287466b,0aeaa886f6b76c7158452418cbf5033adc5747e9e9b5d3b2303db96936528557,,,ba9ab867131f8e4586d792fb080c14e3c0e2e82277c9ef0d52d1027c5d78b5c4,f51557790948938ea7badbe7340afcc523a8b816164a2c4dcfc24695c9ad76d8,case0:bad[valid_x(-x-u)];case1:bad[valid_x(-x-u)];case2:info[v=0]&ok;case3:ok;case4:bad[valid_x(-x-u)];case5:bad[valid_x(-x-u)];case6:info[v=0]&ok;case7:ok 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