294 lines
12 KiB
JavaScript
294 lines
12 KiB
JavaScript
/**
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* SECG secp256k1. See [pdf](https://www.secg.org/sec2-v2.pdf).
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*
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* Belongs to Koblitz curves: it has efficiently-computable GLV endomorphism ψ,
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* check out {@link EndomorphismOpts}. Seems to be rigid (not backdoored).
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* @module
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*/
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/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
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import { sha256 } from '@noble/hashes/sha2.js';
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import { randomBytes } from '@noble/hashes/utils.js';
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import { createCurve } from "./_shortw_utils.js";
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import { createHasher, isogenyMap, } from "./abstract/hash-to-curve.js";
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import { Field, mapHashToField, mod, pow2 } from "./abstract/modular.js";
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import { _normFnElement, mapToCurveSimpleSWU, } from "./abstract/weierstrass.js";
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import { bytesToNumberBE, concatBytes, ensureBytes, inRange, numberToBytesBE, utf8ToBytes, } from "./utils.js";
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// Seems like generator was produced from some seed:
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// `Point.BASE.multiply(Point.Fn.inv(2n, N)).toAffine().x`
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// // gives short x 0x3b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63n
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const secp256k1_CURVE = {
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p: BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f'),
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n: BigInt('0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141'),
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h: BigInt(1),
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a: BigInt(0),
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b: BigInt(7),
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Gx: BigInt('0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798'),
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Gy: BigInt('0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8'),
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};
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const secp256k1_ENDO = {
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beta: BigInt('0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee'),
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basises: [
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[BigInt('0x3086d221a7d46bcde86c90e49284eb15'), -BigInt('0xe4437ed6010e88286f547fa90abfe4c3')],
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[BigInt('0x114ca50f7a8e2f3f657c1108d9d44cfd8'), BigInt('0x3086d221a7d46bcde86c90e49284eb15')],
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],
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};
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const _0n = /* @__PURE__ */ BigInt(0);
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const _1n = /* @__PURE__ */ BigInt(1);
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const _2n = /* @__PURE__ */ BigInt(2);
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/**
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* √n = n^((p+1)/4) for fields p = 3 mod 4. We unwrap the loop and multiply bit-by-bit.
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* (P+1n/4n).toString(2) would produce bits [223x 1, 0, 22x 1, 4x 0, 11, 00]
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*/
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function sqrtMod(y) {
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const P = secp256k1_CURVE.p;
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// prettier-ignore
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const _3n = BigInt(3), _6n = BigInt(6), _11n = BigInt(11), _22n = BigInt(22);
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// prettier-ignore
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const _23n = BigInt(23), _44n = BigInt(44), _88n = BigInt(88);
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const b2 = (y * y * y) % P; // x^3, 11
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const b3 = (b2 * b2 * y) % P; // x^7
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const b6 = (pow2(b3, _3n, P) * b3) % P;
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const b9 = (pow2(b6, _3n, P) * b3) % P;
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const b11 = (pow2(b9, _2n, P) * b2) % P;
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const b22 = (pow2(b11, _11n, P) * b11) % P;
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const b44 = (pow2(b22, _22n, P) * b22) % P;
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const b88 = (pow2(b44, _44n, P) * b44) % P;
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const b176 = (pow2(b88, _88n, P) * b88) % P;
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const b220 = (pow2(b176, _44n, P) * b44) % P;
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const b223 = (pow2(b220, _3n, P) * b3) % P;
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const t1 = (pow2(b223, _23n, P) * b22) % P;
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const t2 = (pow2(t1, _6n, P) * b2) % P;
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const root = pow2(t2, _2n, P);
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if (!Fpk1.eql(Fpk1.sqr(root), y))
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throw new Error('Cannot find square root');
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return root;
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}
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const Fpk1 = Field(secp256k1_CURVE.p, { sqrt: sqrtMod });
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/**
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* secp256k1 curve, ECDSA and ECDH methods.
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*
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* Field: `2n**256n - 2n**32n - 2n**9n - 2n**8n - 2n**7n - 2n**6n - 2n**4n - 1n`
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*
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* @example
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* ```js
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* import { secp256k1 } from '@noble/curves/secp256k1';
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* const { secretKey, publicKey } = secp256k1.keygen();
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* const msg = new TextEncoder().encode('hello');
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* const sig = secp256k1.sign(msg, secretKey);
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* const isValid = secp256k1.verify(sig, msg, publicKey) === true;
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* ```
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*/
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export const secp256k1 = createCurve({ ...secp256k1_CURVE, Fp: Fpk1, lowS: true, endo: secp256k1_ENDO }, sha256);
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// Schnorr signatures are superior to ECDSA from above. Below is Schnorr-specific BIP0340 code.
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// https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki
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/** An object mapping tags to their tagged hash prefix of [SHA256(tag) | SHA256(tag)] */
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const TAGGED_HASH_PREFIXES = {};
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function taggedHash(tag, ...messages) {
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let tagP = TAGGED_HASH_PREFIXES[tag];
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if (tagP === undefined) {
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const tagH = sha256(utf8ToBytes(tag));
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tagP = concatBytes(tagH, tagH);
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TAGGED_HASH_PREFIXES[tag] = tagP;
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}
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return sha256(concatBytes(tagP, ...messages));
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}
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// ECDSA compact points are 33-byte. Schnorr is 32: we strip first byte 0x02 or 0x03
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const pointToBytes = (point) => point.toBytes(true).slice(1);
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const Pointk1 = /* @__PURE__ */ (() => secp256k1.Point)();
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const hasEven = (y) => y % _2n === _0n;
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// Calculate point, scalar and bytes
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function schnorrGetExtPubKey(priv) {
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const { Fn, BASE } = Pointk1;
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const d_ = _normFnElement(Fn, priv);
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const p = BASE.multiply(d_); // P = d'⋅G; 0 < d' < n check is done inside
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const scalar = hasEven(p.y) ? d_ : Fn.neg(d_);
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return { scalar, bytes: pointToBytes(p) };
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}
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/**
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* lift_x from BIP340. Convert 32-byte x coordinate to elliptic curve point.
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* @returns valid point checked for being on-curve
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*/
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function lift_x(x) {
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const Fp = Fpk1;
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if (!Fp.isValidNot0(x))
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throw new Error('invalid x: Fail if x ≥ p');
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const xx = Fp.create(x * x);
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const c = Fp.create(xx * x + BigInt(7)); // Let c = x³ + 7 mod p.
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let y = Fp.sqrt(c); // Let y = c^(p+1)/4 mod p. Same as sqrt().
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// Return the unique point P such that x(P) = x and
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// y(P) = y if y mod 2 = 0 or y(P) = p-y otherwise.
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if (!hasEven(y))
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y = Fp.neg(y);
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const p = Pointk1.fromAffine({ x, y });
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p.assertValidity();
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return p;
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}
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const num = bytesToNumberBE;
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/**
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* Create tagged hash, convert it to bigint, reduce modulo-n.
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*/
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function challenge(...args) {
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return Pointk1.Fn.create(num(taggedHash('BIP0340/challenge', ...args)));
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}
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/**
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* Schnorr public key is just `x` coordinate of Point as per BIP340.
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*/
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function schnorrGetPublicKey(secretKey) {
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return schnorrGetExtPubKey(secretKey).bytes; // d'=int(sk). Fail if d'=0 or d'≥n. Ret bytes(d'⋅G)
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}
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/**
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* Creates Schnorr signature as per BIP340. Verifies itself before returning anything.
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* auxRand is optional and is not the sole source of k generation: bad CSPRNG won't be dangerous.
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*/
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function schnorrSign(message, secretKey, auxRand = randomBytes(32)) {
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const { Fn } = Pointk1;
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const m = ensureBytes('message', message);
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const { bytes: px, scalar: d } = schnorrGetExtPubKey(secretKey); // checks for isWithinCurveOrder
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const a = ensureBytes('auxRand', auxRand, 32); // Auxiliary random data a: a 32-byte array
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const t = Fn.toBytes(d ^ num(taggedHash('BIP0340/aux', a))); // Let t be the byte-wise xor of bytes(d) and hash/aux(a)
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const rand = taggedHash('BIP0340/nonce', t, px, m); // Let rand = hash/nonce(t || bytes(P) || m)
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// Let k' = int(rand) mod n. Fail if k' = 0. Let R = k'⋅G
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const { bytes: rx, scalar: k } = schnorrGetExtPubKey(rand);
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const e = challenge(rx, px, m); // Let e = int(hash/challenge(bytes(R) || bytes(P) || m)) mod n.
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const sig = new Uint8Array(64); // Let sig = bytes(R) || bytes((k + ed) mod n).
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sig.set(rx, 0);
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sig.set(Fn.toBytes(Fn.create(k + e * d)), 32);
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// If Verify(bytes(P), m, sig) (see below) returns failure, abort
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if (!schnorrVerify(sig, m, px))
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throw new Error('sign: Invalid signature produced');
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return sig;
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}
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/**
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* Verifies Schnorr signature.
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* Will swallow errors & return false except for initial type validation of arguments.
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*/
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function schnorrVerify(signature, message, publicKey) {
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const { Fn, BASE } = Pointk1;
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const sig = ensureBytes('signature', signature, 64);
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const m = ensureBytes('message', message);
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const pub = ensureBytes('publicKey', publicKey, 32);
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try {
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const P = lift_x(num(pub)); // P = lift_x(int(pk)); fail if that fails
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const r = num(sig.subarray(0, 32)); // Let r = int(sig[0:32]); fail if r ≥ p.
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if (!inRange(r, _1n, secp256k1_CURVE.p))
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return false;
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const s = num(sig.subarray(32, 64)); // Let s = int(sig[32:64]); fail if s ≥ n.
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if (!inRange(s, _1n, secp256k1_CURVE.n))
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return false;
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// int(challenge(bytes(r)||bytes(P)||m))%n
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const e = challenge(Fn.toBytes(r), pointToBytes(P), m);
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// R = s⋅G - e⋅P, where -eP == (n-e)P
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const R = BASE.multiplyUnsafe(s).add(P.multiplyUnsafe(Fn.neg(e)));
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const { x, y } = R.toAffine();
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// Fail if is_infinite(R) / not has_even_y(R) / x(R) ≠ r.
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if (R.is0() || !hasEven(y) || x !== r)
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return false;
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return true;
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}
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catch (error) {
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return false;
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}
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}
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/**
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* Schnorr signatures over secp256k1.
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* https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki
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* @example
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* ```js
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* import { schnorr } from '@noble/curves/secp256k1';
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* const { secretKey, publicKey } = schnorr.keygen();
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* // const publicKey = schnorr.getPublicKey(secretKey);
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* const msg = new TextEncoder().encode('hello');
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* const sig = schnorr.sign(msg, secretKey);
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* const isValid = schnorr.verify(sig, msg, publicKey);
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* ```
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*/
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export const schnorr = /* @__PURE__ */ (() => {
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const size = 32;
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const seedLength = 48;
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const randomSecretKey = (seed = randomBytes(seedLength)) => {
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return mapHashToField(seed, secp256k1_CURVE.n);
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};
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// TODO: remove
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secp256k1.utils.randomSecretKey;
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function keygen(seed) {
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const secretKey = randomSecretKey(seed);
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return { secretKey, publicKey: schnorrGetPublicKey(secretKey) };
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}
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return {
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keygen,
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getPublicKey: schnorrGetPublicKey,
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sign: schnorrSign,
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verify: schnorrVerify,
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Point: Pointk1,
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utils: {
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randomSecretKey: randomSecretKey,
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randomPrivateKey: randomSecretKey,
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taggedHash,
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// TODO: remove
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lift_x,
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pointToBytes,
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numberToBytesBE,
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bytesToNumberBE,
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mod,
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},
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lengths: {
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secretKey: size,
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publicKey: size,
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publicKeyHasPrefix: false,
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signature: size * 2,
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seed: seedLength,
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},
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};
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})();
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const isoMap = /* @__PURE__ */ (() => isogenyMap(Fpk1, [
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// xNum
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[
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'0x8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa8c7',
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'0x7d3d4c80bc321d5b9f315cea7fd44c5d595d2fc0bf63b92dfff1044f17c6581',
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'0x534c328d23f234e6e2a413deca25caece4506144037c40314ecbd0b53d9dd262',
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'0x8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa88c',
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],
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// xDen
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[
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'0xd35771193d94918a9ca34ccbb7b640dd86cd409542f8487d9fe6b745781eb49b',
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'0xedadc6f64383dc1df7c4b2d51b54225406d36b641f5e41bbc52a56612a8c6d14',
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'0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1
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],
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// yNum
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[
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'0x4bda12f684bda12f684bda12f684bda12f684bda12f684bda12f684b8e38e23c',
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'0xc75e0c32d5cb7c0fa9d0a54b12a0a6d5647ab046d686da6fdffc90fc201d71a3',
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'0x29a6194691f91a73715209ef6512e576722830a201be2018a765e85a9ecee931',
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'0x2f684bda12f684bda12f684bda12f684bda12f684bda12f684bda12f38e38d84',
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],
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// yDen
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[
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'0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffff93b',
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'0x7a06534bb8bdb49fd5e9e6632722c2989467c1bfc8e8d978dfb425d2685c2573',
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'0x6484aa716545ca2cf3a70c3fa8fe337e0a3d21162f0d6299a7bf8192bfd2a76f',
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'0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1
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],
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].map((i) => i.map((j) => BigInt(j)))))();
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const mapSWU = /* @__PURE__ */ (() => mapToCurveSimpleSWU(Fpk1, {
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A: BigInt('0x3f8731abdd661adca08a5558f0f5d272e953d363cb6f0e5d405447c01a444533'),
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B: BigInt('1771'),
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Z: Fpk1.create(BigInt('-11')),
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}))();
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/** Hashing / encoding to secp256k1 points / field. RFC 9380 methods. */
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export const secp256k1_hasher = /* @__PURE__ */ (() => createHasher(secp256k1.Point, (scalars) => {
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const { x, y } = mapSWU(Fpk1.create(scalars[0]));
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return isoMap(x, y);
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}, {
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DST: 'secp256k1_XMD:SHA-256_SSWU_RO_',
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encodeDST: 'secp256k1_XMD:SHA-256_SSWU_NU_',
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p: Fpk1.ORDER,
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m: 1,
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k: 128,
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expand: 'xmd',
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hash: sha256,
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}))();
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/** @deprecated use `import { secp256k1_hasher } from '@noble/curves/secp256k1.js';` */
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export const hashToCurve = /* @__PURE__ */ (() => secp256k1_hasher.hashToCurve)();
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/** @deprecated use `import { secp256k1_hasher } from '@noble/curves/secp256k1.js';` */
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export const encodeToCurve = /* @__PURE__ */ (() => secp256k1_hasher.encodeToCurve)();
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//# sourceMappingURL=secp256k1.js.map
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