@proton/ccxt
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A JavaScript / TypeScript / Python / C# / PHP cryptocurrency trading library with support for 130+ exchanges
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JavaScript
// ----------------------------------------------------------------------------
// PLEASE DO NOT EDIT THIS FILE, IT IS GENERATED AND WILL BE OVERWRITTEN:
// https://github.com/ccxt/ccxt/blob/master/CONTRIBUTING.md#how-to-contribute-code
// EDIT THE CORRESPONDENT .ts FILE INSTEAD
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { sha256 } from '../noble-hashes/sha256.js';
import { randomBytes } from '../noble-hashes/utils.js';
import { Fp as Field, mod, pow2 } from './abstract/modular.js';
import { mapToCurveSimpleSWU } from './abstract/weierstrass.js';
import { bytesToNumberBE, concatBytes, ensureBytes, numberToBytesBE } from './abstract/utils.js';
import * as htf from './abstract/hash-to-curve.js';
import { createCurve } from './_shortw_utils.js';
const secp256k1P = BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f');
const secp256k1N = BigInt('0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141');
const _1n = BigInt(1);
const _2n = BigInt(2);
const divNearest = (a, b) => (a + b / _2n) / b;
/**
* √n = n^((p+1)/4) for fields p = 3 mod 4. We unwrap the loop and multiply bit-by-bit.
* (P+1n/4n).toString(2) would produce bits [223x 1, 0, 22x 1, 4x 0, 11, 00]
*/
function sqrtMod(y) {
const P = secp256k1P;
// prettier-ignore
const _3n = BigInt(3), _6n = BigInt(6), _11n = BigInt(11), _22n = BigInt(22);
// prettier-ignore
const _23n = BigInt(23), _44n = BigInt(44), _88n = BigInt(88);
const b2 = (y * y * y) % P; // x^3, 11
const b3 = (b2 * b2 * y) % P; // x^7
const b6 = (pow2(b3, _3n, P) * b3) % P;
const b9 = (pow2(b6, _3n, P) * b3) % P;
const b11 = (pow2(b9, _2n, P) * b2) % P;
const b22 = (pow2(b11, _11n, P) * b11) % P;
const b44 = (pow2(b22, _22n, P) * b22) % P;
const b88 = (pow2(b44, _44n, P) * b44) % P;
const b176 = (pow2(b88, _88n, P) * b88) % P;
const b220 = (pow2(b176, _44n, P) * b44) % P;
const b223 = (pow2(b220, _3n, P) * b3) % P;
const t1 = (pow2(b223, _23n, P) * b22) % P;
const t2 = (pow2(t1, _6n, P) * b2) % P;
const root = pow2(t2, _2n, P);
if (!Fp.eql(Fp.sqr(root), y))
throw new Error('Cannot find square root');
return root;
}
const Fp = Field(secp256k1P, undefined, undefined, { sqrt: sqrtMod });
export const secp256k1 = createCurve({
a: BigInt(0),
b: BigInt(7),
Fp,
n: secp256k1N,
// Base point (x, y) aka generator point
Gx: BigInt('55066263022277343669578718895168534326250603453777594175500187360389116729240'),
Gy: BigInt('32670510020758816978083085130507043184471273380659243275938904335757337482424'),
h: BigInt(1),
lowS: true,
/**
* secp256k1 belongs to Koblitz curves: it has efficiently computable endomorphism.
* Endomorphism uses 2x less RAM, speeds up precomputation by 2x and ECDH / key recovery by 20%.
* For precomputed wNAF it trades off 1/2 init time & 1/3 ram for 20% perf hit.
* Explanation: https://gist.github.com/paulmillr/eb670806793e84df628a7c434a873066
*/
endo: {
beta: BigInt('0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee'),
splitScalar: (k) => {
const n = secp256k1N;
const a1 = BigInt('0x3086d221a7d46bcde86c90e49284eb15');
const b1 = -_1n * BigInt('0xe4437ed6010e88286f547fa90abfe4c3');
const a2 = BigInt('0x114ca50f7a8e2f3f657c1108d9d44cfd8');
const b2 = a1;
const POW_2_128 = BigInt('0x100000000000000000000000000000000'); // (2n**128n).toString(16)
const c1 = divNearest(b2 * k, n);
const c2 = divNearest(-b1 * k, n);
let k1 = mod(k - c1 * a1 - c2 * a2, n);
let k2 = mod(-c1 * b1 - c2 * b2, n);
const k1neg = k1 > POW_2_128;
const k2neg = k2 > POW_2_128;
if (k1neg)
k1 = n - k1;
if (k2neg)
k2 = n - k2;
if (k1 > POW_2_128 || k2 > POW_2_128) {
throw new Error('splitScalar: Endomorphism failed, k=' + k);
}
return { k1neg, k1, k2neg, k2 };
},
},
}, sha256);
// Schnorr signatures are superior to ECDSA from above. Below is Schnorr-specific BIP0340 code.
// https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki
const _0n = BigInt(0);
const fe = (x) => typeof x === 'bigint' && _0n < x && x < secp256k1P;
const ge = (x) => typeof x === 'bigint' && _0n < x && x < secp256k1N;
/** An object mapping tags to their tagged hash prefix of [SHA256(tag) | SHA256(tag)] */
const TAGGED_HASH_PREFIXES = {};
function taggedHash(tag, ...messages) {
let tagP = TAGGED_HASH_PREFIXES[tag];
if (tagP === undefined) {
const tagH = sha256(Uint8Array.from(tag, (c) => c.charCodeAt(0)));
tagP = concatBytes(tagH, tagH);
TAGGED_HASH_PREFIXES[tag] = tagP;
}
return sha256(concatBytes(tagP, ...messages));
}
// ECDSA compact points are 33-byte. Schnorr is 32: we strip first byte 0x02 or 0x03
const pointToBytes = (point) => point.toRawBytes(true).slice(1);
const numTo32b = (n) => numberToBytesBE(n, 32);
const modP = (x) => mod(x, secp256k1P);
const modN = (x) => mod(x, secp256k1N);
const Point = secp256k1.ProjectivePoint;
const GmulAdd = (Q, a, b) => Point.BASE.multiplyAndAddUnsafe(Q, a, b);
// Calculate point, scalar and bytes
function schnorrGetExtPubKey(priv) {
let d_ = secp256k1.utils.normPrivateKeyToScalar(priv); // same method executed in fromPrivateKey
let p = Point.fromPrivateKey(d_); // P = d'⋅G; 0 < d' < n check is done inside
const scalar = p.hasEvenY() ? d_ : modN(-d_);
return { scalar: scalar, bytes: pointToBytes(p) };
}
/**
* lift_x from BIP340. Convert 32-byte x coordinate to elliptic curve point.
* @returns valid point checked for being on-curve
*/
function lift_x(x) {
if (!fe(x))
throw new Error('bad x: need 0 < x < p'); // Fail if x ≥ p.
const xx = modP(x * x);
const c = modP(xx * x + BigInt(7)); // Let c = x³ + 7 mod p.
let y = sqrtMod(c); // Let y = c^(p+1)/4 mod p.
if (y % 2n !== 0n)
y = modP(-y); // Return the unique point P such that x(P) = x and
const p = new Point(x, y, _1n); // y(P) = y if y mod 2 = 0 or y(P) = p-y otherwise.
p.assertValidity();
return p;
}
/**
* Create tagged hash, convert it to bigint, reduce modulo-n.
*/
function challenge(...args) {
return modN(bytesToNumberBE(taggedHash('BIP0340/challenge', ...args)));
}
/**
* Schnorr public key is just `x` coordinate of Point as per BIP340.
*/
function schnorrGetPublicKey(privateKey) {
return schnorrGetExtPubKey(privateKey).bytes; // d'=int(sk). Fail if d'=0 or d'≥n. Ret bytes(d'⋅G)
}
/**
* Creates Schnorr signature as per BIP340. Verifies itself before returning anything.
* auxRand is optional and is not the sole source of k generation: bad CSPRNG won't be dangerous.
*/
function schnorrSign(message, privateKey, auxRand = randomBytes(32)) {
const m = ensureBytes('message', message);
const { bytes: px, scalar: d } = schnorrGetExtPubKey(privateKey); // checks for isWithinCurveOrder
const a = ensureBytes('auxRand', auxRand, 32); // Auxiliary random data a: a 32-byte array
const t = numTo32b(d ^ bytesToNumberBE(taggedHash('BIP0340/aux', a))); // Let t be the byte-wise xor of bytes(d) and hash/aux(a)
const rand = taggedHash('BIP0340/nonce', t, px, m); // Let rand = hash/nonce(t || bytes(P) || m)
const k_ = modN(bytesToNumberBE(rand)); // Let k' = int(rand) mod n
if (k_ === _0n)
throw new Error('sign failed: k is zero'); // Fail if k' = 0.
const { bytes: rx, scalar: k } = schnorrGetExtPubKey(k_); // Let R = k'⋅G.
const e = challenge(rx, px, m); // Let e = int(hash/challenge(bytes(R) || bytes(P) || m)) mod n.
const sig = new Uint8Array(64); // Let sig = bytes(R) || bytes((k + ed) mod n).
sig.set(rx, 0);
sig.set(numTo32b(modN(k + e * d)), 32);
// If Verify(bytes(P), m, sig) (see below) returns failure, abort
if (!schnorrVerify(sig, m, px))
throw new Error('sign: Invalid signature produced');
return sig;
}
/**
* Verifies Schnorr signature.
* Will swallow errors & return false except for initial type validation of arguments.
*/
function schnorrVerify(signature, message, publicKey) {
const sig = ensureBytes('signature', signature, 64);
const m = ensureBytes('message', message);
const pub = ensureBytes('publicKey', publicKey, 32);
try {
const P = lift_x(bytesToNumberBE(pub)); // P = lift_x(int(pk)); fail if that fails
const r = bytesToNumberBE(sig.subarray(0, 32)); // Let r = int(sig[0:32]); fail if r ≥ p.
if (!fe(r))
return false;
const s = bytesToNumberBE(sig.subarray(32, 64)); // Let s = int(sig[32:64]); fail if s ≥ n.
if (!ge(s))
return false;
const e = challenge(numTo32b(r), pointToBytes(P), m); // int(challenge(bytes(r)||bytes(P)||m))%n
const R = GmulAdd(P, s, modN(-e)); // R = s⋅G - e⋅P
if (!R || !R.hasEvenY() || R.toAffine().x !== r)
return false; // -eP == (n-e)P
return true; // Fail if is_infinite(R) / not has_even_y(R) / x(R) ≠ r.
}
catch (error) {
return false;
}
}
export const schnorr = {
getPublicKey: schnorrGetPublicKey,
sign: schnorrSign,
verify: schnorrVerify,
utils: {
randomPrivateKey: secp256k1.utils.randomPrivateKey,
lift_x,
pointToBytes,
numberToBytesBE,
bytesToNumberBE,
taggedHash,
mod,
},
};
const isoMap = htf.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))));
const mapSWU = mapToCurveSimpleSWU(Fp, {
A: BigInt('0x3f8731abdd661adca08a5558f0f5d272e953d363cb6f0e5d405447c01a444533'),
B: BigInt('1771'),
Z: Fp.create(BigInt('-11')),
});
export const { hashToCurve, encodeToCurve } = htf.createHasher(secp256k1.ProjectivePoint, (scalars) => {
const { x, y } = mapSWU(Fp.create(scalars[0]));
return isoMap(x, y);
}, {
DST: 'secp256k1_XMD:SHA-256_SSWU_RO_',
encodeDST: 'secp256k1_XMD:SHA-256_SSWU_NU_',
p: Fp.ORDER,
m: 1,
k: 128,
expand: 'xmd',
hash: sha256,
});