opnet
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The perfect library for building Bitcoin-based applications.
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JavaScript
import { r as requireUtils$2, a as requireHmac, b as requireSha2, c as bytesToHex, i as isBytes, h as hexToBytes, d as abytes, e as concatBytes, f as anumber, g as ahash, j as randomBytes, k as hmac, s as sha256 } from './noble-hashes.js';
function getDefaultExportFromCjs(x) {
return x && x.__esModule && Object.prototype.hasOwnProperty.call(x, "default") ? x["default"] : x;
}
function getAugmentedNamespace(n) {
if (Object.prototype.hasOwnProperty.call(n, "__esModule")) return n;
var f = n.default;
if (typeof f == "function") {
var a = function a2() {
var isInstance = false;
try {
isInstance = this instanceof a2;
} catch {
}
if (isInstance) {
return Reflect.construct(f, arguments, this.constructor);
}
return f.apply(this, arguments);
};
a.prototype = f.prototype;
} else a = {};
Object.defineProperty(a, "__esModule", { value: true });
Object.keys(n).forEach(function(k) {
var d = Object.getOwnPropertyDescriptor(n, k);
Object.defineProperty(a, k, d.get ? d : {
enumerable: true,
get: function() {
return n[k];
}
});
});
return a;
}
var secp256k1$1 = {};
var _shortw_utils = {};
var weierstrass$1 = {};
var utils$1 = {};
var hasRequiredUtils$1;
function requireUtils$1 () {
if (hasRequiredUtils$1) return utils$1;
hasRequiredUtils$1 = 1;
(function (exports$1) {
Object.defineProperty(exports$1, "__esModule", { value: true });
exports$1.notImplemented = exports$1.bitMask = exports$1.utf8ToBytes = exports$1.randomBytes = exports$1.isBytes = exports$1.hexToBytes = exports$1.concatBytes = exports$1.bytesToUtf8 = exports$1.bytesToHex = exports$1.anumber = exports$1.abytes = void 0;
exports$1.abool = abool;
exports$1._abool2 = _abool2;
exports$1._abytes2 = _abytes2;
exports$1.numberToHexUnpadded = numberToHexUnpadded;
exports$1.hexToNumber = hexToNumber;
exports$1.bytesToNumberBE = bytesToNumberBE;
exports$1.bytesToNumberLE = bytesToNumberLE;
exports$1.numberToBytesBE = numberToBytesBE;
exports$1.numberToBytesLE = numberToBytesLE;
exports$1.numberToVarBytesBE = numberToVarBytesBE;
exports$1.ensureBytes = ensureBytes;
exports$1.equalBytes = equalBytes;
exports$1.copyBytes = copyBytes;
exports$1.asciiToBytes = asciiToBytes;
exports$1.inRange = inRange;
exports$1.aInRange = aInRange;
exports$1.bitLen = bitLen;
exports$1.bitGet = bitGet;
exports$1.bitSet = bitSet;
exports$1.createHmacDrbg = createHmacDrbg;
exports$1.validateObject = validateObject;
exports$1.isHash = isHash;
exports$1._validateObject = _validateObject;
exports$1.memoized = memoized;
/**
* Hex, bytes and number utilities.
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
const utils_js_1 = /*@__PURE__*/ requireUtils$2();
var utils_js_2 = /*@__PURE__*/ requireUtils$2();
Object.defineProperty(exports$1, "abytes", { enumerable: true, get: function () { return utils_js_2.abytes; } });
Object.defineProperty(exports$1, "anumber", { enumerable: true, get: function () { return utils_js_2.anumber; } });
Object.defineProperty(exports$1, "bytesToHex", { enumerable: true, get: function () { return utils_js_2.bytesToHex; } });
Object.defineProperty(exports$1, "bytesToUtf8", { enumerable: true, get: function () { return utils_js_2.bytesToUtf8; } });
Object.defineProperty(exports$1, "concatBytes", { enumerable: true, get: function () { return utils_js_2.concatBytes; } });
Object.defineProperty(exports$1, "hexToBytes", { enumerable: true, get: function () { return utils_js_2.hexToBytes; } });
Object.defineProperty(exports$1, "isBytes", { enumerable: true, get: function () { return utils_js_2.isBytes; } });
Object.defineProperty(exports$1, "randomBytes", { enumerable: true, get: function () { return utils_js_2.randomBytes; } });
Object.defineProperty(exports$1, "utf8ToBytes", { enumerable: true, get: function () { return utils_js_2.utf8ToBytes; } });
const _0n = /* @__PURE__ */ BigInt(0);
const _1n = /* @__PURE__ */ BigInt(1);
function abool(title, value) {
if (typeof value !== 'boolean')
throw new Error(title + ' boolean expected, got ' + value);
}
// tmp name until v2
function _abool2(value, title = '') {
if (typeof value !== 'boolean') {
const prefix = title && `"${title}"`;
throw new Error(prefix + 'expected boolean, got type=' + typeof value);
}
return value;
}
// tmp name until v2
/** Asserts something is Uint8Array. */
function _abytes2(value, length, title = '') {
const bytes = (0, utils_js_1.isBytes)(value);
const len = value?.length;
const needsLen = length !== undefined;
if (!bytes || (needsLen && len !== length)) {
const prefix = title && `"${title}" `;
const ofLen = needsLen ? ` of length ${length}` : '';
const got = bytes ? `length=${len}` : `type=${typeof value}`;
throw new Error(prefix + 'expected Uint8Array' + ofLen + ', got ' + got);
}
return value;
}
// Used in weierstrass, der
function numberToHexUnpadded(num) {
const hex = num.toString(16);
return hex.length & 1 ? '0' + hex : hex;
}
function hexToNumber(hex) {
if (typeof hex !== 'string')
throw new Error('hex string expected, got ' + typeof hex);
return hex === '' ? _0n : BigInt('0x' + hex); // Big Endian
}
// BE: Big Endian, LE: Little Endian
function bytesToNumberBE(bytes) {
return hexToNumber((0, utils_js_1.bytesToHex)(bytes));
}
function bytesToNumberLE(bytes) {
(0, utils_js_1.abytes)(bytes);
return hexToNumber((0, utils_js_1.bytesToHex)(Uint8Array.from(bytes).reverse()));
}
function numberToBytesBE(n, len) {
return (0, utils_js_1.hexToBytes)(n.toString(16).padStart(len * 2, '0'));
}
function numberToBytesLE(n, len) {
return numberToBytesBE(n, len).reverse();
}
// Unpadded, rarely used
function numberToVarBytesBE(n) {
return (0, utils_js_1.hexToBytes)(numberToHexUnpadded(n));
}
/**
* Takes hex string or Uint8Array, converts to Uint8Array.
* Validates output length.
* Will throw error for other types.
* @param title descriptive title for an error e.g. 'secret key'
* @param hex hex string or Uint8Array
* @param expectedLength optional, will compare to result array's length
* @returns
*/
function ensureBytes(title, hex, expectedLength) {
let res;
if (typeof hex === 'string') {
try {
res = (0, utils_js_1.hexToBytes)(hex);
}
catch (e) {
throw new Error(title + ' must be hex string or Uint8Array, cause: ' + e);
}
}
else if ((0, utils_js_1.isBytes)(hex)) {
// Uint8Array.from() instead of hash.slice() because node.js Buffer
// is instance of Uint8Array, and its slice() creates **mutable** copy
res = Uint8Array.from(hex);
}
else {
throw new Error(title + ' must be hex string or Uint8Array');
}
const len = res.length;
if (typeof expectedLength === 'number' && len !== expectedLength)
throw new Error(title + ' of length ' + expectedLength + ' expected, got ' + len);
return res;
}
// Compares 2 u8a-s in kinda constant time
function equalBytes(a, b) {
if (a.length !== b.length)
return false;
let diff = 0;
for (let i = 0; i < a.length; i++)
diff |= a[i] ^ b[i];
return diff === 0;
}
/**
* Copies Uint8Array. We can't use u8a.slice(), because u8a can be Buffer,
* and Buffer#slice creates mutable copy. Never use Buffers!
*/
function copyBytes(bytes) {
return Uint8Array.from(bytes);
}
/**
* Decodes 7-bit ASCII string to Uint8Array, throws on non-ascii symbols
* Should be safe to use for things expected to be ASCII.
* Returns exact same result as utf8ToBytes for ASCII or throws.
*/
function asciiToBytes(ascii) {
return Uint8Array.from(ascii, (c, i) => {
const charCode = c.charCodeAt(0);
if (c.length !== 1 || charCode > 127) {
throw new Error(`string contains non-ASCII character "${ascii[i]}" with code ${charCode} at position ${i}`);
}
return charCode;
});
}
/**
* @example utf8ToBytes('abc') // new Uint8Array([97, 98, 99])
*/
// export const utf8ToBytes: typeof utf8ToBytes_ = utf8ToBytes_;
/**
* Converts bytes to string using UTF8 encoding.
* @example bytesToUtf8(Uint8Array.from([97, 98, 99])) // 'abc'
*/
// export const bytesToUtf8: typeof bytesToUtf8_ = bytesToUtf8_;
// Is positive bigint
const isPosBig = (n) => typeof n === 'bigint' && _0n <= n;
function inRange(n, min, max) {
return isPosBig(n) && isPosBig(min) && isPosBig(max) && min <= n && n < max;
}
/**
* Asserts min <= n < max. NOTE: It's < max and not <= max.
* @example
* aInRange('x', x, 1n, 256n); // would assume x is in (1n..255n)
*/
function aInRange(title, n, min, max) {
// Why min <= n < max and not a (min < n < max) OR b (min <= n <= max)?
// consider P=256n, min=0n, max=P
// - a for min=0 would require -1: `inRange('x', x, -1n, P)`
// - b would commonly require subtraction: `inRange('x', x, 0n, P - 1n)`
// - our way is the cleanest: `inRange('x', x, 0n, P)
if (!inRange(n, min, max))
throw new Error('expected valid ' + title + ': ' + min + ' <= n < ' + max + ', got ' + n);
}
// Bit operations
/**
* Calculates amount of bits in a bigint.
* Same as `n.toString(2).length`
* TODO: merge with nLength in modular
*/
function bitLen(n) {
let len;
for (len = 0; n > _0n; n >>= _1n, len += 1)
;
return len;
}
/**
* Gets single bit at position.
* NOTE: first bit position is 0 (same as arrays)
* Same as `!!+Array.from(n.toString(2)).reverse()[pos]`
*/
function bitGet(n, pos) {
return (n >> BigInt(pos)) & _1n;
}
/**
* Sets single bit at position.
*/
function bitSet(n, pos, value) {
return n | ((value ? _1n : _0n) << BigInt(pos));
}
/**
* Calculate mask for N bits. Not using ** operator with bigints because of old engines.
* Same as BigInt(`0b${Array(i).fill('1').join('')}`)
*/
const bitMask = (n) => (_1n << BigInt(n)) - _1n;
exports$1.bitMask = bitMask;
/**
* Minimal HMAC-DRBG from NIST 800-90 for RFC6979 sigs.
* @returns function that will call DRBG until 2nd arg returns something meaningful
* @example
* const drbg = createHmacDRBG<Key>(32, 32, hmac);
* drbg(seed, bytesToKey); // bytesToKey must return Key or undefined
*/
function createHmacDrbg(hashLen, qByteLen, hmacFn) {
if (typeof hashLen !== 'number' || hashLen < 2)
throw new Error('hashLen must be a number');
if (typeof qByteLen !== 'number' || qByteLen < 2)
throw new Error('qByteLen must be a number');
if (typeof hmacFn !== 'function')
throw new Error('hmacFn must be a function');
// Step B, Step C: set hashLen to 8*ceil(hlen/8)
const u8n = (len) => new Uint8Array(len); // creates Uint8Array
const u8of = (byte) => Uint8Array.of(byte); // another shortcut
let v = u8n(hashLen); // Minimal non-full-spec HMAC-DRBG from NIST 800-90 for RFC6979 sigs.
let k = u8n(hashLen); // Steps B and C of RFC6979 3.2: set hashLen, in our case always same
let i = 0; // Iterations counter, will throw when over 1000
const reset = () => {
v.fill(1);
k.fill(0);
i = 0;
};
const h = (...b) => hmacFn(k, v, ...b); // hmac(k)(v, ...values)
const reseed = (seed = u8n(0)) => {
// HMAC-DRBG reseed() function. Steps D-G
k = h(u8of(0x00), seed); // k = hmac(k || v || 0x00 || seed)
v = h(); // v = hmac(k || v)
if (seed.length === 0)
return;
k = h(u8of(0x01), seed); // k = hmac(k || v || 0x01 || seed)
v = h(); // v = hmac(k || v)
};
const gen = () => {
// HMAC-DRBG generate() function
if (i++ >= 1000)
throw new Error('drbg: tried 1000 values');
let len = 0;
const out = [];
while (len < qByteLen) {
v = h();
const sl = v.slice();
out.push(sl);
len += v.length;
}
return (0, utils_js_1.concatBytes)(...out);
};
const genUntil = (seed, pred) => {
reset();
reseed(seed); // Steps D-G
let res = undefined; // Step H: grind until k is in [1..n-1]
while (!(res = pred(gen())))
reseed();
reset();
return res;
};
return genUntil;
}
// Validating curves and fields
const validatorFns = {
bigint: (val) => typeof val === 'bigint',
function: (val) => typeof val === 'function',
boolean: (val) => typeof val === 'boolean',
string: (val) => typeof val === 'string',
stringOrUint8Array: (val) => typeof val === 'string' || (0, utils_js_1.isBytes)(val),
isSafeInteger: (val) => Number.isSafeInteger(val),
array: (val) => Array.isArray(val),
field: (val, object) => object.Fp.isValid(val),
hash: (val) => typeof val === 'function' && Number.isSafeInteger(val.outputLen),
};
// type Record<K extends string | number | symbol, T> = { [P in K]: T; }
function validateObject(object, validators, optValidators = {}) {
const checkField = (fieldName, type, isOptional) => {
const checkVal = validatorFns[type];
if (typeof checkVal !== 'function')
throw new Error('invalid validator function');
const val = object[fieldName];
if (isOptional && val === undefined)
return;
if (!checkVal(val, object)) {
throw new Error('param ' + String(fieldName) + ' is invalid. Expected ' + type + ', got ' + val);
}
};
for (const [fieldName, type] of Object.entries(validators))
checkField(fieldName, type, false);
for (const [fieldName, type] of Object.entries(optValidators))
checkField(fieldName, type, true);
return object;
}
// validate type tests
// const o: { a: number; b: number; c: number } = { a: 1, b: 5, c: 6 };
// const z0 = validateObject(o, { a: 'isSafeInteger' }, { c: 'bigint' }); // Ok!
// // Should fail type-check
// const z1 = validateObject(o, { a: 'tmp' }, { c: 'zz' });
// const z2 = validateObject(o, { a: 'isSafeInteger' }, { c: 'zz' });
// const z3 = validateObject(o, { test: 'boolean', z: 'bug' });
// const z4 = validateObject(o, { a: 'boolean', z: 'bug' });
function isHash(val) {
return typeof val === 'function' && Number.isSafeInteger(val.outputLen);
}
function _validateObject(object, fields, optFields = {}) {
if (!object || typeof object !== 'object')
throw new Error('expected valid options object');
function checkField(fieldName, expectedType, isOpt) {
const val = object[fieldName];
if (isOpt && val === undefined)
return;
const current = typeof val;
if (current !== expectedType || val === null)
throw new Error(`param "${fieldName}" is invalid: expected ${expectedType}, got ${current}`);
}
Object.entries(fields).forEach(([k, v]) => checkField(k, v, false));
Object.entries(optFields).forEach(([k, v]) => checkField(k, v, true));
}
/**
* throws not implemented error
*/
const notImplemented = () => {
throw new Error('not implemented');
};
exports$1.notImplemented = notImplemented;
/**
* Memoizes (caches) computation result.
* Uses WeakMap: the value is going auto-cleaned by GC after last reference is removed.
*/
function memoized(fn) {
const map = new WeakMap();
return (arg, ...args) => {
const val = map.get(arg);
if (val !== undefined)
return val;
const computed = fn(arg, ...args);
map.set(arg, computed);
return computed;
};
}
} (utils$1));
return utils$1;
}
var curve = {};
var modular = {};
var hasRequiredModular;
function requireModular () {
if (hasRequiredModular) return modular;
hasRequiredModular = 1;
Object.defineProperty(modular, "__esModule", { value: true });
modular.isNegativeLE = void 0;
modular.mod = mod;
modular.pow = pow;
modular.pow2 = pow2;
modular.invert = invert;
modular.tonelliShanks = tonelliShanks;
modular.FpSqrt = FpSqrt;
modular.validateField = validateField;
modular.FpPow = FpPow;
modular.FpInvertBatch = FpInvertBatch;
modular.FpDiv = FpDiv;
modular.FpLegendre = FpLegendre;
modular.FpIsSquare = FpIsSquare;
modular.nLength = nLength;
modular.Field = Field;
modular.FpSqrtOdd = FpSqrtOdd;
modular.FpSqrtEven = FpSqrtEven;
modular.hashToPrivateScalar = hashToPrivateScalar;
modular.getFieldBytesLength = getFieldBytesLength;
modular.getMinHashLength = getMinHashLength;
modular.mapHashToField = mapHashToField;
/**
* Utils for modular division and fields.
* Field over 11 is a finite (Galois) field is integer number operations `mod 11`.
* There is no division: it is replaced by modular multiplicative inverse.
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
const utils_ts_1 = /*@__PURE__*/ requireUtils$1();
// prettier-ignore
const _0n = BigInt(0), _1n = BigInt(1), _2n = /* @__PURE__ */ BigInt(2), _3n = /* @__PURE__ */ BigInt(3);
// prettier-ignore
const _4n = /* @__PURE__ */ BigInt(4), _5n = /* @__PURE__ */ BigInt(5), _7n = /* @__PURE__ */ BigInt(7);
// prettier-ignore
const _8n = /* @__PURE__ */ BigInt(8), _9n = /* @__PURE__ */ BigInt(9), _16n = /* @__PURE__ */ BigInt(16);
// Calculates a modulo b
function mod(a, b) {
const result = a % b;
return result >= _0n ? result : b + result;
}
/**
* Efficiently raise num to power and do modular division.
* Unsafe in some contexts: uses ladder, so can expose bigint bits.
* @example
* pow(2n, 6n, 11n) // 64n % 11n == 9n
*/
function pow(num, power, modulo) {
return FpPow(Field(modulo), num, power);
}
/** Does `x^(2^power)` mod p. `pow2(30, 4)` == `30^(2^4)` */
function pow2(x, power, modulo) {
let res = x;
while (power-- > _0n) {
res *= res;
res %= modulo;
}
return res;
}
/**
* Inverses number over modulo.
* Implemented using [Euclidean GCD](https://brilliant.org/wiki/extended-euclidean-algorithm/).
*/
function invert(number, modulo) {
if (number === _0n)
throw new Error('invert: expected non-zero number');
if (modulo <= _0n)
throw new Error('invert: expected positive modulus, got ' + modulo);
// Fermat's little theorem "CT-like" version inv(n) = n^(m-2) mod m is 30x slower.
let a = mod(number, modulo);
let b = modulo;
// prettier-ignore
let x = _0n, u = _1n;
while (a !== _0n) {
// JIT applies optimization if those two lines follow each other
const q = b / a;
const r = b % a;
const m = x - u * q;
// prettier-ignore
b = a, a = r, x = u, u = m;
}
const gcd = b;
if (gcd !== _1n)
throw new Error('invert: does not exist');
return mod(x, modulo);
}
function assertIsSquare(Fp, root, n) {
if (!Fp.eql(Fp.sqr(root), n))
throw new Error('Cannot find square root');
}
// Not all roots are possible! Example which will throw:
// const NUM =
// n = 72057594037927816n;
// Fp = Field(BigInt('0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab'));
function sqrt3mod4(Fp, n) {
const p1div4 = (Fp.ORDER + _1n) / _4n;
const root = Fp.pow(n, p1div4);
assertIsSquare(Fp, root, n);
return root;
}
function sqrt5mod8(Fp, n) {
const p5div8 = (Fp.ORDER - _5n) / _8n;
const n2 = Fp.mul(n, _2n);
const v = Fp.pow(n2, p5div8);
const nv = Fp.mul(n, v);
const i = Fp.mul(Fp.mul(nv, _2n), v);
const root = Fp.mul(nv, Fp.sub(i, Fp.ONE));
assertIsSquare(Fp, root, n);
return root;
}
// Based on RFC9380, Kong algorithm
// prettier-ignore
function sqrt9mod16(P) {
const Fp_ = Field(P);
const tn = tonelliShanks(P);
const c1 = tn(Fp_, Fp_.neg(Fp_.ONE)); // 1. c1 = sqrt(-1) in F, i.e., (c1^2) == -1 in F
const c2 = tn(Fp_, c1); // 2. c2 = sqrt(c1) in F, i.e., (c2^2) == c1 in F
const c3 = tn(Fp_, Fp_.neg(c1)); // 3. c3 = sqrt(-c1) in F, i.e., (c3^2) == -c1 in F
const c4 = (P + _7n) / _16n; // 4. c4 = (q + 7) / 16 # Integer arithmetic
return (Fp, n) => {
let tv1 = Fp.pow(n, c4); // 1. tv1 = x^c4
let tv2 = Fp.mul(tv1, c1); // 2. tv2 = c1 * tv1
const tv3 = Fp.mul(tv1, c2); // 3. tv3 = c2 * tv1
const tv4 = Fp.mul(tv1, c3); // 4. tv4 = c3 * tv1
const e1 = Fp.eql(Fp.sqr(tv2), n); // 5. e1 = (tv2^2) == x
const e2 = Fp.eql(Fp.sqr(tv3), n); // 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.eql(Fp.sqr(tv2), n); // 9. e3 = (tv2^2) == x
const root = Fp.cmov(tv1, tv2, e3); // 10. z = CMOV(tv1, tv2, e3) # Select sqrt from tv1 & tv2
assertIsSquare(Fp, root, n);
return root;
};
}
/**
* Tonelli-Shanks square root search algorithm.
* 1. https://eprint.iacr.org/2012/685.pdf (page 12)
* 2. Square Roots from 1; 24, 51, 10 to Dan Shanks
* @param P field order
* @returns function that takes field Fp (created from P) and number n
*/
function tonelliShanks(P) {
// Initialization (precomputation).
// Caching initialization could boost perf by 7%.
if (P < _3n)
throw new Error('sqrt is not defined for small field');
// Factor P - 1 = Q * 2^S, where Q is odd
let Q = P - _1n;
let S = 0;
while (Q % _2n === _0n) {
Q /= _2n;
S++;
}
// Find the first quadratic non-residue Z >= 2
let Z = _2n;
const _Fp = Field(P);
while (FpLegendre(_Fp, Z) === 1) {
// Basic primality test for P. After x iterations, chance of
// not finding quadratic non-residue is 2^x, so 2^1000.
if (Z++ > 1000)
throw new Error('Cannot find square root: probably non-prime P');
}
// Fast-path; usually done before Z, but we do "primality test".
if (S === 1)
return sqrt3mod4;
// Slow-path
// TODO: test on Fp2 and others
let cc = _Fp.pow(Z, Q); // c = z^Q
const Q1div2 = (Q + _1n) / _2n;
return function tonelliSlow(Fp, n) {
if (Fp.is0(n))
return n;
// Check if n is a quadratic residue using Legendre symbol
if (FpLegendre(Fp, n) !== 1)
throw new Error('Cannot find square root');
// Initialize variables for the main loop
let M = S;
let c = Fp.mul(Fp.ONE, cc); // c = z^Q, move cc from field _Fp into field Fp
let t = Fp.pow(n, Q); // t = n^Q, first guess at the fudge factor
let R = Fp.pow(n, Q1div2); // R = n^((Q+1)/2), first guess at the square root
// Main loop
// while t != 1
while (!Fp.eql(t, Fp.ONE)) {
if (Fp.is0(t))
return Fp.ZERO; // if t=0 return R=0
let i = 1;
// Find the smallest i >= 1 such that t^(2^i) ≡ 1 (mod P)
let t_tmp = Fp.sqr(t); // t^(2^1)
while (!Fp.eql(t_tmp, Fp.ONE)) {
i++;
t_tmp = Fp.sqr(t_tmp); // t^(2^2)...
if (i === M)
throw new Error('Cannot find square root');
}
// Calculate the exponent for b: 2^(M - i - 1)
const exponent = _1n << BigInt(M - i - 1); // bigint is important
const b = Fp.pow(c, exponent); // b = 2^(M - i - 1)
// Update variables
M = i;
c = Fp.sqr(b); // c = b^2
t = Fp.mul(t, c); // t = (t * b^2)
R = Fp.mul(R, b); // R = R*b
}
return R;
};
}
/**
* Square root for a finite field. Will try optimized versions first:
*
* 1. P ≡ 3 (mod 4)
* 2. P ≡ 5 (mod 8)
* 3. P ≡ 9 (mod 16)
* 4. Tonelli-Shanks algorithm
*
* Different algorithms can give different roots, it is up to user to decide which one they want.
* For example there is FpSqrtOdd/FpSqrtEven to choice root based on oddness (used for hash-to-curve).
*/
function FpSqrt(P) {
// P ≡ 3 (mod 4) => √n = n^((P+1)/4)
if (P % _4n === _3n)
return sqrt3mod4;
// P ≡ 5 (mod 8) => Atkin algorithm, page 10 of https://eprint.iacr.org/2012/685.pdf
if (P % _8n === _5n)
return sqrt5mod8;
// P ≡ 9 (mod 16) => Kong algorithm, page 11 of https://eprint.iacr.org/2012/685.pdf (algorithm 4)
if (P % _16n === _9n)
return sqrt9mod16(P);
// Tonelli-Shanks algorithm
return tonelliShanks(P);
}
// Little-endian check for first LE bit (last BE bit);
const isNegativeLE = (num, modulo) => (mod(num, modulo) & _1n) === _1n;
modular.isNegativeLE = isNegativeLE;
// prettier-ignore
const FIELD_FIELDS = [
'create', 'isValid', 'is0', 'neg', 'inv', 'sqrt', 'sqr',
'eql', 'add', 'sub', 'mul', 'pow', 'div',
'addN', 'subN', 'mulN', 'sqrN'
];
function validateField(field) {
const initial = {
ORDER: 'bigint',
MASK: 'bigint',
BYTES: 'number',
BITS: 'number',
};
const opts = FIELD_FIELDS.reduce((map, val) => {
map[val] = 'function';
return map;
}, initial);
(0, utils_ts_1._validateObject)(field, opts);
// const max = 16384;
// if (field.BYTES < 1 || field.BYTES > max) throw new Error('invalid field');
// if (field.BITS < 1 || field.BITS > 8 * max) throw new Error('invalid field');
return field;
}
// Generic field functions
/**
* Same as `pow` but for Fp: non-constant-time.
* Unsafe in some contexts: uses ladder, so can expose bigint bits.
*/
function FpPow(Fp, num, power) {
if (power < _0n)
throw new Error('invalid exponent, negatives unsupported');
if (power === _0n)
return Fp.ONE;
if (power === _1n)
return num;
let p = Fp.ONE;
let d = num;
while (power > _0n) {
if (power & _1n)
p = Fp.mul(p, d);
d = Fp.sqr(d);
power >>= _1n;
}
return p;
}
/**
* Efficiently invert an array of Field elements.
* Exception-free. Will return `undefined` for 0 elements.
* @param passZero map 0 to 0 (instead of undefined)
*/
function FpInvertBatch(Fp, nums, passZero = false) {
const inverted = new Array(nums.length).fill(passZero ? Fp.ZERO : undefined);
// Walk from first to last, multiply them by each other MOD p
const multipliedAcc = nums.reduce((acc, num, i) => {
if (Fp.is0(num))
return acc;
inverted[i] = acc;
return Fp.mul(acc, num);
}, Fp.ONE);
// Invert last element
const invertedAcc = Fp.inv(multipliedAcc);
// Walk from last to first, multiply them by inverted each other MOD p
nums.reduceRight((acc, num, i) => {
if (Fp.is0(num))
return acc;
inverted[i] = Fp.mul(acc, inverted[i]);
return Fp.mul(acc, num);
}, invertedAcc);
return inverted;
}
// TODO: remove
function FpDiv(Fp, lhs, rhs) {
return Fp.mul(lhs, typeof rhs === 'bigint' ? invert(rhs, Fp.ORDER) : Fp.inv(rhs));
}
/**
* Legendre symbol.
* Legendre constant is used to calculate Legendre symbol (a | p)
* which denotes the value of a^((p-1)/2) (mod p).
*
* * (a | p) ≡ 1 if a is a square (mod p), quadratic residue
* * (a | p) ≡ -1 if a is not a square (mod p), quadratic non residue
* * (a | p) ≡ 0 if a ≡ 0 (mod p)
*/
function FpLegendre(Fp, n) {
// We can use 3rd argument as optional cache of this value
// but seems unneeded for now. The operation is very fast.
const p1mod2 = (Fp.ORDER - _1n) / _2n;
const powered = Fp.pow(n, p1mod2);
const yes = Fp.eql(powered, Fp.ONE);
const zero = Fp.eql(powered, Fp.ZERO);
const no = Fp.eql(powered, Fp.neg(Fp.ONE));
if (!yes && !zero && !no)
throw new Error('invalid Legendre symbol result');
return yes ? 1 : zero ? 0 : -1;
}
// This function returns True whenever the value x is a square in the field F.
function FpIsSquare(Fp, n) {
const l = FpLegendre(Fp, n);
return l === 1;
}
// CURVE.n lengths
function nLength(n, nBitLength) {
// Bit size, byte size of CURVE.n
if (nBitLength !== undefined)
(0, utils_ts_1.anumber)(nBitLength);
const _nBitLength = nBitLength !== undefined ? nBitLength : n.toString(2).length;
const nByteLength = Math.ceil(_nBitLength / 8);
return { nBitLength: _nBitLength, nByteLength };
}
/**
* Creates a finite field. Major performance optimizations:
* * 1. Denormalized operations like mulN instead of mul.
* * 2. Identical object shape: never add or remove keys.
* * 3. `Object.freeze`.
* Fragile: always run a benchmark on a change.
* Security note: operations don't check 'isValid' for all elements for performance reasons,
* it is caller responsibility to check this.
* This is low-level code, please make sure you know what you're doing.
*
* Note about field properties:
* * CHARACTERISTIC p = prime number, number of elements in main subgroup.
* * ORDER q = similar to cofactor in curves, may be composite `q = p^m`.
*
* @param ORDER field order, probably prime, or could be composite
* @param bitLen how many bits the field consumes
* @param isLE (default: false) if encoding / decoding should be in little-endian
* @param redef optional faster redefinitions of sqrt and other methods
*/
function Field(ORDER, bitLenOrOpts, // TODO: use opts only in v2?
isLE = false, opts = {}) {
if (ORDER <= _0n)
throw new Error('invalid field: expected ORDER > 0, got ' + ORDER);
let _nbitLength = undefined;
let _sqrt = undefined;
let modFromBytes = false;
let allowedLengths = undefined;
if (typeof bitLenOrOpts === 'object' && bitLenOrOpts != null) {
if (opts.sqrt || isLE)
throw new Error('cannot specify opts in two arguments');
const _opts = bitLenOrOpts;
if (_opts.BITS)
_nbitLength = _opts.BITS;
if (_opts.sqrt)
_sqrt = _opts.sqrt;
if (typeof _opts.isLE === 'boolean')
isLE = _opts.isLE;
if (typeof _opts.modFromBytes === 'boolean')
modFromBytes = _opts.modFromBytes;
allowedLengths = _opts.allowedLengths;
}
else {
if (typeof bitLenOrOpts === 'number')
_nbitLength = bitLenOrOpts;
if (opts.sqrt)
_sqrt = opts.sqrt;
}
const { nBitLength: BITS, nByteLength: BYTES } = nLength(ORDER, _nbitLength);
if (BYTES > 2048)
throw new Error('invalid field: expected ORDER of <= 2048 bytes');
let sqrtP; // cached sqrtP
const f = Object.freeze({
ORDER,
isLE,
BITS,
BYTES,
MASK: (0, utils_ts_1.bitMask)(BITS),
ZERO: _0n,
ONE: _1n,
allowedLengths: allowedLengths,
create: (num) => mod(num, ORDER),
isValid: (num) => {
if (typeof num !== 'bigint')
throw new Error('invalid field element: expected bigint, got ' + typeof num);
return _0n <= num && num < ORDER; // 0 is valid element, but it's not invertible
},
is0: (num) => num === _0n,
// is valid and invertible
isValidNot0: (num) => !f.is0(num) && f.isValid(num),
isOdd: (num) => (num & _1n) === _1n,
neg: (num) => mod(-num, ORDER),
eql: (lhs, rhs) => lhs === rhs,
sqr: (num) => mod(num * num, ORDER),
add: (lhs, rhs) => mod(lhs + rhs, ORDER),
sub: (lhs, rhs) => mod(lhs - rhs, ORDER),
mul: (lhs, rhs) => mod(lhs * rhs, ORDER),
pow: (num, power) => FpPow(f, num, power),
div: (lhs, rhs) => mod(lhs * invert(rhs, ORDER), ORDER),
// Same as above, but doesn't normalize
sqrN: (num) => num * num,
addN: (lhs, rhs) => lhs + rhs,
subN: (lhs, rhs) => lhs - rhs,
mulN: (lhs, rhs) => lhs * rhs,
inv: (num) => invert(num, ORDER),
sqrt: _sqrt ||
((n) => {
if (!sqrtP)
sqrtP = FpSqrt(ORDER);
return sqrtP(f, n);
}),
toBytes: (num) => (isLE ? (0, utils_ts_1.numberToBytesLE)(num, BYTES) : (0, utils_ts_1.numberToBytesBE)(num, BYTES)),
fromBytes: (bytes, skipValidation = true) => {
if (allowedLengths) {
if (!allowedLengths.includes(bytes.length) || bytes.length > BYTES) {
throw new Error('Field.fromBytes: expected ' + allowedLengths + ' bytes, got ' + bytes.length);
}
const padded = new Uint8Array(BYTES);
// isLE add 0 to right, !isLE to the left.
padded.set(bytes, isLE ? 0 : padded.length - bytes.length);
bytes = padded;
}
if (bytes.length !== BYTES)
throw new Error('Field.fromBytes: expected ' + BYTES + ' bytes, got ' + bytes.length);
let scalar = isLE ? (0, utils_ts_1.bytesToNumberLE)(bytes) : (0, utils_ts_1.bytesToNumberBE)(bytes);
if (modFromBytes)
scalar = mod(scalar, ORDER);
if (!skipValidation)
if (!f.isValid(scalar))
throw new Error('invalid field element: outside of range 0..ORDER');
// NOTE: we don't validate scalar here, please use isValid. This done such way because some
// protocol may allow non-reduced scalar that reduced later or changed some other way.
return scalar;
},
// TODO: we don't need it here, move out to separate fn
invertBatch: (lst) => FpInvertBatch(f, lst),
// We can't move this out because Fp6, Fp12 implement it
// and it's unclear what to return in there.
cmov: (a, b, c) => (c ? b : a),
});
return Object.freeze(f);
}
// Generic random scalar, we can do same for other fields if via Fp2.mul(Fp2.ONE, Fp2.random)?
// This allows unsafe methods like ignore bias or zero. These unsafe, but often used in different protocols (if deterministic RNG).
// which mean we cannot force this via opts.
// Not sure what to do with randomBytes, we can accept it inside opts if wanted.
// Probably need to export getMinHashLength somewhere?
// random(bytes?: Uint8Array, unsafeAllowZero = false, unsafeAllowBias = false) {
// const LEN = !unsafeAllowBias ? getMinHashLength(ORDER) : BYTES;
// if (bytes === undefined) bytes = randomBytes(LEN); // _opts.randomBytes?
// const num = isLE ? bytesToNumberLE(bytes) : bytesToNumberBE(bytes);
// // `mod(x, 11)` can sometimes produce 0. `mod(x, 10) + 1` is the same, but no 0
// const reduced = unsafeAllowZero ? mod(num, ORDER) : mod(num, ORDER - _1n) + _1n;
// return reduced;
// },
function FpSqrtOdd(Fp, elm) {
if (!Fp.isOdd)
throw new Error("Field doesn't have isOdd");
const root = Fp.sqrt(elm);
return Fp.isOdd(root) ? root : Fp.neg(root);
}
function FpSqrtEven(Fp, elm) {
if (!Fp.isOdd)
throw new Error("Field doesn't have isOdd");
const root = Fp.sqrt(elm);
return Fp.isOdd(root) ? Fp.neg(root) : root;
}
/**
* "Constant-time" private key generation utility.
* Same as mapKeyToField, but accepts less bytes (40 instead of 48 for 32-byte field).
* Which makes it slightly more biased, less secure.
* @deprecated use `mapKeyToField` instead
*/
function hashToPrivateScalar(hash, groupOrder, isLE = false) {
hash = (0, utils_ts_1.ensureBytes)('privateHash', hash);
const hashLen = hash.length;
const minLen = nLength(groupOrder).nByteLength + 8;
if (minLen < 24 || hashLen < minLen || hashLen > 1024)
throw new Error('hashToPrivateScalar: expected ' + minLen + '-1024 bytes of input, got ' + hashLen);
const num = isLE ? (0, utils_ts_1.bytesToNumberLE)(hash) : (0, utils_ts_1.bytesToNumberBE)(hash);
return mod(num, groupOrder - _1n) + _1n;
}
/**
* Returns total number of bytes consumed by the field element.
* For example, 32 bytes for usual 256-bit weierstrass curve.
* @param fieldOrder number of field elements, usually CURVE.n
* @returns byte length of field
*/
function getFieldBytesLength(fieldOrder) {
if (typeof fieldOrder !== 'bigint')
throw new Error('field order must be bigint');
const bitLength = fieldOrder.toString(2).length;
return Math.ceil(bitLength / 8);
}
/**
* Returns minimal amount of bytes that can be safely reduced
* by field order.
* Should be 2^-128 for 128-bit curve such as P256.
* @param fieldOrder number of field elements, usually CURVE.n
* @returns byte length of target hash
*/
function getMinHashLength(fieldOrder) {
const length = getFieldBytesLength(fieldOrder);
return length + Math.ceil(length / 2);
}
/**
* "Constant-time" private key generation utility.
* Can take (n + n/2) or more bytes of uniform input e.g. from CSPRNG or KDF
* and convert them into private scalar, with the modulo bias being negligible.
* Needs at least 48 bytes of input for 32-byte private key.
* https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
* FIPS 186-5, A.2 https://csrc.nist.gov/publications/detail/fips/186/5/final
* RFC 9380, https://www.rfc-editor.org/rfc/rfc9380#section-5
* @param hash hash output from SHA3 or a similar function
* @param groupOrder size of subgroup - (e.g. secp256k1.CURVE.n)
* @param isLE interpret hash bytes as LE num
* @returns valid private scalar
*/
function mapHashToField(key, fieldOrder, isLE = false) {
const len = key.length;
const fieldLen = getFieldBytesLength(fieldOrder);
const minLen = getMinHashLength(fieldOrder);
// No small numbers: need to understand bias story. No huge numbers: easier to detect JS timings.
if (len < 16 || len < minLen || len > 1024)
throw new Error('expected ' + minLen + '-1024 bytes of input, got ' + len);
const num = isLE ? (0, utils_ts_1.bytesToNumberLE)(key) : (0, utils_ts_1.bytesToNumberBE)(key);
// `mod(x, 11)` can sometimes produce 0. `mod(x, 10) + 1` is the same, but no 0
const reduced = mod(num, fieldOrder - _1n) + _1n;
return isLE ? (0, utils_ts_1.numberToBytesLE)(reduced, fieldLen) : (0, utils_ts_1.numberToBytesBE)(reduced, fieldLen);
}
return modular;
}
var hasRequiredCurve;
function requireCurve () {
if (hasRequiredCurve) return curve;
hasRequiredCurve = 1;
Object.defineProperty(curve, "__esModule", { value: true });
curve.wNAF = void 0;
curve.negateCt = negateCt;
curve.normalizeZ = normalizeZ;
curve.mulEndoUnsafe = mulEndoUnsafe;
curve.pippenger = pippenger;
curve.precomputeMSMUnsafe = precomputeMSMUnsafe;
curve.validateBasic = validateBasic;
curve._createCurveFields = _createCurveFields;
/**
* Methods for elliptic curve multiplication by scalars.
* Contains wNAF, pippenger.
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
const utils_ts_1 = /*@__PURE__*/ requireUtils$1();
const modular_ts_1 = /*@__PURE__*/ requireModular();
const _0n = BigInt(0);
const _1n = BigInt(1);
function negateCt(condition, item) {
const neg = item.negate();
return condition ? neg : item;
}
/**
* Takes a bunch of Projective Points but executes only one
* inversion on all of them. Inversion is very slow operation,
* so this improves performance massively.
* Optimization: converts a list of projective points to a list of identical points with Z=1.
*/
function normalizeZ(c, points) {
const invertedZs = (0, modular_ts_1.FpInvertBatch)(c.Fp, points.map((p) => p.Z));
return points.map((p, i) => c.fromAffine(p.toAffine(invertedZs[i])));
}
function validateW(W, bits) {
if (!Number.isSafeInteger(W) || W <= 0 || W > bits)
throw new Error('invalid window size, expected [1..' + bits + '], got W=' + W);
}
function calcWOpts(W, scalarBits) {
validateW(W, scalarBits);
const windows = Math.ceil(scalarBits / W) + 1; // W=8 33. Not 32, because we skip zero
const windowSize = 2 ** (W - 1); // W=8 128. Not 256, because we skip zero
const maxNumber = 2 ** W; // W=8 256
const mask = (0, utils_ts_1.bitMask)(W); // W=8 255 == mask 0b11111111
const shiftBy = BigInt(W); // W=8 8
return { windows, windowSize, mask, maxNumber, shiftBy };
}
function calcOffsets(n, window, wOpts) {
const { windowSize, mask, maxNumber, shiftBy } = wOpts;
let wbits = Number(n & mask); // extract W bits.
let nextN = n >> shiftBy; // shift number by W bits.
// What actually happens here:
// const highestBit = Number(mask ^ (mask >> 1n));
// let wbits2 = wbits - 1; // skip zero
// if (wbits2 & highestBit) { wbits2 ^= Number(mask); // (~);
// split if bits > max: +224 => 256-32
if (wbits > windowSize) {
// we skip zero, which means instead of `>= size-1`, we do `> size`
wbits -= maxNumber; // -32, can be maxNumber - wbits, but then we need to set isNeg here.
nextN += _1n; // +256 (carry)
}
const offsetStart = window * windowSize;
const offset = offsetStart + Math.abs(wbits) - 1; // -1 because we skip zero
const isZero = wbits === 0; // is current window slice a 0?
const isNeg = wbits < 0; // is current window slice negative?
const isNegF = window % 2 !== 0; // fake random statement for noise
const offsetF = offsetStart; // fake offset for noise
return { nextN, offset, isZero, isNeg, isNegF, offsetF };
}
function validateMSMPoints(points, c) {
if (!Array.isArray(points))
throw new Error('array expected');
points.forEach((p, i) => {
if (!(p instanceof c))
throw new Error('invalid point at index ' + i);
});
}
function validateMSMScalars(scalars, field) {
if (!Array.isArray(scalars))
throw new Error('array of scalars expected');
scalars.forEach((s, i) => {
if (!field.isValid(s))
throw new Error('invalid scalar at index ' + i);
});
}
// Since points in different groups cannot be equal (different object constructor),
// we can have single place to store precomputes.
// Allows to make points frozen / immutable.
const pointPrecomputes = new WeakMap();
const pointWindowSizes = new WeakMap();
function getW(P) {
// To disable precomputes:
// return 1;
return pointWindowSizes.get(P) || 1;
}
function assert0(n) {
if (n !== _0n)
throw new Error('invalid wNAF');
}
/**
* Elliptic curve multiplication of Point by scalar. Fragile.
* Table generation takes **30MB of ram and 10ms on high-end CPU**,
* but may take much longer on slow devices. Actual generation will happen on
* first call of `multiply()`. By default, `BASE` point is precomputed.
*
* Scalars should always be less than curve order: this should be checked inside of a curve itself.
* Creates precomputation tables for fast multiplication:
* - private scalar is split by fixed size windows of W bits
* - every window point is collected from window's table & added to accumulator
* - since windows are different, same point inside tables won't be accessed more than once per calc
* - each multiplication is 'Math.ceil(CURVE_ORDER / 𝑊) + 1' point additions (fixed for any scalar)
* - +1 window is neccessary for wNAF
* - wNAF reduces table size: 2x less memory + 2x faster generation, but 10% slower multiplication
*
* @todo Research returning 2d JS array of windows, instead of a single window.
* This would allow windows to be in different memory locations
*/
class wNAF {
// Parametrized with a given Point class (not individual point)
constructor(Point, bits) {
this.BASE = Point.BASE;
this.ZERO = Point.ZERO;
this.Fn = Point.Fn;
this.bits = bits;
}
// non-const time multiplication ladder
_unsafeLadder(elm, n, p = this.ZERO) {
let d = elm;
while (n > _0n) {
if (n & _1n)
p = p.add(d);
d = d.double();
n >>= _1n;
}
return p;
}
/**
* Creates a wNAF precomputation window. Used for caching.
* Default window size is set by `utils.precompute()` and is equal to 8.
* Number of precomputed points depends on the curve size:
* 2^(𝑊−1) * (Math.ceil(𝑛 / 𝑊) + 1), where:
* - 𝑊 is the window size
* - 𝑛 is the bitlength of the curve order.
* For a 256-bit curve and window size 8, the number of precomputed points is 128 * 33 = 4224.
* @param point Point instance
* @param W window size
* @returns precomputed point tables flattened to a single array
*/
precomputeWindow(point, W) {
const { windows, windowSize } = calcWOpts(W, this.bits);
const points = [];
let p = point;
let base = p;
for (let window = 0; window < windows; window++) {
base = p;
points.push(base);
// i=1, bc we skip 0
for (let i = 1; i < windowSize; i++) {
base = base.add(p);
points.push(base);
}
p = base.double();
}
return points;
}
/**
* Implements ec multiplication using precomputed tables and w-ary non-adjacent form.
* More compact implementation:
* https://github.com/paulmillr/noble-secp256k1/blob/47cb1669b6e506ad66b35fe7d76132ae97465da2/index.ts#L502-L541
* @returns real and fake (for const-time) points
*/
wNAF(W, precomputes, n) {
// Scalar should be smaller than field order
if (!this.Fn.isValid(n))
throw new Error('invalid scalar');
// Accumulators
let p = this.ZERO;
let f = this.BASE;
// This code was first written with assumption that 'f' and 'p' will never be infinity point:
// since each addition is multiplied by 2 ** W, it cannot cancel each other. However,
// there is negate now: it is possible that negated element from low value
// would be the same as high element, which will create carry into next window.
// It's not obvious how this can fail, but still worth investigating later.
const wo = calcWOpts(W, this.bits);
for (let window = 0; window < wo.windows; window++) {
// (n === _0n) is handled and not early-exited. isEven and offsetF are used for noise
const { nextN, offset, isZero, isNeg, isNegF, offsetF } = calcOffsets(n, window, wo);
n = nextN;
if (isZero) {
// bits are 0: add garbage to fake point
// Important part for const-time getPublicKey: add random "noise" point to f.
f = f.add(negateCt(isNegF, precomputes[offsetF]));
}
else {
// bits are 1: add to result point
p = p.add(negateCt(isNeg, precomputes[offset]));
}
}
assert0(n);
// Return both real and fake points: JIT won't eliminate f.
// At this point there is a way to F be infinity-point even if p is not,
// which makes it less const-time: around 1 bigint multiply.
return { p, f };
}
/**
* Implements ec unsafe (non const-time) multiplication using precomputed tables and w-ary non-adjacent form.
* @param acc accumulator point to add result of multiplication
* @returns point
*/
wNAFUnsafe(W, precomputes, n, acc = this.ZERO) {
const wo = calcWOpts(W, this.bits);
for (let window = 0; window < wo.windows; window++) {
if (n === _0n)
break; // Early-exit, skip 0 value
const { nextN, offset, isZero, isNeg } = calcOffsets(n, window, wo);
n = nextN;
if (isZero) {
// Window bits are 0: skip processing.
// Move to next window.
continue;
}
else {
const item = precomputes[offset];
acc = acc.add(isNeg ? item.negate() : item); // Re-using acc allows to save adds in MSM
}
}
assert0(n);
return acc;
}
getPrecomputes(W, point, transform) {
// Calculate precomputes on a first run, reuse them after
let comp = pointPrecomputes.get(point);
if (!comp) {
comp = this.precomputeWindow(point, W);
if (W !== 1) {
// Doing transform outside of if brings 15% perf hit
if (typeof transform === 'function')
comp = transform(comp);
pointPrecomputes.set(point, comp);
}
}
return comp;
}
cached(point, scalar, transform) {
const W = getW(point);
return this.wNAF(W, this.getPrecomputes(W, point, transform), scalar)