PHP WebShell
Текущая директория: /usr/lib/node_modules/bitgo/node_modules/@noble/curves/abstract
Просмотр файла: modular.js
"use strict";
Object.defineProperty(exports, "__esModule", { value: true });
exports.isNegativeLE = void 0;
exports.mod = mod;
exports.pow = pow;
exports.pow2 = pow2;
exports.invert = invert;
exports.tonelliShanks = tonelliShanks;
exports.FpSqrt = FpSqrt;
exports.validateField = validateField;
exports.FpPow = FpPow;
exports.FpInvertBatch = FpInvertBatch;
exports.FpDiv = FpDiv;
exports.FpLegendre = FpLegendre;
exports.FpIsSquare = FpIsSquare;
exports.nLength = nLength;
exports.Field = Field;
exports.FpSqrtOdd = FpSqrtOdd;
exports.FpSqrtEven = FpSqrtEven;
exports.hashToPrivateScalar = hashToPrivateScalar;
exports.getFieldBytesLength = getFieldBytesLength;
exports.getMinHashLength = getMinHashLength;
exports.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 = require("../utils.js");
// 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, y = _1n, u = _1n, v = _0n;
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;
const n = y - v * q;
// prettier-ignore
b = a, a = r, x = u, y = v, u = m, v = n;
}
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;
exports.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);
}
//# sourceMappingURL=modular.js.mapВыполнить команду
Для локальной разработки. Не используйте в интернете!