@0xfutbol/id
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React component library with shared providers for 0xFutbol ID
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JavaScript
import {s as sha256}from'./sha256-DQJaatHj.js';import {b4 as Hash,bz as ahash,b7 as toBytes,b6 as aexists,bA as abytes,bB as numberToBytesLE,bC as numberToBytesBE,bD as bitMask,bE as bytesToNumberLE,bF as bytesToNumberBE,bG as validateObject,bH as bitLen,bI as concatBytes,bJ as ensureBytes,bK as aInRange,bL as bytesToHex,bM as hexToBytes,bN as isBytes,bO as createHmacDrbg,bP as memoized,bQ as abool,bR as inRange,bS as ut,bT as abytes$1,bU as numberToHexUnpadded,bV as randomBytes,bW as concatBytes$1}from'./index-BJCJzM2_.js';import'react';import'react/jsx-runtime';import'@0xfutbol/id-sign';import'react-use';import'@0xfutbol/constants';import'thirdweb';import'@matchain/matchid-sdk-react';import'@tanstack/react-query';import'@matchain/matchid-sdk-react/index.css';import'react-dom';/**
* HMAC: RFC2104 message authentication code.
* @module
*/
class HMAC extends Hash {
constructor(hash, _key) {
super();
this.finished = false;
this.destroyed = false;
ahash(hash);
const key = toBytes(_key);
this.iHash = hash.create();
if (typeof this.iHash.update !== 'function')
throw new Error('Expected instance of class which extends utils.Hash');
this.blockLen = this.iHash.blockLen;
this.outputLen = this.iHash.outputLen;
const blockLen = this.blockLen;
const pad = new Uint8Array(blockLen);
// blockLen can be bigger than outputLen
pad.set(key.length > blockLen ? hash.create().update(key).digest() : key);
for (let i = 0; i < pad.length; i++)
pad[i] ^= 0x36;
this.iHash.update(pad);
// By doing update (processing of first block) of outer hash here we can re-use it between multiple calls via clone
this.oHash = hash.create();
// Undo internal XOR && apply outer XOR
for (let i = 0; i < pad.length; i++)
pad[i] ^= 0x36 ^ 0x5c;
this.oHash.update(pad);
pad.fill(0);
}
update(buf) {
aexists(this);
this.iHash.update(buf);
return this;
}
digestInto(out) {
aexists(this);
abytes(out, this.outputLen);
this.finished = true;
this.iHash.digestInto(out);
this.oHash.update(out);
this.oHash.digestInto(out);
this.destroy();
}
digest() {
const out = new Uint8Array(this.oHash.outputLen);
this.digestInto(out);
return out;
}
_cloneInto(to) {
// Create new instance without calling constructor since key already in state and we don't know it.
to || (to = Object.create(Object.getPrototypeOf(this), {}));
const { oHash, iHash, finished, destroyed, blockLen, outputLen } = this;
to = to;
to.finished = finished;
to.destroyed = destroyed;
to.blockLen = blockLen;
to.outputLen = outputLen;
to.oHash = oHash._cloneInto(to.oHash);
to.iHash = iHash._cloneInto(to.iHash);
return to;
}
destroy() {
this.destroyed = true;
this.oHash.destroy();
this.iHash.destroy();
}
}
/**
* HMAC: RFC2104 message authentication code.
* @param hash - function that would be used e.g. sha256
* @param key - message key
* @param message - message data
* @example
* import { hmac } from '@noble/hashes/hmac';
* import { sha256 } from '@noble/hashes/sha2';
* const mac1 = hmac(sha256, 'key', 'message');
*/
const hmac = (hash, key, message) => new HMAC(hash, key).update(message).digest();
hmac.create = (hash, key) => new HMAC(hash, key);/**
* Utils for modular division and finite fields.
* A finite field over 11 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) */
// prettier-ignore
const _0n$2 = BigInt(0), _1n$3 = BigInt(1), _2n$1 = /* @__PURE__ */ BigInt(2), _3n$1 = /* @__PURE__ */ BigInt(3);
// prettier-ignore
const _4n = /* @__PURE__ */ BigInt(4), _5n = /* @__PURE__ */ BigInt(5), _8n = /* @__PURE__ */ BigInt(8);
// Calculates a modulo b
function mod(a, b) {
const result = a % b;
return result >= _0n$2 ? result : b + result;
}
/**
* Efficiently raise num to power and do modular division.
* Unsafe in some contexts: uses ladder, so can expose bigint bits.
* @todo use field version && remove
* @example
* pow(2n, 6n, 11n) // 64n % 11n == 9n
*/
function pow(num, power, modulo) {
if (power < _0n$2)
throw new Error('invalid exponent, negatives unsupported');
if (modulo <= _0n$2)
throw new Error('invalid modulus');
if (modulo === _1n$3)
return _0n$2;
let res = _1n$3;
while (power > _0n$2) {
if (power & _1n$3)
res = (res * num) % modulo;
num = (num * num) % modulo;
power >>= _1n$3;
}
return res;
}
/** Does `x^(2^power)` mod p. `pow2(30, 4)` == `30^(2^4)` */
function pow2(x, power, modulo) {
let res = x;
while (power-- > _0n$2) {
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$2)
throw new Error('invert: expected non-zero number');
if (modulo <= _0n$2)
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$2, u = _1n$3;
while (a !== _0n$2) {
// 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$3)
throw new Error('invert: does not exist');
return mod(x, modulo);
}
/**
* 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
* Will start an infinite loop if field order P is not prime.
* @param P field order
* @returns function that takes field Fp (created from P) and number n
*/
function tonelliShanks(P) {
// Legendre constant: 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)
// (a | p) ≡ -1 if a is not a square (mod p)
// (a | p) ≡ 0 if a ≡ 0 (mod p)
const legendreC = (P - _1n$3) / _2n$1;
let Q, S, Z;
// Step 1: By factoring out powers of 2 from p - 1,
// find q and s such that p - 1 = q*(2^s) with q odd
for (Q = P - _1n$3, S = 0; Q % _2n$1 === _0n$2; Q /= _2n$1, S++)
;
// Step 2: Select a non-square z such that (z | p) ≡ -1 and set c ≡ zq
for (Z = _2n$1; Z < P && pow(Z, legendreC, P) !== P - _1n$3; Z++) {
// Crash instead of infinity loop, we cannot reasonable count until P.
if (Z > 1000)
throw new Error('Cannot find square root: likely non-prime P');
}
// Fast-path
if (S === 1) {
const p1div4 = (P + _1n$3) / _4n;
return function tonelliFast(Fp, n) {
const root = Fp.pow(n, p1div4);
if (!Fp.eql(Fp.sqr(root), n))
throw new Error('Cannot find square root');
return root;
};
}
// Slow-path
const Q1div2 = (Q + _1n$3) / _2n$1;
return function tonelliSlow(Fp, n) {
// Step 0: Check that n is indeed a square: (n | p) should not be ≡ -1
if (Fp.pow(n, legendreC) === Fp.neg(Fp.ONE))
throw new Error('Cannot find square root');
let r = S;
// TODO: will fail at Fp2/etc
let g = Fp.pow(Fp.mul(Fp.ONE, Z), Q); // will update both x and b
let x = Fp.pow(n, Q1div2); // first guess at the square root
let b = Fp.pow(n, Q); // first guess at the fudge factor
while (!Fp.eql(b, Fp.ONE)) {
if (Fp.eql(b, Fp.ZERO))
return Fp.ZERO; // https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm (4. If t = 0, return r = 0)
// Find m such b^(2^m)==1
let m = 1;
for (let t2 = Fp.sqr(b); m < r; m++) {
if (Fp.eql(t2, Fp.ONE))
break;
t2 = Fp.sqr(t2); // t2 *= t2
}
// NOTE: r-m-1 can be bigger than 32, need to convert to bigint before shift, otherwise there will be overflow
const ge = Fp.pow(g, _1n$3 << BigInt(r - m - 1)); // ge = 2^(r-m-1)
g = Fp.sqr(ge); // g = ge * ge
x = Fp.mul(x, ge); // x *= ge
b = Fp.mul(b, g); // b *= g
r = m;
}
return x;
};
}
/**
* Square root for a finite field. It will try to check if optimizations are applicable and fall back to 4:
*
* 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$1) {
// Not all roots possible!
// const ORDER =
// 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaabn;
// const NUM = 72057594037927816n;
const p1div4 = (P + _1n$3) / _4n;
return function sqrt3mod4(Fp, n) {
const root = Fp.pow(n, p1div4);
// Throw if root**2 != n
if (!Fp.eql(Fp.sqr(root), n))
throw new Error('Cannot find square root');
return root;
};
}
// Atkin algorithm for q ≡ 5 (mod 8), https://eprint.iacr.org/2012/685.pdf (page 10)
if (P % _8n === _5n) {
const c1 = (P - _5n) / _8n;
return function sqrt5mod8(Fp, n) {
const n2 = Fp.mul(n, _2n$1);
const v = Fp.pow(n2, c1);
const nv = Fp.mul(n, v);
const i = Fp.mul(Fp.mul(nv, _2n$1), v);
const root = Fp.mul(nv, Fp.sub(i, Fp.ONE));
if (!Fp.eql(Fp.sqr(root), n))
throw new Error('Cannot find square root');
return root;
};
}
// Other cases: Tonelli-Shanks algorithm
return tonelliShanks(P);
}
// 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: 'isSafeInteger',
BITS: 'isSafeInteger',
};
const opts = FIELD_FIELDS.reduce((map, val) => {
map[val] = 'function';
return map;
}, initial);
return validateObject(field, opts);
}
// 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(f, num, power) {
// Should have same speed as pow for bigints
// TODO: benchmark!
if (power < _0n$2)
throw new Error('invalid exponent, negatives unsupported');
if (power === _0n$2)
return f.ONE;
if (power === _1n$3)
return num;
let p = f.ONE;
let d = num;
while (power > _0n$2) {
if (power & _1n$3)
p = f.mul(p, d);
d = f.sqr(d);
power >>= _1n$3;
}
return p;
}
/**
* Efficiently invert an array of Field elements.
* `inv(0)` will return `undefined` here: make sure to throw an error.
*/
function FpInvertBatch(f, nums) {
const tmp = new Array(nums.length);
// Walk from first to last, multiply them by each other MOD p
const lastMultiplied = nums.reduce((acc, num, i) => {
if (f.is0(num))
return acc;
tmp[i] = acc;
return f.mul(acc, num);
}, f.ONE);
// Invert last element
const inverted = f.inv(lastMultiplied);
// Walk from last to first, multiply them by inverted each other MOD p
nums.reduceRight((acc, num, i) => {
if (f.is0(num))
return acc;
tmp[i] = f.mul(acc, tmp[i]);
return f.mul(acc, num);
}, inverted);
return tmp;
}
// CURVE.n lengths
function nLength(n, nBitLength) {
// Bit size, byte size of CURVE.n
const _nBitLength = nBitLength !== undefined ? nBitLength : n.toString(2).length;
const nByteLength = Math.ceil(_nBitLength / 8);
return { nBitLength: _nBitLength, nByteLength };
}
/**
* Initializes a finite field over prime.
* Major performance optimizations:
* * a) denormalized operations like mulN instead of mul
* * b) same object shape: never add or remove keys
* * c) 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.
* @param ORDER prime positive bigint
* @param bitLen how many bits the field consumes
* @param isLE (def: false) if encoding / decoding should be in little-endian
* @param redef optional faster redefinitions of sqrt and other methods
*/
function Field(ORDER, bitLen, isLE = false, redef = {}) {
if (ORDER <= _0n$2)
throw new Error('invalid field: expected ORDER > 0, got ' + ORDER);
const { nBitLength: BITS, nByteLength: BYTES } = nLength(ORDER, bitLen);
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: bitMask(BITS),
ZERO: _0n$2,
ONE: _1n$3,
create: (num) => mod(num, ORDER),
isValid: (num) => {
if (typeof num !== 'bigint')
throw new Error('invalid field element: expected bigint, got ' + typeof num);
return _0n$2 <= num && num < ORDER; // 0 is valid element, but it's not invertible
},
is0: (num) => num === _0n$2,
isOdd: (num) => (num & _1n$3) === _1n$3,
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: redef.sqrt ||
((n) => {
if (!sqrtP)
sqrtP = FpSqrt(ORDER);
return sqrtP(f, n);
}),
invertBatch: (lst) => FpInvertBatch(f, lst),
// TODO: do we really need constant cmov?
// We don't have const-time bigints anyway, so probably will be not very useful
cmov: (a, b, c) => (c ? b : a),
toBytes: (num) => (isLE ? numberToBytesLE(num, BYTES) : numberToBytesBE(num, BYTES)),
fromBytes: (bytes) => {
if (bytes.length !== BYTES)
throw new Error('Field.fromBytes: expected ' + BYTES + ' bytes, got ' + bytes.length);
return isLE ? bytesToNumberLE(bytes) : bytesToNumberBE(bytes);
},
});
return Object.freeze(f);
}
/**
* 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 ? bytesToNumberLE(key) : 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$3) + _1n$3;
return isLE ? numberToBytesLE(reduced, fieldLen) : numberToBytesBE(reduced, fieldLen);
}/**
* Methods for elliptic curve multiplication by scalars.
* Contains wNAF, pippenger
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
const _0n$1 = BigInt(0);
const _1n$2 = BigInt(1);
function constTimeNegate(condition, item) {
const neg = item.negate();
return condition ? neg : item;
}
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, bits) {
validateW(W, bits);
const windows = Math.ceil(bits / W) + 1; // +1, because
const windowSize = 2 ** (W - 1); // -1 because we skip zero
return { windows, windowSize };
}
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
const pointPrecomputes = new WeakMap();
const pointWindowSizes = new WeakMap(); // This allows use make points immutable (nothing changes inside)
function getW(P) {
return pointWindowSizes.get(P) || 1;
}
/**
* Elliptic curve multiplication of Point by scalar. Fragile.
* 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
*/
function wNAF(c, bits) {
return {
constTimeNegate,
hasPrecomputes(elm) {
return getW(elm) !== 1;
},
// non-const time multiplication ladder
unsafeLadder(elm, n, p = c.ZERO) {
let d = elm;
while (n > _0n$1) {
if (n & _1n$2)
p = p.add(d);
d = d.double();
n >>= _1n$2;
}
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 elm Point instance
* @param W window size
* @returns precomputed point tables flattened to a single array
*/
precomputeWindow(elm, W) {
const { windows, windowSize } = calcWOpts(W, bits);
const points = [];
let p = elm;
let base = p;
for (let window = 0; window < windows; window++) {
base = p;
points.push(base);
// =1, because we skip zero
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.
* @param W window size
* @param precomputes precomputed tables
* @param n scalar (we don't check here, but should be less than curve order)
* @returns real and fake (for const-time) points
*/
wNAF(W, precomputes, n) {
// TODO: maybe check that scalar is less than group order? wNAF behavious is undefined otherwise
// But need to carefully remove other checks before wNAF. ORDER == bits here
const { windows, windowSize } = calcWOpts(W, bits);
let p = c.ZERO;
let f = c.BASE;
const mask = BigInt(2 ** W - 1); // Create mask with W ones: 0b1111 for W=4 etc.
const maxNumber = 2 ** W;
const shiftBy = BigInt(W);
for (let window = 0; window < windows; window++) {
const offset = window * windowSize;
// Extract W bits.
let wbits = Number(n & mask);
// Shift number by W bits.
n >>= shiftBy;
// If the bits are bigger than max size, we'll split those.
// +224 => 256 - 32
if (wbits > windowSize) {
wbits -= maxNumber;
n += _1n$2;
}
// 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.
// Check if we're onto Zero point.
// Add random point inside current window to f.
const offset1 = offset;
const offset2 = offset + Math.abs(wbits) - 1; // -1 because we skip zero
const cond1 = window % 2 !== 0;
const cond2 = wbits < 0;
if (wbits === 0) {
// The most important part for const-time getPublicKey
f = f.add(constTimeNegate(cond1, precomputes[offset1]));
}
else {
p = p.add(constTimeNegate(cond2, precomputes[offset2]));
}
}
// JIT-compiler should not eliminate f here, since it will later be used in normalizeZ()
// Even if the variable is still unused, there are some checks which will
// throw an exception, so compiler needs to prove they won't happen, which is hard.
// 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 W window size
* @param precomputes precomputed tables
* @param n scalar (we don't check here, but should be less than curve order)
* @param acc accumulator point to add result of multiplication
* @returns point
*/
wNAFUnsafe(W, precomputes, n, acc = c.ZERO) {
const { windows, windowSize } = calcWOpts(W, bits);
const mask = BigInt(2 ** W - 1); // Create mask with W ones: 0b1111 for W=4 etc.
const maxNumber = 2 ** W;
const shiftBy = BigInt(W);
for (let window = 0; window < windows; window++) {
const offset = window * windowSize;
if (n === _0n$1)
break; // No need to go over empty scalar
// Extract W bits.
let wbits = Number(n & mask);
// Shift number by W bits.
n >>= shiftBy;
// If the bits are bigger than max size, we'll split those.
// +224 => 256 - 32
if (wbits > windowSize) {
wbits -= maxNumber;
n += _1n$2;
}
if (wbits === 0)
continue;
let curr = precomputes[offset + Math.abs(wbits) - 1]; // -1 because we skip zero
if (wbits < 0)
curr = curr.negate();
// NOTE: by re-using acc, we can save a lot of additions in case of MSM
acc = acc.add(curr);
}
return acc;
},
getPrecomputes(W, P, transform) {
// Calculate precomputes on a first run, reuse them after
let comp = pointPrecomputes.get(P);
if (!comp) {
comp = this.precomputeWindow(P, W);
if (W !== 1)
pointPrecomputes.set(P, transform(comp));
}
return comp;
},
wNAFCached(P, n, transform) {
const W = getW(P);
return this.wNAF(W, this.getPrecomputes(W, P, transform), n);
},
wNAFCachedUnsafe(P, n, transform, prev) {
const W = getW(P);
if (W === 1)
return this.unsafeLadder(P, n, prev); // For W=1 ladder is ~x2 faster
return this.wNAFUnsafe(W, this.getPrecomputes(W, P, transform), n, prev);
},
// We calculate precomputes for elliptic curve point multiplication
// using windowed method. This specifies window size and
// stores precomputed values. Usually only base point would be precomputed.
setWindowSize(P, W) {
validateW(W, bits);
pointWindowSizes.set(P, W);
pointPrecomputes.delete(P);
},
};
}
/**
* Pippenger algorithm for multi-scalar multiplication (MSM, Pa + Qb + Rc + ...).
* 30x faster vs naive addition on L=4096, 10x faster with precomputes.
* For N=254bit, L=1, it does: 1024 ADD + 254 DBL. For L=5: 1536 ADD + 254 DBL.
* Algorithmically constant-time (for same L), even when 1 point + scalar, or when scalar = 0.
* @param c Curve Point constructor
* @param fieldN field over CURVE.N - important that it's not over CURVE.P
* @param points array of L curve points
* @param scalars array of L scalars (aka private keys / bigints)
*/
function pippenger(c, fieldN, points, scalars) {
// If we split scalars by some window (let's say 8 bits), every chunk will only
// take 256 buckets even if there are 4096 scalars, also re-uses double.
// TODO:
// - https://eprint.iacr.org/2024/750.pdf
// - https://tches.iacr.org/index.php/TCHES/article/view/10287
// 0 is accepted in scalars
validateMSMPoints(points, c);
validateMSMScalars(scalars, fieldN);
if (points.length !== scalars.length)
throw new Error('arrays of points and scalars must have equal length');
const zero = c.ZERO;
const wbits = bitLen(BigInt(points.length));
const windowSize = wbits > 12 ? wbits - 3 : wbits > 4 ? wbits - 2 : wbits ? 2 : 1; // in bits
const MASK = (1 << windowSize) - 1;
const buckets = new Array(MASK + 1).fill(zero); // +1 for zero array
const lastBits = Math.floor((fieldN.BITS - 1) / windowSize) * windowSize;
let sum = zero;
for (let i = lastBits; i >= 0; i -= windowSize) {
buckets.fill(zero);
for (let j = 0; j < scalars.length; j++) {
const scalar = scalars[j];
const wbits = Number((scalar >> BigInt(i)) & BigInt(MASK));
buckets[wbits] = buckets[wbits].add(points[j]);
}
let resI = zero; // not using this will do small speed-up, but will lose ct
// Skip first bucket, because it is zero
for (let j = buckets.length - 1, sumI = zero; j > 0; j--) {
sumI = sumI.add(buckets[j]);
resI = resI.add(sumI);
}
sum = sum.add(resI);
if (i !== 0)
for (let j = 0; j < windowSize; j++)
sum = sum.double();
}
return sum;
}
function validateBasic(curve) {
validateField(curve.Fp);
validateObject(curve, {
n: 'bigint',
h: 'bigint',
Gx: 'field',
Gy: 'field',
}, {
nBitLength: 'isSafeInteger',
nByteLength: 'isSafeInteger',
});
// Set defaults
return Object.freeze({
...nLength(curve.n, curve.nBitLength),
...curve,
...{ p: curve.Fp.ORDER },
});
}/**
* Short Weierstrass curve methods. The formula is: y² = x³ + ax + b.
*
* ### Design rationale for types
*
* * Interaction between classes from different curves should fail:
* `k256.Point.BASE.add(p256.Point.BASE)`
* * For this purpose we want to use `instanceof` operator, which is fast and works during runtime
* * Different calls of `curve()` would return different classes -
* `curve(params) !== curve(params)`: if somebody decided to monkey-patch their curve,
* it won't affect others
*
* TypeScript can't infer types for classes created inside a function. Classes is one instance
* of nominative types in TypeScript and interfaces only check for shape, so it's hard to create
* unique type for every function call.
*
* We can use generic types via some param, like curve opts, but that would:
* 1. Enable interaction between `curve(params)` and `curve(params)` (curves of same params)
* which is hard to debug.
* 2. Params can be generic and we can't enforce them to be constant value:
* if somebody creates curve from non-constant params,
* it would be allowed to interact with other curves with non-constant params
*
* @todo https://www.typescriptlang.org/docs/handbook/release-notes/typescript-2-7.html#unique-symbol
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
function validateSigVerOpts(opts) {
if (opts.lowS !== undefined)
abool('lowS', opts.lowS);
if (opts.prehash !== undefined)
abool('prehash', opts.prehash);
}
function validatePointOpts(curve) {
const opts = validateBasic(curve);
validateObject(opts, {
a: 'field',
b: 'field',
}, {
allowedPrivateKeyLengths: 'array',
wrapPrivateKey: 'boolean',
isTorsionFree: 'function',
clearCofactor: 'function',
allowInfinityPoint: 'boolean',
fromBytes: 'function',
toBytes: 'function',
});
const { endo, Fp, a } = opts;
if (endo) {
if (!Fp.eql(a, Fp.ZERO)) {
throw new Error('invalid endomorphism, can only be defined for Koblitz curves that have a=0');
}
if (typeof endo !== 'object' ||
typeof endo.beta !== 'bigint' ||
typeof endo.splitScalar !== 'function') {
throw new Error('invalid endomorphism, expected beta: bigint and splitScalar: function');
}
}
return Object.freeze({ ...opts });
}
const { bytesToNumberBE: b2n, hexToBytes: h2b } = ut;
class DERErr extends Error {
constructor(m = '') {
super(m);
}
}
/**
* ASN.1 DER encoding utilities. ASN is very complex & fragile. Format:
*
* [0x30 (SEQUENCE), bytelength, 0x02 (INTEGER), intLength, R, 0x02 (INTEGER), intLength, S]
*
* Docs: https://letsencrypt.org/docs/a-warm-welcome-to-asn1-and-der/, https://luca.ntop.org/Teaching/Appunti/asn1.html
*/
const DER = {
// asn.1 DER encoding utils
Err: DERErr,
// Basic building block is TLV (Tag-Length-Value)
_tlv: {
encode: (tag, data) => {
const { Err: E } = DER;
if (tag < 0 || tag > 256)
throw new E('tlv.encode: wrong tag');
if (data.length & 1)
throw new E('tlv.encode: unpadded data');
const dataLen = data.length / 2;
const len = numberToHexUnpadded(dataLen);
if ((len.length / 2) & 128)
throw new E('tlv.encode: long form length too big');
// length of length with long form flag
const lenLen = dataLen > 127 ? numberToHexUnpadded((len.length / 2) | 128) : '';
const t = numberToHexUnpadded(tag);
return t + lenLen + len + data;
},
// v - value, l - left bytes (unparsed)
decode(tag, data) {
const { Err: E } = DER;
let pos = 0;
if (tag < 0 || tag > 256)
throw new E('tlv.encode: wrong tag');
if (data.length < 2 || data[pos++] !== tag)
throw new E('tlv.decode: wrong tlv');
const first = data[pos++];
const isLong = !!(first & 128); // First bit of first length byte is flag for short/long form
let length = 0;
if (!isLong)
length = first;
else {
// Long form: [longFlag(1bit), lengthLength(7bit), length (BE)]
const lenLen = first & 127;
if (!lenLen)
throw new E('tlv.decode(long): indefinite length not supported');
if (lenLen > 4)
throw new E('tlv.decode(long): byte length is too big'); // this will overflow u32 in js
const lengthBytes = data.subarray(pos, pos + lenLen);
if (lengthBytes.length !== lenLen)
throw new E('tlv.decode: length bytes not complete');
if (lengthBytes[0] === 0)
throw new E('tlv.decode(long): zero leftmost byte');
for (const b of lengthBytes)
length = (length << 8) | b;
pos += lenLen;
if (length < 128)
throw new E('tlv.decode(long): not minimal encoding');
}
const v = data.subarray(pos, pos + length);
if (v.length !== length)
throw new E('tlv.decode: wrong value length');
return { v, l: data.subarray(pos + length) };
},
},
// https://crypto.stackexchange.com/a/57734 Leftmost bit of first byte is 'negative' flag,
// since we always use positive integers here. It must always be empty:
// - add zero byte if exists
// - if next byte doesn't have a flag, leading zero is not allowed (minimal encoding)
_int: {
encode(num) {
const { Err: E } = DER;
if (num < _0n)
throw new E('integer: negative integers are not allowed');
let hex = numberToHexUnpadded(num);
// Pad with zero byte if negative flag is present
if (Number.parseInt(hex[0], 16) & 0b1000)
hex = '00' + hex;
if (hex.length & 1)
throw new E('unexpected DER parsing assertion: unpadded hex');
return hex;
},
decode(data) {
const { Err: E } = DER;
if (data[0] & 128)
throw new E('invalid signature integer: negative');
if (data[0] === 0x00 && !(data[1] & 128))
throw new E('invalid signature integer: unnecessary leading zero');
return b2n(data);
},
},
toSig(hex) {
// parse DER signature
const { Err: E, _int: int, _tlv: tlv } = DER;
const data = typeof hex === 'string' ? h2b(hex) : hex;
abytes$1(data);
const { v: seqBytes, l: seqLeftBytes } = tlv.decode(0x30, data);
if (seqLeftBytes.length)
throw new E('invalid signature: left bytes after parsing');
const { v: rBytes, l: rLeftBytes } = tlv.decode(0x02, seqBytes);
const { v: sBytes, l: sLeftBytes } = tlv.decode(0x02, rLeftBytes);
if (sLeftBytes.length)
throw new E('invalid signature: left bytes after parsing');
return { r: int.decode(rBytes), s: int.decode(sBytes) };
},
hexFromSig(sig) {
const { _tlv: tlv, _int: int } = DER;
const rs = tlv.encode(0x02, int.encode(sig.r));
const ss = tlv.encode(0x02, int.encode(sig.s));
const seq = rs + ss;
return tlv.encode(0x30, seq);
},
};
// Be friendly to bad ECMAScript parsers by not using bigint literals
// prettier-ignore
const _0n = BigInt(0), _1n$1 = BigInt(1); BigInt(2); const _3n = BigInt(3); BigInt(4);
function weierstrassPoints(opts) {
const CURVE = validatePointOpts(opts);
const { Fp } = CURVE; // All curves has same field / group length as for now, but they can differ
const Fn = Field(CURVE.n, CURVE.nBitLength);
const toBytes = CURVE.toBytes ||
((_c, point, _isCompressed) => {
const a = point.toAffine();
return concatBytes(Uint8Array.from([0x04]), Fp.toBytes(a.x), Fp.toBytes(a.y));
});
const fromBytes = CURVE.fromBytes ||
((bytes) => {
// const head = bytes[0];
const tail = bytes.subarray(1);
// if (head !== 0x04) throw new Error('Only non-compressed encoding is supported');
const x = Fp.fromBytes(tail.subarray(0, Fp.BYTES));
const y = Fp.fromBytes(tail.subarray(Fp.BYTES, 2 * Fp.BYTES));
return { x, y };
});
/**
* y² = x³ + ax + b: Short weierstrass curve formula
* @returns y²
*/
function weierstrassEquation(x) {
const { a, b } = CURVE;
const x2 = Fp.sqr(x); // x * x
const x3 = Fp.mul(x2, x); // x2 * x
return Fp.add(Fp.add(x3, Fp.mul(x, a)), b); // x3 + a * x + b
}
// Validate whether the passed curve params are valid.
// We check if curve equation works for generator point.
// `assertValidity()` won't work: `isTorsionFree()` is not available at this point in bls12-381.
// ProjectivePoint class has not been initialized yet.
if (!Fp.eql(Fp.sqr(CURVE.Gy), weierstrassEquation(CURVE.Gx)))
throw new Error('bad generator point: equation left != right');
// Valid group elements reside in range 1..n-1
function isWithinCurveOrder(num) {
return inRange(num, _1n$1, CURVE.n);
}
// Validates if priv key is valid and converts it to bigint.
// Supports options allowedPrivateKeyLengths and wrapPrivateKey.
function normPrivateKeyToScalar(key) {
const { allowedPrivateKeyLengths: lengths, nByteLength, wrapPrivateKey, n: N } = CURVE;
if (lengths && typeof key !== 'bigint') {
if (isBytes(key))
key = bytesToHex(key);
// Normalize to hex string, pad. E.g. P521 would norm 130-132 char hex to 132-char bytes
if (typeof key !== 'string' || !lengths.includes(key.length))
throw new Error('invalid private key');
key = key.padStart(nByteLength * 2, '0');
}
let num;
try {
num =
typeof key === 'bigint'
? key
: bytesToNumberBE(ensureBytes('private key', key, nByteLength));
}
catch (error) {
throw new Error('invalid private key, expected hex or ' + nByteLength + ' bytes, got ' + typeof key);
}
if (wrapPrivateKey)
num = mod(num, N); // disabled by default, enabled for BLS
aInRange('private key', num, _1n$1, N); // num in range [1..N-1]
return num;
}
function assertPrjPoint(other) {
if (!(other instanceof Point))
throw new Error('ProjectivePoint expected');
}
// Memoized toAffine / validity check. They are heavy. Points are immutable.
// Converts Projective point to affine (x, y) coordinates.
// Can accept precomputed Z^-1 - for example, from invertBatch.
// (x, y, z) ∋ (x=x/z, y=y/z)
const toAffineMemo = memoized((p, iz) => {
const { px: x, py: y, pz: z } = p;
// Fast-path for normalized points
if (Fp.eql(z, Fp.ONE))
return { x, y };
const is0 = p.is0();
// If invZ was 0, we return zero point. However we still want to execute
// all operations, so we replace invZ with a random number, 1.
if (iz == null)
iz = is0 ? Fp.ONE : Fp.inv(z);
const ax = Fp.mul(x, iz);
const ay = Fp.mul(y, iz);
const zz = Fp.mul(z, iz);
if (is0)
return { x: Fp.ZERO, y: Fp.ZERO };
if (!Fp.eql(zz, Fp.ONE))
throw new Error('invZ was invalid');
return { x: ax, y: ay };
});
// NOTE: on exception this will crash 'cached' and no value will be set.
// Otherwise true will be return
const assertValidMemo = memoized((p) => {
if (p.is0()) {
// (0, 1, 0) aka ZERO is invalid in most contexts.
// In BLS, ZERO can be serialized, so we allow it.
// (0, 0, 0) is invalid representation of ZERO.
if (CURVE.allowInfinityPoint && !Fp.is0(p.py))
return;
throw new Error('bad point: ZERO');
}
// Some 3rd-party test vectors require different wording between here & `fromCompressedHex`
const { x, y } = p.toAffine();
// Check if x, y are valid field elements
if (!Fp.isValid(x) || !Fp.isValid(y))
throw new Error('bad point: x or y not FE');
const left = Fp.sqr(y); // y²
const right = weierstrassEquation(x); // x³ + ax + b
if (!Fp.eql(left, right))
throw new Error('bad point: equation left != right');
if (!p.isTorsionFree())
throw new Error('bad point: not in prime-order subgroup');
return true;
});
/**
* Projective Point works in 3d / projective (homogeneous) coordinates: (x, y, z) ∋ (x=x/z, y=y/z)
* Default Point works in 2d / affine coordinates: (x, y)
* We're doing calculations in projective, because its operations don't require costly inversion.
*/
class Point {
constructor(px, py, pz) {
this.px = px;
this.py = py;
this.pz = pz;
if (px == null || !Fp.isValid(px))
throw new Error('x required');
if (py == null || !Fp.isValid(py))
throw new Error('y required');
if (pz == null || !Fp.isValid(pz))
throw new Error('z required');
Object.freeze(this);
}
// Does not validate if the point is on-curve.
// Use fromHex instead, or call assertValidity() later.
static fromAffine(p) {
const { x, y } = p || {};
if (!p || !Fp.isValid(x) || !Fp.isValid(y))
throw new Error('invalid affine point');
if (p instanceof Point)
throw new Error('projective point not allowed');
const is0 = (i) => Fp.eql(i, Fp.ZERO);
// fromAffine(x:0, y:0) would produce (x:0, y:0, z:1), but we need (x:0, y:1, z:0)
if (is0(x) && is0(y))
return Point.ZERO;
return new Point(x, y, Fp.ONE);
}
get x() {
return this.toAffine().x;
}
get y() {
return this.toAffine().y;
}
/**
* 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.
*/
static normalizeZ(points) {
const toInv = Fp.invertBatch(points.map((p) => p.pz));
return points.map((p, i) => p.toAffine(toInv[i])).map(Point.fromAffine);
}
/**
* Converts hash string or Uint8Array to Point.
* @param hex short/long ECDSA hex
*/
static fromHex(hex) {
const P = Point.fromAffine(fromBytes(ensureBytes('pointHex', hex)));
P.assertValidity();
return P;
}
// Multiplies generator point by privateKey.
static fromPrivateKey(privateKey) {
return Point.BASE.multiply(normPrivateKeyToScalar(privateKey));
}
// Multiscalar Multiplication
static msm(points, scalars) {
return pippenger(Point, Fn, points, scalars);
}
// "Private method", don't use it directly
_setWindowSize(windowSize) {
wnaf.setWindowSize(this, windowSize);
}
// A point on curve is valid if it conforms to equation.
assertValidity() {
assertValidMemo(this);
}
hasEvenY() {
const { y } = this.toAffine();
if (Fp.isOdd)
return !Fp.isOdd(y);
throw new Error("Field doesn't support isOdd");
}
/**
* Compare one point to another.
*/
equals(other) {
assertPrjPoint(other);
const { px: X1, py: Y1, pz: Z1 } = this;
const { px: X2, py: Y2, pz: Z2 } = other;
const U1 = Fp.eql(Fp.mul(X1, Z2), Fp.mul(X2, Z1));
const U2 = Fp.eql(Fp.mul(Y1, Z2), Fp.mul(Y2, Z1));
return U1 && U2;
}
/**
* Flips point to one corresponding to (x, -y) in Affine coordinates.
*/
negate() {
return new Point(this.px, Fp.neg(this.py), this.pz);
}
// Renes-Costello-Batina exception-free doubling formula.
// There is 30% faster Jacobian formula, but it is not complete.
// https://eprint.iacr.org/2015/1060, algorithm 3
// Cost: 8M + 3S + 3*a + 2*b3 + 15add.
double() {
const { a, b } = CURVE;
const b3 = Fp.mul(b, _3n);
const { px: X1, py: Y1, pz: Z1 } = this;
let X3 = Fp.ZERO, Y3 = Fp.ZERO, Z3 = Fp.ZERO; // prettier-ignore
let t0 = Fp.mul(X1, X1); // step 1
let t1 = Fp.mul(Y1, Y1);
let t2 = Fp.mul(Z1, Z1);
let t3 = Fp.mul(X1, Y1);
t3 = Fp.add(t3, t3); // step 5
Z3 = Fp.mul(X1, Z1);
Z3 = Fp.add(Z3, Z3);
X3 = Fp.mul(a, Z3);
Y3 = Fp.mul(b3, t2);
Y3 = Fp.add(X3, Y3); // step 10
X3 = Fp.sub(t1, Y3);
Y3 = Fp.add(t1, Y3);
Y3 = Fp.mul(X3, Y3);
X3 = Fp.mul(t3, X3);
Z3 = Fp.mul(b3, Z3); // step 15
t2 = Fp.mul(a, t2);
t3 = Fp.sub(t0, t2);
t3 = Fp.mul(a, t3);
t3 = Fp.add(t3, Z3);
Z3 = Fp.add(t0, t0); // step 20
t0 = Fp.add(Z3, t0);
t0 = Fp.add(t0, t2);
t0 = Fp.mul(t0, t3);
Y3 = Fp.add(Y3, t0);
t2 = Fp.mul(Y1, Z1); // step 25
t2 = Fp.add(t2, t2);
t0 = Fp.mul(t2, t3);
X3 = Fp.sub(X3, t0);
Z3 = Fp.mul(t2, t1);
Z3 = Fp.add(Z3, Z3); // step 30
Z3 = Fp.add(Z3, Z3);
return new Point(X3, Y3, Z3);
}
// Renes-Costello-Batina exception-free addition formula.
// There is 30% faster Jacobian formula, but it is not complete.
// https://eprint.iacr.org/2015/1060, algorithm 1
// Cost: 12M + 0S + 3*a + 3*b3 + 23add.
add(other) {
assertPrjPoint(other);
const { px: X1, py: Y1, pz: Z1 } = this;
const { px: X2, py: Y2, pz: Z2 } = other;
let X3 = Fp.ZERO, Y3 = Fp.ZERO, Z3 = Fp.ZERO; // prettier-ignore
const a = CURVE.a;
const b3 = Fp.mul(CURVE.b, _3n);
let t0 = Fp.mul(X1, X2); // step 1
let t1 = Fp.mul(Y1, Y2);
let t2 = Fp.mul(Z1, Z2);
let t3 = Fp.add(X1, Y1);