openpgp
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OpenPGP.js is a Javascript implementation of the OpenPGP protocol. This is defined in RFC 4880.
2,995 lines • 125 kB
JavaScript
/*! OpenPGP.js v6.1.0 - 2025-01-30 - this is LGPL licensed code, see LICENSE/our website https://openpgpjs.org/ for more information. */
const globalThis = typeof window !== 'undefined' ? window : typeof global !== 'undefined' ? global : typeof self !== 'undefined' ? self : {};
import { H as Hash, h as hash, t as toBytes, e as exists, b as bytes, c as concatBytes$1, r as randomBytes, s as sha256, a as sha384, d as sha512, w as wrapConstructor, u as utf8ToBytes$1, f as shake256 } from './sha3.mjs';
// HMAC (RFC 2104)
class HMAC extends Hash {
constructor(hash$1, _key) {
super();
this.finished = false;
this.destroyed = false;
hash(hash$1);
const key = toBytes(_key);
this.iHash = hash$1.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$1.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$1.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) {
exists(this);
this.iHash.update(buf);
return this;
}
digestInto(out) {
exists(this);
bytes(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);
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
// 100 lines of code in the file are duplicated from noble-hashes (utils).
// This is OK: `abstract` directory does not use noble-hashes.
// User may opt-in into using different hashing library. This way, noble-hashes
// won't be included into their bundle.
const _0n$5 = /* @__PURE__ */ BigInt(0);
const _1n$7 = /* @__PURE__ */ BigInt(1);
const _2n$4 = /* @__PURE__ */ BigInt(2);
function isBytes(a) {
return (a instanceof Uint8Array ||
(a != null && typeof a === 'object' && a.constructor.name === 'Uint8Array'));
}
function abytes(item) {
if (!isBytes(item))
throw new Error('Uint8Array expected');
}
function abool(title, value) {
if (typeof value !== 'boolean')
throw new Error(`${title} must be valid boolean, got "${value}".`);
}
// Array where index 0xf0 (240) is mapped to string 'f0'
const hexes = /* @__PURE__ */ Array.from({ length: 256 }, (_, i) => i.toString(16).padStart(2, '0'));
/**
* @example bytesToHex(Uint8Array.from([0xca, 0xfe, 0x01, 0x23])) // 'cafe0123'
*/
function bytesToHex(bytes) {
abytes(bytes);
// pre-caching improves the speed 6x
let hex = '';
for (let i = 0; i < bytes.length; i++) {
hex += hexes[bytes[i]];
}
return hex;
}
function numberToHexUnpadded(num) {
const hex = num.toString(16);
return hex.length & 1 ? `0${hex}` : hex;
}
function hexToNumber(hex) {
if (typeof hex !== 'string')
throw new Error('hex string expected, got ' + typeof hex);
// Big Endian
return BigInt(hex === '' ? '0' : `0x${hex}`);
}
// We use optimized technique to convert hex string to byte array
const asciis = { _0: 48, _9: 57, _A: 65, _F: 70, _a: 97, _f: 102 };
function asciiToBase16(char) {
if (char >= asciis._0 && char <= asciis._9)
return char - asciis._0;
if (char >= asciis._A && char <= asciis._F)
return char - (asciis._A - 10);
if (char >= asciis._a && char <= asciis._f)
return char - (asciis._a - 10);
return;
}
/**
* @example hexToBytes('cafe0123') // Uint8Array.from([0xca, 0xfe, 0x01, 0x23])
*/
function hexToBytes(hex) {
if (typeof hex !== 'string')
throw new Error('hex string expected, got ' + typeof hex);
const hl = hex.length;
const al = hl / 2;
if (hl % 2)
throw new Error('padded hex string expected, got unpadded hex of length ' + hl);
const array = new Uint8Array(al);
for (let ai = 0, hi = 0; ai < al; ai++, hi += 2) {
const n1 = asciiToBase16(hex.charCodeAt(hi));
const n2 = asciiToBase16(hex.charCodeAt(hi + 1));
if (n1 === undefined || n2 === undefined) {
const char = hex[hi] + hex[hi + 1];
throw new Error('hex string expected, got non-hex character "' + char + '" at index ' + hi);
}
array[ai] = n1 * 16 + n2;
}
return array;
}
// BE: Big Endian, LE: Little Endian
function bytesToNumberBE(bytes) {
return hexToNumber(bytesToHex(bytes));
}
function bytesToNumberLE(bytes) {
abytes(bytes);
return hexToNumber(bytesToHex(Uint8Array.from(bytes).reverse()));
}
function numberToBytesBE(n, len) {
return hexToBytes(n.toString(16).padStart(len * 2, '0'));
}
function numberToBytesLE(n, len) {
return numberToBytesBE(n, len).reverse();
}
// Unpadded, rarely used
function numberToVarBytesBE(n) {
return 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. 'private 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 = hexToBytes(hex);
}
catch (e) {
throw new Error(`${title} must be valid hex string, got "${hex}". Cause: ${e}`);
}
}
else if (isBytes(hex)) {
// Uint8Array.from() instead of hash.slice() because node.js Buffer
// is instance of Uint8Array, and its slice() creates **mutable** copy
res = Uint8Array.from(hex);
}
else {
throw new Error(`${title} must be hex string or Uint8Array`);
}
const len = res.length;
if (typeof expectedLength === 'number' && len !== expectedLength)
throw new Error(`${title} expected ${expectedLength} bytes, got ${len}`);
return res;
}
/**
* Copies several Uint8Arrays into one.
*/
function concatBytes(...arrays) {
let sum = 0;
for (let i = 0; i < arrays.length; i++) {
const a = arrays[i];
abytes(a);
sum += a.length;
}
const res = new Uint8Array(sum);
for (let i = 0, pad = 0; i < arrays.length; i++) {
const a = arrays[i];
res.set(a, pad);
pad += a.length;
}
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;
}
/**
* @example utf8ToBytes('abc') // new Uint8Array([97, 98, 99])
*/
function utf8ToBytes(str) {
if (typeof str !== 'string')
throw new Error(`utf8ToBytes expected string, got ${typeof str}`);
return new Uint8Array(new TextEncoder().encode(str)); // https://bugzil.la/1681809
}
// Is positive bigint
const isPosBig = (n) => typeof n === 'bigint' && _0n$5 <= 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 ${typeof n} ${n}`);
}
// Bit operations
/**
* Calculates amount of bits in a bigint.
* Same as `n.toString(2).length`
*/
function bitLen(n) {
let len;
for (len = 0; n > _0n$5; n >>= _1n$7, 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$7;
}
/**
* Sets single bit at position.
*/
function bitSet(n, pos, value) {
return n | ((value ? _1n$7 : _0n$5) << BigInt(pos));
}
/**
* Calculate mask for N bits. Not using ** operator with bigints because of old engines.
* Same as BigInt(`0b${Array(i).fill('1').join('')}`)
*/
const bitMask = (n) => (_2n$4 << BigInt(n - 1)) - _1n$7;
// DRBG
const u8n = (data) => new Uint8Array(data); // creates Uint8Array
const u8fr = (arr) => Uint8Array.from(arr); // another shortcut
/**
* 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)
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()) => {
// HMAC-DRBG reseed() function. Steps D-G
k = h(u8fr([0x00]), seed); // k = hmac(k || v || 0x00 || seed)
v = h(); // v = hmac(k || v)
if (seed.length === 0)
return;
k = h(u8fr([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 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' || 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 "${type}", expected function`);
const val = object[fieldName];
if (isOptional && val === undefined)
return;
if (!checkVal(val, object)) {
throw new Error(`Invalid param ${String(fieldName)}=${val} (${typeof val}), expected ${type}`);
}
};
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' });
/**
* throws not implemented error
*/
const notImplemented = () => {
throw new Error('not implemented');
};
/**
* 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;
};
}
var ut = /*#__PURE__*/Object.freeze({
__proto__: null,
aInRange: aInRange,
abool: abool,
abytes: abytes,
bitGet: bitGet,
bitLen: bitLen,
bitMask: bitMask,
bitSet: bitSet,
bytesToHex: bytesToHex,
bytesToNumberBE: bytesToNumberBE,
bytesToNumberLE: bytesToNumberLE,
concatBytes: concatBytes,
createHmacDrbg: createHmacDrbg,
ensureBytes: ensureBytes,
equalBytes: equalBytes,
hexToBytes: hexToBytes,
hexToNumber: hexToNumber,
inRange: inRange,
isBytes: isBytes,
memoized: memoized,
notImplemented: notImplemented,
numberToBytesBE: numberToBytesBE,
numberToBytesLE: numberToBytesLE,
numberToHexUnpadded: numberToHexUnpadded,
numberToVarBytesBE: numberToVarBytesBE,
utf8ToBytes: utf8ToBytes,
validateObject: validateObject
});
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
// Utilities for modular arithmetics and finite fields
// prettier-ignore
const _0n$4 = BigInt(0), _1n$6 = BigInt(1), _2n$3 = BigInt(2), _3n$2 = BigInt(3);
// prettier-ignore
const _4n = BigInt(4), _5n = BigInt(5), _8n$1 = BigInt(8);
// prettier-ignore
BigInt(9); BigInt(16);
// Calculates a modulo b
function mod(a, b) {
const result = a % b;
return result >= _0n$4 ? 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
*/
// TODO: use field version && remove
function pow(num, power, modulo) {
if (modulo <= _0n$4 || power < _0n$4)
throw new Error('Expected power/modulo > 0');
if (modulo === _1n$6)
return _0n$4;
let res = _1n$6;
while (power > _0n$4) {
if (power & _1n$6)
res = (res * num) % modulo;
num = (num * num) % modulo;
power >>= _1n$6;
}
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$4) {
res *= res;
res %= modulo;
}
return res;
}
// Inverses number over modulo
function invert(number, modulo) {
if (number === _0n$4 || modulo <= _0n$4) {
throw new Error(`invert: expected positive integers, got n=${number} mod=${modulo}`);
}
// Euclidean GCD https://brilliant.org/wiki/extended-euclidean-algorithm/
// 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$4, u = _1n$6;
while (a !== _0n$4) {
// 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$6)
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$6) / _2n$3;
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$6, S = 0; Q % _2n$3 === _0n$4; Q /= _2n$3, S++)
;
// Step 2: Select a non-square z such that (z | p) ≡ -1 and set c ≡ zq
for (Z = _2n$3; Z < P && pow(Z, legendreC, P) !== P - _1n$6; Z++)
;
// Fast-path
if (S === 1) {
const p1div4 = (P + _1n$6) / _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$6) / _2n$3;
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$6 << 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;
};
}
function FpSqrt(P) {
// NOTE: 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).
// P ≡ 3 (mod 4)
// √n = n^((P+1)/4)
if (P % _4n === _3n$2) {
// Not all roots possible!
// const ORDER =
// 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaabn;
// const NUM = 72057594037927816n;
const p1div4 = (P + _1n$6) / _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$1 === _5n) {
const c1 = (P - _5n) / _8n$1;
return function sqrt5mod8(Fp, n) {
const n2 = Fp.mul(n, _2n$3);
const v = Fp.pow(n2, c1);
const nv = Fp.mul(n, v);
const i = Fp.mul(Fp.mul(nv, _2n$3), 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$4)
throw new Error('Expected power > 0');
if (power === _0n$4)
return f.ONE;
if (power === _1n$6)
return num;
let p = f.ONE;
let d = num;
while (power > _0n$4) {
if (power & _1n$6)
p = f.mul(p, d);
d = f.sqr(d);
power >>= _1n$6;
}
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. **Non-primes are not supported.**
* Do not init in loop: slow. Very fragile: always run a benchmark on a change.
* Major performance optimizations:
* * a) denormalized operations like mulN instead of mul
* * b) same object shape: never add or remove keys
* * c) Object.freeze
* 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 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$4)
throw new Error(`Expected Field ORDER > 0, got ${ORDER}`);
const { nBitLength: BITS, nByteLength: BYTES } = nLength(ORDER, bitLen);
if (BYTES > 2048)
throw new Error('Field lengths over 2048 bytes are not supported');
const sqrtP = FpSqrt(ORDER);
const f = Object.freeze({
ORDER,
BITS,
BYTES,
MASK: bitMask(BITS),
ZERO: _0n$4,
ONE: _1n$6,
create: (num) => mod(num, ORDER),
isValid: (num) => {
if (typeof num !== 'bigint')
throw new Error(`Invalid field element: expected bigint, got ${typeof num}`);
return _0n$4 <= num && num < ORDER; // 0 is valid element, but it's not invertible
},
is0: (num) => num === _0n$4,
isOdd: (num) => (num & _1n$6) === _1n$6,
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) => 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(`Fp.fromBytes: expected ${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 ? bytesToNumberBE(key) : bytesToNumberLE(key);
// `mod(x, 11)` can sometimes produce 0. `mod(x, 10) + 1` is the same, but no 0
const reduced = mod(num, fieldOrder - _1n$6) + _1n$6;
return isLE ? numberToBytesLE(reduced, fieldLen) : numberToBytesBE(reduced, fieldLen);
}
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
// Abelian group utilities
const _0n$3 = BigInt(0);
const _1n$5 = BigInt(1);
// Since points in different groups cannot be equal (different object constructor),
// we can have single place to store precomputes
const pointPrecomputes = new WeakMap();
const pointWindowSizes = new WeakMap(); // This allows use make points immutable (nothing changes inside)
// Elliptic curve multiplication of Point by scalar. Fragile.
// Scalars should always be less than curve order: this should be checked inside of a curve itself.
// Creates precomputation tables for fast multiplication:
// - private scalar is split by fixed size windows of W bits
// - every window point is collected from window's table & added to accumulator
// - since windows are different, same point inside tables won't be accessed more than once per calc
// - each multiplication is 'Math.ceil(CURVE_ORDER / 𝑊) + 1' point additions (fixed for any scalar)
// - +1 window is neccessary for wNAF
// - wNAF reduces table size: 2x less memory + 2x faster generation, but 10% slower multiplication
// TODO: Research returning 2d JS array of windows, instead of a single window. This would allow
// windows to be in different memory locations
function wNAF(c, bits) {
const constTimeNegate = (condition, item) => {
const neg = item.negate();
return condition ? neg : item;
};
const validateW = (W) => {
if (!Number.isSafeInteger(W) || W <= 0 || W > bits)
throw new Error(`Wrong window size=${W}, should be [1..${bits}]`);
};
const opts = (W) => {
validateW(W);
const windows = Math.ceil(bits / W) + 1; // +1, because
const windowSize = 2 ** (W - 1); // -1 because we skip zero
return { windows, windowSize };
};
return {
constTimeNegate,
// non-const time multiplication ladder
unsafeLadder(elm, n) {
let p = c.ZERO;
let d = elm;
while (n > _0n$3) {
if (n & _1n$5)
p = p.add(d);
d = d.double();
n >>= _1n$5;
}
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.
* @returns precomputed point tables flattened to a single array
*/
precomputeWindow(elm, W) {
const { windows, windowSize } = opts(W);
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 } = opts(W);
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$5;
}
// 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 };
},
wNAFCached(P, n, transform) {
const W = pointWindowSizes.get(P) || 1;
// 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 this.wNAF(W, comp, n);
},
// 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);
pointWindowSizes.set(P, W);
pointPrecomputes.delete(P);
},
};
}
/**
* Pippenger algorithm for multi-scalar multiplication (MSM).
* MSM is basically (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 field 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, field, 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
if (!Array.isArray(points) || !Array.isArray(scalars) || scalars.length !== points.length)
throw new Error('arrays of points and scalars must have equal length');
scalars.forEach((s, i) => {
if (!field.isValid(s))
throw new Error(`wrong scalar at index ${i}`);
});
points.forEach((p, i) => {
if (!(p instanceof c))
throw new Error(`wrong point at index ${i}`);
});
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(c.ZERO); // +1 for zero array
const lastBits = Math.floor((field.BITS - 1) / windowSize) * windowSize;
let sum = c.ZERO;
for (let i = lastBits; i >= 0; i -= windowSize) {
buckets.fill(c.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 = c.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 = c.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 },
});
}
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
// Short Weierstrass curve. The formula is: y² = x³ + ax + b
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('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('Expected endomorphism with beta: bigint and splitScalar: function');
}
}
return Object.freeze({ ...opts });
}
const { bytesToNumberBE: b2n, hexToBytes: h2b } = ut;
/**
* 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: class DERErr extends Error {
constructor(m = '') {
super(m);
}
},
// 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) : '';
return `${numberToHexUnpadded(tag)}${lenLen}${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$2)
throw new E('integer: negative integers are not allowed');
let hex = numberToHexUnpadded(num);
// Pad with zero byte if negative flag is present
if (Number.parseInt(hex[0], 16) & 0b1000)
hex = '00' + hex;
if (hex.length & 1)
throw new E('unexpected assertion');
return hex;
},
decode(data) {
const { Err: E } = DER;
if (data[0] & 128)
throw new E('Invalid signature integer: negative');
if (data[0] === 0x00 && !(data[1] & 128))
throw new E('Invalid signature integer: unnecessary leading zero');
return b2n(data);
},
},
toSig(hex) {
// parse DER signature
const { Err: E, _int: int, _tlv: tlv } = DER;
const data = typeof hex === 'string' ? h2b(hex) : hex;
abytes(data);
const { v: seqBytes, l: seqLeftBytes } = tlv.decode(0x30, data);
if (seqLeftBytes.length)
throw new E('Invalid signature: left bytes after parsing');
const { v: rBytes, l: rLeftBytes } = tlv.decode(0x02, seqBytes);
const { v: sBytes, l: sLeftBytes } = tlv.decode(0x02, rLeftBytes);
if (sLeftBytes.length)
throw new E('Invalid signature: left bytes after parsing');
return { r: int.decode(rBytes), s: int.decode(sBytes) };
},
hexFromSig(sig) {
const { _tlv: tlv, _int: int } = DER;
const seq = `${tlv.encode(0x02, int.encode(sig.r))}${tlv.encode(0x02, int.encode(sig.s))}`;
return tlv.encode(0x30, seq);
},
};
// Be friendly to bad ECMAScript parsers by not using bigint literals
// prettier-ignore
const _0n$2 = BigInt(0), _1n$4 = BigInt(1); BigInt(2); const _3n$1 = 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$4, 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 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(`private key must be ${nByteLength} bytes, hex or bigint, not ${typeof key}`);
}
if (wrapPrivateKey)
num = mod(num, N); // disabled by default, enabled for BLS
aInRange('private key', num, _1n$4, 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 wrong representation of ZERO and is always invalid.
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$1);
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$1);
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);
let t4 = Fp.add(X2, Y2); // step 5
t3 = Fp.mul(t3, t4);
t4 = Fp.add(t0, t1);
t3 = Fp.sub(t3, t4);
t4 = Fp.add(X1, Z1);
let t5 = Fp.add(X2, Z2); // step 10
t4 = Fp.mul(t4, t5);
t5 = Fp.add(t0, t2);
t4 = Fp.sub(t4, t5);
t5 = Fp.add(Y1, Z1);
X3 = Fp.add(Y2, Z2); // step 15
t5 = Fp.mul(t5, X3);
X3 = Fp.add(t1, t2);
t5 = Fp.sub(t5, X3);
Z3 = Fp.mul(a, t4);
X3 = Fp.mul(b3, t2); // step 20
Z3 = Fp.add(X3, Z3);
X3 = Fp.sub(t1, Z3);
Z3 = Fp.add(t1, Z3);
Y3 = Fp.mul(X3, Z3);
t1 = Fp.add(t0, t0); // step 25
t1 = Fp.add(t1, t0);
t2 = Fp.mul(a, t2);
t4 = Fp.mul(b3, t4);
t1 = Fp.add(t1, t2);
t2 = Fp.sub(t0, t2); // step 30
t2 = Fp.mul(a, t2);
t4 = Fp.add(t4, t2);
t0 = Fp.mul(t1, t4);
Y3 = Fp.add(Y3, t0);
t0 = Fp.mul(t5, t4); // step 35
X3 = Fp.mul(t3, X3);
X3 = Fp.sub(X3, t0);
t0 = Fp.mul(t3, t1);
Z3 = Fp.mul(t5, Z3);
Z3 = Fp.add(Z3, t0); // step 40
return new Point(X3, Y3, Z3);
}
subtract(other) {
return this.add(other.negate());
}
is0() {
return this.equals(Point.ZERO);
}
wNAF(n) {
return wnaf.wNAFCached(this, n, Point.normalizeZ);
}
/**
* Non-constant-time multiplication. Uses double-and-add algorithm.
* It's faster, but should only be used when you don't care about
* an exposed private key e.g. sig verification, which works over *public* keys.
*/
multiplyUnsafe(sc) {
aInRange('scalar', sc, _0n$2, CURVE.n);
const I = Point.ZERO;
if (sc === _0n$2)
return I;
if (sc === _1n$4)
return this;
const { endo } = CURVE;
if (!endo)
return wnaf.unsafeLadder(this, sc);
// Apply endomorphism
let { k1neg, k1, k2neg, k2 } = endo.splitScalar(sc);
let k1p = I;
let k2p = I;
let d = this;
while (k1 > _0n$2 || k2 > _0n$2) {
if (k1 & _1n$4)
k1p = k1p.add(d);
if (k2 & _1n$4)
k2p = k2p.add(d);
d = d.double();
k1 >>= _1n$4;
k2 >>= _1n$4;
}
if (k1neg)
k1p = k1p.negate();
if (k2neg)
k2p = k2p.negate();
k2p = new Point(Fp.mul(k2p.px, endo.beta), k2p.py, k2p.pz);
return k1p.add(k2p);
}
/**
* Constant time multiplication.
* Uses wNAF method. Windowed method may be 10% faster,
* but takes 2x longer to generate and consumes 2x memory.
* Uses precomputes when available.
* Uses endomorphism for Koblitz curves.
* @param scalar by which the point would be multiplied
* @returns New point
*/
multiply(scalar) {
const { endo, n: N } = CURVE;
aInRange('scalar', scalar, _1n$4, N);
let point, fake; // Fake point is used to const-time mult
if (endo) {
const { k1neg, k1, k2neg, k2 } = endo.splitScalar(scalar);
let { p: k1p, f: f1p } = this.wNAF(k1);
let { p: k2p, f: f2p } = this.wNAF(k2);
k1p = wnaf.constTimeNegate(k1neg, k1p);
k2p = wnaf.constTimeNegate(k2neg, k2p);
k2p = new Point(Fp.mul(k2p.px, endo.beta), k2p.py, k2p.pz);
point = k1p.add(k2p);
fake = f1p.add(f2p);
}
else {
const { p, f } = this.wNAF(scalar);
point = p;
fake = f;
}
// Normalize `z` for both points, but return only real one
return Point.normalizeZ([point, fake])[0];
}
/**
* Efficiently calculate `aP + bQ`. Unsafe, can expose private key, if used incorrectly.
* Not using Strauss-Shamir trick: precomputation tables are faster.
* The trick could be useful if both P and Q are not G (not in our case).
* @returns non-zero affine point
*/
multiplyAndAddUnsafe(Q, a, b) {
const G = Point.BASE; // No Strauss-Shamir trick: we have 10% faster G precomputes
const mul = (P, a // Select faster multiply() method
) => (a === _0n$2 || a === _1n$4 || !P.equals(G) ? P.multiplyUnsafe(a) : P.multiply(a));
const sum = mul(this, a).add(mul(Q, b));
return sum.is0() ? undefined : sum;
}
// 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)
toAffine(iz) {
return toAffineMemo(this, iz);
}
isTorsionFree() {
const { h: cofactor, isTorsionFree } = CURVE;
if (cofactor === _1n$4)
return true; // No subgroups, always torsion-free
if (isTorsionFree)
return isTorsionFree(Point, this);
throw new Error('isTorsionFree() has not been declared for the elliptic curve');
}
clearCofactor() {
const { h: cofactor, clearCofactor } = CURVE;
if (cofactor === _1n$4)
return this; // Fast-path
if (clearCofactor)
return clearCofactor(Point, this);
return this.multiplyUnsafe(CURVE.h);
}
toRawBytes(isCompressed = true) {
abool('isCompressed', isCompressed);
this.assertValidity();
return toBytes(Point, this, isCompressed);
}
toHex(isCompressed = true) {
abool('isCompressed', isCompressed);
return bytesToHex(this.toRawBytes(isCompressed));
}
}
Point.BASE = new Point(CURVE.Gx, CURVE.Gy, Fp.ONE);
Point.ZERO = new Point(Fp.ZERO, Fp.ONE, Fp.ZERO);
const _bits = CURVE.nBitLength;
const wnaf = wNAF(Point, CURVE.endo ? Math.ceil(_bits / 2) : _bits);
// Validate if generator point is on curve
return {
CURVE,
ProjectivePoint: Point,
normPrivateKeyToScalar,
weierstrassEquation,
isWithinCurveOrder,
};
}
function validateOpts$2(curve) {
const opts = validateBasic(curve);
validateObject(opts, {
hash: 'hash',
hmac: 'function',
randomBytes: 'function',
}, {
bits2int: 'function',
bits2int_modN: 'function',
lowS: 'boolean',
});
return Object.freeze({ lowS: true, ...opts });
}
/**
* Creates short weierstrass curve and ECDSA signature methods for it.
* @example
* import { Field } from '@noble/curves/abstract/modular';
* // Before that, define BigInt-s: a, b, p, n, Gx, Gy
* const curve = weierstrass({ a, b, Fp: Field(p), n, Gx, Gy, h: 1n })
*/
function weierstrass(curveDef) {
const CURVE = validateOpts$2(curveDef);
const { Fp, n: CURVE_ORDER } = CURVE;
const compressedLen = Fp.BYTES + 1; // e.g. 33 for 32
const uncompressedLen = 2 * Fp.BYTES + 1; // e.g. 65 for 32
function modN(a) {
return mod(a, CURVE_ORDER);
}
function invN(a) {
return invert(a, CURVE_ORDER);
}
const { ProjectivePoint: Point, normPrivateKeyToScalar, weierstrassEquation, isWithinCurveOrder, } = weierstrassPoints({
...CURVE,
toBytes(_c, point, isCompressed) {
const a = point.toAffine();
const x = Fp.toBytes(a.x);
const cat = concatBytes;
abool('isCompressed', isCompressed);
if (isCompressed) {
return cat(Uint8Array.from([point.hasEvenY() ? 0x02 : 0x03]), x);
}
else {
return cat(Uint8Array.from([0x04]), x, Fp.toBytes(a.y));
}
},
fromBytes(bytes) {
const len = bytes.length;
const head = bytes[0];
const tail = bytes.subarray(1);
// this.assertValidity() is done inside of fromHex
if (len === compressedLen && (head === 0x02 || head === 0x03)) {
const x = bytesToNumberBE(tail);
if (!inRange(x, _1n$4, Fp.ORDER))
throw new Error('Point is not on curve');
const y2 = weierstrassEquation(x); // y² = x³ + ax + b
let y;
try {
y = Fp.sqrt(y2); // y = y² ^ (p+1)/4
}
catch (sqrtError) {
const suffix = sqrtError instanceof Error ? ': ' + sqrtError.message : '';
throw new Error('Point is not on curve' + suffix);
}
const isYOdd = (y & _1n$4) === _1n$4;
// ECDSA
const isHeadOdd = (head & 1) === 1;
if (isHeadOdd !== isYOdd)
y = Fp.neg(y);
return { x, y };
}
else if (len === uncompressedLen && head === 0x04) {
const x = Fp.fromBytes(tail.subarray(0, Fp.BYTES));
const y = Fp.fromBytes(tail.subarray(Fp.BYTES, 2 * Fp.BYTES));
return { x, y };
}
else {
throw new Error(`Point of length ${len} was invalid. Expected ${compressedLen} compressed bytes or ${uncompressedLen} uncompressed bytes`);
}
},
});
const numToNByteStr = (num) => bytesToHex(numberToBytesBE(num, CURVE.nByteLength));
function isBiggerThanHalfOrder(number) {
const HALF = CURVE_ORDER >> _1n$4;
return number > HALF;
}
function normalizeS(s) {
return isBiggerThanHalfOrder(s) ? modN(-s) : s;
}
// slice bytes num
const slcNum = (b, from, to) => bytesToNumberBE(b.slice(from, to));
/**
* ECDSA signature with its (r, s) properties. Supports DER & compact representations.
*/
class Signature {
constructor(r, s, recovery) {
this.r = r;
this.s = s;
this.recovery = recovery;
this.assertValidity();
}
// pair (bytes of r, bytes of s)
static fromCompact(hex) {
const l = CURVE.nByteLength;
hex = ensureBytes('compactSignature', hex, l * 2);
return new Signature(slcNum(hex, 0, l), slcNum(hex, l, 2 * l));
}
// DER encoded ECDSA signature
// https://bitcoin.stackexchange.com/questions/57644/what-are-the-parts-of-a-bitcoin-transaction-input-script
static fromDER(hex) {
const { r, s } = DER.toSig(ensureBytes('DER', hex));
return new Signature(r, s);
}
assertValidity() {
aInRange('r', this.r, _1n$4, CURVE_ORDER); // r in [1..N]
aInRange('s', this.s, _1n$4, CURVE_ORDER); // s in [1..N]
}
addRecoveryBit(recovery) {
return new Signature(this.r, this.s, recovery);
}
recoverPublicKey(msgHash) {
const { r, s, recovery: rec } = this;
const h = bits2int_modN(ensureBytes('msgHash', msgHash)); // Truncate hash
if (rec == null || ![0, 1, 2, 3].includes(rec))
throw new Error('recovery id invalid');
const radj = rec === 2 || rec === 3 ? r + CURVE.n : r;
if (radj >= Fp.ORDER)
throw new Error('recovery id 2 or 3 invalid');
const prefix = (rec & 1) === 0 ? '02' : '03';
const R = Point.fromHex(prefix + numToNByteStr(radj));
const ir = invN(radj); // r^-1
const u1 = modN(-h * ir); // -hr^-1
const u2 = modN(s * ir); // sr^-1
const Q = Point.BASE.multiplyAndAddUnsafe(R, u1, u2); // (sr^-1)R-(hr^-1)G = -(hr^-1)G + (sr^-1)
if (!Q)
throw new Error('point at infinify'); // unsafe is fine: no priv data leaked
Q.assertValidity();
return Q;
}
// Signatures should be low-s, to prevent malleability.
hasHighS() {
return isBiggerThanHalfOrder(this.s);
}
normalizeS() {
return this.hasHighS() ? new Signature(this.r, modN(-this.s), this.recovery) : this;
}
// DER-encoded
toDERRawBytes() {
return hexToBytes(this.toDERHex());
}
toDERHex() {
return DER.hexFromSig({ r: this.r, s: this.s });
}
// padded bytes of r, then padded bytes of s
toCompactRawBytes() {
return hexToBytes(this.toCompactHex());
}
toCompactHex() {
return numToNByteStr(this.r) + numToNByteStr(this.s);
}
}
const utils = {
isValidPrivateKey(privateKey) {
try {
normPrivateKeyToScalar(privateKey);
return true;
}
catch (error) {
return false;
}
},
normPrivateKeyToScalar: normPrivateKeyToScalar,
/**
* Produces cryptographically secure private key from random of size
* (groupLen + ceil(groupLen / 2)) with modulo bias being negligible.
*/
randomPrivateKey: () => {
const length = getMinHashLength(CURVE.n);
return mapHashToField(CURVE.randomBytes(length), CURVE.n);
},
/**
* Creates precompute table for an arbitrary EC point. Makes point "cached".
* Allows to massively speed-up `point.multiply(scalar)`.
* @returns cached point
* @example
* const fast = utils.precompute(8, ProjectivePoint.fromHex(someonesPubKey));
* fast.multiply(privKey); // much faster ECDH now
*/
precompute(windowSize = 8, point = Point.BASE) {
point._setWindowSize(windowSize);
point.multiply(BigInt(3)); // 3 is arbitrary, just need any number here
return point;
},
};
/**
* Computes public key for a private key. Checks for validity of the private key.
* @param privateKey private key
* @param isCompressed whether to return compact (default), or full key
* @returns Public key, full when isCompressed=false; short when isCompressed=true
*/
function getPublicKey(privateKey, isCompressed = true) {
return Point.fromPrivateKey(privateKey).toRawBytes(isCompressed);
}
/**
* Quick and dirty check for item being public key. Does not validate hex, or being on-curve.
*/
function isProbPub(item) {
const arr = isBytes(item);
const str = typeof item === 'string';
const len = (arr || str) && item.length;
if (arr)
return len === compressedLen || len === uncompressedLen;
if (str)
return len === 2 * compressedLen || len === 2 * uncompressedLen;
if (item instanceof Point)
return true;
return false;
}
/**
* ECDH (Elliptic Curve Diffie Hellman).
* Computes shared public key from private key and public key.
* Checks: 1) private key validity 2) shared key is on-curve.
* Does NOT hash the result.
* @param privateA private key
* @param publicB different public key
* @param isCompressed whether to return compact (default), or full key
* @returns shared public key
*/
function getSharedSecret(privateA, publicB, isCompressed = true) {
if (isProbPub(privateA))
throw new Error('first arg must be private key');
if (!isProbPub(publicB))
throw new Error('second arg must be public key');
const b = Point.fromHex(publicB); // check for being on-curve
return b.multiply(normPrivateKeyToScalar(privateA)).toRawBytes(isCompressed);
}
// RFC6979: ensure ECDSA msg is X bytes and < N. RFC suggests optional truncating via bits2octets.
// FIPS 186-4 4.6 suggests the leftmost min(nBitLen, outLen) bits, which matches bits2int.
// bits2int can produce res>N, we can do mod(res, N) since the bitLen is the same.
// int2octets can't be used; pads small msgs with 0: unacceptatble for trunc as per RFC vectors
const bits2int = CURVE.bits2int ||
function (bytes) {
// For curves with nBitLength % 8 !== 0: bits2octets(bits2octets(m)) !== bits2octets(m)
// for some cases, since bytes.length * 8 is not actual bitLength.
const num = bytesToNumberBE(bytes); // check for == u8 done here
const delta = bytes.length * 8 - CURVE.nBitLength; // truncate to nBitLength leftmost bits
return delta > 0 ? num >> BigInt(delta) : num;
};
const bits2int_modN = CURVE.bits2int_modN ||
function (bytes) {
return modN(bits2int(bytes)); // can't use bytesToNumberBE here
};
// NOTE: pads output with zero as per spec
const ORDER_MASK = bitMask(CURVE.nBitLength);
/**
* Converts to bytes. Checks if num in `[0..ORDER_MASK-1]` e.g.: `[0..2^256-1]`.
*/
function int2octets(num) {
aInRange(`num < 2^${CURVE.nBitLength}`, num, _0n$2, ORDER_MASK);
// works with order, can have different size than numToField!
return numberToBytesBE(num, CURVE.nByteLength);
}
// Steps A, D of RFC6979 3.2
// Creates RFC6979 seed; converts msg/privKey to numbers.
// Used only in sign, not in verify.
// NOTE: we cannot assume here that msgHash has same amount of bytes as curve order, this will be wrong at least for P521.
// Also it can be bigger for P224 + SHA256
function prepSig(msgHash, privateKey, opts = defaultSigOpts) {
if (['recovered', 'canonical'].some((k) => k in opts))
throw new Error('sign() legacy options not supported');
const { hash, randomBytes } = CURVE;
let { lowS, prehash, extraEntropy: ent } = opts; // generates low-s sigs by default
if (lowS == null)
lowS = true; // RFC6979 3.2: we skip step A, because we already provide hash
msgHash = ensureBytes('msgHash', msgHash);
validateSigVerOpts(opts);
if (prehash)
msgHash = ensureBytes('prehashed msgHash', hash(msgHash));
// We can't later call bits2octets, since nested bits2int is broken for curves
// with nBitLength % 8 !== 0. Because of that, we unwrap it here as int2octets call.
// const bits2octets = (bits) => int2octets(bits2int_modN(bits))
const h1int = bits2int_modN(msgHash);
const d = normPrivateKeyToScalar(privateKey); // validate private key, convert to bigint
const seedArgs = [int2octets(d), int2octets(h1int)];
// extraEntropy. RFC6979 3.6: additional k' (optional).
if (ent != null && ent !== false) {
// K = HMAC_K(V || 0x00 || int2octets(x) || bits2octets(h1) || k')
const e = ent === true ? randomBytes(Fp.BYTES) : ent; // generate random bytes OR pass as-is
seedArgs.push(ensureBytes('extraEntropy', e)); // check for being bytes
}
const seed = concatBytes(...seedArgs); // Step D of RFC6979 3.2
const m = h1int; // NOTE: no need to call bits2int second time here, it is inside truncateHash!
// Converts signature params into point w r/s, checks result for validity.
function k2sig(kBytes) {
// RFC 6979 Section 3.2, step 3: k = bits2int(T)
const k = bits2int(kBytes); // Cannot use fields methods, since it is group element
if (!isWithinCurveOrder(k))
return; // Important: all mod() calls here must be done over N
const ik = invN(k); // k^-1 mod n
const q = Point.BASE.multiply(k).toAffine(); // q = Gk
const r = modN(q.x); // r = q.x mod n
if (r === _0n$2)
return;
// Can use scalar blinding b^-1(bm + bdr) where b ∈ [1,q−1] according to
// https://tches.iacr.org/index.php/TCHES/article/view/7337/6509. We've decided against it:
// a) dependency on CSPRNG b) 15% slowdown c) doesn't really help since bigints are not CT
const s = modN(ik * modN(m + r * d)); // Not using blinding here
if (s === _0n$2)
return;
let recovery = (q.x === r ? 0 : 2) | Number(q.y & _1n$4); // recovery bit (2 or 3, when q.x > n)
let normS = s;
if (lowS && isBiggerThanHalfOrder(s)) {
normS = normalizeS(s); // if lowS was passed, ensure s is always
recovery ^= 1; // // in the bottom half of N
}
return new Signature(r, normS, recovery); // use normS, not s
}
return { seed, k2sig };
}
const defaultSigOpts = { lowS: CURVE.lowS, prehash: false };
const defaultVerOpts = { lowS: CURVE.lowS, prehash: false };
/**
* Signs message hash with a private key.
* ```
* sign(m, d, k) where
* (x, y) = G × k
* r = x mod n
* s = (m + dr)/k mod n
* ```
* @param msgHash NOT message. msg needs to be hashed to `msgHash`, or use `prehash`.
* @param privKey private key
* @param opts lowS for non-malleable sigs. extraEntropy for mixing randomness into k. prehash will hash first arg.
* @returns signature with recovery param
*/
function sign(msgHash, privKey, opts = defaultSigOpts) {
const { seed, k2sig } = prepSig(msgHash, privKey, opts); // Steps A, D of RFC6979 3.2.
const C = CURVE;
const drbg = createHmacDrbg(C.hash.outputLen, C.nByteLength, C.hmac);
return drbg(seed, k2sig); // Steps B, C, D, E, F, G
}
// Enable precomputes. Slows down first publicKey computation by 20ms.
Point.BASE._setWindowSize(8);
// utils.precompute(8, ProjectivePoint.BASE)
/**
* Verifies a signature against message hash and public key.
* Rejects lowS signatures by default: to override,
* specify option `{lowS: false}`. Implements section 4.1.4 from https://www.secg.org/sec1-v2.pdf:
*
* ```
* verify(r, s, h, P) where
* U1 = hs^-1 mod n
* U2 = rs^-1 mod n
* R = U1⋅G - U2⋅P
* mod(R.x, n) == r
* ```
*/
function verify(signature, msgHash, publicKey, opts = defaultVerOpts) {
const sg = signature;
msgHash = ensureBytes('msgHash', msgHash);
publicKey = ensureBytes('publicKey', publicKey);
if ('strict' in opts)
throw new Error('options.strict was renamed to lowS');
validateSigVerOpts(opts);
const { lowS, prehash } = opts;
let _sig = undefined;
let P;
try {
if (typeof sg === 'string' || isBytes(sg)) {
// Signature can be represented in 2 ways: compact (2*nByteLength) & DER (variable-length).
// Since DER can also be 2*nByteLength bytes, we check for it first.
try {
_sig = Signature.fromDER(sg);
}
catch (derError) {
if (!(derError instanceof DER.Err))
throw derError;
_sig = Signature.fromCompact(sg);
}
}
else if (typeof sg === 'object' && typeof sg.r === 'bigint' && typeof sg.s === 'bigint') {
const { r, s } = sg;
_sig = new Signature(r, s);
}
else {
throw new Error('PARSE');
}
P = Point.fromHex(publicKey);
}
catch (error) {
if (error.message === 'PARSE')
throw new Error(`signature must be Signature instance, Uint8Array or hex string`);
return false;
}
if (lowS && _sig.hasHighS())
return false;
if (prehash)
msgHash = CURVE.hash(msgHash);
const { r, s } = _sig;
const h = bits2int_modN(msgHash); // Cannot use fields methods, since it is group element
const is = invN(s); // s^-1
const u1 = modN(h * is); // u1 = hs^-1 mod n
const u2 = modN(r * is); // u2 = rs^-1 mod n
const R = Point.BASE.multiplyAndAddUnsafe(P, u1, u2)?.toAffine(); // R = u1⋅G + u2⋅P
if (!R)
return false;
const v = modN(R.x);
return v === r;
}
return {
CURVE,
getPublicKey,
getSharedSecret,
sign,
verify,
ProjectivePoint: Point,
Signature,
utils,
};
}
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
// connects noble-curves to noble-hashes
function getHash(hash) {
return {
hash,
hmac: (key, ...msgs) => hmac(hash, key, concatBytes$1(...msgs)),
randomBytes,
};
}
function createCurve(curveDef, defHash) {
const create = (hash) => weierstrass({ ...curveDef, ...getHash(hash) });
return Object.freeze({ ...create(defHash), create });
}
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
// NIST secp256r1 aka p256
// https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-256
const Fp$7 = Field(BigInt('0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff'));
const CURVE_A$4 = Fp$7.create(BigInt('-3'));
const CURVE_B$4 = BigInt('0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b');
// prettier-ignore
const p256 = createCurve({
a: CURVE_A$4, // Equation params: a, b
b: CURVE_B$4,
Fp: Fp$7, // Field: 2n**224n * (2n**32n-1n) + 2n**192n + 2n**96n-1n
// Curve order, total count of valid points in the field
n: BigInt('0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551'),
// Base (generator) point (x, y)
Gx: BigInt('0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296'),
Gy: BigInt('0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5'),
h: BigInt(1),
lowS: false,
}, sha256);
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
// NIST secp384r1 aka p384
// https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-384
// Field over which we'll do calculations.
// prettier-ignore
const P$1 = BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff');
const Fp$6 = Field(P$1);
const CURVE_A$3 = Fp$6.create(BigInt('-3'));
// prettier-ignore
const CURVE_B$3 = BigInt('0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef');
// prettier-ignore
const p384 = createCurve({
a: CURVE_A$3, // Equation params: a, b
b: CURVE_B$3,
Fp: Fp$6, // Field: 2n**384n - 2n**128n - 2n**96n + 2n**32n - 1n
// Curve order, total count of valid points in the field.
n: BigInt('0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973'),
// Base (generator) point (x, y)
Gx: BigInt('0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7'),
Gy: BigInt('0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f'),
h: BigInt(1),
lowS: false,
}, sha384);
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
// NIST secp521r1 aka p521
// Note that it's 521, which differs from 512 of its hash function.
// https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-521
// Field over which we'll do calculations.
// prettier-ignore
const P = BigInt('0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff');
const Fp$5 = Field(P);
const CURVE = {
a: Fp$5.create(BigInt('-3')),
b: BigInt('0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00'),
Fp: Fp$5,
n: BigInt('0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409'),
Gx: BigInt('0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66'),
Gy: BigInt('0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650'),
h: BigInt(1),
};
// prettier-ignore
const p521 = createCurve({
a: CURVE.a, // Equation params: a, b
b: CURVE.b,
Fp: Fp$5, // Field: 2n**521n - 1n
// Curve order, total count of valid points in the field
n: CURVE.n,
Gx: CURVE.Gx, // Base point (x, y) aka generator point
Gy: CURVE.Gy,
h: CURVE.h,
lowS: false,
allowedPrivateKeyLengths: [130, 131, 132] // P521 keys are variable-length. Normalize to 132b
}, sha512);
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
// Twisted Edwards curve. The formula is: ax² + y² = 1 + dx²y²
// Be friendly to bad ECMAScript parsers by not using bigint literals
// prettier-ignore
const _0n$1 = BigInt(0), _1n$3 = BigInt(1), _2n$2 = BigInt(2), _8n = BigInt(8);
// verification rule is either zip215 or rfc8032 / nist186-5. Consult fromHex:
const VERIFY_DEFAULT = { zip215: true };
function validateOpts$1(curve) {
const opts = validateBasic(curve);
validateObject(curve, {
hash: 'function',
a: 'bigint',
d: 'bigint',
randomBytes: 'function',
}, {
adjustScalarBytes: 'function',
domain: 'function',
uvRatio: 'function',
mapToCurve: 'function',
});
// Set defaults
return Object.freeze({ ...opts });
}
/**
* Creates Twisted Edwards curve with EdDSA signatures.
* @example
* import { Field } from '@noble/curves/abstract/modular';
* // Before that, define BigInt-s: a, d, p, n, Gx, Gy, h
* const curve = twistedEdwards({ a, d, Fp: Field(p), n, Gx, Gy, h })
*/
function twistedEdwards(curveDef) {
const CURVE = validateOpts$1(curveDef);
const { Fp, n: CURVE_ORDER, prehash: prehash, hash: cHash, randomBytes, nByteLength, h: cofactor, } = CURVE;
const MASK = _2n$2 << (BigInt(nByteLength * 8) - _1n$3);
const modP = Fp.create; // Function overrides
const Fn = Field(CURVE.n, CURVE.nBitLength);
// sqrt(u/v)
const uvRatio = CURVE.uvRatio ||
((u, v) => {
try {
return { isValid: true, value: Fp.sqrt(u * Fp.inv(v)) };
}
catch (e) {
return { isValid: false, value: _0n$1 };
}
});
const adjustScalarBytes = CURVE.adjustScalarBytes || ((bytes) => bytes); // NOOP
const domain = CURVE.domain ||
((data, ctx, phflag) => {
abool('phflag', phflag);
if (ctx.length || phflag)
throw new Error('Contexts/pre-hash are not supported');
return data;
}); // NOOP
// 0 <= n < MASK
// Coordinates larger than Fp.ORDER are allowed for zip215
function aCoordinate(title, n) {
aInRange('coordinate ' + title, n, _0n$1, MASK);
}
function assertPoint(other) {
if (!(other instanceof Point))
throw new Error('ExtendedPoint expected');
}
// Converts Extended point to default (x, y) coordinates.
// Can accept precomputed Z^-1 - for example, from invertBatch.
const toAffineMemo = memoized((p, iz) => {
const { ex: x, ey: y, ez: z } = p;
const is0 = p.is0();
if (iz == null)
iz = is0 ? _8n : Fp.inv(z); // 8 was chosen arbitrarily
const ax = modP(x * iz);
const ay = modP(y * iz);
const zz = modP(z * iz);
if (is0)
return { x: _0n$1, y: _1n$3 };
if (zz !== _1n$3)
throw new Error('invZ was invalid');
return { x: ax, y: ay };
});
const assertValidMemo = memoized((p) => {
const { a, d } = CURVE;
if (p.is0())
throw new Error('bad point: ZERO'); // TODO: optimize, with vars below?
// Equation in affine coordinates: ax² + y² = 1 + dx²y²
// Equation in projective coordinates (X/Z, Y/Z, Z): (aX² + Y²)Z² = Z⁴ + dX²Y²
const { ex: X, ey: Y, ez: Z, et: T } = p;
const X2 = modP(X * X); // X²
const Y2 = modP(Y * Y); // Y²
const Z2 = modP(Z * Z); // Z²
const Z4 = modP(Z2 * Z2); // Z⁴
const aX2 = modP(X2 * a); // aX²
const left = modP(Z2 * modP(aX2 + Y2)); // (aX² + Y²)Z²
const right = modP(Z4 + modP(d * modP(X2 * Y2))); // Z⁴ + dX²Y²
if (left !== right)
throw new Error('bad point: equation left != right (1)');
// In Extended coordinates we also have T, which is x*y=T/Z: check X*Y == Z*T
const XY = modP(X * Y);
const ZT = modP(Z * T);
if (XY !== ZT)
throw new Error('bad point: equation left != right (2)');
return true;
});
// Extended Point works in extended coordinates: (x, y, z, t) ∋ (x=x/z, y=y/z, t=xy).
// https://en.wikipedia.org/wiki/Twisted_Edwards_curve#Extended_coordinates
class Point {
constructor(ex, ey, ez, et) {
this.ex = ex;
this.ey = ey;
this.ez = ez;
this.et = et;
aCoordinate('x', ex);
aCoordinate('y', ey);
aCoordinate('z', ez);
aCoordinate('t', et);
Object.freeze(this);
}
get x() {
return this.toAffine().x;
}
get y() {
return this.toAffine().y;
}
static fromAffine(p) {
if (p instanceof Point)
throw new Error('extended point not allowed');
const { x, y } = p || {};
aCoordinate('x', x);
aCoordinate('y', y);
return new Point(x, y, _1n$3, modP(x * y));
}
static normalizeZ(points) {
const toInv = Fp.invertBatch(points.map((p) => p.ez));
return points.map((p, i) => p.toAffine(toInv[i])).map(Point.fromAffine);
}
// 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);
}
// Not required for fromHex(), which always creates valid points.
// Could be useful for fromAffine().
assertValidity() {
assertValidMemo(this);
}
// Compare one point to another.
equals(other) {
assertPoint(other);
const { ex: X1, ey: Y1, ez: Z1 } = this;
const { ex: X2, ey: Y2, ez: Z2 } = other;
const X1Z2 = modP(X1 * Z2);
const X2Z1 = modP(X2 * Z1);
const Y1Z2 = modP(Y1 * Z2);
const Y2Z1 = modP(Y2 * Z1);
return X1Z2 === X2Z1 && Y1Z2 === Y2Z1;
}
is0() {
return this.equals(Point.ZERO);
}
negate() {
// Flips point sign to a negative one (-x, y in affine coords)
return new Point(modP(-this.ex), this.ey, this.ez, modP(-this.et));
}
// Fast algo for doubling Extended Point.
// https://hyperelliptic.org/EFD/g1p/auto-twisted-extended.html#doubling-dbl-2008-hwcd
// Cost: 4M + 4S + 1*a + 6add + 1*2.
double() {
const { a } = CURVE;
const { ex: X1, ey: Y1, ez: Z1 } = this;
const A = modP(X1 * X1); // A = X12
const B = modP(Y1 * Y1); // B = Y12
const C = modP(_2n$2 * modP(Z1 * Z1)); // C = 2*Z12
const D = modP(a * A); // D = a*A
const x1y1 = X1 + Y1;
const E = modP(modP(x1y1 * x1y1) - A - B); // E = (X1+Y1)2-A-B
const G = D + B; // G = D+B
const F = G - C; // F = G-C
const H = D - B; // H = D-B
const X3 = modP(E * F); // X3 = E*F
const Y3 = modP(G * H); // Y3 = G*H
const T3 = modP(E * H); // T3 = E*H
const Z3 = modP(F * G); // Z3 = F*G
return new Point(X3, Y3, Z3, T3);
}
// Fast algo for adding 2 Extended Points.
// https://hyperelliptic.org/EFD/g1p/auto-twisted-extended.html#addition-add-2008-hwcd
// Cost: 9M + 1*a + 1*d + 7add.
add(other) {
assertPoint(other);
const { a, d } = CURVE;
const { ex: X1, ey: Y1, ez: Z1, et: T1 } = this;
const { ex: X2, ey: Y2, ez: Z2, et: T2 } = other;
// Faster algo for adding 2 Extended Points when curve's a=-1.
// http://hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#addition-add-2008-hwcd-4
// Cost: 8M + 8add + 2*2.
// Note: It does not check whether the `other` point is valid.
if (a === BigInt(-1)) {
const A = modP((Y1 - X1) * (Y2 + X2));
const B = modP((Y1 + X1) * (Y2 - X2));
const F = modP(B - A);
if (F === _0n$1)
return this.double(); // Same point. Tests say it doesn't affect timing
const C = modP(Z1 * _2n$2 * T2);
const D = modP(T1 * _2n$2 * Z2);
const E = D + C;
const G = B + A;
const H = D - C;
const X3 = modP(E * F);
const Y3 = modP(G * H);
const T3 = modP(E * H);
const Z3 = modP(F * G);
return new Point(X3, Y3, Z3, T3);
}
const A = modP(X1 * X2); // A = X1*X2
const B = modP(Y1 * Y2); // B = Y1*Y2
const C = modP(T1 * d * T2); // C = T1*d*T2
const D = modP(Z1 * Z2); // D = Z1*Z2
const E = modP((X1 + Y1) * (X2 + Y2) - A - B); // E = (X1+Y1)*(X2+Y2)-A-B
const F = D - C; // F = D-C
const G = D + C; // G = D+C
const H = modP(B - a * A); // H = B-a*A
const X3 = modP(E * F); // X3 = E*F
const Y3 = modP(G * H); // Y3 = G*H
const T3 = modP(E * H); // T3 = E*H
const Z3 = modP(F * G); // Z3 = F*G
return new Point(X3, Y3, Z3, T3);
}
subtract(other) {
return this.add(other.negate());
}
wNAF(n) {
return wnaf.wNAFCached(this, n, Point.normalizeZ);
}
// Constant-time multiplication.
multiply(scalar) {
const n = scalar;
aInRange('scalar', n, _1n$3, CURVE_ORDER); // 1 <= scalar < L
const { p, f } = this.wNAF(n);
return Point.normalizeZ([p, f])[0];
}
// Non-constant-time multiplication. Uses double-and-add algorithm.
// It's faster, but should only be used when you don't care about
// an exposed private key e.g. sig verification.
// Does NOT allow scalars higher than CURVE.n.
multiplyUnsafe(scalar) {
const n = scalar;
aInRange('scalar', n, _0n$1, CURVE_ORDER); // 0 <= scalar < L
if (n === _0n$1)
return I;
if (this.equals(I) || n === _1n$3)
return this;
if (this.equals(G))
return this.wNAF(n).p;
return wnaf.unsafeLadder(this, n);
}
// Checks if point is of small order.
// If you add something to small order point, you will have "dirty"
// point with torsion component.
// Multiplies point by cofactor and checks if the result is 0.
isSmallOrder() {
return this.multiplyUnsafe(cofactor).is0();
}
// Multiplies point by curve order and checks if the result is 0.
// Returns `false` is the point is dirty.
isTorsionFree() {
return wnaf.unsafeLadder(this, CURVE_ORDER).is0();
}
// Converts Extended point to default (x, y) coordinates.
// Can accept precomputed Z^-1 - for example, from invertBatch.
toAffine(iz) {
return toAffineMemo(this, iz);
}
clearCofactor() {
const { h: cofactor } = CURVE;
if (cofactor === _1n$3)
return this;
return this.multiplyUnsafe(cofactor);
}
// Converts hash string or Uint8Array to Point.
// Uses algo from RFC8032 5.1.3.
static fromHex(hex, zip215 = false) {
const { d, a } = CURVE;
const len = Fp.BYTES;
hex = ensureBytes('pointHex', hex, len); // copy hex to a new array
abool('zip215', zip215);
const normed = hex.slice(); // copy again, we'll manipulate it
const lastByte = hex[len - 1]; // select last byte
normed[len - 1] = lastByte & ~0x80; // clear last bit
const y = bytesToNumberLE(normed);
// RFC8032 prohibits >= p, but ZIP215 doesn't
// zip215=true: 0 <= y < MASK (2^256 for ed25519)
// zip215=false: 0 <= y < P (2^255-19 for ed25519)
const max = zip215 ? MASK : Fp.ORDER;
aInRange('pointHex.y', y, _0n$1, max);
// Ed25519: x² = (y²-1)/(dy²+1) mod p. Ed448: x² = (y²-1)/(dy²-1) mod p. Generic case:
// ax²+y²=1+dx²y² => y²-1=dx²y²-ax² => y²-1=x²(dy²-a) => x²=(y²-1)/(dy²-a)
const y2 = modP(y * y); // denominator is always non-0 mod p.
const u = modP(y2 - _1n$3); // u = y² - 1
const v = modP(d * y2 - a); // v = d y² + 1.
let { isValid, value: x } = uvRatio(u, v); // √(u/v)
if (!isValid)
throw new Error('Point.fromHex: invalid y coordinate');
const isXOdd = (x & _1n$3) === _1n$3; // There are 2 square roots. Use x_0 bit to select proper
const isLastByteOdd = (lastByte & 0x80) !== 0; // x_0, last bit
if (!zip215 && x === _0n$1 && isLastByteOdd)
// if x=0 and x_0 = 1, fail
throw new Error('Point.fromHex: x=0 and x_0=1');
if (isLastByteOdd !== isXOdd)
x = modP(-x); // if x_0 != x mod 2, set x = p-x
return Point.fromAffine({ x, y });
}
static fromPrivateKey(privKey) {
return getExtendedPublicKey(privKey).point;
}
toRawBytes() {
const { x, y } = this.toAffine();
const bytes = numberToBytesLE(y, Fp.BYTES); // each y has 2 x values (x, -y)
bytes[bytes.length - 1] |= x & _1n$3 ? 0x80 : 0; // when compressing, it's enough to store y
return bytes; // and use the last byte to encode sign of x
}
toHex() {
return bytesToHex(this.toRawBytes()); // Same as toRawBytes, but returns string.
}
}
Point.BASE = new Point(CURVE.Gx, CURVE.Gy, _1n$3, modP(CURVE.Gx * CURVE.Gy));
Point.ZERO = new Point(_0n$1, _1n$3, _1n$3, _0n$1); // 0, 1, 1, 0
const { BASE: G, ZERO: I } = Point;
const wnaf = wNAF(Point, nByteLength * 8);
function modN(a) {
return mod(a, CURVE_ORDER);
}
// Little-endian SHA512 with modulo n
function modN_LE(hash) {
return modN(bytesToNumberLE(hash));
}
/** Convenience method that creates public key and other stuff. RFC8032 5.1.5 */
function getExtendedPublicKey(key) {
const len = nByteLength;
key = ensureBytes('private key', key, len);
// Hash private key with curve's hash function to produce uniformingly random input
// Check byte lengths: ensure(64, h(ensure(32, key)))
const hashed = ensureBytes('hashed private key', cHash(key), 2 * len);
const head = adjustScalarBytes(hashed.slice(0, len)); // clear first half bits, produce FE
const prefix = hashed.slice(len, 2 * len); // second half is called key prefix (5.1.6)
const scalar = modN_LE(head); // The actual private scalar
const point = G.multiply(scalar); // Point on Edwards curve aka public key
const pointBytes = point.toRawBytes(); // Uint8Array representation
return { head, prefix, scalar, point, pointBytes };
}
// Calculates EdDSA pub key. RFC8032 5.1.5. Privkey is hashed. Use first half with 3 bits cleared
function getPublicKey(privKey) {
return getExtendedPublicKey(privKey).pointBytes;
}
// int('LE', SHA512(dom2(F, C) || msgs)) mod N
function hashDomainToScalar(context = new Uint8Array(), ...msgs) {
const msg = concatBytes(...msgs);
return modN_LE(cHash(domain(msg, ensureBytes('context', context), !!prehash)));
}
/** Signs message with privateKey. RFC8032 5.1.6 */
function sign(msg, privKey, options = {}) {
msg = ensureBytes('message', msg);
if (prehash)
msg = prehash(msg); // for ed25519ph etc.
const { prefix, scalar, pointBytes } = getExtendedPublicKey(privKey);
const r = hashDomainToScalar(options.context, prefix, msg); // r = dom2(F, C) || prefix || PH(M)
const R = G.multiply(r).toRawBytes(); // R = rG
const k = hashDomainToScalar(options.context, R, pointBytes, msg); // R || A || PH(M)
const s = modN(r + k * scalar); // S = (r + k * s) mod L
aInRange('signature.s', s, _0n$1, CURVE_ORDER); // 0 <= s < l
const res = concatBytes(R, numberToBytesLE(s, Fp.BYTES));
return ensureBytes('result', res, nByteLength * 2); // 64-byte signature
}
const verifyOpts = VERIFY_DEFAULT;
function verify(sig, msg, publicKey, options = verifyOpts) {
const { context, zip215 } = options;
const len = Fp.BYTES; // Verifies EdDSA signature against message and public key. RFC8032 5.1.7.
sig = ensureBytes('signature', sig, 2 * len); // An extended group equation is checked.
msg = ensureBytes('message', msg);
if (zip215 !== undefined)
abool('zip215', zip215);
if (prehash)
msg = prehash(msg); // for ed25519ph, etc
const s = bytesToNumberLE(sig.slice(len, 2 * len));
// zip215: true is good for consensus-critical apps and allows points < 2^256
// zip215: false follows RFC8032 / NIST186-5 and restricts points to CURVE.p
let A, R, SB;
try {
A = Point.fromHex(publicKey, zip215);
R = Point.fromHex(sig.slice(0, len), zip215);
SB = G.multiplyUnsafe(s); // 0 <= s < l is done inside
}
catch (error) {
return false;
}
if (!zip215 && A.isSmallOrder())
return false;
const k = hashDomainToScalar(context, R.toRawBytes(), A.toRawBytes(), msg);
const RkA = R.add(A.multiplyUnsafe(k));
// [8][S]B = [8]R + [8][k]A'
return RkA.subtract(SB).clearCofactor().equals(Point.ZERO);
}
G._setWindowSize(8); // Enable precomputes. Slows down first publicKey computation by 20ms.
const utils = {
getExtendedPublicKey,
// ed25519 private keys are uniform 32b. No need to check for modulo bias, like in secp256k1.
randomPrivateKey: () => randomBytes(Fp.BYTES),
/**
* We're doing scalar multiplication (used in getPublicKey etc) with precomputed BASE_POINT
* values. This slows down first getPublicKey() by milliseconds (see Speed section),
* but allows to speed-up subsequent getPublicKey() calls up to 20x.
* @param windowSize 2, 4, 8, 16
*/
precompute(windowSize = 8, point = Point.BASE) {
point._setWindowSize(windowSize);
point.multiply(BigInt(3));
return point;
},
};
return {
CURVE,
getPublicKey,
sign,
verify,
ExtendedPoint: Point,
utils,
};
}
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
const _0n = BigInt(0);
const _1n$2 = BigInt(1);
function validateOpts(curve) {
validateObject(curve, {
a: 'bigint',
}, {
montgomeryBits: 'isSafeInteger',
nByteLength: 'isSafeInteger',
adjustScalarBytes: 'function',
domain: 'function',
powPminus2: 'function',
Gu: 'bigint',
});
// Set defaults
return Object.freeze({ ...curve });
}
// NOTE: not really montgomery curve, just bunch of very specific methods for X25519/X448 (RFC 7748, https://www.rfc-editor.org/rfc/rfc7748)
// Uses only one coordinate instead of two
function montgomery(curveDef) {
const CURVE = validateOpts(curveDef);
const { P } = CURVE;
const modP = (n) => mod(n, P);
const montgomeryBits = CURVE.montgomeryBits;
const montgomeryBytes = Math.ceil(montgomeryBits / 8);
const fieldLen = CURVE.nByteLength;
const adjustScalarBytes = CURVE.adjustScalarBytes || ((bytes) => bytes);
const powPminus2 = CURVE.powPminus2 || ((x) => pow(x, P - BigInt(2), P));
// cswap from RFC7748. But it is not from RFC7748!
/*
cswap(swap, x_2, x_3):
dummy = mask(swap) AND (x_2 XOR x_3)
x_2 = x_2 XOR dummy
x_3 = x_3 XOR dummy
Return (x_2, x_3)
Where mask(swap) is the all-1 or all-0 word of the same length as x_2
and x_3, computed, e.g., as mask(swap) = 0 - swap.
*/
function cswap(swap, x_2, x_3) {
const dummy = modP(swap * (x_2 - x_3));
x_2 = modP(x_2 - dummy);
x_3 = modP(x_3 + dummy);
return [x_2, x_3];
}
// x25519 from 4
// The constant a24 is (486662 - 2) / 4 = 121665 for curve25519/X25519
const a24 = (CURVE.a - BigInt(2)) / BigInt(4);
/**
*
* @param pointU u coordinate (x) on Montgomery Curve 25519
* @param scalar by which the point would be multiplied
* @returns new Point on Montgomery curve
*/
function montgomeryLadder(u, scalar) {
aInRange('u', u, _0n, P);
aInRange('scalar', scalar, _0n, P);
// Section 5: Implementations MUST accept non-canonical values and process them as
// if they had been reduced modulo the field prime.
const k = scalar;
const x_1 = u;
let x_2 = _1n$2;
let z_2 = _0n;
let x_3 = u;
let z_3 = _1n$2;
let swap = _0n;
let sw;
for (let t = BigInt(montgomeryBits - 1); t >= _0n; t--) {
const k_t = (k >> t) & _1n$2;
swap ^= k_t;
sw = cswap(swap, x_2, x_3);
x_2 = sw[0];
x_3 = sw[1];
sw = cswap(swap, z_2, z_3);
z_2 = sw[0];
z_3 = sw[1];
swap = k_t;
const A = x_2 + z_2;
const AA = modP(A * A);
const B = x_2 - z_2;
const BB = modP(B * B);
const E = AA - BB;
const C = x_3 + z_3;
const D = x_3 - z_3;
const DA = modP(D * A);
const CB = modP(C * B);
const dacb = DA + CB;
const da_cb = DA - CB;
x_3 = modP(dacb * dacb);
z_3 = modP(x_1 * modP(da_cb * da_cb));
x_2 = modP(AA * BB);
z_2 = modP(E * (AA + modP(a24 * E)));
}
// (x_2, x_3) = cswap(swap, x_2, x_3)
sw = cswap(swap, x_2, x_3);
x_2 = sw[0];
x_3 = sw[1];
// (z_2, z_3) = cswap(swap, z_2, z_3)
sw = cswap(swap, z_2, z_3);
z_2 = sw[0];
z_3 = sw[1];
// z_2^(p - 2)
const z2 = powPminus2(z_2);
// Return x_2 * (z_2^(p - 2))
return modP(x_2 * z2);
}
function encodeUCoordinate(u) {
return numberToBytesLE(modP(u), montgomeryBytes);
}
function decodeUCoordinate(uEnc) {
// Section 5: When receiving such an array, implementations of X25519
// MUST mask the most significant bit in the final byte.
const u = ensureBytes('u coordinate', uEnc, montgomeryBytes);
if (fieldLen === 32)
u[31] &= 127; // 0b0111_1111
return bytesToNumberLE(u);
}
function decodeScalar(n) {
const bytes = ensureBytes('scalar', n);
const len = bytes.length;
if (len !== montgomeryBytes && len !== fieldLen)
throw new Error(`Expected ${montgomeryBytes} or ${fieldLen} bytes, got ${len}`);
return bytesToNumberLE(adjustScalarBytes(bytes));
}
function scalarMult(scalar, u) {
const pointU = decodeUCoordinate(u);
const _scalar = decodeScalar(scalar);
const pu = montgomeryLadder(pointU, _scalar);
// The result was not contributory
// https://cr.yp.to/ecdh.html#validate
if (pu === _0n)
throw new Error('Invalid private or public key received');
return encodeUCoordinate(pu);
}
// Computes public key from private. By doing scalar multiplication of base point.
const GuBytes = encodeUCoordinate(CURVE.Gu);
function scalarMultBase(scalar) {
return scalarMult(scalar, GuBytes);
}
return {
scalarMult,
scalarMultBase,
getSharedSecret: (privateKey, publicKey) => scalarMult(privateKey, publicKey),
getPublicKey: (privateKey) => scalarMultBase(privateKey),
utils: { randomPrivateKey: () => CURVE.randomBytes(CURVE.nByteLength) },
GuBytes: GuBytes,
};
}
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
/**
* Edwards448 (not Ed448-Goldilocks) curve with following addons:
* - X448 ECDH
* - Decaf cofactor elimination
* - Elligator hash-to-group / point indistinguishability
* Conforms to RFC 8032 https://www.rfc-editor.org/rfc/rfc8032.html#section-5.2
*/
const shake256_114 = wrapConstructor(() => shake256.create({ dkLen: 114 }));
const shake256_64 = wrapConstructor(() => shake256.create({ dkLen: 64 }));
const ed448P = BigInt('726838724295606890549323807888004534353641360687318060281490199180612328166730772686396383698676545930088884461843637361053498018365439');
// prettier-ignore
const _1n$1 = BigInt(1), _2n$1 = BigInt(2), _3n = BigInt(3); BigInt(4); const _11n = BigInt(11);
// prettier-ignore
const _22n = BigInt(22), _44n = BigInt(44), _88n = BigInt(88), _223n = BigInt(223);
// powPminus3div4 calculates z = x^k mod p, where k = (p-3)/4.
// Used for efficient square root calculation.
// ((P-3)/4).toString(2) would produce bits [223x 1, 0, 222x 1]
function ed448_pow_Pminus3div4(x) {
const P = ed448P;
const b2 = (x * x * x) % P;
const b3 = (b2 * b2 * x) % P;
const b6 = (pow2(b3, _3n, P) * b3) % P;
const b9 = (pow2(b6, _3n, P) * b3) % P;
const b11 = (pow2(b9, _2n$1, P) * b2) % P;
const b22 = (pow2(b11, _11n, P) * b11) % P;
const b44 = (pow2(b22, _22n, P) * b22) % P;
const b88 = (pow2(b44, _44n, P) * b44) % P;
const b176 = (pow2(b88, _88n, P) * b88) % P;
const b220 = (pow2(b176, _44n, P) * b44) % P;
const b222 = (pow2(b220, _2n$1, P) * b2) % P;
const b223 = (pow2(b222, _1n$1, P) * x) % P;
return (pow2(b223, _223n, P) * b222) % P;
}
function adjustScalarBytes(bytes) {
// Section 5: Likewise, for X448, set the two least significant bits of the first byte to 0, and the most
// significant bit of the last byte to 1.
bytes[0] &= 252; // 0b11111100
// and the most significant bit of the last byte to 1.
bytes[55] |= 128; // 0b10000000
// NOTE: is is NOOP for 56 bytes scalars (X25519/X448)
bytes[56] = 0; // Byte outside of group (456 buts vs 448 bits)
return bytes;
}
// Constant-time ratio of u to v. Allows to combine inversion and square root u/√v.
// Uses algo from RFC8032 5.1.3.
function uvRatio(u, v) {
const P = ed448P;
// https://www.rfc-editor.org/rfc/rfc8032#section-5.2.3
// To compute the square root of (u/v), the first step is to compute the
// candidate root x = (u/v)^((p+1)/4). This can be done using the
// following trick, to use a single modular powering for both the
// inversion of v and the square root:
// x = (u/v)^((p+1)/4) = u³v(u⁵v³)^((p-3)/4) (mod p)
const u2v = mod(u * u * v, P); // u²v
const u3v = mod(u2v * u, P); // u³v
const u5v3 = mod(u3v * u2v * v, P); // u⁵v³
const root = ed448_pow_Pminus3div4(u5v3);
const x = mod(u3v * root, P);
// Verify that root is exists
const x2 = mod(x * x, P); // x²
// If vx² = u, the recovered x-coordinate is x. Otherwise, no
// square root exists, and the decoding fails.
return { isValid: mod(x2 * v, P) === u, value: x };
}
const Fp$4 = Field(ed448P, 456, true);
const ED448_DEF = {
// Param: a
a: BigInt(1),
// -39081. Negative number is P - number
d: BigInt('726838724295606890549323807888004534353641360687318060281490199180612328166730772686396383698676545930088884461843637361053498018326358'),
// Finite field 𝔽p over which we'll do calculations; 2n**448n - 2n**224n - 1n
Fp: Fp$4,
// Subgroup order: how many points curve has;
// 2n**446n - 13818066809895115352007386748515426880336692474882178609894547503885n
n: BigInt('181709681073901722637330951972001133588410340171829515070372549795146003961539585716195755291692375963310293709091662304773755859649779'),
// RFC 7748 has 56-byte keys, RFC 8032 has 57-byte keys
nBitLength: 456,
// Cofactor
h: BigInt(4),
// Base point (x, y) aka generator point
Gx: BigInt('224580040295924300187604334099896036246789641632564134246125461686950415467406032909029192869357953282578032075146446173674602635247710'),
Gy: BigInt('298819210078481492676017930443930673437544040154080242095928241372331506189835876003536878655418784733982303233503462500531545062832660'),
// SHAKE256(dom4(phflag,context)||x, 114)
hash: shake256_114,
randomBytes,
adjustScalarBytes,
// dom4
domain: (data, ctx, phflag) => {
if (ctx.length > 255)
throw new Error(`Context is too big: ${ctx.length}`);
return concatBytes$1(utf8ToBytes$1('SigEd448'), new Uint8Array([phflag ? 1 : 0, ctx.length]), ctx, data);
},
uvRatio,
};
const ed448 = /* @__PURE__ */ twistedEdwards(ED448_DEF);
// NOTE: there is no ed448ctx, since ed448 supports ctx by default
/* @__PURE__ */ twistedEdwards({ ...ED448_DEF, prehash: shake256_64 });
const x448 = /* @__PURE__ */ (() => montgomery({
a: BigInt(156326),
// RFC 7748 has 56-byte keys, RFC 8032 has 57-byte keys
montgomeryBits: 448,
nByteLength: 56,
P: ed448P,
Gu: BigInt(5),
powPminus2: (x) => {
const P = ed448P;
const Pminus3div4 = ed448_pow_Pminus3div4(x);
const Pminus3 = pow2(Pminus3div4, BigInt(2), P);
return mod(Pminus3 * x, P); // Pminus3 * x = Pminus2
},
adjustScalarBytes,
randomBytes,
}))();
// TODO: add edwardsToMontgomeryPriv, similar to ed25519 version
// Hash To Curve Elligator2 Map
(Fp$4.ORDER - BigInt(3)) / BigInt(4); // 1. c1 = (q - 3) / 4 # Integer arithmetic
BigInt(156326);
// 1-d
BigInt('39082');
// 1-2d
BigInt('78163');
// √(-d)
BigInt('98944233647732219769177004876929019128417576295529901074099889598043702116001257856802131563896515373927712232092845883226922417596214');
// 1 / √(-d)
BigInt('315019913931389607337177038330951043522456072897266928557328499619017160722351061360252776265186336876723201881398623946864393857820716');
BigInt('0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff');
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
const secp256k1P = BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f');
const secp256k1N = BigInt('0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141');
const _1n = BigInt(1);
const _2n = BigInt(2);
const divNearest = (a, b) => (a + b / _2n) / b;
/**
* √n = n^((p+1)/4) for fields p = 3 mod 4. We unwrap the loop and multiply bit-by-bit.
* (P+1n/4n).toString(2) would produce bits [223x 1, 0, 22x 1, 4x 0, 11, 00]
*/
function sqrtMod(y) {
const P = secp256k1P;
// prettier-ignore
const _3n = BigInt(3), _6n = BigInt(6), _11n = BigInt(11), _22n = BigInt(22);
// prettier-ignore
const _23n = BigInt(23), _44n = BigInt(44), _88n = BigInt(88);
const b2 = (y * y * y) % P; // x^3, 11
const b3 = (b2 * b2 * y) % P; // x^7
const b6 = (pow2(b3, _3n, P) * b3) % P;
const b9 = (pow2(b6, _3n, P) * b3) % P;
const b11 = (pow2(b9, _2n, P) * b2) % P;
const b22 = (pow2(b11, _11n, P) * b11) % P;
const b44 = (pow2(b22, _22n, P) * b22) % P;
const b88 = (pow2(b44, _44n, P) * b44) % P;
const b176 = (pow2(b88, _88n, P) * b88) % P;
const b220 = (pow2(b176, _44n, P) * b44) % P;
const b223 = (pow2(b220, _3n, P) * b3) % P;
const t1 = (pow2(b223, _23n, P) * b22) % P;
const t2 = (pow2(t1, _6n, P) * b2) % P;
const root = pow2(t2, _2n, P);
if (!Fp$3.eql(Fp$3.sqr(root), y))
throw new Error('Cannot find square root');
return root;
}
const Fp$3 = Field(secp256k1P, undefined, undefined, { sqrt: sqrtMod });
/**
* secp256k1 short weierstrass curve and ECDSA signatures over it.
*/
const secp256k1 = createCurve({
a: BigInt(0), // equation params: a, b
b: BigInt(7), // Seem to be rigid: bitcointalk.org/index.php?topic=289795.msg3183975#msg3183975
Fp: Fp$3, // Field's prime: 2n**256n - 2n**32n - 2n**9n - 2n**8n - 2n**7n - 2n**6n - 2n**4n - 1n
n: secp256k1N, // Curve order, total count of valid points in the field
// Base point (x, y) aka generator point
Gx: BigInt('55066263022277343669578718895168534326250603453777594175500187360389116729240'),
Gy: BigInt('32670510020758816978083085130507043184471273380659243275938904335757337482424'),
h: BigInt(1), // Cofactor
lowS: true, // Allow only low-S signatures by default in sign() and verify()
/**
* secp256k1 belongs to Koblitz curves: it has efficiently computable endomorphism.
* Endomorphism uses 2x less RAM, speeds up precomputation by 2x and ECDH / key recovery by 20%.
* For precomputed wNAF it trades off 1/2 init time & 1/3 ram for 20% perf hit.
* Explanation: https://gist.github.com/paulmillr/eb670806793e84df628a7c434a873066
*/
endo: {
beta: BigInt('0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee'),
splitScalar: (k) => {
const n = secp256k1N;
const a1 = BigInt('0x3086d221a7d46bcde86c90e49284eb15');
const b1 = -_1n * BigInt('0xe4437ed6010e88286f547fa90abfe4c3');
const a2 = BigInt('0x114ca50f7a8e2f3f657c1108d9d44cfd8');
const b2 = a1;
const POW_2_128 = BigInt('0x100000000000000000000000000000000'); // (2n**128n).toString(16)
const c1 = divNearest(b2 * k, n);
const c2 = divNearest(-b1 * k, n);
let k1 = mod(k - c1 * a1 - c2 * a2, n);
let k2 = mod(-c1 * b1 - c2 * b2, n);
const k1neg = k1 > POW_2_128;
const k2neg = k2 > POW_2_128;
if (k1neg)
k1 = n - k1;
if (k2neg)
k2 = n - k2;
if (k1 > POW_2_128 || k2 > POW_2_128) {
throw new Error('splitScalar: Endomorphism failed, k=' + k);
}
return { k1neg, k1, k2neg, k2 };
},
},
}, sha256);
// Schnorr signatures are superior to ECDSA from above. Below is Schnorr-specific BIP0340 code.
// https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki
BigInt(0);
secp256k1.ProjectivePoint;
// brainpoolP256r1: https://datatracker.ietf.org/doc/html/rfc5639#section-3.4
// eslint-disable-next-line new-cap
const Fp$2 = Field(BigInt('0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377'));
const CURVE_A$2 = Fp$2.create(BigInt('0x7d5a0975fc2c3057eef67530417affe7fb8055c126dc5c6ce94a4b44f330b5d9'));
const CURVE_B$2 = BigInt('0x26dc5c6ce94a4b44f330b5d9bbd77cbf958416295cf7e1ce6bccdc18ff8c07b6');
// prettier-ignore
const brainpoolP256r1 = createCurve({
a: CURVE_A$2, // Equation params: a, b
b: CURVE_B$2,
Fp: Fp$2,
// Curve order (q), total count of valid points in the field
n: BigInt('0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7'),
// Base (generator) point (x, y)
Gx: BigInt('0x8bd2aeb9cb7e57cb2c4b482ffc81b7afb9de27e1e3bd23c23a4453bd9ace3262'),
Gy: BigInt('0x547ef835c3dac4fd97f8461a14611dc9c27745132ded8e545c1d54c72f046997'),
h: BigInt(1),
lowS: false
}, sha256);
// brainpoolP384 r1: https://datatracker.ietf.org/doc/html/rfc5639#section-3.6
// eslint-disable-next-line new-cap
const Fp$1 = Field(BigInt('0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53'));
const CURVE_A$1 = Fp$1.create(BigInt('0x7bc382c63d8c150c3c72080ace05afa0c2bea28e4fb22787139165efba91f90f8aa5814a503ad4eb04a8c7dd22ce2826'));
const CURVE_B$1 = BigInt('0x04a8c7dd22ce28268b39b55416f0447c2fb77de107dcd2a62e880ea53eeb62d57cb4390295dbc9943ab78696fa504c11');
// prettier-ignore
const brainpoolP384r1 = createCurve({
a: CURVE_A$1, // Equation params: a, b
b: CURVE_B$1,
Fp: Fp$1,
// Curve order (q), total count of valid points in the field
n: BigInt('0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565'),
// Base (generator) point (x, y)
Gx: BigInt('0x1d1c64f068cf45ffa2a63a81b7c13f6b8847a3e77ef14fe3db7fcafe0cbd10e8e826e03436d646aaef87b2e247d4af1e'),
Gy: BigInt('0x8abe1d7520f9c2a45cb1eb8e95cfd55262b70b29feec5864e19c054ff99129280e4646217791811142820341263c5315'),
h: BigInt(1),
lowS: false
}, sha384);
// brainpoolP512r1: https://datatracker.ietf.org/doc/html/rfc5639#section-3.7
// eslint-disable-next-line new-cap
const Fp = Field(BigInt('0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3'));
const CURVE_A = Fp.create(BigInt('0x7830a3318b603b89e2327145ac234cc594cbdd8d3df91610a83441caea9863bc2ded5d5aa8253aa10a2ef1c98b9ac8b57f1117a72bf2c7b9e7c1ac4d77fc94ca'));
const CURVE_B = BigInt('0x3df91610a83441caea9863bc2ded5d5aa8253aa10a2ef1c98b9ac8b57f1117a72bf2c7b9e7c1ac4d77fc94cadc083e67984050b75ebae5dd2809bd638016f723');
// prettier-ignore
const brainpoolP512r1 = createCurve({
a: CURVE_A, // Equation params: a, b
b: CURVE_B,
Fp,
// Curve order (q), total count of valid points in the field
n: BigInt('0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069'),
// Base (generator) point (x, y)
Gx: BigInt('0x81aee4bdd82ed9645a21322e9c4c6a9385ed9f70b5d916c1b43b62eef4d0098eff3b1f78e2d0d48d50d1687b93b97d5f7c6d5047406a5e688b352209bcb9f822'),
Gy: BigInt('0x7dde385d566332ecc0eabfa9cf7822fdf209f70024a57b1aa000c55b881f8111b2dcde494a5f485e5bca4bd88a2763aed1ca2b2fa8f0540678cd1e0f3ad80892'),
h: BigInt(1),
lowS: false
}, sha512);
/**
* This file is needed to dynamic import the noble-curves.
* Separate dynamic imports are not convenient as they result in too many chunks,
* which share a lot of code anyway.
*/
const nobleCurves = new Map(Object.entries({
nistP256: p256,
nistP384: p384,
nistP521: p521,
brainpoolP256r1,
brainpoolP384r1,
brainpoolP512r1,
secp256k1,
x448,
ed448
}));
export { nobleCurves };