openpgp/dist/lightweight/noble_curves.min.mjs.map

OpenPGP.js is a Javascript implementation of the OpenPGP protocol. This is defined in RFC 4880.

{"version":3,"file":"noble_curves.min.mjs","sources":["../../node_modules/@noble/hashes/esm/hmac.js","../../node_modules/@noble/curves/esm/abstract/utils.js","../../node_modules/@noble/curves/esm/abstract/modular.js","../../node_modules/@noble/curves/esm/abstract/curve.js","../../node_modules/@noble/curves/esm/abstract/weierstrass.js","../../node_modules/@noble/curves/esm/_shortw_utils.js","../../node_modules/@noble/curves/esm/p256.js","../../node_modules/@noble/curves/esm/p384.js","../../node_modules/@noble/curves/esm/p521.js","../../node_modules/@noble/curves/esm/abstract/edwards.js","../../node_modules/@noble/curves/esm/abstract/montgomery.js","../../node_modules/@noble/curves/esm/ed448.js","../../node_modules/@noble/curves/esm/secp256k1.js","../../../../../src/crypto/public_key/elliptic/brainpool/brainpoolP256r1.ts","../../../../../src/crypto/public_key/elliptic/brainpool/brainpoolP384r1.ts","../../../../../src/crypto/public_key/elliptic/brainpool/brainpoolP512r1.ts","../../src/crypto/public_key/elliptic/noble_curves.js"],"sourcesContent":["import { hash as assertHash, bytes as assertBytes, exists as assertExists } from './_assert.js';\nimport { Hash, toBytes } from './utils.js';\n// HMAC (RFC 2104)\nexport class HMAC extends Hash {\n    constructor(hash, _key) {\n        super();\n        this.finished = false;\n        this.destroyed = false;\n        assertHash(hash);\n        const key = toBytes(_key);\n        this.iHash = hash.create();\n        if (typeof this.iHash.update !== 'function')\n            throw new Error('Expected instance of class which extends utils.Hash');\n        this.blockLen = this.iHash.blockLen;\n        this.outputLen = this.iHash.outputLen;\n        const blockLen = this.blockLen;\n        const pad = new Uint8Array(blockLen);\n        // blockLen can be bigger than outputLen\n        pad.set(key.length > blockLen ? hash.create().update(key).digest() : key);\n        for (let i = 0; i < pad.length; i++)\n            pad[i] ^= 0x36;\n        this.iHash.update(pad);\n        // By doing update (processing of first block) of outer hash here we can re-use it between multiple calls via clone\n        this.oHash = hash.create();\n        // Undo internal XOR && apply outer XOR\n        for (let i = 0; i < pad.length; i++)\n            pad[i] ^= 0x36 ^ 0x5c;\n        this.oHash.update(pad);\n        pad.fill(0);\n    }\n    update(buf) {\n        assertExists(this);\n        this.iHash.update(buf);\n        return this;\n    }\n    digestInto(out) {\n        assertExists(this);\n        assertBytes(out, this.outputLen);\n        this.finished = true;\n        this.iHash.digestInto(out);\n        this.oHash.update(out);\n        this.oHash.digestInto(out);\n        this.destroy();\n    }\n    digest() {\n        const out = new Uint8Array(this.oHash.outputLen);\n        this.digestInto(out);\n        return out;\n    }\n    _cloneInto(to) {\n        // Create new instance without calling constructor since key already in state and we don't know it.\n        to || (to = Object.create(Object.getPrototypeOf(this), {}));\n        const { oHash, iHash, finished, destroyed, blockLen, outputLen } = this;\n        to = to;\n        to.finished = finished;\n        to.destroyed = destroyed;\n        to.blockLen = blockLen;\n        to.outputLen = outputLen;\n        to.oHash = oHash._cloneInto(to.oHash);\n        to.iHash = iHash._cloneInto(to.iHash);\n        return to;\n    }\n    destroy() {\n        this.destroyed = true;\n        this.oHash.destroy();\n        this.iHash.destroy();\n    }\n}\n/**\n * HMAC: RFC2104 message authentication code.\n * @param hash - function that would be used e.g. sha256\n * @param key - message key\n * @param message - message data\n * @example\n * import { hmac } from '@noble/hashes/hmac';\n * import { sha256 } from '@noble/hashes/sha2';\n * const mac1 = hmac(sha256, 'key', 'message');\n */\nexport const hmac = (hash, key, message) => new HMAC(hash, key).update(message).digest();\nhmac.create = (hash, key) => new HMAC(hash, key);\n//# sourceMappingURL=hmac.js.map","/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n// 100 lines of code in the file are duplicated from noble-hashes (utils).\n// This is OK: `abstract` directory does not use noble-hashes.\n// User may opt-in into using different hashing library. This way, noble-hashes\n// won't be included into their bundle.\nconst _0n = /* @__PURE__ */ BigInt(0);\nconst _1n = /* @__PURE__ */ BigInt(1);\nconst _2n = /* @__PURE__ */ BigInt(2);\nexport function isBytes(a) {\n    return (a instanceof Uint8Array ||\n        (a != null && typeof a === 'object' && a.constructor.name === 'Uint8Array'));\n}\nexport function abytes(item) {\n    if (!isBytes(item))\n        throw new Error('Uint8Array expected');\n}\nexport function abool(title, value) {\n    if (typeof value !== 'boolean')\n        throw new Error(`${title} must be valid boolean, got \"${value}\".`);\n}\n// Array where index 0xf0 (240) is mapped to string 'f0'\nconst hexes = /* @__PURE__ */ Array.from({ length: 256 }, (_, i) => i.toString(16).padStart(2, '0'));\n/**\n * @example bytesToHex(Uint8Array.from([0xca, 0xfe, 0x01, 0x23])) // 'cafe0123'\n */\nexport function bytesToHex(bytes) {\n    abytes(bytes);\n    // pre-caching improves the speed 6x\n    let hex = '';\n    for (let i = 0; i < bytes.length; i++) {\n        hex += hexes[bytes[i]];\n    }\n    return hex;\n}\nexport function numberToHexUnpadded(num) {\n    const hex = num.toString(16);\n    return hex.length & 1 ? `0${hex}` : hex;\n}\nexport function hexToNumber(hex) {\n    if (typeof hex !== 'string')\n        throw new Error('hex string expected, got ' + typeof hex);\n    // Big Endian\n    return BigInt(hex === '' ? '0' : `0x${hex}`);\n}\n// We use optimized technique to convert hex string to byte array\nconst asciis = { _0: 48, _9: 57, _A: 65, _F: 70, _a: 97, _f: 102 };\nfunction asciiToBase16(char) {\n    if (char >= asciis._0 && char <= asciis._9)\n        return char - asciis._0;\n    if (char >= asciis._A && char <= asciis._F)\n        return char - (asciis._A - 10);\n    if (char >= asciis._a && char <= asciis._f)\n        return char - (asciis._a - 10);\n    return;\n}\n/**\n * @example hexToBytes('cafe0123') // Uint8Array.from([0xca, 0xfe, 0x01, 0x23])\n */\nexport function hexToBytes(hex) {\n    if (typeof hex !== 'string')\n        throw new Error('hex string expected, got ' + typeof hex);\n    const hl = hex.length;\n    const al = hl / 2;\n    if (hl % 2)\n        throw new Error('padded hex string expected, got unpadded hex of length ' + hl);\n    const array = new Uint8Array(al);\n    for (let ai = 0, hi = 0; ai < al; ai++, hi += 2) {\n        const n1 = asciiToBase16(hex.charCodeAt(hi));\n        const n2 = asciiToBase16(hex.charCodeAt(hi + 1));\n        if (n1 === undefined || n2 === undefined) {\n            const char = hex[hi] + hex[hi + 1];\n            throw new Error('hex string expected, got non-hex character \"' + char + '\" at index ' + hi);\n        }\n        array[ai] = n1 * 16 + n2;\n    }\n    return array;\n}\n// BE: Big Endian, LE: Little Endian\nexport function bytesToNumberBE(bytes) {\n    return hexToNumber(bytesToHex(bytes));\n}\nexport function bytesToNumberLE(bytes) {\n    abytes(bytes);\n    return hexToNumber(bytesToHex(Uint8Array.from(bytes).reverse()));\n}\nexport function numberToBytesBE(n, len) {\n    return hexToBytes(n.toString(16).padStart(len * 2, '0'));\n}\nexport function numberToBytesLE(n, len) {\n    return numberToBytesBE(n, len).reverse();\n}\n// Unpadded, rarely used\nexport function numberToVarBytesBE(n) {\n    return hexToBytes(numberToHexUnpadded(n));\n}\n/**\n * Takes hex string or Uint8Array, converts to Uint8Array.\n * Validates output length.\n * Will throw error for other types.\n * @param title descriptive title for an error e.g. 'private key'\n * @param hex hex string or Uint8Array\n * @param expectedLength optional, will compare to result array's length\n * @returns\n */\nexport function ensureBytes(title, hex, expectedLength) {\n    let res;\n    if (typeof hex === 'string') {\n        try {\n            res = hexToBytes(hex);\n        }\n        catch (e) {\n            throw new Error(`${title} must be valid hex string, got \"${hex}\". Cause: ${e}`);\n        }\n    }\n    else if (isBytes(hex)) {\n        // Uint8Array.from() instead of hash.slice() because node.js Buffer\n        // is instance of Uint8Array, and its slice() creates **mutable** copy\n        res = Uint8Array.from(hex);\n    }\n    else {\n        throw new Error(`${title} must be hex string or Uint8Array`);\n    }\n    const len = res.length;\n    if (typeof expectedLength === 'number' && len !== expectedLength)\n        throw new Error(`${title} expected ${expectedLength} bytes, got ${len}`);\n    return res;\n}\n/**\n * Copies several Uint8Arrays into one.\n */\nexport function concatBytes(...arrays) {\n    let sum = 0;\n    for (let i = 0; i < arrays.length; i++) {\n        const a = arrays[i];\n        abytes(a);\n        sum += a.length;\n    }\n    const res = new Uint8Array(sum);\n    for (let i = 0, pad = 0; i < arrays.length; i++) {\n        const a = arrays[i];\n        res.set(a, pad);\n        pad += a.length;\n    }\n    return res;\n}\n// Compares 2 u8a-s in kinda constant time\nexport function equalBytes(a, b) {\n    if (a.length !== b.length)\n        return false;\n    let diff = 0;\n    for (let i = 0; i < a.length; i++)\n        diff |= a[i] ^ b[i];\n    return diff === 0;\n}\n/**\n * @example utf8ToBytes('abc') // new Uint8Array([97, 98, 99])\n */\nexport function utf8ToBytes(str) {\n    if (typeof str !== 'string')\n        throw new Error(`utf8ToBytes expected string, got ${typeof str}`);\n    return new Uint8Array(new TextEncoder().encode(str)); // https://bugzil.la/1681809\n}\n// Is positive bigint\nconst isPosBig = (n) => typeof n === 'bigint' && _0n <= n;\nexport function inRange(n, min, max) {\n    return isPosBig(n) && isPosBig(min) && isPosBig(max) && min <= n && n < max;\n}\n/**\n * Asserts min <= n < max. NOTE: It's < max and not <= max.\n * @example\n * aInRange('x', x, 1n, 256n); // would assume x is in (1n..255n)\n */\nexport function aInRange(title, n, min, max) {\n    // Why min <= n < max and not a (min < n < max) OR b (min <= n <= max)?\n    // consider P=256n, min=0n, max=P\n    // - a for min=0 would require -1:          `inRange('x', x, -1n, P)`\n    // - b would commonly require subtraction:  `inRange('x', x, 0n, P - 1n)`\n    // - our way is the cleanest:               `inRange('x', x, 0n, P)\n    if (!inRange(n, min, max))\n        throw new Error(`expected valid ${title}: ${min} <= n < ${max}, got ${typeof n} ${n}`);\n}\n// Bit operations\n/**\n * Calculates amount of bits in a bigint.\n * Same as `n.toString(2).length`\n */\nexport function bitLen(n) {\n    let len;\n    for (len = 0; n > _0n; n >>= _1n, len += 1)\n        ;\n    return len;\n}\n/**\n * Gets single bit at position.\n * NOTE: first bit position is 0 (same as arrays)\n * Same as `!!+Array.from(n.toString(2)).reverse()[pos]`\n */\nexport function bitGet(n, pos) {\n    return (n >> BigInt(pos)) & _1n;\n}\n/**\n * Sets single bit at position.\n */\nexport function bitSet(n, pos, value) {\n    return n | ((value ? _1n : _0n) << BigInt(pos));\n}\n/**\n * Calculate mask for N bits. Not using ** operator with bigints because of old engines.\n * Same as BigInt(`0b${Array(i).fill('1').join('')}`)\n */\nexport const bitMask = (n) => (_2n << BigInt(n - 1)) - _1n;\n// DRBG\nconst u8n = (data) => new Uint8Array(data); // creates Uint8Array\nconst u8fr = (arr) => Uint8Array.from(arr); // another shortcut\n/**\n * Minimal HMAC-DRBG from NIST 800-90 for RFC6979 sigs.\n * @returns function that will call DRBG until 2nd arg returns something meaningful\n * @example\n *   const drbg = createHmacDRBG<Key>(32, 32, hmac);\n *   drbg(seed, bytesToKey); // bytesToKey must return Key or undefined\n */\nexport function createHmacDrbg(hashLen, qByteLen, hmacFn) {\n    if (typeof hashLen !== 'number' || hashLen < 2)\n        throw new Error('hashLen must be a number');\n    if (typeof qByteLen !== 'number' || qByteLen < 2)\n        throw new Error('qByteLen must be a number');\n    if (typeof hmacFn !== 'function')\n        throw new Error('hmacFn must be a function');\n    // Step B, Step C: set hashLen to 8*ceil(hlen/8)\n    let v = u8n(hashLen); // Minimal non-full-spec HMAC-DRBG from NIST 800-90 for RFC6979 sigs.\n    let k = u8n(hashLen); // Steps B and C of RFC6979 3.2: set hashLen, in our case always same\n    let i = 0; // Iterations counter, will throw when over 1000\n    const reset = () => {\n        v.fill(1);\n        k.fill(0);\n        i = 0;\n    };\n    const h = (...b) => hmacFn(k, v, ...b); // hmac(k)(v, ...values)\n    const reseed = (seed = u8n()) => {\n        // HMAC-DRBG reseed() function. Steps D-G\n        k = h(u8fr([0x00]), seed); // k = hmac(k || v || 0x00 || seed)\n        v = h(); // v = hmac(k || v)\n        if (seed.length === 0)\n            return;\n        k = h(u8fr([0x01]), seed); // k = hmac(k || v || 0x01 || seed)\n        v = h(); // v = hmac(k || v)\n    };\n    const gen = () => {\n        // HMAC-DRBG generate() function\n        if (i++ >= 1000)\n            throw new Error('drbg: tried 1000 values');\n        let len = 0;\n        const out = [];\n        while (len < qByteLen) {\n            v = h();\n            const sl = v.slice();\n            out.push(sl);\n            len += v.length;\n        }\n        return concatBytes(...out);\n    };\n    const genUntil = (seed, pred) => {\n        reset();\n        reseed(seed); // Steps D-G\n        let res = undefined; // Step H: grind until k is in [1..n-1]\n        while (!(res = pred(gen())))\n            reseed();\n        reset();\n        return res;\n    };\n    return genUntil;\n}\n// Validating curves and fields\nconst validatorFns = {\n    bigint: (val) => typeof val === 'bigint',\n    function: (val) => typeof val === 'function',\n    boolean: (val) => typeof val === 'boolean',\n    string: (val) => typeof val === 'string',\n    stringOrUint8Array: (val) => typeof val === 'string' || isBytes(val),\n    isSafeInteger: (val) => Number.isSafeInteger(val),\n    array: (val) => Array.isArray(val),\n    field: (val, object) => object.Fp.isValid(val),\n    hash: (val) => typeof val === 'function' && Number.isSafeInteger(val.outputLen),\n};\n// type Record<K extends string | number | symbol, T> = { [P in K]: T; }\nexport function validateObject(object, validators, optValidators = {}) {\n    const checkField = (fieldName, type, isOptional) => {\n        const checkVal = validatorFns[type];\n        if (typeof checkVal !== 'function')\n            throw new Error(`Invalid validator \"${type}\", expected function`);\n        const val = object[fieldName];\n        if (isOptional && val === undefined)\n            return;\n        if (!checkVal(val, object)) {\n            throw new Error(`Invalid param ${String(fieldName)}=${val} (${typeof val}), expected ${type}`);\n        }\n    };\n    for (const [fieldName, type] of Object.entries(validators))\n        checkField(fieldName, type, false);\n    for (const [fieldName, type] of Object.entries(optValidators))\n        checkField(fieldName, type, true);\n    return object;\n}\n// validate type tests\n// const o: { a: number; b: number; c: number } = { a: 1, b: 5, c: 6 };\n// const z0 = validateObject(o, { a: 'isSafeInteger' }, { c: 'bigint' }); // Ok!\n// // Should fail type-check\n// const z1 = validateObject(o, { a: 'tmp' }, { c: 'zz' });\n// const z2 = validateObject(o, { a: 'isSafeInteger' }, { c: 'zz' });\n// const z3 = validateObject(o, { test: 'boolean', z: 'bug' });\n// const z4 = validateObject(o, { a: 'boolean', z: 'bug' });\n/**\n * throws not implemented error\n */\nexport const notImplemented = () => {\n    throw new Error('not implemented');\n};\n/**\n * Memoizes (caches) computation result.\n * Uses WeakMap: the value is going auto-cleaned by GC after last reference is removed.\n */\nexport function memoized(fn) {\n    const map = new WeakMap();\n    return (arg, ...args) => {\n        const val = map.get(arg);\n        if (val !== undefined)\n            return val;\n        const computed = fn(arg, ...args);\n        map.set(arg, computed);\n        return computed;\n    };\n}\n//# sourceMappingURL=utils.js.map","/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n// Utilities for modular arithmetics and finite fields\nimport { bitMask, bytesToNumberBE, bytesToNumberLE, ensureBytes, numberToBytesBE, numberToBytesLE, validateObject, } from './utils.js';\n// prettier-ignore\nconst _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);\n// prettier-ignore\nconst _4n = BigInt(4), _5n = BigInt(5), _8n = BigInt(8);\n// prettier-ignore\nconst _9n = BigInt(9), _16n = BigInt(16);\n// Calculates a modulo b\nexport function mod(a, b) {\n    const result = a % b;\n    return result >= _0n ? result : b + result;\n}\n/**\n * Efficiently raise num to power and do modular division.\n * Unsafe in some contexts: uses ladder, so can expose bigint bits.\n * @example\n * pow(2n, 6n, 11n) // 64n % 11n == 9n\n */\n// TODO: use field version && remove\nexport function pow(num, power, modulo) {\n    if (modulo <= _0n || power < _0n)\n        throw new Error('Expected power/modulo > 0');\n    if (modulo === _1n)\n        return _0n;\n    let res = _1n;\n    while (power > _0n) {\n        if (power & _1n)\n            res = (res * num) % modulo;\n        num = (num * num) % modulo;\n        power >>= _1n;\n    }\n    return res;\n}\n// Does x ^ (2 ^ power) mod p. pow2(30, 4) == 30 ^ (2 ^ 4)\nexport function pow2(x, power, modulo) {\n    let res = x;\n    while (power-- > _0n) {\n        res *= res;\n        res %= modulo;\n    }\n    return res;\n}\n// Inverses number over modulo\nexport function invert(number, modulo) {\n    if (number === _0n || modulo <= _0n) {\n        throw new Error(`invert: expected positive integers, got n=${number} mod=${modulo}`);\n    }\n    // Euclidean GCD https://brilliant.org/wiki/extended-euclidean-algorithm/\n    // Fermat's little theorem \"CT-like\" version inv(n) = n^(m-2) mod m is 30x slower.\n    let a = mod(number, modulo);\n    let b = modulo;\n    // prettier-ignore\n    let x = _0n, y = _1n, u = _1n, v = _0n;\n    while (a !== _0n) {\n        // JIT applies optimization if those two lines follow each other\n        const q = b / a;\n        const r = b % a;\n        const m = x - u * q;\n        const n = y - v * q;\n        // prettier-ignore\n        b = a, a = r, x = u, y = v, u = m, v = n;\n    }\n    const gcd = b;\n    if (gcd !== _1n)\n        throw new Error('invert: does not exist');\n    return mod(x, modulo);\n}\n/**\n * Tonelli-Shanks square root search algorithm.\n * 1. https://eprint.iacr.org/2012/685.pdf (page 12)\n * 2. Square Roots from 1; 24, 51, 10 to Dan Shanks\n * Will start an infinite loop if field order P is not prime.\n * @param P field order\n * @returns function that takes field Fp (created from P) and number n\n */\nexport function tonelliShanks(P) {\n    // Legendre constant: used to calculate Legendre symbol (a | p),\n    // which denotes the value of a^((p-1)/2) (mod p).\n    // (a | p) ≡ 1    if a is a square (mod p)\n    // (a | p) ≡ -1   if a is not a square (mod p)\n    // (a | p) ≡ 0    if a ≡ 0 (mod p)\n    const legendreC = (P - _1n) / _2n;\n    let Q, S, Z;\n    // Step 1: By factoring out powers of 2 from p - 1,\n    // find q and s such that p - 1 = q*(2^s) with q odd\n    for (Q = P - _1n, S = 0; Q % _2n === _0n; Q /= _2n, S++)\n        ;\n    // Step 2: Select a non-square z such that (z | p) ≡ -1 and set c ≡ zq\n    for (Z = _2n; Z < P && pow(Z, legendreC, P) !== P - _1n; Z++)\n        ;\n    // Fast-path\n    if (S === 1) {\n        const p1div4 = (P + _1n) / _4n;\n        return function tonelliFast(Fp, n) {\n            const root = Fp.pow(n, p1div4);\n            if (!Fp.eql(Fp.sqr(root), n))\n                throw new Error('Cannot find square root');\n            return root;\n        };\n    }\n    // Slow-path\n    const Q1div2 = (Q + _1n) / _2n;\n    return function tonelliSlow(Fp, n) {\n        // Step 0: Check that n is indeed a square: (n | p) should not be ≡ -1\n        if (Fp.pow(n, legendreC) === Fp.neg(Fp.ONE))\n            throw new Error('Cannot find square root');\n        let r = S;\n        // TODO: will fail at Fp2/etc\n        let g = Fp.pow(Fp.mul(Fp.ONE, Z), Q); // will update both x and b\n        let x = Fp.pow(n, Q1div2); // first guess at the square root\n        let b = Fp.pow(n, Q); // first guess at the fudge factor\n        while (!Fp.eql(b, Fp.ONE)) {\n            if (Fp.eql(b, Fp.ZERO))\n                return Fp.ZERO; // https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm (4. If t = 0, return r = 0)\n            // Find m such b^(2^m)==1\n            let m = 1;\n            for (let t2 = Fp.sqr(b); m < r; m++) {\n                if (Fp.eql(t2, Fp.ONE))\n                    break;\n                t2 = Fp.sqr(t2); // t2 *= t2\n            }\n            // NOTE: r-m-1 can be bigger than 32, need to convert to bigint before shift, otherwise there will be overflow\n            const ge = Fp.pow(g, _1n << BigInt(r - m - 1)); // ge = 2^(r-m-1)\n            g = Fp.sqr(ge); // g = ge * ge\n            x = Fp.mul(x, ge); // x *= ge\n            b = Fp.mul(b, g); // b *= g\n            r = m;\n        }\n        return x;\n    };\n}\nexport function FpSqrt(P) {\n    // NOTE: different algorithms can give different roots, it is up to user to decide which one they want.\n    // For example there is FpSqrtOdd/FpSqrtEven to choice root based on oddness (used for hash-to-curve).\n    // P ≡ 3 (mod 4)\n    // √n = n^((P+1)/4)\n    if (P % _4n === _3n) {\n        // Not all roots possible!\n        // const ORDER =\n        //   0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaabn;\n        // const NUM = 72057594037927816n;\n        const p1div4 = (P + _1n) / _4n;\n        return function sqrt3mod4(Fp, n) {\n            const root = Fp.pow(n, p1div4);\n            // Throw if root**2 != n\n            if (!Fp.eql(Fp.sqr(root), n))\n                throw new Error('Cannot find square root');\n            return root;\n        };\n    }\n    // Atkin algorithm for q ≡ 5 (mod 8), https://eprint.iacr.org/2012/685.pdf (page 10)\n    if (P % _8n === _5n) {\n        const c1 = (P - _5n) / _8n;\n        return function sqrt5mod8(Fp, n) {\n            const n2 = Fp.mul(n, _2n);\n            const v = Fp.pow(n2, c1);\n            const nv = Fp.mul(n, v);\n            const i = Fp.mul(Fp.mul(nv, _2n), v);\n            const root = Fp.mul(nv, Fp.sub(i, Fp.ONE));\n            if (!Fp.eql(Fp.sqr(root), n))\n                throw new Error('Cannot find square root');\n            return root;\n        };\n    }\n    // P ≡ 9 (mod 16)\n    if (P % _16n === _9n) {\n        // NOTE: tonelli is too slow for bls-Fp2 calculations even on start\n        // Means we cannot use sqrt for constants at all!\n        //\n        // const c1 = Fp.sqrt(Fp.negate(Fp.ONE)); //  1. c1 = sqrt(-1) in F, i.e., (c1^2) == -1 in F\n        // const c2 = Fp.sqrt(c1);                //  2. c2 = sqrt(c1) in F, i.e., (c2^2) == c1 in F\n        // const c3 = Fp.sqrt(Fp.negate(c1));     //  3. c3 = sqrt(-c1) in F, i.e., (c3^2) == -c1 in F\n        // const c4 = (P + _7n) / _16n;           //  4. c4 = (q + 7) / 16        # Integer arithmetic\n        // sqrt = (x) => {\n        //   let tv1 = Fp.pow(x, c4);             //  1. tv1 = x^c4\n        //   let tv2 = Fp.mul(c1, tv1);           //  2. tv2 = c1 * tv1\n        //   const tv3 = Fp.mul(c2, tv1);         //  3. tv3 = c2 * tv1\n        //   let tv4 = Fp.mul(c3, tv1);           //  4. tv4 = c3 * tv1\n        //   const e1 = Fp.equals(Fp.square(tv2), x); //  5.  e1 = (tv2^2) == x\n        //   const e2 = Fp.equals(Fp.square(tv3), x); //  6.  e2 = (tv3^2) == x\n        //   tv1 = Fp.cmov(tv1, tv2, e1); //  7. tv1 = CMOV(tv1, tv2, e1)  # Select tv2 if (tv2^2) == x\n        //   tv2 = Fp.cmov(tv4, tv3, e2); //  8. tv2 = CMOV(tv4, tv3, e2)  # Select tv3 if (tv3^2) == x\n        //   const e3 = Fp.equals(Fp.square(tv2), x); //  9.  e3 = (tv2^2) == x\n        //   return Fp.cmov(tv1, tv2, e3); //  10.  z = CMOV(tv1, tv2, e3)  # Select the sqrt from tv1 and tv2\n        // }\n    }\n    // Other cases: Tonelli-Shanks algorithm\n    return tonelliShanks(P);\n}\n// Little-endian check for first LE bit (last BE bit);\nexport const isNegativeLE = (num, modulo) => (mod(num, modulo) & _1n) === _1n;\n// prettier-ignore\nconst FIELD_FIELDS = [\n    'create', 'isValid', 'is0', 'neg', 'inv', 'sqrt', 'sqr',\n    'eql', 'add', 'sub', 'mul', 'pow', 'div',\n    'addN', 'subN', 'mulN', 'sqrN'\n];\nexport function validateField(field) {\n    const initial = {\n        ORDER: 'bigint',\n        MASK: 'bigint',\n        BYTES: 'isSafeInteger',\n        BITS: 'isSafeInteger',\n    };\n    const opts = FIELD_FIELDS.reduce((map, val) => {\n        map[val] = 'function';\n        return map;\n    }, initial);\n    return validateObject(field, opts);\n}\n// Generic field functions\n/**\n * Same as `pow` but for Fp: non-constant-time.\n * Unsafe in some contexts: uses ladder, so can expose bigint bits.\n */\nexport function FpPow(f, num, power) {\n    // Should have same speed as pow for bigints\n    // TODO: benchmark!\n    if (power < _0n)\n        throw new Error('Expected power > 0');\n    if (power === _0n)\n        return f.ONE;\n    if (power === _1n)\n        return num;\n    let p = f.ONE;\n    let d = num;\n    while (power > _0n) {\n        if (power & _1n)\n            p = f.mul(p, d);\n        d = f.sqr(d);\n        power >>= _1n;\n    }\n    return p;\n}\n/**\n * Efficiently invert an array of Field elements.\n * `inv(0)` will return `undefined` here: make sure to throw an error.\n */\nexport function FpInvertBatch(f, nums) {\n    const tmp = new Array(nums.length);\n    // Walk from first to last, multiply them by each other MOD p\n    const lastMultiplied = nums.reduce((acc, num, i) => {\n        if (f.is0(num))\n            return acc;\n        tmp[i] = acc;\n        return f.mul(acc, num);\n    }, f.ONE);\n    // Invert last element\n    const inverted = f.inv(lastMultiplied);\n    // Walk from last to first, multiply them by inverted each other MOD p\n    nums.reduceRight((acc, num, i) => {\n        if (f.is0(num))\n            return acc;\n        tmp[i] = f.mul(acc, tmp[i]);\n        return f.mul(acc, num);\n    }, inverted);\n    return tmp;\n}\nexport function FpDiv(f, lhs, rhs) {\n    return f.mul(lhs, typeof rhs === 'bigint' ? invert(rhs, f.ORDER) : f.inv(rhs));\n}\nexport function FpLegendre(order) {\n    // (a | p) ≡ 1    if a is a square (mod p), quadratic residue\n    // (a | p) ≡ -1   if a is not a square (mod p), quadratic non residue\n    // (a | p) ≡ 0    if a ≡ 0 (mod p)\n    const legendreConst = (order - _1n) / _2n; // Integer arithmetic\n    return (f, x) => f.pow(x, legendreConst);\n}\n// This function returns True whenever the value x is a square in the field F.\nexport function FpIsSquare(f) {\n    const legendre = FpLegendre(f.ORDER);\n    return (x) => {\n        const p = legendre(f, x);\n        return f.eql(p, f.ZERO) || f.eql(p, f.ONE);\n    };\n}\n// CURVE.n lengths\nexport function nLength(n, nBitLength) {\n    // Bit size, byte size of CURVE.n\n    const _nBitLength = nBitLength !== undefined ? nBitLength : n.toString(2).length;\n    const nByteLength = Math.ceil(_nBitLength / 8);\n    return { nBitLength: _nBitLength, nByteLength };\n}\n/**\n * Initializes a finite field over prime. **Non-primes are not supported.**\n * Do not init in loop: slow. Very fragile: always run a benchmark on a change.\n * Major performance optimizations:\n * * a) denormalized operations like mulN instead of mul\n * * b) same object shape: never add or remove keys\n * * c) Object.freeze\n * NOTE: operations don't check 'isValid' for all elements for performance reasons,\n * it is caller responsibility to check this.\n * This is low-level code, please make sure you know what you doing.\n * @param ORDER prime positive bigint\n * @param bitLen how many bits the field consumes\n * @param isLE (def: false) if encoding / decoding should be in little-endian\n * @param redef optional faster redefinitions of sqrt and other methods\n */\nexport function Field(ORDER, bitLen, isLE = false, redef = {}) {\n    if (ORDER <= _0n)\n        throw new Error(`Expected Field ORDER > 0, got ${ORDER}`);\n    const { nBitLength: BITS, nByteLength: BYTES } = nLength(ORDER, bitLen);\n    if (BYTES > 2048)\n        throw new Error('Field lengths over 2048 bytes are not supported');\n    const sqrtP = FpSqrt(ORDER);\n    const f = Object.freeze({\n        ORDER,\n        BITS,\n        BYTES,\n        MASK: bitMask(BITS),\n        ZERO: _0n,\n        ONE: _1n,\n        create: (num) => mod(num, ORDER),\n        isValid: (num) => {\n            if (typeof num !== 'bigint')\n                throw new Error(`Invalid field element: expected bigint, got ${typeof num}`);\n            return _0n <= num && num < ORDER; // 0 is valid element, but it's not invertible\n        },\n        is0: (num) => num === _0n,\n        isOdd: (num) => (num & _1n) === _1n,\n        neg: (num) => mod(-num, ORDER),\n        eql: (lhs, rhs) => lhs === rhs,\n        sqr: (num) => mod(num * num, ORDER),\n        add: (lhs, rhs) => mod(lhs + rhs, ORDER),\n        sub: (lhs, rhs) => mod(lhs - rhs, ORDER),\n        mul: (lhs, rhs) => mod(lhs * rhs, ORDER),\n        pow: (num, power) => FpPow(f, num, power),\n        div: (lhs, rhs) => mod(lhs * invert(rhs, ORDER), ORDER),\n        // Same as above, but doesn't normalize\n        sqrN: (num) => num * num,\n        addN: (lhs, rhs) => lhs + rhs,\n        subN: (lhs, rhs) => lhs - rhs,\n        mulN: (lhs, rhs) => lhs * rhs,\n        inv: (num) => invert(num, ORDER),\n        sqrt: redef.sqrt || ((n) => sqrtP(f, n)),\n        invertBatch: (lst) => FpInvertBatch(f, lst),\n        // TODO: do we really need constant cmov?\n        // We don't have const-time bigints anyway, so probably will be not very useful\n        cmov: (a, b, c) => (c ? b : a),\n        toBytes: (num) => (isLE ? numberToBytesLE(num, BYTES) : numberToBytesBE(num, BYTES)),\n        fromBytes: (bytes) => {\n            if (bytes.length !== BYTES)\n                throw new Error(`Fp.fromBytes: expected ${BYTES}, got ${bytes.length}`);\n            return isLE ? bytesToNumberLE(bytes) : bytesToNumberBE(bytes);\n        },\n    });\n    return Object.freeze(f);\n}\nexport function FpSqrtOdd(Fp, elm) {\n    if (!Fp.isOdd)\n        throw new Error(`Field doesn't have isOdd`);\n    const root = Fp.sqrt(elm);\n    return Fp.isOdd(root) ? root : Fp.neg(root);\n}\nexport function FpSqrtEven(Fp, elm) {\n    if (!Fp.isOdd)\n        throw new Error(`Field doesn't have isOdd`);\n    const root = Fp.sqrt(elm);\n    return Fp.isOdd(root) ? Fp.neg(root) : root;\n}\n/**\n * \"Constant-time\" private key generation utility.\n * Same as mapKeyToField, but accepts less bytes (40 instead of 48 for 32-byte field).\n * Which makes it slightly more biased, less secure.\n * @deprecated use mapKeyToField instead\n */\nexport function hashToPrivateScalar(hash, groupOrder, isLE = false) {\n    hash = ensureBytes('privateHash', hash);\n    const hashLen = hash.length;\n    const minLen = nLength(groupOrder).nByteLength + 8;\n    if (minLen < 24 || hashLen < minLen || hashLen > 1024)\n        throw new Error(`hashToPrivateScalar: expected ${minLen}-1024 bytes of input, got ${hashLen}`);\n    const num = isLE ? bytesToNumberLE(hash) : bytesToNumberBE(hash);\n    return mod(num, groupOrder - _1n) + _1n;\n}\n/**\n * Returns total number of bytes consumed by the field element.\n * For example, 32 bytes for usual 256-bit weierstrass curve.\n * @param fieldOrder number of field elements, usually CURVE.n\n * @returns byte length of field\n */\nexport function getFieldBytesLength(fieldOrder) {\n    if (typeof fieldOrder !== 'bigint')\n        throw new Error('field order must be bigint');\n    const bitLength = fieldOrder.toString(2).length;\n    return Math.ceil(bitLength / 8);\n}\n/**\n * Returns minimal amount of bytes that can be safely reduced\n * by field order.\n * Should be 2^-128 for 128-bit curve such as P256.\n * @param fieldOrder number of field elements, usually CURVE.n\n * @returns byte length of target hash\n */\nexport function getMinHashLength(fieldOrder) {\n    const length = getFieldBytesLength(fieldOrder);\n    return length + Math.ceil(length / 2);\n}\n/**\n * \"Constant-time\" private key generation utility.\n * Can take (n + n/2) or more bytes of uniform input e.g. from CSPRNG or KDF\n * and convert them into private scalar, with the modulo bias being negligible.\n * Needs at least 48 bytes of input for 32-byte private key.\n * https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/\n * FIPS 186-5, A.2 https://csrc.nist.gov/publications/detail/fips/186/5/final\n * RFC 9380, https://www.rfc-editor.org/rfc/rfc9380#section-5\n * @param hash hash output from SHA3 or a similar function\n * @param groupOrder size of subgroup - (e.g. secp256k1.CURVE.n)\n * @param isLE interpret hash bytes as LE num\n * @returns valid private scalar\n */\nexport function mapHashToField(key, fieldOrder, isLE = false) {\n    const len = key.length;\n    const fieldLen = getFieldBytesLength(fieldOrder);\n    const minLen = getMinHashLength(fieldOrder);\n    // No small numbers: need to understand bias story. No huge numbers: easier to detect JS timings.\n    if (len < 16 || len < minLen || len > 1024)\n        throw new Error(`expected ${minLen}-1024 bytes of input, got ${len}`);\n    const num = isLE ? bytesToNumberBE(key) : bytesToNumberLE(key);\n    // `mod(x, 11)` can sometimes produce 0. `mod(x, 10) + 1` is the same, but no 0\n    const reduced = mod(num, fieldOrder - _1n) + _1n;\n    return isLE ? numberToBytesLE(reduced, fieldLen) : numberToBytesBE(reduced, fieldLen);\n}\n//# sourceMappingURL=modular.js.map","/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n// Abelian group utilities\nimport { validateField, nLength } from './modular.js';\nimport { validateObject, bitLen } from './utils.js';\nconst _0n = BigInt(0);\nconst _1n = BigInt(1);\n// Since points in different groups cannot be equal (different object constructor),\n// we can have single place to store precomputes\nconst pointPrecomputes = new WeakMap();\nconst pointWindowSizes = new WeakMap(); // This allows use make points immutable (nothing changes inside)\n// Elliptic curve multiplication of Point by scalar. Fragile.\n// Scalars should always be less than curve order: this should be checked inside of a curve itself.\n// Creates precomputation tables for fast multiplication:\n// - private scalar is split by fixed size windows of W bits\n// - every window point is collected from window's table & added to accumulator\n// - since windows are different, same point inside tables won't be accessed more than once per calc\n// - each multiplication is 'Math.ceil(CURVE_ORDER / 𝑊) + 1' point additions (fixed for any scalar)\n// - +1 window is neccessary for wNAF\n// - wNAF reduces table size: 2x less memory + 2x faster generation, but 10% slower multiplication\n// TODO: Research returning 2d JS array of windows, instead of a single window. This would allow\n// windows to be in different memory locations\nexport function wNAF(c, bits) {\n    const constTimeNegate = (condition, item) => {\n        const neg = item.negate();\n        return condition ? neg : item;\n    };\n    const validateW = (W) => {\n        if (!Number.isSafeInteger(W) || W <= 0 || W > bits)\n            throw new Error(`Wrong window size=${W}, should be [1..${bits}]`);\n    };\n    const opts = (W) => {\n        validateW(W);\n        const windows = Math.ceil(bits / W) + 1; // +1, because\n        const windowSize = 2 ** (W - 1); // -1 because we skip zero\n        return { windows, windowSize };\n    };\n    return {\n        constTimeNegate,\n        // non-const time multiplication ladder\n        unsafeLadder(elm, n) {\n            let p = c.ZERO;\n            let d = elm;\n            while (n > _0n) {\n                if (n & _1n)\n                    p = p.add(d);\n                d = d.double();\n                n >>= _1n;\n            }\n            return p;\n        },\n        /**\n         * Creates a wNAF precomputation window. Used for caching.\n         * Default window size is set by `utils.precompute()` and is equal to 8.\n         * Number of precomputed points depends on the curve size:\n         * 2^(𝑊−1) * (Math.ceil(𝑛 / 𝑊) + 1), where:\n         * - 𝑊 is the window size\n         * - 𝑛 is the bitlength of the curve order.\n         * For a 256-bit curve and window size 8, the number of precomputed points is 128 * 33 = 4224.\n         * @returns precomputed point tables flattened to a single array\n         */\n        precomputeWindow(elm, W) {\n            const { windows, windowSize } = opts(W);\n            const points = [];\n            let p = elm;\n            let base = p;\n            for (let window = 0; window < windows; window++) {\n                base = p;\n                points.push(base);\n                // =1, because we skip zero\n                for (let i = 1; i < windowSize; i++) {\n                    base = base.add(p);\n                    points.push(base);\n                }\n                p = base.double();\n            }\n            return points;\n        },\n        /**\n         * Implements ec multiplication using precomputed tables and w-ary non-adjacent form.\n         * @param W window size\n         * @param precomputes precomputed tables\n         * @param n scalar (we don't check here, but should be less than curve order)\n         * @returns real and fake (for const-time) points\n         */\n        wNAF(W, precomputes, n) {\n            // TODO: maybe check that scalar is less than group order? wNAF behavious is undefined otherwise\n            // But need to carefully remove other checks before wNAF. ORDER == bits here\n            const { windows, windowSize } = opts(W);\n            let p = c.ZERO;\n            let f = c.BASE;\n            const mask = BigInt(2 ** W - 1); // Create mask with W ones: 0b1111 for W=4 etc.\n            const maxNumber = 2 ** W;\n            const shiftBy = BigInt(W);\n            for (let window = 0; window < windows; window++) {\n                const offset = window * windowSize;\n                // Extract W bits.\n                let wbits = Number(n & mask);\n                // Shift number by W bits.\n                n >>= shiftBy;\n                // If the bits are bigger than max size, we'll split those.\n                // +224 => 256 - 32\n                if (wbits > windowSize) {\n                    wbits -= maxNumber;\n                    n += _1n;\n                }\n                // This code was first written with assumption that 'f' and 'p' will never be infinity point:\n                // since each addition is multiplied by 2 ** W, it cannot cancel each other. However,\n                // there is negate now: it is possible that negated element from low value\n                // would be the same as high element, which will create carry into next window.\n                // It's not obvious how this can fail, but still worth investigating later.\n                // Check if we're onto Zero point.\n                // Add random point inside current window to f.\n                const offset1 = offset;\n                const offset2 = offset + Math.abs(wbits) - 1; // -1 because we skip zero\n                const cond1 = window % 2 !== 0;\n                const cond2 = wbits < 0;\n                if (wbits === 0) {\n                    // The most important part for const-time getPublicKey\n                    f = f.add(constTimeNegate(cond1, precomputes[offset1]));\n                }\n                else {\n                    p = p.add(constTimeNegate(cond2, precomputes[offset2]));\n                }\n            }\n            // JIT-compiler should not eliminate f here, since it will later be used in normalizeZ()\n            // Even if the variable is still unused, there are some checks which will\n            // throw an exception, so compiler needs to prove they won't happen, which is hard.\n            // At this point there is a way to F be infinity-point even if p is not,\n            // which makes it less const-time: around 1 bigint multiply.\n            return { p, f };\n        },\n        wNAFCached(P, n, transform) {\n            const W = pointWindowSizes.get(P) || 1;\n            // Calculate precomputes on a first run, reuse them after\n            let comp = pointPrecomputes.get(P);\n            if (!comp) {\n                comp = this.precomputeWindow(P, W);\n                if (W !== 1)\n                    pointPrecomputes.set(P, transform(comp));\n            }\n            return this.wNAF(W, comp, n);\n        },\n        // We calculate precomputes for elliptic curve point multiplication\n        // using windowed method. This specifies window size and\n        // stores precomputed values. Usually only base point would be precomputed.\n        setWindowSize(P, W) {\n            validateW(W);\n            pointWindowSizes.set(P, W);\n            pointPrecomputes.delete(P);\n        },\n    };\n}\n/**\n * Pippenger algorithm for multi-scalar multiplication (MSM).\n * MSM is basically (Pa + Qb + Rc + ...).\n * 30x faster vs naive addition on L=4096, 10x faster with precomputes.\n * For N=254bit, L=1, it does: 1024 ADD + 254 DBL. For L=5: 1536 ADD + 254 DBL.\n * Algorithmically constant-time (for same L), even when 1 point + scalar, or when scalar = 0.\n * @param c Curve Point constructor\n * @param field field over CURVE.N - important that it's not over CURVE.P\n * @param points array of L curve points\n * @param scalars array of L scalars (aka private keys / bigints)\n */\nexport function pippenger(c, field, points, scalars) {\n    // If we split scalars by some window (let's say 8 bits), every chunk will only\n    // take 256 buckets even if there are 4096 scalars, also re-uses double.\n    // TODO:\n    // - https://eprint.iacr.org/2024/750.pdf\n    // - https://tches.iacr.org/index.php/TCHES/article/view/10287\n    // 0 is accepted in scalars\n    if (!Array.isArray(points) || !Array.isArray(scalars) || scalars.length !== points.length)\n        throw new Error('arrays of points and scalars must have equal length');\n    scalars.forEach((s, i) => {\n        if (!field.isValid(s))\n            throw new Error(`wrong scalar at index ${i}`);\n    });\n    points.forEach((p, i) => {\n        if (!(p instanceof c))\n            throw new Error(`wrong point at index ${i}`);\n    });\n    const wbits = bitLen(BigInt(points.length));\n    const windowSize = wbits > 12 ? wbits - 3 : wbits > 4 ? wbits - 2 : wbits ? 2 : 1; // in bits\n    const MASK = (1 << windowSize) - 1;\n    const buckets = new Array(MASK + 1).fill(c.ZERO); // +1 for zero array\n    const lastBits = Math.floor((field.BITS - 1) / windowSize) * windowSize;\n    let sum = c.ZERO;\n    for (let i = lastBits; i >= 0; i -= windowSize) {\n        buckets.fill(c.ZERO);\n        for (let j = 0; j < scalars.length; j++) {\n            const scalar = scalars[j];\n            const wbits = Number((scalar >> BigInt(i)) & BigInt(MASK));\n            buckets[wbits] = buckets[wbits].add(points[j]);\n        }\n        let resI = c.ZERO; // not using this will do small speed-up, but will lose ct\n        // Skip first bucket, because it is zero\n        for (let j = buckets.length - 1, sumI = c.ZERO; j > 0; j--) {\n            sumI = sumI.add(buckets[j]);\n            resI = resI.add(sumI);\n        }\n        sum = sum.add(resI);\n        if (i !== 0)\n            for (let j = 0; j < windowSize; j++)\n                sum = sum.double();\n    }\n    return sum;\n}\nexport function validateBasic(curve) {\n    validateField(curve.Fp);\n    validateObject(curve, {\n        n: 'bigint',\n        h: 'bigint',\n        Gx: 'field',\n        Gy: 'field',\n    }, {\n        nBitLength: 'isSafeInteger',\n        nByteLength: 'isSafeInteger',\n    });\n    // Set defaults\n    return Object.freeze({\n        ...nLength(curve.n, curve.nBitLength),\n        ...curve,\n        ...{ p: curve.Fp.ORDER },\n    });\n}\n//# sourceMappingURL=curve.js.map","/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n// Short Weierstrass curve. The formula is: y² = x³ + ax + b\nimport { validateBasic, wNAF, pippenger, } from './curve.js';\nimport * as mod from './modular.js';\nimport * as ut from './utils.js';\nimport { ensureBytes, memoized, abool } from './utils.js';\nfunction validateSigVerOpts(opts) {\n    if (opts.lowS !== undefined)\n        abool('lowS', opts.lowS);\n    if (opts.prehash !== undefined)\n        abool('prehash', opts.prehash);\n}\nfunction validatePointOpts(curve) {\n    const opts = validateBasic(curve);\n    ut.validateObject(opts, {\n        a: 'field',\n        b: 'field',\n    }, {\n        allowedPrivateKeyLengths: 'array',\n        wrapPrivateKey: 'boolean',\n        isTorsionFree: 'function',\n        clearCofactor: 'function',\n        allowInfinityPoint: 'boolean',\n        fromBytes: 'function',\n        toBytes: 'function',\n    });\n    const { endo, Fp, a } = opts;\n    if (endo) {\n        if (!Fp.eql(a, Fp.ZERO)) {\n            throw new Error('Endomorphism can only be defined for Koblitz curves that have a=0');\n        }\n        if (typeof endo !== 'object' ||\n            typeof endo.beta !== 'bigint' ||\n            typeof endo.splitScalar !== 'function') {\n            throw new Error('Expected endomorphism with beta: bigint and splitScalar: function');\n        }\n    }\n    return Object.freeze({ ...opts });\n}\nconst { bytesToNumberBE: b2n, hexToBytes: h2b } = ut;\n/**\n * ASN.1 DER encoding utilities. ASN is very complex & fragile. Format:\n *\n *     [0x30 (SEQUENCE), bytelength, 0x02 (INTEGER), intLength, R, 0x02 (INTEGER), intLength, S]\n *\n * Docs: https://letsencrypt.org/docs/a-warm-welcome-to-asn1-and-der/, https://luca.ntop.org/Teaching/Appunti/asn1.html\n */\nexport const DER = {\n    // asn.1 DER encoding utils\n    Err: class DERErr extends Error {\n        constructor(m = '') {\n            super(m);\n        }\n    },\n    // Basic building block is TLV (Tag-Length-Value)\n    _tlv: {\n        encode: (tag, data) => {\n            const { Err: E } = DER;\n            if (tag < 0 || tag > 256)\n                throw new E('tlv.encode: wrong tag');\n            if (data.length & 1)\n                throw new E('tlv.encode: unpadded data');\n            const dataLen = data.length / 2;\n            const len = ut.numberToHexUnpadded(dataLen);\n            if ((len.length / 2) & 128)\n                throw new E('tlv.encode: long form length too big');\n            // length of length with long form flag\n            const lenLen = dataLen > 127 ? ut.numberToHexUnpadded((len.length / 2) | 128) : '';\n            return `${ut.numberToHexUnpadded(tag)}${lenLen}${len}${data}`;\n        },\n        // v - value, l - left bytes (unparsed)\n        decode(tag, data) {\n            const { Err: E } = DER;\n            let pos = 0;\n            if (tag < 0 || tag > 256)\n                throw new E('tlv.encode: wrong tag');\n            if (data.length < 2 || data[pos++] !== tag)\n                throw new E('tlv.decode: wrong tlv');\n            const first = data[pos++];\n            const isLong = !!(first & 128); // First bit of first length byte is flag for short/long form\n            let length = 0;\n            if (!isLong)\n                length = first;\n            else {\n                // Long form: [longFlag(1bit), lengthLength(7bit), length (BE)]\n                const lenLen = first & 127;\n                if (!lenLen)\n                    throw new E('tlv.decode(long): indefinite length not supported');\n                if (lenLen > 4)\n                    throw new E('tlv.decode(long): byte length is too big'); // this will overflow u32 in js\n                const lengthBytes = data.subarray(pos, pos + lenLen);\n                if (lengthBytes.length !== lenLen)\n                    throw new E('tlv.decode: length bytes not complete');\n                if (lengthBytes[0] === 0)\n                    throw new E('tlv.decode(long): zero leftmost byte');\n                for (const b of lengthBytes)\n                    length = (length << 8) | b;\n                pos += lenLen;\n                if (length < 128)\n                    throw new E('tlv.decode(long): not minimal encoding');\n            }\n            const v = data.subarray(pos, pos + length);\n            if (v.length !== length)\n                throw new E('tlv.decode: wrong value length');\n            return { v, l: data.subarray(pos + length) };\n        },\n    },\n    // https://crypto.stackexchange.com/a/57734 Leftmost bit of first byte is 'negative' flag,\n    // since we always use positive integers here. It must always be empty:\n    // - add zero byte if exists\n    // - if next byte doesn't have a flag, leading zero is not allowed (minimal encoding)\n    _int: {\n        encode(num) {\n            const { Err: E } = DER;\n            if (num < _0n)\n                throw new E('integer: negative integers are not allowed');\n            let hex = ut.numberToHexUnpadded(num);\n            // Pad with zero byte if negative flag is present\n            if (Number.parseInt(hex[0], 16) & 0b100