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atchOwners.ts","../src/utils/addressMap.ts","../src/utils/getTransferableInputsByTx.ts","../src/utils/getTransferableOutputsByTx.ts","../src/utils/getBurnedAmountByTx.ts","../src/utils/devutils.ts","../src/utils/validateBurnedAmount.ts","../src/serializable/avax/utxo.ts","../src/signer/signing.ts","../src/constants/public-urls.ts","../src/vms/common/rpc.ts","../src/vms/common/baseApi.ts","../src/vms/common/chainAPI.ts","../src/vms/common/avaxApi.ts","../src/vms/avm/api.ts","../src/utils/builderUtils.ts","../src/utils/sort.ts","../src/utils/transferableAmounts.ts","../src/vms/common/defaultSpendOptions.ts","../src/constants/zeroValue.ts","../src/vms/common/unsignedTx.ts","../src/vms/utils/calculateSpend/calculateSpend.ts","../src/utils/bigintMath.ts","../src/vms/utils/calculateSpend/utils/verifySignaturesMatch.ts","../src/vms/avm/utxoCalculationFns/useAvmAndCorethUTXOs.ts","../src/vms/common/builder.ts","../src/vms/avm/builder.ts","../src/vms/common/evmUnsignedTx.ts","../src/info/info.ts","../src/vms/context/context.ts","../src/vms/evm/api.ts","../src/vms/evm/builder.ts","../src/vms/pvm/utxoCalculationFns/useSpendableLockedUTXOs.ts","../src/vms/pvm/utxoCalculationFns/useUnlockedUTXOs.ts","../src/utils/consolidate.ts","../src/vms/utils/consolidateOutputs.ts","../src/vms/pvm/utxoCalculationFns/useConsolidateOutputs.ts","../src/vms/pvm/api.ts","../src/vms/pvm/builder.ts","../src/signer/addTxSignatures.ts"],"sourcesContent":["/******************************************************************************\r\nCopyright 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Promise.resolve(r.value.v).then(fulfill, reject) : settle(q[0][2], r); }\r\n    function fulfill(value) { resume(\"next\", value); }\r\n    function reject(value) { resume(\"throw\", value); }\r\n    function settle(f, v) { if (f(v), q.shift(), q.length) resume(q[0][0], q[0][1]); }\r\n}\r\n\r\nexport function __asyncDelegator(o) {\r\n    var i, p;\r\n    return i = {}, verb(\"next\"), verb(\"throw\", function (e) { throw e; }), verb(\"return\"), i[Symbol.iterator] = function () { return this; }, i;\r\n    function verb(n, f) { i[n] = o[n] ? function (v) { return (p = !p) ? { value: __await(o[n](v)), done: n === \"return\" } : f ? f(v) : v; } : f; }\r\n}\r\n\r\nexport function __asyncValues(o) {\r\n    if (!Symbol.asyncIterator) throw new TypeError(\"Symbol.asyncIterator is not defined.\");\r\n    var m = o[Symbol.asyncIterator], i;\r\n    return m ? m.call(o) : (o = typeof __values === \"function\" ? __values(o) : o[Symbol.iterator](), i = {}, verb(\"next\"), verb(\"throw\"), verb(\"return\"), i[Symbol.asyncIterator] = function () { return this; }, i);\r\n    function verb(n) { i[n] = o[n] && function (v) { return new Promise(function (resolve, reject) { v = o[n](v), settle(resolve, reject, v.done, v.value); }); }; }\r\n    function settle(resolve, reject, d, v) { Promise.resolve(v).then(function(v) { resolve({ value: v, done: d }); }, reject); }\r\n}\r\n\r\nexport function __makeTemplateObject(cooked, raw) {\r\n    if (Object.defineProperty) { Object.defineProperty(cooked, \"raw\", { value: raw }); } else { cooked.raw = raw; }\r\n    return cooked;\r\n};\r\n\r\nvar __setModuleDefault = Object.create ? (function(o, v) {\r\n    Object.defineProperty(o, \"default\", { enumerable: true, value: v });\r\n}) : function(o, v) {\r\n    o[\"default\"] = v;\r\n};\r\n\r\nexport function __importStar(mod) {\r\n    if (mod && mod.__esModule) return mod;\r\n    var result = {};\r\n    if (mod != null) for (var k in mod) if (k !== \"default\" && Object.prototype.hasOwnProperty.call(mod, k)) __createBinding(result, mod, k);\r\n    __setModuleDefault(result, mod);\r\n    return result;\r\n}\r\n\r\nexport function __importDefault(mod) {\r\n    return (mod && mod.__esModule) ? mod : { default: mod };\r\n}\r\n\r\nexport function __classPrivateFieldGet(receiver, state, kind, f) {\r\n    if (kind === \"a\" && !f) throw new TypeError(\"Private accessor was defined without a getter\");\r\n    if (typeof state === \"function\" ? receiver !== state || !f : !state.has(receiver)) throw new TypeError(\"Cannot read private member from an object whose class did not declare it\");\r\n    return kind === \"m\" ? f : kind === \"a\" ? f.call(receiver) : f ? f.value : state.get(receiver);\r\n}\r\n\r\nexport function __classPrivateFieldSet(receiver, state, value, kind, f) {\r\n    if (kind === \"m\") throw new TypeError(\"Private method is not writable\");\r\n    if (kind === \"a\" && !f) throw new TypeError(\"Private accessor was defined without a setter\");\r\n    if (typeof state === \"function\" ? receiver !== state || !f : !state.has(receiver)) throw new TypeError(\"Cannot write private member to an object whose class did not declare it\");\r\n    return (kind === \"a\" ? f.call(receiver, value) : f ? f.value = value : state.set(receiver, value)), value;\r\n}\r\n\r\nexport function __classPrivateFieldIn(state, receiver) {\r\n    if (receiver === null || (typeof receiver !== \"object\" && typeof receiver !== \"function\")) throw new TypeError(\"Cannot use 'in' operator on non-object\");\r\n    return typeof state === \"function\" ? receiver === state : state.has(receiver);\r\n}\r\n",null,null,"function number(n) {\n    if (!Number.isSafeInteger(n) || n < 0)\n        throw new Error(`Wrong positive integer: ${n}`);\n}\nfunction bool(b) {\n    if (typeof b !== 'boolean')\n        throw new Error(`Expected boolean, not ${b}`);\n}\n// copied from utils\nfunction isBytes(a) {\n    return (a instanceof Uint8Array ||\n        (a != null && typeof a === 'object' && a.constructor.name === 'Uint8Array'));\n}\nfunction bytes(b, ...lengths) {\n    if (!isBytes(b))\n        throw new Error('Expected Uint8Array');\n    if (lengths.length > 0 && !lengths.includes(b.length))\n        throw new Error(`Expected Uint8Array of length ${lengths}, not of length=${b.length}`);\n}\nfunction hash(hash) {\n    if (typeof hash !== 'function' || typeof hash.create !== 'function')\n        throw new Error('Hash should be wrapped by utils.wrapConstructor');\n    number(hash.outputLen);\n    number(hash.blockLen);\n}\nfunction exists(instance, checkFinished = true) {\n    if (instance.destroyed)\n        throw new Error('Hash instance has been destroyed');\n    if (checkFinished && instance.finished)\n        throw new Error('Hash#digest() has already been called');\n}\nfunction output(out, instance) {\n    bytes(out);\n    const min = instance.outputLen;\n    if (out.length < min) {\n        throw new Error(`digestInto() expects output buffer of length at least ${min}`);\n    }\n}\nexport { number, bool, bytes, hash, exists, output };\nconst assert = { number, bool, bytes, hash, exists, output };\nexport default assert;\n//# sourceMappingURL=_assert.js.map","const U32_MASK64 = /* @__PURE__ */ BigInt(2 ** 32 - 1);\nconst _32n = /* @__PURE__ */ BigInt(32);\n// We are not using BigUint64Array, because they are extremely slow as per 2022\nfunction fromBig(n, le = false) {\n    if (le)\n        return { h: Number(n & U32_MASK64), l: Number((n >> _32n) & U32_MASK64) };\n    return { h: Number((n >> _32n) & U32_MASK64) | 0, l: Number(n & U32_MASK64) | 0 };\n}\nfunction split(lst, le = false) {\n    let Ah = new Uint32Array(lst.length);\n    let Al = new Uint32Array(lst.length);\n    for (let i = 0; i < lst.length; i++) {\n        const { h, l } = fromBig(lst[i], le);\n        [Ah[i], Al[i]] = [h, l];\n    }\n    return [Ah, Al];\n}\nconst toBig = (h, l) => (BigInt(h >>> 0) << _32n) | BigInt(l >>> 0);\n// for Shift in [0, 32)\nconst shrSH = (h, _l, s) => h >>> s;\nconst shrSL = (h, l, s) => (h << (32 - s)) | (l >>> s);\n// Right rotate for Shift in [1, 32)\nconst rotrSH = (h, l, s) => (h >>> s) | (l << (32 - s));\nconst rotrSL = (h, l, s) => (h << (32 - s)) | (l >>> s);\n// Right rotate for Shift in (32, 64), NOTE: 32 is special case.\nconst rotrBH = (h, l, s) => (h << (64 - s)) | (l >>> (s - 32));\nconst rotrBL = (h, l, s) => (h >>> (s - 32)) | (l << (64 - s));\n// Right rotate for shift===32 (just swaps l&h)\nconst rotr32H = (_h, l) => l;\nconst rotr32L = (h, _l) => h;\n// Left rotate for Shift in [1, 32)\nconst rotlSH = (h, l, s) => (h << s) | (l >>> (32 - s));\nconst rotlSL = (h, l, s) => (l << s) | (h >>> (32 - s));\n// Left rotate for Shift in (32, 64), NOTE: 32 is special case.\nconst rotlBH = (h, l, s) => (l << (s - 32)) | (h >>> (64 - s));\nconst rotlBL = (h, l, s) => (h << (s - 32)) | (l >>> (64 - s));\n// JS uses 32-bit signed integers for bitwise operations which means we cannot\n// simple take carry out of low bit sum by shift, we need to use division.\nfunction add(Ah, Al, Bh, Bl) {\n    const l = (Al >>> 0) + (Bl >>> 0);\n    return { h: (Ah + Bh + ((l / 2 ** 32) | 0)) | 0, l: l | 0 };\n}\n// Addition with more than 2 elements\nconst add3L = (Al, Bl, Cl) => (Al >>> 0) + (Bl >>> 0) + (Cl >>> 0);\nconst add3H = (low, Ah, Bh, Ch) => (Ah + Bh + Ch + ((low / 2 ** 32) | 0)) | 0;\nconst add4L = (Al, Bl, Cl, Dl) => (Al >>> 0) + (Bl >>> 0) + (Cl >>> 0) + (Dl >>> 0);\nconst add4H = (low, Ah, Bh, Ch, Dh) => (Ah + Bh + Ch + Dh + ((low / 2 ** 32) | 0)) | 0;\nconst add5L = (Al, Bl, Cl, Dl, El) => (Al >>> 0) + (Bl >>> 0) + (Cl >>> 0) + (Dl >>> 0) + (El >>> 0);\nconst add5H = (low, Ah, Bh, Ch, Dh, Eh) => (Ah + Bh + Ch + Dh + Eh + ((low / 2 ** 32) | 0)) | 0;\n// prettier-ignore\nexport { fromBig, split, toBig, shrSH, shrSL, rotrSH, rotrSL, rotrBH, rotrBL, rotr32H, rotr32L, rotlSH, rotlSL, rotlBH, rotlBL, add, add3L, add3H, add4L, add4H, add5H, add5L, };\n// prettier-ignore\nconst u64 = {\n    fromBig, split, toBig,\n    shrSH, shrSL,\n    rotrSH, rotrSL, rotrBH, rotrBL,\n    rotr32H, rotr32L,\n    rotlSH, rotlSL, rotlBH, rotlBL,\n    add, add3L, add3H, add4L, add4H, add5H, add5L,\n};\nexport default u64;\n//# sourceMappingURL=_u64.js.map","/*! noble-hashes - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n// We use WebCrypto aka globalThis.crypto, which exists in browsers and node.js 16+.\n// node.js versions earlier than v19 don't declare it in global scope.\n// For node.js, package.json#exports field mapping rewrites import\n// from `crypto` to `cryptoNode`, which imports native module.\n// Makes the utils un-importable in browsers without a bundler.\n// Once node.js 18 is deprecated (2025-04-30), we can just drop the import.\nimport { crypto } from '@noble/hashes/crypto';\n// Cast array to different type\nexport const u8 = (arr) => new Uint8Array(arr.buffer, arr.byteOffset, arr.byteLength);\nexport const u32 = (arr) => new Uint32Array(arr.buffer, arr.byteOffset, Math.floor(arr.byteLength / 4));\nfunction isBytes(a) {\n    return (a instanceof Uint8Array ||\n        (a != null && typeof a === 'object' && a.constructor.name === 'Uint8Array'));\n}\n// Cast array to view\nexport const createView = (arr) => new DataView(arr.buffer, arr.byteOffset, arr.byteLength);\n// The rotate right (circular right shift) operation for uint32\nexport const rotr = (word, shift) => (word << (32 - shift)) | (word >>> shift);\n// big-endian hardware is rare. Just in case someone still decides to run hashes:\n// early-throw an error because we don't support BE yet.\n// Other libraries would silently corrupt the data instead of throwing an error,\n// when they don't support it.\nexport const isLE = new Uint8Array(new Uint32Array([0x11223344]).buffer)[0] === 0x44;\nif (!isLE)\n    throw new Error('Non little-endian hardware is not supported');\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    if (!isBytes(bytes))\n        throw new Error('Uint8Array expected');\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}\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// There is no setImmediate in browser and setTimeout is slow.\n// call of async fn will return Promise, which will be fullfiled only on\n// next scheduler queue processing step and this is exactly what we need.\nexport const nextTick = async () => { };\n// Returns control to thread each 'tick' ms to avoid blocking\nexport async function asyncLoop(iters, tick, cb) {\n    let ts = Date.now();\n    for (let i = 0; i < iters; i++) {\n        cb(i);\n        // Date.now() is not monotonic, so in case if clock goes backwards we return return control too\n        const diff = Date.now() - ts;\n        if (diff >= 0 && diff < tick)\n            continue;\n        await nextTick();\n        ts += diff;\n    }\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/**\n * Normalizes (non-hex) string or Uint8Array to Uint8Array.\n * Warning: when Uint8Array is passed, it would NOT get copied.\n * Keep in mind for future mutable operations.\n */\nexport function toBytes(data) {\n    if (typeof data === 'string')\n        data = utf8ToBytes(data);\n    if (!isBytes(data))\n        throw new Error(`expected Uint8Array, got ${typeof data}`);\n    return data;\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        if (!isBytes(a))\n            throw new Error('Uint8Array expected');\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// For runtime check if class implements interface\nexport class Hash {\n    // Safe version that clones internal state\n    clone() {\n        return this._cloneInto();\n    }\n}\nconst toStr = {}.toString;\nexport function checkOpts(defaults, opts) {\n    if (opts !== undefined && toStr.call(opts) !== '[object Object]')\n        throw new Error('Options should be object or undefined');\n    const merged = Object.assign(defaults, opts);\n    return merged;\n}\nexport function wrapConstructor(hashCons) {\n    const hashC = (msg) => hashCons().update(toBytes(msg)).digest();\n    const tmp = hashCons();\n    hashC.outputLen = tmp.outputLen;\n    hashC.blockLen = tmp.blockLen;\n    hashC.create = () => hashCons();\n    return hashC;\n}\nexport function wrapConstructorWithOpts(hashCons) {\n    const hashC = (msg, opts) => hashCons(opts).update(toBytes(msg)).digest();\n    const tmp = hashCons({});\n    hashC.outputLen = tmp.outputLen;\n    hashC.blockLen = tmp.blockLen;\n    hashC.create = (opts) => hashCons(opts);\n    return hashC;\n}\nexport function wrapXOFConstructorWithOpts(hashCons) {\n    const hashC = (msg, opts) => hashCons(opts).update(toBytes(msg)).digest();\n    const tmp = hashCons({});\n    hashC.outputLen = tmp.outputLen;\n    hashC.blockLen = tmp.blockLen;\n    hashC.create = (opts) => hashCons(opts);\n    return hashC;\n}\n/**\n * Secure PRNG. Uses `crypto.getRandomValues`, which defers to OS.\n */\nexport function randomBytes(bytesLength = 32) {\n    if (crypto && typeof crypto.getRandomValues === 'function') {\n        return crypto.getRandomValues(new Uint8Array(bytesLength));\n    }\n    throw new Error('crypto.getRandomValues must be defined');\n}\n//# sourceMappingURL=utils.js.map","import { bytes, exists, number, output } from './_assert.js';\nimport { rotlBH, rotlBL, rotlSH, rotlSL, split } from './_u64.js';\nimport { Hash, u32, toBytes, wrapConstructor, wrapXOFConstructorWithOpts, } from './utils.js';\n// SHA3 (keccak) is based on a new design: basically, the internal state is bigger than output size.\n// It's called a sponge function.\n// Various per round constants calculations\nconst [SHA3_PI, SHA3_ROTL, _SHA3_IOTA] = [[], [], []];\nconst _0n = /* @__PURE__ */ BigInt(0);\nconst _1n = /* @__PURE__ */ BigInt(1);\nconst _2n = /* @__PURE__ */ BigInt(2);\nconst _7n = /* @__PURE__ */ BigInt(7);\nconst _256n = /* @__PURE__ */ BigInt(256);\nconst _0x71n = /* @__PURE__ */ BigInt(0x71);\nfor (let round = 0, R = _1n, x = 1, y = 0; round < 24; round++) {\n    // Pi\n    [x, y] = [y, (2 * x + 3 * y) % 5];\n    SHA3_PI.push(2 * (5 * y + x));\n    // Rotational\n    SHA3_ROTL.push((((round + 1) * (round + 2)) / 2) % 64);\n    // Iota\n    let t = _0n;\n    for (let j = 0; j < 7; j++) {\n        R = ((R << _1n) ^ ((R >> _7n) * _0x71n)) % _256n;\n        if (R & _2n)\n            t ^= _1n << ((_1n << /* @__PURE__ */ BigInt(j)) - _1n);\n    }\n    _SHA3_IOTA.push(t);\n}\nconst [SHA3_IOTA_H, SHA3_IOTA_L] = /* @__PURE__ */ split(_SHA3_IOTA, true);\n// Left rotation (without 0, 32, 64)\nconst rotlH = (h, l, s) => (s > 32 ? rotlBH(h, l, s) : rotlSH(h, l, s));\nconst rotlL = (h, l, s) => (s > 32 ? rotlBL(h, l, s) : rotlSL(h, l, s));\n// Same as keccakf1600, but allows to skip some rounds\nexport function keccakP(s, rounds = 24) {\n    const B = new Uint32Array(5 * 2);\n    // NOTE: all indices are x2 since we store state as u32 instead of u64 (bigints to slow in js)\n    for (let round = 24 - rounds; round < 24; round++) {\n        // Theta θ\n        for (let x = 0; x < 10; x++)\n            B[x] = s[x] ^ s[x + 10] ^ s[x + 20] ^ s[x + 30] ^ s[x + 40];\n        for (let x = 0; x < 10; x += 2) {\n            const idx1 = (x + 8) % 10;\n            const idx0 = (x + 2) % 10;\n            const B0 = B[idx0];\n            const B1 = B[idx0 + 1];\n            const Th = rotlH(B0, B1, 1) ^ B[idx1];\n            const Tl = rotlL(B0, B1, 1) ^ B[idx1 + 1];\n            for (let y = 0; y < 50; y += 10) {\n                s[x + y] ^= Th;\n                s[x + y + 1] ^= Tl;\n            }\n        }\n        // Rho (ρ) and Pi (π)\n        let curH = s[2];\n        let curL = s[3];\n        for (let t = 0; t < 24; t++) {\n            const shift = SHA3_ROTL[t];\n            const Th = rotlH(curH, curL, shift);\n            const Tl = rotlL(curH, curL, shift);\n            const PI = SHA3_PI[t];\n            curH = s[PI];\n            curL = s[PI + 1];\n            s[PI] = Th;\n            s[PI + 1] = Tl;\n        }\n        // Chi (χ)\n        for (let y = 0; y < 50; y += 10) {\n            for (let x = 0; x < 10; x++)\n                B[x] = s[y + x];\n            for (let x = 0; x < 10; x++)\n                s[y + x] ^= ~B[(x + 2) % 10] & B[(x + 4) % 10];\n        }\n        // Iota (ι)\n        s[0] ^= SHA3_IOTA_H[round];\n        s[1] ^= SHA3_IOTA_L[round];\n    }\n    B.fill(0);\n}\nexport class Keccak extends Hash {\n    // NOTE: we accept arguments in bytes instead of bits here.\n    constructor(blockLen, suffix, outputLen, enableXOF = false, rounds = 24) {\n        super();\n        this.blockLen = blockLen;\n        this.suffix = suffix;\n        this.outputLen = outputLen;\n        this.enableXOF = enableXOF;\n        this.rounds = rounds;\n        this.pos = 0;\n        this.posOut = 0;\n        this.finished = false;\n        this.destroyed = false;\n        // Can be passed from user as dkLen\n        number(outputLen);\n        // 1600 = 5x5 matrix of 64bit.  1600 bits === 200 bytes\n        if (0 >= this.blockLen || this.blockLen >= 200)\n            throw new Error('Sha3 supports only keccak-f1600 function');\n        this.state = new Uint8Array(200);\n        this.state32 = u32(this.state);\n    }\n    keccak() {\n        keccakP(this.state32, this.rounds);\n        this.posOut = 0;\n        this.pos = 0;\n    }\n    update(data) {\n        exists(this);\n        const { blockLen, state } = this;\n        data = toBytes(data);\n        const len = data.length;\n        for (let pos = 0; pos < len;) {\n            const take = Math.min(blockLen - this.pos, len - pos);\n            for (let i = 0; i < take; i++)\n                state[this.pos++] ^= data[pos++];\n            if (this.pos === blockLen)\n                this.keccak();\n        }\n        return this;\n    }\n    finish() {\n        if (this.finished)\n            return;\n        this.finished = true;\n        const { state, suffix, pos, blockLen } = this;\n        // Do the padding\n        state[pos] ^= suffix;\n        if ((suffix & 0x80) !== 0 && pos === blockLen - 1)\n            this.keccak();\n        state[blockLen - 1] ^= 0x80;\n        this.keccak();\n    }\n    writeInto(out) {\n        exists(this, false);\n        bytes(out);\n        this.finish();\n        const bufferOut = this.state;\n        const { blockLen } = this;\n        for (let pos = 0, len = out.length; pos < len;) {\n            if (this.posOut >= blockLen)\n                this.keccak();\n            const take = Math.min(blockLen - this.posOut, len - pos);\n            out.set(bufferOut.subarray(this.posOut, this.posOut + take), pos);\n            this.posOut += take;\n            pos += take;\n        }\n        return out;\n    }\n    xofInto(out) {\n        // Sha3/Keccak usage with XOF is probably mistake, only SHAKE instances can do XOF\n        if (!this.enableXOF)\n            throw new Error('XOF is not possible for this instance');\n        return this.writeInto(out);\n    }\n    xof(bytes) {\n        number(bytes);\n        return this.xofInto(new Uint8Array(bytes));\n    }\n    digestInto(out) {\n        output(out, this);\n        if (this.finished)\n            throw new Error('digest() was already called');\n        this.writeInto(out);\n        this.destroy();\n        return out;\n    }\n    digest() {\n        return this.digestInto(new Uint8Array(this.outputLen));\n    }\n    destroy() {\n        this.destroyed = true;\n        this.state.fill(0);\n    }\n    _cloneInto(to) {\n        const { blockLen, suffix, outputLen, rounds, enableXOF } = this;\n        to || (to = new Keccak(blockLen, suffix, outputLen, enableXOF, rounds));\n        to.state32.set(this.state32);\n        to.pos = this.pos;\n        to.posOut = this.posOut;\n        to.finished = this.finished;\n        to.rounds = rounds;\n        // Suffix can change in cSHAKE\n        to.suffix = suffix;\n        to.outputLen = outputLen;\n        to.enableXOF = enableXOF;\n        to.destroyed = this.destroyed;\n        return to;\n    }\n}\nconst gen = (suffix, blockLen, outputLen) => wrapConstructor(() => new Keccak(blockLen, suffix, outputLen));\nexport const sha3_224 = /* @__PURE__ */ gen(0x06, 144, 224 / 8);\n/**\n * SHA3-256 hash function\n * @param message - that would be hashed\n */\nexport const sha3_256 = /* @__PURE__ */ gen(0x06, 136, 256 / 8);\nexport const sha3_384 = /* @__PURE__ */ gen(0x06, 104, 384 / 8);\nexport const sha3_512 = /* @__PURE__ */ gen(0x06, 72, 512 / 8);\nexport const keccak_224 = /* @__PURE__ */ gen(0x01, 144, 224 / 8);\n/**\n * keccak-256 hash function. Different from SHA3-256.\n * @param message - that would be hashed\n */\nexport const keccak_256 = /* @__PURE__ */ gen(0x01, 136, 256 / 8);\nexport const keccak_384 = /* @__PURE__ */ gen(0x01, 104, 384 / 8);\nexport const keccak_512 = /* @__PURE__ */ gen(0x01, 72, 512 / 8);\nconst genShake = (suffix, blockLen, outputLen) => wrapXOFConstructorWithOpts((opts = {}) => new Keccak(blockLen, suffix, opts.dkLen === undefined ? outputLen : opts.dkLen, true));\nexport const shake128 = /* @__PURE__ */ genShake(0x1f, 168, 128 / 8);\nexport const shake256 = /* @__PURE__ */ genShake(0x1f, 136, 256 / 8);\n//# sourceMappingURL=sha3.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 = BigInt(0);\nconst _1n = BigInt(1);\nconst _2n = BigInt(2);\nexport function isBytes(a) {\n    return (a instanceof Uint8Array ||\n        (a != null && typeof a === 'object' && a.constructor.name === 'Uint8Array'));\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    if (!isBytes(bytes))\n        throw new Error('Uint8Array expected');\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    if (!isBytes(bytes))\n        throw new Error('Uint8Array expected');\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        if (!isBytes(a))\n            throw new Error('Uint8Array expected');\n        sum += a.length;\n    }\n    let res = new Uint8Array(sum);\n    let pad = 0;\n    for (let i = 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 ${typeof str}`);\n    return new Uint8Array(new TextEncoder().encode(str)); // https://bugzil.la/1681809\n}\n// Bit operations\n/**\n * Calculates amount of bits in a bigint.\n * Same as `n.toString(2).length`\n */\nexport function bitLen(n) {\n    let len;\n    for (len = 0; n > _0n; n >>= _1n, len += 1)\n        ;\n    return len;\n}\n/**\n * Gets single bit at position.\n * NOTE: first bit position is 0 (same as arrays)\n * Same as `!!+Array.from(n.toString(2)).reverse()[pos]`\n */\nexport function bitGet(n, pos) {\n    return (n >> BigInt(pos)) & _1n;\n}\n/**\n * Sets single bit at position.\n */\nexport const bitSet = (n, pos, value) => {\n    return n | ((value ? _1n : _0n) << BigInt(pos));\n};\n/**\n * Calculate mask for N bits. Not using ** operator with bigints because of old engines.\n * Same as BigInt(`0b${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//# sourceMappingURL=utils.js.map","/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n// Utilities for modular arithmetics and finite fields\nimport { bitMask, numberToBytesBE, numberToBytesLE, bytesToNumberBE, bytesToNumberLE, ensureBytes, 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}\n// This function returns True whenever the value x is a square in the field F.\nexport function FpIsSquare(f) {\n    const legendreConst = (f.ORDER - _1n) / _2n; // Integer arithmetic\n    return (x) => {\n        const p = f.pow(x, legendreConst);\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 * @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 } from './utils.js';\nconst _0n = BigInt(0);\nconst _1n = BigInt(1);\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 opts = (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, precomputesMap, n, transform) {\n            // @ts-ignore\n            const W = P._WINDOW_SIZE || 1;\n            // Calculate precomputes on a first run, reuse them after\n            let comp = precomputesMap.get(P);\n            if (!comp) {\n                comp = this.precomputeWindow(P, W);\n                if (W !== 1) {\n                    precomputesMap.set(P, transform(comp));\n                }\n            }\n            return this.wNAF(W, comp, n);\n        },\n    };\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 * as mod from './modular.js';\nimport * as ut from './utils.js';\nimport { ensureBytes } from './utils.js';\nimport { wNAF, validateBasic } from './curve.js';\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}\n// ASN.1 DER encoding utilities\nconst { bytesToNumberBE: b2n, hexToBytes: h2b } = ut;\nexport const DER = {\n    // asn.1 DER encoding utils\n    Err: class DERErr extends Error {\n        constructor(m = '') {\n            super(m);\n        }\n    },\n    _parseInt(data) {\n        const { Err: E } = DER;\n        if (data.length < 2 || data[0] !== 0x02)\n            throw new E('Invalid signature integer tag');\n        const len = data[1];\n        const res = data.subarray(2, len + 2);\n        if (!len || res.length !== len)\n            throw new E('Invalid signature integer: wrong length');\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        if (res[0] & 0b10000000)\n            throw new E('Invalid signature integer: negative');\n        if (res[0] === 0x00 && !(res[1] & 0b10000000))\n            throw new E('Invalid signature integer: unnecessary leading zero');\n        return { d: b2n(res), l: data.subarray(len + 2) }; // d is data, l is left\n    },\n    toSig(hex) {\n        // parse DER signature\n        const { Err: E } = DER;\n        const data = typeof hex === 'string' ? h2b(hex) : hex;\n        if (!ut.isBytes(data))\n            throw new Error('ui8a expected');\n        let l = data.length;\n        if (l < 2 || data[0] != 0x30)\n            throw new E('Invalid signature tag');\n        if (data[1] !== l - 2)\n            throw new E('Invalid signature: incorrect length');\n        const { d: r, l: sBytes } = DER._parseInt(data.subarray(2));\n        const { d: s, l: rBytesLeft } = DER._parseInt(sBytes);\n        if (rBytesLeft.length)\n            throw new E('Invalid signature: left bytes after parsing');\n        return { r, s };\n    },\n    hexFromSig(sig) {\n        // Add leading zero if first byte has negative bit enabled. More details in '_parseInt'\n        const slice = (s) => (Number.parseInt(s[0], 16) & 0b1000 ? '00' + s : s);\n        const h = (num) => {\n            const hex = num.toString(16);\n            return hex.length & 1 ? `0${hex}` : hex;\n        };\n        const s = slice(h(sig.s));\n        const r = slice(h(sig.r));\n        const shl = s.length / 2;\n        const rhl = r.length / 2;\n        const sl = h(shl);\n        const rl = h(rhl);\n        return `30${h(rhl + shl + 4)}02${rl}${r}02${sl}${s}`;\n    },\n};\n// Be friendly to bad ECMAScript parsers by not using bigint literals\n// prettier-ignore\nconst _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3), _4n = BigInt(4);\nexport function weierstrassPoints(opts) {\n    const CURVE = validatePointOpts(opts);\n    const { Fp } = CURVE; // All curves has same field / group length as for now, but they can differ\n    const toBytes = CURVE.toBytes ||\n        ((_c, point, _isCompressed) => {\n            const a = point.toAffine();\n            return ut.concatBytes(Uint8Array.from([0x04]), Fp.toBytes(a.x), Fp.toBytes(a.y));\n        });\n    const fromBytes = CURVE.fromBytes ||\n        ((bytes) => {\n            // const head = bytes[0];\n            const tail = bytes.subarray(1);\n            // if (head !== 0x04) throw new Error('Only non-compressed encoding is supported');\n            const x = Fp.fromBytes(tail.subarray(0, Fp.BYTES));\n            const y = Fp.fromBytes(tail.subarray(Fp.BYTES, 2 * Fp.BYTES));\n            return { x, y };\n        });\n    /**\n     * y² = x³ + ax + b: Short weierstrass curve formula\n     * @returns y²\n     */\n    function weierstrassEquation(x) {\n        const { a, b } = CURVE;\n        const x2 = Fp.sqr(x); // x * x\n        const x3 = Fp.mul(x2, x); // x2 * x\n        return Fp.add(Fp.add(x3, Fp.mul(x, a)), b); // x3 + a * x + b\n    }\n    // Validate whether the passed curve params are valid.\n    // We check if curve equation works for generator point.\n    // `assertValidity()` won't work: `isTorsionFree()` is not available at this point in bls12-381.\n    // ProjectivePoint class has not been initialized yet.\n    if (!Fp.eql(Fp.sqr(CURVE.Gy), weierstrassEquation(CURVE.Gx)))\n        throw new Error('bad generator point: equation left != right');\n    // Valid group elements reside in range 1..n-1\n    function isWithinCurveOrder(num) {\n        return typeof num === 'bigint' && _0n < num && num < CURVE.n;\n    }\n    function assertGE(num) {\n        if (!isWithinCurveOrder(num))\n            throw new Error('Expected valid bigint: 0 < bigint < curve.n');\n    }\n    // Validates if priv key is valid and converts it to bigint.\n    // Supports options allowedPrivateKeyLengths and wrapPrivateKey.\n    function normPrivateKeyToScalar(key) {\n        const { allowedPrivateKeyLengths: lengths, nByteLength, wrapPrivateKey, n } = CURVE;\n        if (lengths && typeof key !== 'bigint') {\n            if (ut.isBytes(key))\n                key = ut.bytesToHex(key);\n            // Normalize to hex string, pad. E.g. P521 would norm 130-132 char hex to 132-char bytes\n            if (typeof key !== 'string' || !lengths.includes(key.length))\n                throw new Error('Invalid key');\n            key = key.padStart(nByteLength * 2, '0');\n        }\n        let num;\n        try {\n            num =\n                typeof key === 'bigint'\n                    ? key\n                    : ut.bytesToNumberBE(ensureBytes('private key', key, nByteLength));\n        }\n        catch (error) {\n            throw new Error(`private key must be ${nByteLength} bytes, hex or bigint, not ${typeof key}`);\n        }\n        if (wrapPrivateKey)\n            num = mod.mod(num, n); // disabled by default, enabled for BLS\n        assertGE(num); // num in range [1..N-1]\n        return num;\n    }\n    const pointPrecomputes = new Map();\n    function assertPrjPoint(other) {\n        if (!(other instanceof Point))\n            throw new Error('ProjectivePoint expected');\n    }\n    /**\n     * Projective Point works in 3d / projective (homogeneous) coordinates: (x, y, z) ∋ (x=x/z, y=y/z)\n     * Default Point works in 2d / affine coordinates: (x, y)\n     * We're doing calculations in projective, because its operations don't require costly inversion.\n     */\n    class Point {\n        constructor(px, py, pz) {\n            this.px = px;\n            this.py = py;\n            this.pz = pz;\n            if (px == null || !Fp.isValid(px))\n                throw new Error('x required');\n            if (py == null || !Fp.isValid(py))\n                throw new Error('y required');\n            if (pz == null || !Fp.isValid(pz))\n                throw new Error('z required');\n        }\n        // Does not validate if the point is on-curve.\n        // Use fromHex instead, or call assertValidity() later.\n        static fromAffine(p) {\n            const { x, y } = p || {};\n            if (!p || !Fp.isValid(x) || !Fp.isValid(y))\n                throw new Error('invalid affine point');\n            if (p instanceof Point)\n                throw new Error('projective point not allowed');\n            const is0 = (i) => Fp.eql(i, Fp.ZERO);\n            // fromAffine(x:0, y:0) would produce (x:0, y:0, z:1), but we need (x:0, y:1, z:0)\n            if (is0(x) && is0(y))\n                return Point.ZERO;\n            return new Point(x, y, Fp.ONE);\n        }\n        get x() {\n            return this.toAffine().x;\n        }\n        get y() {\n            return this.toAffine().y;\n        }\n        /**\n         * Takes a bunch of Projective Points but executes only one\n         * inversion on all of them. Inversion is very slow operation,\n         * so this improves performance massively.\n         * Optimization: converts a list of projective points to a list of identical points with Z=1.\n         */\n        static normalizeZ(points) {\n            const toInv = Fp.invertBatch(points.map((p) => p.pz));\n            return points.map((p, i) => p.toAffine(toInv[i])).map(Point.fromAffine);\n        }\n        /**\n         * Converts hash string or Uint8Array to Point.\n         * @param hex short/long ECDSA hex\n         */\n        static fromHex(hex) {\n            const P = Point.fromAffine(fromBytes(ensureBytes('pointHex', hex)));\n            P.assertValidity();\n            return P;\n        }\n        // Multiplies generator point by privateKey.\n        static fromPrivateKey(privateKey) {\n            return Point.BASE.multiply(normPrivateKeyToScalar(privateKey));\n        }\n        // \"Private method\", don't use it directly\n        _setWindowSize(windowSize) {\n            this._WINDOW_SIZE = windowSize;\n            pointPrecomputes.delete(this);\n        }\n        // A point on curve is valid if it conforms to equation.\n        assertValidity() {\n            if (this.is0()) {\n                // (0, 1, 0) aka ZERO is invalid in most contexts.\n                // In BLS, ZERO can be serialized, so we allow it.\n                // (0, 0, 0) is wrong representation of ZERO and is always invalid.\n                if (CURVE.allowInfinityPoint && !Fp.is0(this.py))\n                    return;\n                throw new Error('bad point: ZERO');\n            }\n            // Some 3rd-party test vectors require different wording between here & `fromCompressedHex`\n            const { x, y } = this.toAffine();\n            // Check if x, y are valid field elements\n            if (!Fp.isValid(x) || !Fp.isValid(y))\n                throw new Error('bad point: x or y not FE');\n            const left = Fp.sqr(y); // y²\n            const right = weierstrassEquation(x); // x³ + ax + b\n            if (!Fp.eql(left, right))\n                throw new Error('bad point: equation left != right');\n            if (!this.isTorsionFree())\n                throw new Error('bad point: not in prime-order subgroup');\n        }\n        hasEvenY() {\n            const { y } = this.toAffine();\n            if (Fp.isOdd)\n                return !Fp.isOdd(y);\n            throw new Error(\"Field doesn't support isOdd\");\n        }\n        /**\n         * Compare one point to another.\n         */\n        equals(other) {\n            assertPrjPoint(other);\n            const { px: X1, py: Y1, pz: Z1 } = this;\n            const { px: X2, py: Y2, pz: Z2 } = other;\n            const U1 = Fp.eql(Fp.mul(X1, Z2), Fp.mul(X2, Z1));\n            const U2 = Fp.eql(Fp.mul(Y1, Z2), Fp.mul(Y2, Z1));\n            return U1 && U2;\n        }\n        /**\n         * Flips point to one corresponding to (x, -y) in Affine coordinates.\n         */\n        negate() {\n            return new Point(this.px, Fp.neg(this.py), this.pz);\n        }\n        // Renes-Costello-Batina exception-free doubling formula.\n        // There is 30% faster Jacobian formula, but it is not complete.\n        // https://eprint.iacr.org/2015/1060, algorithm 3\n        // Cost: 8M + 3S + 3*a + 2*b3 + 15add.\n        double() {\n            const { a, b } = CURVE;\n            const b3 = Fp.mul(b, _3n);\n            const { px: X1, py: Y1, pz: Z1 } = this;\n            let X3 = Fp.ZERO, Y3 = Fp.ZERO, Z3 = Fp.ZERO; // prettier-ignore\n            let t0 = Fp.mul(X1, X1); // step 1\n            let t1 = Fp.mul(Y1, Y1);\n            let t2 = Fp.mul(Z1, Z1);\n            let t3 = Fp.mul(X1, Y1);\n            t3 = Fp.add(t3, t3); // step 5\n            Z3 = Fp.mul(X1, Z1);\n            Z3 = Fp.add(Z3, Z3);\n            X3 = Fp.mul(a, Z3);\n            Y3 = Fp.mul(b3, t2);\n            Y3 = Fp.add(X3, Y3); // step 10\n            X3 = Fp.sub(t1, Y3);\n            Y3 = Fp.add(t1, Y3);\n            Y3 = Fp.mul(X3, Y3);\n            X3 = Fp.mul(t3, X3);\n            Z3 = Fp.mul(b3, Z3); // step 15\n            t2 = Fp.mul(a, t2);\n            t3 = Fp.sub(t0, t2);\n            t3 = Fp.mul(a, t3);\n            t3 = Fp.add(t3, Z3);\n            Z3 = Fp.add(t0, t0); // step 20\n            t0 = Fp.add(Z3, t0);\n            t0 = Fp.add(t0, t2);\n            t0 = Fp.mul(t0, t3);\n            Y3 = Fp.add(Y3, t0);\n            t2 = Fp.mul(Y1, Z1); // step 25\n            t2 = Fp.add(t2, t2);\n            t0 = Fp.mul(t2, t3);\n            X3 = Fp.sub(X3, t0);\n            Z3 = Fp.mul(t2, t1);\n            Z3 = Fp.add(Z3, Z3); // step 30\n            Z3 = Fp.add(Z3, Z3);\n            return new Point(X3, Y3, Z3);\n        }\n        // Renes-Costello-Batina exception-free addition formula.\n        // There is 30% faster Jacobian formula, but it is not complete.\n        // https://eprint.iacr.org/2015/1060, algorithm 1\n        // Cost: 12M + 0S + 3*a + 3*b3 + 23add.\n        add(other) {\n            assertPrjPoint(other);\n            const { px: X1, py: Y1, pz: Z1 } = this;\n            const { px: X2, py: Y2, pz: Z2 } = other;\n            let X3 = Fp.ZERO, Y3 = Fp.ZERO, Z3 = Fp.ZERO; // prettier-ignore\n            const a = CURVE.a;\n            const b3 = Fp.mul(CURVE.b, _3n);\n            let t0 = Fp.mul(X1, X2); // step 1\n            let t1 = Fp.mul(Y1, Y2);\n            let t2 = Fp.mul(Z1, Z2);\n            let t3 = Fp.add(X1, Y1);\n            let t4 = Fp.add(X2, Y2); // step 5\n            t3 = Fp.mul(t3, t4);\n            t4 = Fp.add(t0, t1);\n            t3 = Fp.sub(t3, t4);\n            t4 = Fp.add(X1, Z1);\n            let t5 = Fp.add(X2, Z2); // step 10\n            t4 = Fp.mul(t4, t5);\n            t5 = Fp.add(t0, t2);\n            t4 = Fp.sub(t4, t5);\n            t5 = Fp.add(Y1, Z1);\n            X3 = Fp.add(Y2, Z2); // step 15\n            t5 = Fp.mul(t5, X3);\n            X3 = Fp.add(t1, t2);\n            t5 = Fp.sub(t5, X3);\n            Z3 = Fp.mul(a, t4);\n            X3 = Fp.mul(b3, t2); // step 20\n            Z3 = Fp.add(X3, Z3);\n            X3 = Fp.sub(t1, Z3);\n            Z3 = Fp.add(t1, Z3);\n            Y3 = Fp.mul(X3, Z3);\n            t1 = Fp.add(t0, t0); // step 25\n            t1 = Fp.add(t1, t0);\n            t2 = Fp.mul(a, t2);\n            t4 = Fp.mul(b3, t4);\n            t1 = Fp.add(t1, t2);\n            t2 = Fp.sub(t0, t2); // step 30\n            t2 = Fp.mul(a, t2);\n            t4 = Fp.add(t4, t2);\n            t0 = Fp.mul(t1, t4);\n            Y3 = Fp.add(Y3, t0);\n            t0 = Fp.mul(t5, t4); // step 35\n            X3 = Fp.mul(t3, X3);\n            X3 = Fp.sub(X3, t0);\n            t0 = Fp.mul(t3, t1);\n            Z3 = Fp.mul(t5, Z3);\n            Z3 = Fp.add(Z3, t0); // step 40\n            return new Point(X3, Y3, Z3);\n        }\n        subtract(other) {\n            return this.add(other.negate());\n        }\n        is0() {\n            return this.equals(Point.ZERO);\n        }\n        wNAF(n) {\n            return wnaf.wNAFCached(this, pointPrecomputes, n, (comp) => {\n                const toInv = Fp.invertBatch(comp.map((p) => p.pz));\n                return comp.map((p, i) => p.toAffine(toInv[i])).map(Point.fromAffine);\n            });\n        }\n        /**\n         * Non-constant-time multiplication. Uses double-and-add algorithm.\n         * It's faster, but should only be used when you don't care about\n         * an exposed private key e.g. sig verification, which works over *public* keys.\n         */\n        multiplyUnsafe(n) {\n            const I = Point.ZERO;\n            if (n === _0n)\n                return I;\n            assertGE(n); // Will throw on 0\n            if (n === _1n)\n                return this;\n            const { endo } = CURVE;\n            if (!endo)\n                return wnaf.unsafeLadder(this, n);\n            // Apply endomorphism\n            let { k1neg, k1, k2neg, k2 } = endo.splitScalar(n);\n            let k1p = I;\n            let k2p = I;\n            let d = this;\n            while (k1 > _0n || k2 > _0n) {\n                if (k1 & _1n)\n                    k1p = k1p.add(d);\n                if (k2 & _1n)\n                    k2p = k2p.add(d);\n                d = d.double();\n                k1 >>= _1n;\n                k2 >>= _1n;\n            }\n            if (k1neg)\n                k1p = k1p.negate();\n            if (k2neg)\n                k2p = k2p.negate();\n            k2p = new Point(Fp.mul(k2p.px, endo.beta), k2p.py, k2p.pz);\n            return k1p.add(k2p);\n        }\n        /**\n         * Constant time multiplication.\n         * Uses wNAF method. Windowed method may be 10% faster,\n         * but takes 2x longer to generate and consumes 2x memory.\n         * Uses precomputes when available.\n         * Uses endomorphism for Koblitz curves.\n         * @param scalar by which the point would be multiplied\n         * @returns New point\n         */\n        multiply(scalar) {\n            assertGE(scalar);\n            let n = scalar;\n            let point, fake; // Fake point is used to const-time mult\n            const { endo } = CURVE;\n            if (endo) {\n                const { k1neg, k1, k2neg, k2 } = endo.splitScalar(n);\n                let { p: k1p, f: f1p } = this.wNAF(k1);\n                let { p: k2p, f: f2p } = this.wNAF(k2);\n                k1p = wnaf.constTimeNegate(k1neg, k1p);\n                k2p = wnaf.constTimeNegate(k2neg, k2p);\n                k2p = new Point(Fp.mul(k2p.px, endo.beta), k2p.py, k2p.pz);\n                point = k1p.add(k2p);\n                fake = f1p.add(f2p);\n            }\n            else {\n                const { p, f } = this.wNAF(n);\n                point = p;\n                fake = f;\n            }\n            // Normalize `z` for both points, but return only real one\n            return Point.normalizeZ([point, fake])[0];\n        }\n        /**\n         * Efficiently calculate `aP + bQ`. Unsafe, can expose private key, if used incorrectly.\n         * Not using Strauss-Shamir trick: precomputation tables are faster.\n         * The trick could be useful if both P and Q are not G (not in our case).\n         * @returns non-zero affine point\n         */\n        multiplyAndAddUnsafe(Q, a, b) {\n            const G = Point.BASE; // No Strauss-Shamir trick: we have 10% faster G precomputes\n            const mul = (P, a // Select faster multiply() method\n            ) => (a === _0n || a === _1n || !P.equals(G) ? P.multiplyUnsafe(a) : P.multiply(a));\n            const sum = mul(this, a).add(mul(Q, b));\n            return sum.is0() ? undefined : sum;\n        }\n        // Converts Projective point to affine (x, y) coordinates.\n        // Can accept precomputed Z^-1 - for example, from invertBatch.\n        // (x, y, z) ∋ (x=x/z, y=y/z)\n        toAffine(iz) {\n            const { px: x, py: y, pz: z } = this;\n            const is0 = this.is0();\n            // If invZ was 0, we return zero point. However we still want to execute\n            // all operations, so we replace invZ with a random number, 1.\n            if (iz == null)\n                iz = is0 ? Fp.ONE : Fp.inv(z);\n            const ax = Fp.mul(x, iz);\n            const ay = Fp.mul(y, iz);\n            const zz = Fp.mul(z, iz);\n            if (is0)\n                return { x: Fp.ZERO, y: Fp.ZERO };\n            if (!Fp.eql(zz, Fp.ONE))\n                throw new Error('invZ was invalid');\n            return { x: ax, y: ay };\n        }\n        isTorsionFree() {\n            const { h: cofactor, isTorsionFree } = CURVE;\n            if (cofactor === _1n)\n                return true; // No subgroups, always torsion-free\n            if (isTorsionFree)\n                return isTorsionFree(Point, this);\n            throw new Error('isTorsionFree() has not been declared for the elliptic curve');\n        }\n        clearCofactor() {\n            const { h: cofactor, clearCofactor } = CURVE;\n            if (cofactor === _1n)\n                return this; // Fast-path\n            if (clearCofactor)\n                return clearCofactor(Point, this);\n            return this.multiplyUnsafe(CURVE.h);\n        }\n        toRawBytes(isCompressed = true) {\n            this.assertValidity();\n            return toBytes(Point, this, isCompressed);\n        }\n        toHex(isCompressed = true) {\n            return ut.bytesToHex(this.toRawBytes(isCompressed));\n        }\n    }\n    Point.BASE = new Point(CURVE.Gx, CURVE.Gy, Fp.ONE);\n    Point.ZERO = new Point(Fp.ZERO, Fp.ONE, Fp.ZERO);\n    const _bits = CURVE.nBitLength;\n    const wnaf = wNAF(Point, CURVE.endo ? Math.ceil(_bits / 2) : _bits);\n    // Validate if generator point is on curve\n    return {\n        CURVE,\n        ProjectivePoint: Point,\n        normPrivateKeyToScalar,\n        weierstrassEquation,\n        isWithinCurveOrder,\n    };\n}\nfunction validateOpts(curve) {\n    const opts = validateBasic(curve);\n    ut.validateObject(opts, {\n        hash: 'hash',\n        hmac: 'function',\n        randomBytes: 'function',\n    }, {\n        bits2int: 'function',\n        bits2int_modN: 'function',\n        lowS: 'boolean',\n    });\n    return Object.freeze({ lowS: true, ...opts });\n}\nexport function weierstrass(curveDef) {\n    const CURVE = validateOpts(curveDef);\n    const { Fp, n: CURVE_ORDER } = CURVE;\n    const compressedLen = Fp.BYTES + 1; // e.g. 33 for 32\n    const uncompressedLen = 2 * Fp.BYTES + 1; // e.g. 65 for 32\n    function isValidFieldElement(num) {\n        return _0n < num && num < Fp.ORDER; // 0 is banned since it's not invertible FE\n    }\n    function modN(a) {\n        return mod.mod(a, CURVE_ORDER);\n    }\n    function invN(a) {\n        return mod.invert(a, CURVE_ORDER);\n    }\n    const { ProjectivePoint: Point, normPrivateKeyToScalar, weierstrassEquation, isWithinCurveOrder, } = weierstrassPoints({\n        ...CURVE,\n        toBytes(_c, point, isCompressed) {\n            const a = point.toAffine();\n            const x = Fp.toBytes(a.x);\n            const cat = ut.concatBytes;\n            if (isCompressed) {\n                return cat(Uint8Array.from([point.hasEvenY() ? 0x02 : 0x03]), x);\n            }\n            else {\n                return cat(Uint8Array.from([0x04]), x, Fp.toBytes(a.y));\n            }\n        },\n        fromBytes(bytes) {\n            const len = bytes.length;\n            const head = bytes[0];\n            const tail = bytes.subarray(1);\n            // this.assertValidity() is done inside of fromHex\n            if (len === compressedLen && (head === 0x02 || head === 0x03)) {\n                const x = ut.bytesToNumberBE(tail);\n                if (!isValidFieldElement(x))\n                    throw new Error('Point is not on curve');\n                const y2 = weierstrassEquation(x); // y² = x³ + ax + b\n                let y = Fp.sqrt(y2); // y = y² ^ (p+1)/4\n                const isYOdd = (y & _1n) === _1n;\n                // ECDSA\n                const isHeadOdd = (head & 1) === 1;\n                if (isHeadOdd !== isYOdd)\n                    y = Fp.neg(y);\n                return { x, y };\n            }\n            else if (len === uncompressedLen && head === 0x04) {\n                const x = Fp.fromBytes(tail.subarray(0, Fp.BYTES));\n                const y = Fp.fromBytes(tail.subarray(Fp.BYTES, 2 * Fp.BYTES));\n                return { x, y };\n            }\n            else {\n                throw new Error(`Point of length ${len} was invalid. Expected ${compressedLen} compressed bytes or ${uncompressedLen} uncompressed bytes`);\n            }\n        },\n    });\n    const numToNByteStr = (num) => ut.bytesToHex(ut.numberToBytesBE(num, CURVE.nByteLength));\n    function isBiggerThanHalfOrder(number) {\n        const HALF = CURVE_ORDER >> _1n;\n        return number > HALF;\n    }\n    function normalizeS(s) {\n        return isBiggerThanHalfOrder(s) ? modN(-s) : s;\n    }\n    // slice bytes num\n    const slcNum = (b, from, to) => ut.bytesToNumberBE(b.slice(from, to));\n    /**\n     * ECDSA signature with its (r, s) properties. Supports DER & compact representations.\n     */\n    class Signature {\n        constructor(r, s, recovery) {\n            this.r = r;\n            this.s = s;\n            this.recovery = recovery;\n            this.assertValidity();\n        }\n        // pair (bytes of r, bytes of s)\n        static fromCompact(hex) {\n            const l = CURVE.nByteLength;\n            hex = ensureBytes('compactSignature', hex, l * 2);\n            return new Signature(slcNum(hex, 0, l), slcNum(hex, l, 2 * l));\n        }\n        // DER encoded ECDSA signature\n        // https://bitcoin.stackexchange.com/questions/57644/what-are-the-parts-of-a-bitcoin-transaction-input-script\n        static fromDER(hex) {\n            const { r, s } = DER.toSig(ensureBytes('DER', hex));\n            return new Signature(r, s);\n        }\n        assertValidity() {\n            // can use assertGE here\n            if (!isWithinCurveOrder(this.r))\n                throw new Error('r must be 0 < r < CURVE.n');\n            if (!isWithinCurveOrder(this.s))\n                throw new Error('s must be 0 < s < CURVE.n');\n        }\n        addRecoveryBit(recovery) {\n            return new Signature(this.r, this.s, recovery);\n        }\n        recoverPublicKey(msgHash) {\n            const { r, s, recovery: rec } = this;\n            const h = bits2int_modN(ensureBytes('msgHash', msgHash)); // Truncate hash\n            if (rec == null || ![0, 1, 2, 3].includes(rec))\n                throw new Error('recovery id invalid');\n            const radj = rec === 2 || rec === 3 ? r + CURVE.n : r;\n            if (radj >= Fp.ORDER)\n                throw new Error('recovery id 2 or 3 invalid');\n            const prefix = (rec & 1) === 0 ? '02' : '03';\n            const R = Point.fromHex(prefix + numToNByteStr(radj));\n            const ir = invN(radj); // r^-1\n            const u1 = modN(-h * ir); // -hr^-1\n            const u2 = modN(s * ir); // sr^-1\n            const Q = Point.BASE.multiplyAndAddUnsafe(R, u1, u2); // (sr^-1)R-(hr^-1)G = -(hr^-1)G + (sr^-1)\n            if (!Q)\n                throw new Error('point at infinify'); // unsafe is fine: no priv data leaked\n            Q.assertValidity();\n            return Q;\n        }\n        // Signatures should be low-s, to prevent malleability.\n        hasHighS() {\n            return isBiggerThanHalfOrder(this.s);\n        }\n        normalizeS() {\n            return this.hasHighS() ? new Signature(this.r, modN(-this.s), this.recovery) : this;\n        }\n        // DER-encoded\n        toDERRawBytes() {\n            return ut.hexToBytes(this.toDERHex());\n        }\n        toDERHex() {\n            return DER.hexFromSig({ r: this.r, s: this.s });\n        }\n        // padded bytes of r, then padded bytes of s\n        toCompactRawBytes() {\n            return ut.hexToBytes(this.toCompactHex());\n        }\n        toCompactHex() {\n            return numToNByteStr(this.r) + numToNByteStr(this.s);\n        }\n    }\n    const utils = {\n        isValidPrivateKey(privateKey) {\n            try {\n                normPrivateKeyToScalar(privateKey);\n                return true;\n            }\n            catch (error) {\n                return false;\n            }\n        },\n        normPrivateKeyToScalar: normPrivateKeyToScalar,\n        /**\n         * Produces cryptographically secure private key from random of size\n         * (groupLen + ceil(groupLen / 2)) with modulo bias being negligible.\n         */\n        randomPrivateKey: () => {\n            const length = mod.getMinHashLength(CURVE.n);\n            return mod.mapHashToField(CURVE.randomBytes(length), CURVE.n);\n        },\n        /**\n         * Creates precompute table for an arbitrary EC point. Makes point \"cached\".\n         * Allows to massively speed-up `point.multiply(scalar)`.\n         * @returns cached point\n         * @example\n         * const fast = utils.precompute(8, ProjectivePoint.fromHex(someonesPubKey));\n         * fast.multiply(privKey); // much faster ECDH now\n         */\n        precompute(windowSize = 8, point = Point.BASE) {\n            point._setWindowSize(windowSize);\n            point.multiply(BigInt(3)); // 3 is arbitrary, just need any number here\n            return point;\n        },\n    };\n    /**\n     * Computes public key for a private key. Checks for validity of the private key.\n     * @param privateKey private key\n     * @param isCompressed whether to return compact (default), or full key\n     * @returns Public key, full when isCompressed=false; short when isCompressed=true\n     */\n    function getPublicKey(privateKey, isCompressed = true) {\n        return Point.fromPrivateKey(privateKey).toRawBytes(isCompressed);\n    }\n    /**\n     * Quick and dirty check for item being public key. Does not validate hex, or being on-curve.\n     */\n    function isProbPub(item) {\n        const arr = ut.isBytes(item);\n        const str = typeof item === 'string';\n        const len = (arr || str) && item.length;\n        if (arr)\n            return len === compressedLen || len === uncompressedLen;\n        if (str)\n            return len === 2 * compressedLen || len === 2 * uncompressedLen;\n        if (item instanceof Point)\n            return true;\n        return false;\n    }\n    /**\n     * ECDH (Elliptic Curve Diffie Hellman).\n     * Computes shared public key from private key and public key.\n     * Checks: 1) private key validity 2) shared key is on-curve.\n     * Does NOT hash the result.\n     * @param privateA private key\n     * @param publicB different public key\n     * @param isCompressed whether to return compact (default), or full key\n     * @returns shared public key\n     */\n    function getSharedSecret(privateA, publicB, isCompressed = true) {\n        if (isProbPub(privateA))\n            throw new Error('first arg must be private key');\n        if (!isProbPub(publicB))\n            throw new Error('second arg must be public key');\n        const b = Point.fromHex(publicB); // check for being on-curve\n        return b.multiply(normPrivateKeyToScalar(privateA)).toRawBytes(isCompressed);\n    }\n    // RFC6979: ensure ECDSA msg is X bytes and < N. RFC suggests optional truncating via bits2octets.\n    // FIPS 186-4 4.6 suggests the leftmost min(nBitLen, outLen) bits, which matches bits2int.\n    // bits2int can produce res>N, we can do mod(res, N) since the bitLen is the same.\n    // int2octets can't be used; pads small msgs with 0: unacceptatble for trunc as per RFC vectors\n    const bits2int = CURVE.bits2int ||\n        function (bytes) {\n            // For curves with nBitLength % 8 !== 0: bits2octets(bits2octets(m)) !== bits2octets(m)\n            // for some cases, since bytes.length * 8 is not actual bitLength.\n            const num = ut.bytesToNumberBE(bytes); // check for == u8 done here\n            const delta = bytes.length * 8 - CURVE.nBitLength; // truncate to nBitLength leftmost bits\n            return delta > 0 ? num >> BigInt(delta) : num;\n        };\n    const bits2int_modN = CURVE.bits2int_modN ||\n        function (bytes) {\n            return modN(bits2int(bytes)); // can't use bytesToNumberBE here\n        };\n    // NOTE: pads output with zero as per spec\n    const ORDER_MASK = ut.bitMask(CURVE.nBitLength);\n    /**\n     * Converts to bytes. Checks if num in `[0..ORDER_MASK-1]` e.g.: `[0..2^256-1]`.\n     */\n    function int2octets(num) {\n        if (typeof num !== 'bigint')\n            throw new Error('bigint expected');\n        if (!(_0n <= num && num < ORDER_MASK))\n            throw new Error(`bigint expected < 2^${CURVE.nBitLength}`);\n        // works with order, can have different size than numToField!\n        return ut.numberToBytesBE(num, CURVE.nByteLength);\n    }\n    // Steps A, D of RFC6979 3.2\n    // Creates RFC6979 seed; converts msg/privKey to numbers.\n    // Used only in sign, not in verify.\n    // NOTE: we cannot assume here that msgHash has same amount of bytes as curve order, this will be wrong at least for P521.\n    // Also it can be bigger for P224 + SHA256\n    function prepSig(msgHash, privateKey, opts = defaultSigOpts) {\n        if (['recovered', 'canonical'].some((k) => k in opts))\n            throw new Error('sign() legacy options not supported');\n        const { hash, randomBytes } = CURVE;\n        let { lowS, prehash, extraEntropy: ent } = opts; // generates low-s sigs by default\n        if (lowS == null)\n            lowS = true; // RFC6979 3.2: we skip step A, because we already provide hash\n        msgHash = ensureBytes('msgHash', msgHash);\n        if (prehash)\n            msgHash = ensureBytes('prehashed msgHash', hash(msgHash));\n        // We can't later call bits2octets, since nested bits2int is broken for curves\n        // with nBitLength % 8 !== 0. Because of that, we unwrap it here as int2octets call.\n        // const bits2octets = (bits) => int2octets(bits2int_modN(bits))\n        const h1int = bits2int_modN(msgHash);\n        const d = normPrivateKeyToScalar(privateKey); // validate private key, convert to bigint\n        const seedArgs = [int2octets(d), int2octets(h1int)];\n        // extraEntropy. RFC6979 3.6: additional k' (optional).\n        if (ent != null) {\n            // K = HMAC_K(V || 0x00 || int2octets(x) || bits2octets(h1) || k')\n            const e = ent === true ? randomBytes(Fp.BYTES) : ent; // generate random bytes OR pass as-is\n            seedArgs.push(ensureBytes('extraEntropy', e)); // check for being bytes\n        }\n        const seed = ut.concatBytes(...seedArgs); // Step D of RFC6979 3.2\n        const m = h1int; // NOTE: no need to call bits2int second time here, it is inside truncateHash!\n        // Converts signature params into point w r/s, checks result for validity.\n        function k2sig(kBytes) {\n            // RFC 6979 Section 3.2, step 3: k = bits2int(T)\n            const k = bits2int(kBytes); // Cannot use fields methods, since it is group element\n            if (!isWithinCurveOrder(k))\n                return; // Important: all mod() calls here must be done over N\n            const ik = invN(k); // k^-1 mod n\n            const q = Point.BASE.multiply(k).toAffine(); // q = Gk\n            const r = modN(q.x); // r = q.x mod n\n            if (r === _0n)\n                return;\n            // Can use scalar blinding b^-1(bm + bdr) where b ∈ [1,q−1] according to\n            // https://tches.iacr.org/index.php/TCHES/article/view/7337/6509. We've decided against it:\n            // a) dependency on CSPRNG b) 15% slowdown c) doesn't really help since bigints are not CT\n            const s = modN(ik * modN(m + r * d)); // Not using blinding here\n            if (s === _0n)\n                return;\n            let recovery = (q.x === r ? 0 : 2) | Number(q.y & _1n); // recovery bit (2 or 3, when q.x > n)\n            let normS = s;\n            if (lowS && isBiggerThanHalfOrder(s)) {\n                normS = normalizeS(s); // if lowS was passed, ensure s is always\n                recovery ^= 1; // // in the bottom half of N\n            }\n            return new Signature(r, normS, recovery); // use normS, not s\n        }\n        return { seed, k2sig };\n    }\n    const defaultSigOpts = { lowS: CURVE.lowS, prehash: false };\n    const defaultVerOpts = { lowS: CURVE.lowS, prehash: false };\n    /**\n     * Signs message hash with a private key.\n     * ```\n     * sign(m, d, k) where\n     *   (x, y) = G × k\n     *   r = x mod n\n     *   s = (m + dr)/k mod n\n     * ```\n     * @param msgHash NOT message. msg needs to be hashed to `msgHash`, or use `prehash`.\n     * @param privKey private key\n     * @param opts lowS for non-malleable sigs. extraEntropy for mixing randomness into k. prehash will hash first arg.\n     * @returns signature with recovery param\n     */\n    function sign(msgHash, privKey, opts = defaultSigOpts) {\n        const { seed, k2sig } = prepSig(msgHash, privKey, opts); // Steps A, D of RFC6979 3.2.\n        const C = CURVE;\n        const drbg = ut.createHmacDrbg(C.hash.outputLen, C.nByteLength, C.hmac);\n        return drbg(seed, k2sig); // Steps B, C, D, E, F, G\n    }\n    // Enable precomputes. Slows down first publicKey computation by 20ms.\n    Point.BASE._setWindowSize(8);\n    // utils.precompute(8, ProjectivePoint.BASE)\n    /**\n     * Verifies a signature against message hash and public key.\n     * Rejects lowS signatures by default: to override,\n     * specify option `{lowS: false}`. Implements section 4.1.4 from https://www.secg.org/sec1-v2.pdf:\n     *\n     * ```\n     * verify(r, s, h, P) where\n     *   U1 = hs^-1 mod n\n     *   U2 = rs^-1 mod n\n     *   R = U1⋅G - U2⋅P\n     *   mod(R.x, n) == r\n     * ```\n     */\n    function verify(signature, msgHash, publicKey, opts = defaultVerOpts) {\n        const sg = signature;\n        msgHash = ensureBytes('msgHash', msgHash);\n        publicKey = ensureBytes('publicKey', publicKey);\n        if ('strict' in opts)\n            throw new Error('options.strict was renamed to lowS');\n        const { lowS, prehash } = opts;\n        let _sig = undefined;\n        let P;\n        try {\n            if (typeof sg === 'string' || ut.isBytes(sg)) {\n                // Signature can be represented in 2 ways: compact (2*nByteLength) & DER (variable-length).\n                // Since DER can also be 2*nByteLength bytes, we check for it first.\n                try {\n                    _sig = Signature.fromDER(sg);\n                }\n                catch (derError) {\n                    if (!(derError instanceof DER.Err))\n                        throw derError;\n                    _sig = Signature.fromCompact(sg);\n                }\n            }\n            else if (typeof sg === 'object' && typeof sg.r === 'bigint' && typeof sg.s === 'bigint') {\n                const { r, s } = sg;\n                _sig = new Signature(r, s);\n            }\n            else {\n                throw new Error('PARSE');\n            }\n            P = Point.fromHex(publicKey);\n        }\n        catch (error) {\n            if (error.message === 'PARSE')\n                throw new Error(`signature must be Signature instance, Uint8Array or hex string`);\n            return false;\n        }\n        if (lowS && _sig.hasHighS())\n            return false;\n        if (prehash)\n            msgHash = CURVE.hash(msgHash);\n        const { r, s } = _sig;\n        const h = bits2int_modN(msgHash); // Cannot use fields methods, since it is group element\n        const is = invN(s); // s^-1\n        const u1 = modN(h * is); // u1 = hs^-1 mod n\n        const u2 = modN(r * is); // u2 = rs^-1 mod n\n        const R = Point.BASE.multiplyAndAddUnsafe(P, u1, u2)?.toAffine(); // R = u1⋅G + u2⋅P\n        if (!R)\n            return false;\n        const v = modN(R.x);\n        return v === r;\n    }\n    return {\n        CURVE,\n        getPublicKey,\n        getSharedSecret,\n        sign,\n        verify,\n        ProjectivePoint: Point,\n        Signature,\n        utils,\n    };\n}\n/**\n * Implementation of the Shallue and van de Woestijne method for any weierstrass curve.\n * TODO: check if there is a way to merge this with uvRatio in Edwards; move to modular.\n * b = True and y = sqrt(u / v) if (u / v) is square in F, and\n * b = False and y = sqrt(Z * (u / v)) otherwise.\n * @param Fp\n * @param Z\n * @returns\n */\nexport function SWUFpSqrtRatio(Fp, Z) {\n    // Generic implementation\n    const q = Fp.ORDER;\n    let l = _0n;\n    for (let o = q - _1n; o % _2n === _0n; o /= _2n)\n        l += _1n;\n    const c1 = l; // 1. c1, the largest integer such that 2^c1 divides q - 1.\n    // We need 2n ** c1 and 2n ** (c1-1). We can't use **; but we can use <<.\n    // 2n ** c1 == 2n << (c1-1)\n    const _2n_pow_c1_1 = _2n << (c1 - _1n - _1n);\n    const _2n_pow_c1 = _2n_pow_c1_1 * _2n;\n    const c2 = (q - _1n) / _2n_pow_c1; // 2. c2 = (q - 1) / (2^c1)  # Integer arithmetic\n    const c3 = (c2 - _1n) / _2n; // 3. c3 = (c2 - 1) / 2            # Integer arithmetic\n    const c4 = _2n_pow_c1 - _1n; // 4. c4 = 2^c1 - 1                # Integer arithmetic\n    const c5 = _2n_pow_c1_1; // 5. c5 = 2^(c1 - 1)                  # Integer arithmetic\n    const c6 = Fp.pow(Z, c2); // 6. c6 = Z^c2\n    const c7 = Fp.pow(Z, (c2 + _1n) / _2n); // 7. c7 = Z^((c2 + 1) / 2)\n    let sqrtRatio = (u, v) => {\n        let tv1 = c6; // 1. tv1 = c6\n        let tv2 = Fp.pow(v, c4); // 2. tv2 = v^c4\n        let tv3 = Fp.sqr(tv2); // 3. tv3 = tv2^2\n        tv3 = Fp.mul(tv3, v); // 4. tv3 = tv3 * v\n        let tv5 = Fp.mul(u, tv3); // 5. tv5 = u * tv3\n        tv5 = Fp.pow(tv5, c3); // 6. tv5 = tv5^c3\n        tv5 = Fp.mul(tv5, tv2); // 7. tv5 = tv5 * tv2\n        tv2 = Fp.mul(tv5, v); // 8. tv2 = tv5 * v\n        tv3 = Fp.mul(tv5, u); // 9. tv3 = tv5 * u\n        let tv4 = Fp.mul(tv3, tv2); // 10. tv4 = tv3 * tv2\n        tv5 = Fp.pow(tv4, c5); // 11. tv5 = tv4^c5\n        let isQR = Fp.eql(tv5, Fp.ONE); // 12. isQR = tv5 == 1\n        tv2 = Fp.mul(tv3, c7); // 13. tv2 = tv3 * c7\n        tv5 = Fp.mul(tv4, tv1); // 14. tv5 = tv4 * tv1\n        tv3 = Fp.cmov(tv2, tv3, isQR); // 15. tv3 = CMOV(tv2, tv3, isQR)\n        tv4 = Fp.cmov(tv5, tv4, isQR); // 16. tv4 = CMOV(tv5, tv4, isQR)\n        // 17. for i in (c1, c1 - 1, ..., 2):\n        for (let i = c1; i > _1n; i--) {\n            let tv5 = i - _2n; // 18.    tv5 = i - 2\n            tv5 = _2n << (tv5 - _1n); // 19.    tv5 = 2^tv5\n            let tvv5 = Fp.pow(tv4, tv5); // 20.    tv5 = tv4^tv5\n            const e1 = Fp.eql(tvv5, Fp.ONE); // 21.    e1 = tv5 == 1\n            tv2 = Fp.mul(tv3, tv1); // 22.    tv2 = tv3 * tv1\n            tv1 = Fp.mul(tv1, tv1); // 23.    tv1 = tv1 * tv1\n            tvv5 = Fp.mul(tv4, tv1); // 24.    tv5 = tv4 * tv1\n            tv3 = Fp.cmov(tv2, tv3, e1); // 25.    tv3 = CMOV(tv2, tv3, e1)\n            tv4 = Fp.cmov(tvv5, tv4, e1); // 26.    tv4 = CMOV(tv5, tv4, e1)\n        }\n        return { isValid: isQR, value: tv3 };\n    };\n    if (Fp.ORDER % _4n === _3n) {\n        // sqrt_ratio_3mod4(u, v)\n        const c1 = (Fp.ORDER - _3n) / _4n; // 1. c1 = (q - 3) / 4     # Integer arithmetic\n        const c2 = Fp.sqrt(Fp.neg(Z)); // 2. c2 = sqrt(-Z)\n        sqrtRatio = (u, v) => {\n            let tv1 = Fp.sqr(v); // 1. tv1 = v^2\n            const tv2 = Fp.mul(u, v); // 2. tv2 = u * v\n            tv1 = Fp.mul(tv1, tv2); // 3. tv1 = tv1 * tv2\n            let y1 = Fp.pow(tv1, c1); // 4. y1 = tv1^c1\n            y1 = Fp.mul(y1, tv2); // 5. y1 = y1 * tv2\n            const y2 = Fp.mul(y1, c2); // 6. y2 = y1 * c2\n            const tv3 = Fp.mul(Fp.sqr(y1), v); // 7. tv3 = y1^2; 8. tv3 = tv3 * v\n            const isQR = Fp.eql(tv3, u); // 9. isQR = tv3 == u\n            let y = Fp.cmov(y2, y1, isQR); // 10. y = CMOV(y2, y1, isQR)\n            return { isValid: isQR, value: y }; // 11. return (isQR, y) isQR ? y : y*c2\n        };\n    }\n    // No curves uses that\n    // if (Fp.ORDER % _8n === _5n) // sqrt_ratio_5mod8\n    return sqrtRatio;\n}\n/**\n * Simplified Shallue-van de Woestijne-Ulas Method\n * https://www.rfc-editor.org/rfc/rfc9380#section-6.6.2\n */\nexport function mapToCurveSimpleSWU(Fp, opts) {\n    mod.validateField(Fp);\n    if (!Fp.isValid(opts.A) || !Fp.isValid(opts.B) || !Fp.isValid(opts.Z))\n        throw new Error('mapToCurveSimpleSWU: invalid opts');\n    const sqrtRatio = SWUFpSqrtRatio(Fp, opts.Z);\n    if (!Fp.isOdd)\n        throw new Error('Fp.isOdd is not implemented!');\n    // Input: u, an element of F.\n    // Output: (x, y), a point on E.\n    return (u) => {\n        // prettier-ignore\n        let tv1, tv2, tv3, tv4, tv5, tv6, x, y;\n        tv1 = Fp.sqr(u); // 1.  tv1 = u^2\n        tv1 = Fp.mul(tv1, opts.Z); // 2.  tv1 = Z * tv1\n        tv2 = Fp.sqr(tv1); // 3.  tv2 = tv1^2\n        tv2 = Fp.add(tv2, tv1); // 4.  tv2 = tv2 + tv1\n        tv3 = Fp.add(tv2, Fp.ONE); // 5.  tv3 = tv2 + 1\n        tv3 = Fp.mul(tv3, opts.B); // 6.  tv3 = B * tv3\n        tv4 = Fp.cmov(opts.Z, Fp.neg(tv2), !Fp.eql(tv2, Fp.ZERO)); // 7.  tv4 = CMOV(Z, -tv2, tv2 != 0)\n        tv4 = Fp.mul(tv4, opts.A); // 8.  tv4 = A * tv4\n        tv2 = Fp.sqr(tv3); // 9.  tv2 = tv3^2\n        tv6 = Fp.sqr(tv4); // 10. tv6 = tv4^2\n        tv5 = Fp.mul(tv6, opts.A); // 11. tv5 = A * tv6\n        tv2 = Fp.add(tv2, tv5); // 12. tv2 = tv2 + tv5\n        tv2 = Fp.mul(tv2, tv3); // 13. tv2 = tv2 * tv3\n        tv6 = Fp.mul(tv6, tv4); // 14. tv6 = tv6 * tv4\n        tv5 = Fp.mul(tv6, opts.B); // 15. tv5 = B * tv6\n        tv2 = Fp.add(tv2, tv5); // 16. tv2 = tv2 + tv5\n        x = Fp.mul(tv1, tv3); // 17.   x = tv1 * tv3\n        const { isValid, value } = sqrtRatio(tv2, tv6); // 18. (is_gx1_square, y1) = sqrt_ratio(tv2, tv6)\n        y = Fp.mul(tv1, u); // 19.   y = tv1 * u  -> Z * u^3 * y1\n        y = Fp.mul(y, value); // 20.   y = y * y1\n        x = Fp.cmov(x, tv3, isValid); // 21.   x = CMOV(x, tv3, is_gx1_square)\n        y = Fp.cmov(y, value, isValid); // 22.   y = CMOV(y, y1, is_gx1_square)\n        const e1 = Fp.isOdd(u) === Fp.isOdd(y); // 23.  e1 = sgn0(u) == sgn0(y)\n        y = Fp.cmov(Fp.neg(y), y, e1); // 24.   y = CMOV(-y, y, e1)\n        x = Fp.div(x, tv4); // 25.   x = x / tv4\n        return { x, y };\n    };\n}\n//# sourceMappingURL=weierstrass.js.map","import { mod } from './modular.js';\nimport { bytesToNumberBE, isBytes, concatBytes, utf8ToBytes, validateObject } from './utils.js';\nfunction validateDST(dst) {\n    if (isBytes(dst))\n        return dst;\n    if (typeof dst === 'string')\n        return utf8ToBytes(dst);\n    throw new Error('DST must be Uint8Array or string');\n}\n// Octet Stream to Integer. \"spec\" implementation of os2ip is 2.5x slower vs bytesToNumberBE.\nconst os2ip = bytesToNumberBE;\n// Integer to Octet Stream (numberToBytesBE)\nfunction i2osp(value, length) {\n    if (value < 0 || value >= 1 << (8 * length)) {\n        throw new Error(`bad I2OSP call: value=${value} length=${length}`);\n    }\n    const res = Array.from({ length }).fill(0);\n    for (let i = length - 1; i >= 0; i--) {\n        res[i] = value & 0xff;\n        value >>>= 8;\n    }\n    return new Uint8Array(res);\n}\nfunction strxor(a, b) {\n    const arr = new Uint8Array(a.length);\n    for (let i = 0; i < a.length; i++) {\n        arr[i] = a[i] ^ b[i];\n    }\n    return arr;\n}\nfunction abytes(item) {\n    if (!isBytes(item))\n        throw new Error('Uint8Array expected');\n}\nfunction isNum(item) {\n    if (!Number.isSafeInteger(item))\n        throw new Error('number expected');\n}\n// Produces a uniformly random byte string using a cryptographic hash function H that outputs b bits\n// https://www.rfc-editor.org/rfc/rfc9380#section-5.3.1\nexport function expand_message_xmd(msg, DST, lenInBytes, H) {\n    abytes(msg);\n    abytes(DST);\n    isNum(lenInBytes);\n    // https://www.rfc-editor.org/rfc/rfc9380#section-5.3.3\n    if (DST.length > 255)\n        DST = H(concatBytes(utf8ToBytes('H2C-OVERSIZE-DST-'), DST));\n    const { outputLen: b_in_bytes, blockLen: r_in_bytes } = H;\n    const ell = Math.ceil(lenInBytes / b_in_bytes);\n    if (ell > 255)\n        throw new Error('Invalid xmd length');\n    const DST_prime = concatBytes(DST, i2osp(DST.length, 1));\n    const Z_pad = i2osp(0, r_in_bytes);\n    const l_i_b_str = i2osp(lenInBytes, 2); // len_in_bytes_str\n    const b = new Array(ell);\n    const b_0 = H(concatBytes(Z_pad, msg, l_i_b_str, i2osp(0, 1), DST_prime));\n    b[0] = H(concatBytes(b_0, i2osp(1, 1), DST_prime));\n    for (let i = 1; i <= ell; i++) {\n        const args = [strxor(b_0, b[i - 1]), i2osp(i + 1, 1), DST_prime];\n        b[i] = H(concatBytes(...args));\n    }\n    const pseudo_random_bytes = concatBytes(...b);\n    return pseudo_random_bytes.slice(0, lenInBytes);\n}\n// Produces a uniformly random byte string using an extendable-output function (XOF) H.\n// 1. The collision resistance of H MUST be at least k bits.\n// 2. H MUST be an XOF that has been proved indifferentiable from\n//    a random oracle under a reasonable cryptographic assumption.\n// https://www.rfc-editor.org/rfc/rfc9380#section-5.3.2\nexport function expand_message_xof(msg, DST, lenInBytes, k, H) {\n    abytes(msg);\n    abytes(DST);\n    isNum(lenInBytes);\n    // https://www.rfc-editor.org/rfc/rfc9380#section-5.3.3\n    // DST = H('H2C-OVERSIZE-DST-' || a_very_long_DST, Math.ceil((lenInBytes * k) / 8));\n    if (DST.length > 255) {\n        const dkLen = Math.ceil((2 * k) / 8);\n        DST = H.create({ dkLen }).update(utf8ToBytes('H2C-OVERSIZE-DST-')).update(DST).digest();\n    }\n    if (lenInBytes > 65535 || DST.length > 255)\n        throw new Error('expand_message_xof: invalid lenInBytes');\n    return (H.create({ dkLen: lenInBytes })\n        .update(msg)\n        .update(i2osp(lenInBytes, 2))\n        // 2. DST_prime = DST || I2OSP(len(DST), 1)\n        .update(DST)\n        .update(i2osp(DST.length, 1))\n        .digest());\n}\n/**\n * Hashes arbitrary-length byte strings to a list of one or more elements of a finite field F\n * https://www.rfc-editor.org/rfc/rfc9380#section-5.2\n * @param msg a byte string containing the message to hash\n * @param count the number of elements of F to output\n * @param options `{DST: string, p: bigint, m: number, k: number, expand: 'xmd' | 'xof', hash: H}`, see above\n * @returns [u_0, ..., u_(count - 1)], a list of field elements.\n */\nexport function hash_to_field(msg, count, options) {\n    validateObject(options, {\n        DST: 'stringOrUint8Array',\n        p: 'bigint',\n        m: 'isSafeInteger',\n        k: 'isSafeInteger',\n        hash: 'hash',\n    });\n    const { p, k, m, hash, expand, DST: _DST } = options;\n    abytes(msg);\n    isNum(count);\n    const DST = validateDST(_DST);\n    const log2p = p.toString(2).length;\n    const L = Math.ceil((log2p + k) / 8); // section 5.1 of ietf draft link above\n    const len_in_bytes = count * m * L;\n    let prb; // pseudo_random_bytes\n    if (expand === 'xmd') {\n        prb = expand_message_xmd(msg, DST, len_in_bytes, hash);\n    }\n    else if (expand === 'xof') {\n        prb = expand_message_xof(msg, DST, len_in_bytes, k, hash);\n    }\n    else if (expand === '_internal_pass') {\n        // for internal tests only\n        prb = msg;\n    }\n    else {\n        throw new Error('expand must be \"xmd\" or \"xof\"');\n    }\n    const u = new Array(count);\n    for (let i = 0; i < count; i++) {\n        const e = new Array(m);\n        for (let j = 0; j < m; j++) {\n            const elm_offset = L * (j + i * m);\n            const tv = prb.subarray(elm_offset, elm_offset + L);\n            e[j] = mod(os2ip(tv), p);\n        }\n        u[i] = e;\n    }\n    return u;\n}\nexport function isogenyMap(field, map) {\n    // Make same order as in spec\n    const COEFF = map.map((i) => Array.from(i).reverse());\n    return (x, y) => {\n        const [xNum, xDen, yNum, yDen] = COEFF.map((val) => val.reduce((acc, i) => field.add(field.mul(acc, x), i)));\n        x = field.div(xNum, xDen); // xNum / xDen\n        y = field.mul(y, field.div(yNum, yDen)); // y * (yNum / yDev)\n        return { x, y };\n    };\n}\nexport function createHasher(Point, mapToCurve, def) {\n    if (typeof mapToCurve !== 'function')\n        throw new Error('mapToCurve() must be defined');\n    return {\n        // Encodes byte string to elliptic curve.\n        // hash_to_curve from https://www.rfc-editor.org/rfc/rfc9380#section-3\n        hashToCurve(msg, options) {\n            const u = hash_to_field(msg, 2, { ...def, DST: def.DST, ...options });\n            const u0 = Point.fromAffine(mapToCurve(u[0]));\n            const u1 = Point.fromAffine(mapToCurve(u[1]));\n            const P = u0.add(u1).clearCofactor();\n            P.assertValidity();\n            return P;\n        },\n        // Encodes byte string to elliptic curve.\n        // encode_to_curve from https://www.rfc-editor.org/rfc/rfc9380#section-3\n        encodeToCurve(msg, options) {\n            const u = hash_to_field(msg, 1, { ...def, DST: def.encodeDST, ...options });\n            const P = Point.fromAffine(mapToCurve(u[0])).clearCofactor();\n            P.assertValidity();\n            return P;\n        },\n    };\n}\n//# sourceMappingURL=hash-to-curve.js.map","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 */\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) */\nimport { hmac } from '@noble/hashes/hmac';\nimport { concatBytes, randomBytes } from '@noble/hashes/utils';\nimport { weierstrass } from './abstract/weierstrass.js';\n// connects noble-curves to noble-hashes\nexport function getHash(hash) {\n    return {\n        hash,\n        hmac: (key, ...msgs) => hmac(hash, key, concatBytes(...msgs)),\n        randomBytes,\n    };\n}\nexport function createCurve(curveDef, defHash) {\n    const create = (hash) => weierstrass({ ...curveDef, ...getHash(hash) });\n    return Object.freeze({ ...create(defHash), create });\n}\n//# sourceMappingURL=_shortw_utils.js.map","/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\nimport { sha256 } from '@noble/hashes/sha256';\nimport { randomBytes } from '@noble/hashes/utils';\nimport { Field, mod, pow2 } from './abstract/modular.js';\nimport { mapToCurveSimpleSWU } from './abstract/weierstrass.js';\nimport { bytesToNumberBE, concatBytes, ensureBytes, numberToBytesBE } from './abstract/utils.js';\nimport { createHasher, isogenyMap } from './abstract/hash-to-curve.js';\nimport { createCurve } from './_shortw_utils.js';\nconst secp256k1P = BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f');\nconst secp256k1N = BigInt('0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141');\nconst _1n = BigInt(1);\nconst _2n = BigInt(2);\nconst divNearest = (a, b) => (a + b / _2n) / b;\n/**\n * √n = n^((p+1)/4) for fields p = 3 mod 4. We unwrap the loop and multiply bit-by-bit.\n * (P+1n/4n).toString(2) would produce bits [223x 1, 0, 22x 1, 4x 0, 11, 00]\n */\nfunction sqrtMod(y) {\n    const P = secp256k1P;\n    // prettier-ignore\n    const _3n = BigInt(3), _6n = BigInt(6), _11n = BigInt(11), _22n = BigInt(22);\n    // prettier-ignore\n    const _23n = BigInt(23), _44n = BigInt(44), _88n = BigInt(88);\n    const b2 = (y * y * y) % P; // x^3, 11\n    const b3 = (b2 * b2 * y) % P; // x^7\n    const b6 = (pow2(b3, _3n, P) * b3) % P;\n    const b9 = (pow2(b6, _3n, P) * b3) % P;\n    const b11 = (pow2(b9, _2n, P) * b2) % P;\n    const b22 = (pow2(b11, _11n, P) * b11) % P;\n    const b44 = (pow2(b22, _22n, P) * b22) % P;\n    const b88 = (pow2(b44, _44n, P) * b44) % P;\n    const b176 = (pow2(b88, _88n, P) * b88) % P;\n    const b220 = (pow2(b176, _44n, P) * b44) % P;\n    const b223 = (pow2(b220, _3n, P) * b3) % P;\n    const t1 = (pow2(b223, _23n, P) * b22) % P;\n    const t2 = (pow2(t1, _6n, P) * b2) % P;\n    const root = pow2(t2, _2n, P);\n    if (!Fp.eql(Fp.sqr(root), y))\n        throw new Error('Cannot find square root');\n    return root;\n}\nconst Fp = Field(secp256k1P, undefined, undefined, { sqrt: sqrtMod });\nexport const secp256k1 = createCurve({\n    a: BigInt(0), // equation params: a, b\n    b: BigInt(7), // Seem to be rigid: bitcointalk.org/index.php?topic=289795.msg3183975#msg3183975\n    Fp, // Field's prime: 2n**256n - 2n**32n - 2n**9n - 2n**8n - 2n**7n - 2n**6n - 2n**4n - 1n\n    n: secp256k1N, // Curve order, total count of valid points in the field\n    // Base point (x, y) aka generator point\n    Gx: BigInt('55066263022277343669578718895168534326250603453777594175500187360389116729240'),\n    Gy: BigInt('32670510020758816978083085130507043184471273380659243275938904335757337482424'),\n    h: BigInt(1), // Cofactor\n    lowS: true, // Allow only low-S signatures by default in sign() and verify()\n    /**\n     * secp256k1 belongs to Koblitz curves: it has efficiently computable endomorphism.\n     * Endomorphism uses 2x less RAM, speeds up precomputation by 2x and ECDH / key recovery by 20%.\n     * For precomputed wNAF it trades off 1/2 init time & 1/3 ram for 20% perf hit.\n     * Explanation: https://gist.github.com/paulmillr/eb670806793e84df628a7c434a873066\n     */\n    endo: {\n        beta: BigInt('0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee'),\n        splitScalar: (k) => {\n            const n = secp256k1N;\n            const a1 = BigInt('0x3086d221a7d46bcde86c90e49284eb15');\n            const b1 = -_1n * BigInt('0xe4437ed6010e88286f547fa90abfe4c3');\n            const a2 = BigInt('0x114ca50f7a8e2f3f657c1108d9d44cfd8');\n            const b2 = a1;\n            const POW_2_128 = BigInt('0x100000000000000000000000000000000'); // (2n**128n).toString(16)\n            const c1 = divNearest(b2 * k, n);\n            const c2 = divNearest(-b1 * k, n);\n            let k1 = mod(k - c1 * a1 - c2 * a2, n);\n            let k2 = mod(-c1 * b1 - c2 * b2, n);\n            const k1neg = k1 > POW_2_128;\n            const k2neg = k2 > POW_2_128;\n            if (k1neg)\n                k1 = n - k1;\n            if (k2neg)\n                k2 = n - k2;\n            if (k1 > POW_2_128 || k2 > POW_2_128) {\n                throw new Error('splitScalar: Endomorphism failed, k=' + k);\n            }\n            return { k1neg, k1, k2neg, k2 };\n        },\n    },\n}, sha256);\n// Schnorr signatures are superior to ECDSA from above. Below is Schnorr-specific BIP0340 code.\n// https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki\nconst _0n = BigInt(0);\nconst fe = (x) => typeof x === 'bigint' && _0n < x && x < secp256k1P;\nconst ge = (x) => typeof x === 'bigint' && _0n < x && x < secp256k1N;\n/** An object mapping tags to their tagged hash prefix of [SHA256(tag) | SHA256(tag)] */\nconst TAGGED_HASH_PREFIXES = {};\nfunction taggedHash(tag, ...messages) {\n    let tagP = TAGGED_HASH_PREFIXES[tag];\n    if (tagP === undefined) {\n        const tagH = sha256(Uint8Array.from(tag, (c) => c.charCodeAt(0)));\n        tagP = concatBytes(tagH, tagH);\n        TAGGED_HASH_PREFIXES[tag] = tagP;\n    }\n    return sha256(concatBytes(tagP, ...messages));\n}\n// ECDSA compact points are 33-byte. Schnorr is 32: we strip first byte 0x02 or 0x03\nconst pointToBytes = (point) => point.toRawBytes(true).slice(1);\nconst numTo32b = (n) => numberToBytesBE(n, 32);\nconst modP = (x) => mod(x, secp256k1P);\nconst modN = (x) => mod(x, secp256k1N);\nconst Point = secp256k1.ProjectivePoint;\nconst GmulAdd = (Q, a, b) => Point.BASE.multiplyAndAddUnsafe(Q, a, b);\n// Calculate point, scalar and bytes\nfunction schnorrGetExtPubKey(priv) {\n    let d_ = secp256k1.utils.normPrivateKeyToScalar(priv); // same method executed in fromPrivateKey\n    let p = Point.fromPrivateKey(d_); // P = d'⋅G; 0 < d' < n check is done inside\n    const scalar = p.hasEvenY() ? d_ : modN(-d_);\n    return { scalar: scalar, bytes: pointToBytes(p) };\n}\n/**\n * lift_x from BIP340. Convert 32-byte x coordinate to elliptic curve point.\n * @returns valid point checked for being on-curve\n */\nfunction lift_x(x) {\n    if (!fe(x))\n        throw new Error('bad x: need 0 < x < p'); // Fail if x ≥ p.\n    const xx = modP(x * x);\n    const c = modP(xx * x + BigInt(7)); // Let c = x³ + 7 mod p.\n    let y = sqrtMod(c); // Let y = c^(p+1)/4 mod p.\n    if (y % _2n !== _0n)\n        y = modP(-y); // Return the unique point P such that x(P) = x and\n    const p = new Point(x, y, _1n); // y(P) = y if y mod 2 = 0 or y(P) = p-y otherwise.\n    p.assertValidity();\n    return p;\n}\n/**\n * Create tagged hash, convert it to bigint, reduce modulo-n.\n */\nfunction challenge(...args) {\n    return modN(bytesToNumberBE(taggedHash('BIP0340/challenge', ...args)));\n}\n/**\n * Schnorr public key is just `x` coordinate of Point as per BIP340.\n */\nfunction schnorrGetPublicKey(privateKey) {\n    return schnorrGetExtPubKey(privateKey).bytes; // d'=int(sk). Fail if d'=0 or d'≥n. Ret bytes(d'⋅G)\n}\n/**\n * Creates Schnorr signature as per BIP340. Verifies itself before returning anything.\n * auxRand is optional and is not the sole source of k generation: bad CSPRNG won't be dangerous.\n */\nfunction schnorrSign(message, privateKey, auxRand = randomBytes(32)) {\n    const m = ensureBytes('message', message);\n    const { bytes: px, scalar: d } = schnorrGetExtPubKey(privateKey); // checks for isWithinCurveOrder\n    const a = ensureBytes('auxRand', auxRand, 32); // Auxiliary random data a: a 32-byte array\n    const t = numTo32b(d ^ bytesToNumberBE(taggedHash('BIP0340/aux', a))); // Let t be the byte-wise xor of bytes(d) and hash/aux(a)\n    const rand = taggedHash('BIP0340/nonce', t, px, m); // Let rand = hash/nonce(t || bytes(P) || m)\n    const k_ = modN(bytesToNumberBE(rand)); // Let k' = int(rand) mod n\n    if (k_ === _0n)\n        throw new Error('sign failed: k is zero'); // Fail if k' = 0.\n    const { bytes: rx, scalar: k } = schnorrGetExtPubKey(k_); // Let R = k'⋅G.\n    const e = challenge(rx, px, m); // Let e = int(hash/challenge(bytes(R) || bytes(P) || m)) mod n.\n    const sig = new Uint8Array(64); // Let sig = bytes(R) || bytes((k + ed) mod n).\n    sig.set(rx, 0);\n    sig.set(numTo32b(modN(k + e * d)), 32);\n    // If Verify(bytes(P), m, sig) (see below) returns failure, abort\n    if (!schnorrVerify(sig, m, px))\n        throw new Error('sign: Invalid signature produced');\n    return sig;\n}\n/**\n * Verifies Schnorr signature.\n * Will swallow errors & return false except for initial type validation of arguments.\n */\nfunction schnorrVerify(signature, message, publicKey) {\n    const sig = ensureBytes('signature', signature, 64);\n    const m = ensureBytes('message', message);\n    const pub = ensureBytes('publicKey', publicKey, 32);\n    try {\n        const P = lift_x(bytesToNumberBE(pub)); // P = lift_x(int(pk)); fail if that fails\n        const r = bytesToNumberBE(sig.subarray(0, 32)); // Let r = int(sig[0:32]); fail if r ≥ p.\n        if (!fe(r))\n            return false;\n        const s = bytesToNumberBE(sig.subarray(32, 64)); // Let s = int(sig[32:64]); fail if s ≥ n.\n        if (!ge(s))\n            return false;\n        const e = challenge(numTo32b(r), pointToBytes(P), m); // int(challenge(bytes(r)||bytes(P)||m))%n\n        const R = GmulAdd(P, s, modN(-e)); // R = s⋅G - e⋅P\n        if (!R || !R.hasEvenY() || R.toAffine().x !== r)\n            return false; // -eP == (n-e)P\n        return true; // Fail if is_infinite(R) / not has_even_y(R) / x(R) ≠ r.\n    }\n    catch (error) {\n        return false;\n    }\n}\nexport const schnorr = /* @__PURE__ */ (() => ({\n    getPublicKey: schnorrGetPublicKey,\n    sign: schnorrSign,\n    verify: schnorrVerify,\n    utils: {\n        randomPrivateKey: secp256k1.utils.randomPrivateKey,\n        lift_x,\n        pointToBytes,\n        numberToBytesBE,\n        bytesToNumberBE,\n        taggedHash,\n        mod,\n    },\n}))();\nconst isoMap = /* @__PURE__ */ (() => isogenyMap(Fp, [\n    // xNum\n    [\n        '0x8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa8c7',\n        '0x7d3d4c80bc321d5b9f315cea7fd44c5d595d2fc0bf63b92dfff1044f17c6581',\n        '0x534c328d23f234e6e2a413deca25caece4506144037c40314ecbd0b53d9dd262',\n        '0x8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa88c',\n    ],\n    // xDen\n    [\n        '0xd35771193d94918a9ca34ccbb7b640dd86cd409542f8487d9fe6b745781eb49b',\n        '0xedadc6f64383dc1df7c4b2d51b54225406d36b641f5e41bbc52a56612a8c6d14',\n        '0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1\n    ],\n    // yNum\n    [\n        '0x4bda12f684bda12f684bda12f684bda12f684bda12f684bda12f684b8e38e23c',\n        '0xc75e0c32d5cb7c0fa9d0a54b12a0a6d5647ab046d686da6fdffc90fc201d71a3',\n        '0x29a6194691f91a73715209ef6512e576722830a201be2018a765e85a9ecee931',\n        '0x2f684bda12f684bda12f684bda12f684bda12f684bda12f684bda12f38e38d84',\n    ],\n    // yDen\n    [\n        '0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffff93b',\n        '0x7a06534bb8bdb49fd5e9e6632722c2989467c1bfc8e8d978dfb425d2685c2573',\n        '0x6484aa716545ca2cf3a70c3fa8fe337e0a3d21162f0d6299a7bf8192bfd2a76f',\n        '0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1\n    ],\n].map((i) => i.map((j) => BigInt(j)))))();\nconst mapSWU = /* @__PURE__ */ (() => mapToCurveSimpleSWU(Fp, {\n    A: BigInt('0x3f8731abdd661adca08a5558f0f5d272e953d363cb6f0e5d405447c01a444533'),\n    B: BigInt('1771'),\n    Z: Fp.create(BigInt('-11')),\n}))();\nconst htf = /* @__PURE__ */ (() => createHasher(secp256k1.ProjectivePoint, (scalars) => {\n    const { x, y } = mapSWU(Fp.create(scalars[0]));\n    return isoMap(x, y);\n}, {\n    DST: 'secp256k1_XMD:SHA-256_SSWU_RO_',\n    encodeDST: 'secp256k1_XMD:SHA-256_SSWU_NU_',\n    p: Fp.ORDER,\n    m: 1,\n    k: 128,\n    expand: 'xmd',\n    hash: sha256,\n}))();\nexport const hashToCurve = /* @__PURE__ */ (() => htf.hashToCurve)();\nexport const encodeToCurve = /* @__PURE__ */ (() => htf.encodeToCurve)();\n//# sourceMappingURL=secp256k1.js.map","/**\n * RLP Encoding based on https://ethereum.org/en/developers/docs/data-structures-and-encoding/rlp/\n * This function takes in data, converts it to Uint8Array if not,\n * and adds a length for recursion.\n * @param input Will be converted to Uint8Array\n * @returns Uint8Array of encoded data\n **/\nexport function encode(input) {\n    if (Array.isArray(input)) {\n        const output = [];\n        let outputLength = 0;\n        for (let i = 0; i < input.length; i++) {\n            const encoded = encode(input[i]);\n            output.push(encoded);\n            outputLength += encoded.length;\n        }\n        return concatBytes(encodeLength(outputLength, 192), ...output);\n    }\n    const inputBuf = toBytes(input);\n    if (inputBuf.length === 1 && inputBuf[0] < 128) {\n        return inputBuf;\n    }\n    return concatBytes(encodeLength(inputBuf.length, 128), inputBuf);\n}\n/**\n * Slices a Uint8Array, throws if the slice goes out-of-bounds of the Uint8Array.\n * E.g. `safeSlice(hexToBytes('aa'), 1, 2)` will throw.\n * @param input\n * @param start\n * @param end\n */\nfunction safeSlice(input, start, end) {\n    if (end > input.length) {\n        throw new Error('invalid RLP (safeSlice): end slice of Uint8Array out-of-bounds');\n    }\n    return input.slice(start, end);\n}\n/**\n * Parse integers. Check if there is no leading zeros\n * @param v The value to parse\n */\nfunction decodeLength(v) {\n    if (v[0] === 0) {\n        throw new Error('invalid RLP: extra zeros');\n    }\n    return parseHexByte(bytesToHex(v));\n}\nfunction encodeLength(len, offset) {\n    if (len < 56) {\n        return Uint8Array.from([len + offset]);\n    }\n    const hexLength = numberToHex(len);\n    const lLength = hexLength.length / 2;\n    const firstByte = numberToHex(offset + 55 + lLength);\n    return Uint8Array.from(hexToBytes(firstByte + hexLength));\n}\nexport function decode(input, stream = false) {\n    if (typeof input === 'undefined' || input === null || input.length === 0) {\n        return Uint8Array.from([]);\n    }\n    const inputBytes = toBytes(input);\n    const decoded = _decode(inputBytes);\n    if (stream) {\n        return decoded;\n    }\n    if (decoded.remainder.length !== 0) {\n        throw new Error('invalid RLP: remainder must be zero');\n    }\n    return decoded.data;\n}\n/** Decode an input with RLP */\nfunction _decode(input) {\n    let length, llength, data, innerRemainder, d;\n    const decoded = [];\n    const firstByte = input[0];\n    if (firstByte <= 0x7f) {\n        // a single byte whose value is in the [0x00, 0x7f] range, that byte is its own RLP encoding.\n        return {\n            data: input.slice(0, 1),\n            remainder: input.slice(1),\n        };\n    }\n    else if (firstByte <= 0xb7) {\n        // string is 0-55 bytes long. A single byte with value 0x80 plus the length of the string followed by the string\n        // The range of the first byte is [0x80, 0xb7]\n        length = firstByte - 0x7f;\n        // set 0x80 null to 0\n        if (firstByte === 0x80) {\n            data = Uint8Array.from([]);\n        }\n        else {\n            data = safeSlice(input, 1, length);\n        }\n        if (length === 2 && data[0] < 0x80) {\n            throw new Error('invalid RLP encoding: invalid prefix, single byte < 0x80 are not prefixed');\n        }\n        return {\n            data,\n            remainder: input.slice(length),\n        };\n    }\n    else if (firstByte <= 0xbf) {\n        // string is greater than 55 bytes long. A single byte with the value (0xb7 plus the length of the length),\n        // followed by the length, followed by the string\n        llength = firstByte - 0xb6;\n        if (input.length - 1 < llength) {\n            throw new Error('invalid RLP: not enough bytes for string length');\n        }\n        length = decodeLength(safeSlice(input, 1, llength));\n        if (length <= 55) {\n            throw new Error('invalid RLP: expected string length to be greater than 55');\n        }\n        data = safeSlice(input, llength, length + llength);\n        return {\n            data,\n            remainder: input.slice(length + llength),\n        };\n    }\n    else if (firstByte <= 0xf7) {\n        // a list between 0-55 bytes long\n        length = firstByte - 0xbf;\n        innerRemainder = safeSlice(input, 1, length);\n        while (innerRemainder.length) {\n            d = _decode(innerRemainder);\n            decoded.push(d.data);\n            innerRemainder = d.remainder;\n        }\n        return {\n            data: decoded,\n            remainder: input.slice(length),\n        };\n    }\n    else {\n        // a list over 55 bytes long\n        llength = firstByte - 0xf6;\n        length = decodeLength(safeSlice(input, 1, llength));\n        if (length < 56) {\n            throw new Error('invalid RLP: encoded list too short');\n        }\n        const totalLength = llength + length;\n        if (totalLength > input.length) {\n            throw new Error('invalid RLP: total length is larger than the data');\n        }\n        innerRemainder = safeSlice(input, llength, totalLength);\n        while (innerRemainder.length) {\n            d = _decode(innerRemainder);\n            decoded.push(d.data);\n            innerRemainder = d.remainder;\n        }\n        return {\n            data: decoded,\n            remainder: input.slice(totalLength),\n        };\n    }\n}\nconst cachedHexes = Array.from({ length: 256 }, (_v, i) => i.toString(16).padStart(2, '0'));\nfunction bytesToHex(uint8a) {\n    // Pre-caching chars with `cachedHexes` speeds this up 6x\n    let hex = '';\n    for (let i = 0; i < uint8a.length; i++) {\n        hex += cachedHexes[uint8a[i]];\n    }\n    return hex;\n}\nfunction parseHexByte(hexByte) {\n    const byte = Number.parseInt(hexByte, 16);\n    if (Number.isNaN(byte))\n        throw new Error('Invalid byte sequence');\n    return byte;\n}\n// Caching slows it down 2-3x\nfunction hexToBytes(hex) {\n    if (typeof hex !== 'string') {\n        throw new TypeError('hexToBytes: expected string, got ' + typeof hex);\n    }\n    if (hex.length % 2)\n        throw new Error('hexToBytes: received invalid unpadded hex');\n    const array = new Uint8Array(hex.length / 2);\n    for (let i = 0; i < array.length; i++) {\n        const j = i * 2;\n        array[i] = parseHexByte(hex.slice(j, j + 2));\n    }\n    return array;\n}\n/** Concatenates two Uint8Arrays into one. */\nfunction concatBytes(...arrays) {\n    if (arrays.length === 1)\n        return arrays[0];\n    const length = arrays.reduce((a, arr) => a + arr.length, 0);\n    const result = new Uint8Array(length);\n    for (let i = 0, pad = 0; i < arrays.length; i++) {\n        const arr = arrays[i];\n        result.set(arr, pad);\n        pad += arr.length;\n    }\n    return result;\n}\nfunction utf8ToBytes(utf) {\n    return new TextEncoder().encode(utf);\n}\n/** Transform an integer into its hexadecimal value */\nfunction numberToHex(integer) {\n    if (integer < 0) {\n        throw new Error('Invalid integer as argument, must be unsigned!');\n    }\n    const hex = integer.toString(16);\n    return hex.length % 2 ? `0${hex}` : hex;\n}\n/** Pad a string to be even */\nfunction padToEven(a) {\n    return a.length % 2 ? `0${a}` : a;\n}\n/** Check if a string is prefixed by 0x */\nfunction isHexPrefixed(str) {\n    return str.length >= 2 && str[0] === '0' && str[1] === 'x';\n}\n/** Removes 0x from a given String */\nfunction stripHexPrefix(str) {\n    if (typeof str !== 'string') {\n        return str;\n    }\n    return isHexPrefixed(str) ? str.slice(2) : str;\n}\n/** Transform anything into a Uint8Array */\nfunction toBytes(v) {\n    if (v instanceof Uint8Array) {\n        return v;\n    }\n    if (typeof v === 'string') {\n        if (isHexPrefixed(v)) {\n            return hexToBytes(padToEven(stripHexPrefix(v)));\n        }\n        return utf8ToBytes(v);\n    }\n    if (typeof v === 'number' || typeof v === 'bigint') {\n        if (!v) {\n            return Uint8Array.from([]);\n        }\n        return hexToBytes(numberToHex(v));\n    }\n    if (v === null || v === undefined) {\n        return Uint8Array.from([]);\n    }\n    throw new Error('toBytes: received unsupported type ' + typeof v);\n}\nexport const utils = {\n    bytesToHex,\n    concatBytes,\n    hexToBytes,\n    utf8ToBytes,\n};\nexport const RLP = { encode, decode };\n//# sourceMappingURL=index.js.map","/*! micro-eth-signer - MIT License (c) 2021 Paul Miller (paulmillr.com) */\nimport { keccak_256 } from '@noble/hashes/sha3';\nimport { bytesToHex, hexToBytes as _hexToBytes } from '@noble/hashes/utils';\nimport { isBytes } from '@noble/curves/abstract/utils';\nimport { secp256k1 } from '@noble/curves/secp256k1';\nimport * as RLP from '@ethereumjs/rlp';\nexport const CHAIN_TYPES = { mainnet: 1, ropsten: 3, rinkeby: 4, goerli: 5, kovan: 42 };\nexport const TRANSACTION_TYPES = { legacy: 0, eip2930: 1, eip1559: 2 };\n// All secp methods are in this object. This makes secp library easily replaceable\nconst secp = {\n    getPublicKey65b: (priv) => secp256k1.getPublicKey(priv, false),\n    normalizePublicKeyTo65b: (pub) => secp256k1.ProjectivePoint.fromHex(pub).toRawBytes(false),\n    sign: (msg, priv, opts) => {\n        return secp256k1.sign(msg, priv, {\n            extraEntropy: opts?.extraEntropy === false ? undefined : true,\n        });\n    },\n    signAsync: async (msg, priv, opts) => {\n        return secp256k1.sign(msg, priv, {\n            extraEntropy: opts?.extraEntropy === false ? undefined : true,\n        });\n    },\n    sigRecoverPub: (rsrec, msg, checkHighS = true) => {\n        const sig = new secp256k1.Signature(rsrec.r, rsrec.s).addRecoveryBit(rsrec.recovery);\n        if (checkHighS && sig.hasHighS())\n            throw new Error('Invalid signature: s is invalid');\n        return sig.recoverPublicKey(msg).toRawBytes();\n    },\n};\nexport function add0x(hex) {\n    return /^0x/i.test(hex) ? hex : `0x${hex}`;\n}\nexport function strip0x(hex) {\n    return hex.replace(/^0x/i, '');\n}\nexport function hexToBytes(hex) {\n    return _hexToBytes(strip0x(hex));\n}\nexport function numberTo0xHex(num) {\n    const hex = num.toString(16);\n    const x2 = hex.length & 1 ? `0${hex}` : hex;\n    return add0x(x2);\n}\nfunction hexToNumber(hex) {\n    if (typeof hex !== 'string') {\n        throw new TypeError('hexToNumber: expected string, got ' + typeof hex);\n    }\n    return hex ? BigInt(add0x(hex)) : 0n;\n}\nfunction isObject(item) {\n    return item != null && typeof item === 'object';\n}\nfunction cloneDeep(obj) {\n    if (Array.isArray(obj)) {\n        return obj.map(cloneDeep);\n    }\n    else if (typeof obj === 'bigint') {\n        return BigInt(obj);\n    }\n    else if (typeof obj === 'object') {\n        // should be last, so it won't catch other types\n        let res = {};\n        for (let key in obj)\n            res[key] = cloneDeep(obj[key]);\n        return res;\n    }\n    else\n        return obj;\n}\n// The order is important.\nconst FIELDS = ['nonce', 'gasPrice', 'gasLimit', 'to', 'value', 'data', 'v', 'r', 's'];\n// prettier-ignore\nconst FIELDS2930 = [\n    'chainId', 'nonce', 'gasPrice', 'gasLimit',\n    'to', 'value', 'data', 'accessList', 'yParity', 'r', 's'\n];\n// prettier-ignore\nconst FIELDS1559 = [\n    'chainId', 'nonce', 'maxPriorityFeePerGas', 'maxFeePerGas', 'gasLimit',\n    'to', 'value', 'data', 'accessList', 'yParity', 'r', 's'\n];\nconst TypeToFields = {\n    legacy: FIELDS,\n    eip2930: FIELDS2930,\n    eip1559: FIELDS1559,\n};\n// Normalizes field to format which can easily be serialized by rlp (strings & arrays)\n// prettier-ignore\nconst FIELD_NUMBER = new Set([\n    'chainId', 'nonce', 'gasPrice', 'maxPriorityFeePerGas', 'maxFeePerGas',\n    'gasLimit', 'value', 'v', 'yParity', 'r', 's'\n]);\nconst FIELD_DATA = new Set(['data', 'to', 'storageKey', 'address']);\nfunction normalizeField(field, value) {\n    // can be number, bignumber, decimal number in string (123), hex number in string (0x123)\n    if (FIELD_NUMBER.has(field)) {\n        // bytes\n        if (isBytes(value))\n            value = add0x(bytesToHex(value));\n        if (field === 'yParity' && typeof value === 'boolean')\n            value = value ? '0x1' : '0x0';\n        // '123' -> 0x7b (handles both hex and non-hex numbers)\n        if (typeof value === 'string')\n            value = BigInt(value === '0x' ? '0x0' : value);\n        // 123 -> '0x7b' && 1 -> 0x01\n        if (typeof value === 'number' || typeof value === 'bigint')\n            value = numberTo0xHex(value);\n        // 21000, default / minimum\n        if (field === 'gasLimit' && (!value || BigInt(value) === 0n))\n            value = '0x5208';\n        if (typeof value !== 'string')\n            throw new TypeError(`Invalid type for field ${field}`);\n        // should be hex string starting with '0x' at this point.\n        if (field === 'gasPrice' && BigInt(value) === 0n)\n            throw new TypeError('The gasPrice must have non-zero value');\n        // '0x00' and '' serializes differently\n        return BigInt(value) === 0n ? '' : value;\n    }\n    // Can be string or Uint8Array\n    if (FIELD_DATA.has(field)) {\n        if (!value)\n            value = '';\n        if (isBytes(value))\n            value = bytesToHex(value);\n        if (typeof value !== 'string')\n            throw new TypeError(`Invalid type for field ${field}`);\n        value = add0x(value);\n        return value === '0x' ? '' : value;\n    }\n    if (field === 'accessList') {\n        if (!value)\n            return [];\n        let res = {};\n        if (Array.isArray(value)) {\n            for (let access of value) {\n                if (Array.isArray(access)) {\n                    // AccessList\n                    if (access.length !== 2 || !Array.isArray(access[1]))\n                        throw new TypeError(`Invalid type for field ${field}`);\n                    const key = normalizeField('address', access[0]);\n                    if (!res[key])\n                        res[key] = new Set();\n                    for (let i of access[1])\n                        res[key].add(normalizeField('storageKey', i));\n                }\n                else {\n                    // {address: string, storageKeys: string[]}[]\n                    if (!isObject(access) || !access.address || !Array.isArray(access.storageKeys))\n                        throw new TypeError(`Invalid type for field ${field}`);\n                    const key = normalizeField('address', access.address);\n                    if (!res[key])\n                        res[key] = new Set();\n                    for (let i of access.storageKeys)\n                        res[key].add(normalizeField('storageKey', i));\n                }\n            }\n        }\n        else {\n            // {[address]: string[]}\n            if (!isObject(value) || isBytes(value))\n                throw new TypeError(`Invalid type for field ${field}`);\n            for (let k in value) {\n                const key = normalizeField('address', k);\n                // undefined/empty allowed\n                if (!value[k])\n                    continue;\n                if (!Array.isArray(value[k]))\n                    throw new TypeError(`Invalid type for field ${field}`);\n                res[key] = new Set(value[k].map((i) => normalizeField('storageKey', i)));\n            }\n        }\n        return Object.keys(res).map((i) => [i, Array.from(res[i])]);\n    }\n    throw new TypeError(`Invalid type for field ${field}`);\n}\nfunction possibleTypes(input) {\n    let types = new Set(Object.keys(TRANSACTION_TYPES));\n    const keys = new Set(Object.keys(input));\n    if (keys.has('maxPriorityFeePerGas') || keys.has('maxFeePerGas')) {\n        types.delete('legacy');\n        types.delete('eip2930');\n    }\n    if (keys.has('accessList') || keys.has('yParity'))\n        types.delete('legacy');\n    if (keys.has('gasPrice'))\n        types.delete('eip1559');\n    return types;\n}\nconst RawTxLength = { 9: 'legacy', 11: 'eip2930', 12: 'eip1559' };\nconst RawTxLengthRev = { legacy: 9, eip2930: 11, eip1559: 12 };\nfunction rawToSerialized(input, chain, type) {\n    let chainId;\n    if (chain)\n        chainId = CHAIN_TYPES[chain];\n    if (Array.isArray(input)) {\n        if (!type)\n            type = RawTxLength[input.length];\n        if (!type || RawTxLengthRev[type] !== input.length)\n            throw new Error(`Invalid fields length for ${type}`);\n    }\n    else {\n        const types = possibleTypes(input);\n        if (type && !types.has(type)) {\n            throw new Error(`Invalid type=${type}. Possible types with current fields: ${Array.from(types)}`);\n        }\n        if (!type) {\n            if (types.has('legacy'))\n                type = 'legacy';\n            else if (!types.size)\n                throw new Error('Impossible fields set');\n            else\n                type = Array.from(types)[0];\n        }\n        if (input.chainId) {\n            if (chain) {\n                const fromChain = normalizeField('chainId', CHAIN_TYPES[chain]);\n                const fromInput = normalizeField('chainId', input.chainId);\n                if (fromChain !== fromInput) {\n                    throw new Error(`Both chain=${chain}(${fromChain}) and chainId=${input.chainId}(${fromInput}) specified at same time`);\n                }\n            }\n            chainId = input.chainId;\n        }\n        else\n            input.chainId = chainId;\n        input = TypeToFields[type].map((key) => input[key]);\n    }\n    if (input) {\n        const sign = input.slice(-3);\n        // remove signature if any of fields is empty\n        if (!sign[0] || !sign[1] || !sign[2]) {\n            input = input.slice(0, -3);\n            // EIP-155\n            if (type === 'legacy' && chainId)\n                input.push(normalizeField('chainId', chainId), '', '');\n        }\n    }\n    let normalized = input.map((value, i) => normalizeField(TypeToFields[type][i], value));\n    if (chainId)\n        chainId = normalizeField('chainId', chainId);\n    if (type !== 'legacy' && chainId && normalized[0] !== chainId)\n        throw new Error(`ChainId=${normalized[0]} incompatible with Chain=${chainId}`);\n    const tNum = TRANSACTION_TYPES[type];\n    return (tNum ? `0x0${tNum}` : '0x') + bytesToHex(RLP.encode(normalized));\n}\nexport const Address = {\n    fromPrivateKey(key) {\n        if (typeof key === 'string')\n            key = hexToBytes(key);\n        return Address.fromPublicKey(secp.getPublicKey65b(key));\n    },\n    fromPublicKey(key) {\n        const pub = secp.normalizePublicKeyTo65b(key);\n        const addr = bytesToHex(keccak_256(pub.subarray(1, 65))).slice(24);\n        return Address.checksum(addr);\n    },\n    // ETH addr checksum is calculated by hashing the string with keccak.\n    // NOTE: it hashes *string*, not a bytearray: keccak('beef') not keccak([0xbe, 0xef])\n    checksum(nonChecksummedAddress) {\n        const addr = strip0x(nonChecksummedAddress.toLowerCase());\n        if (addr.length !== 40)\n            throw new Error('Invalid address, must have 40 chars');\n        const hash = strip0x(bytesToHex(keccak_256(addr)));\n        let checksummed = '';\n        for (let i = 0; i < addr.length; i++) {\n            // If ith character is 9 to f then make it uppercase\n            const nth = Number.parseInt(hash[i], 16);\n            let char = addr[i];\n            if (nth > 7)\n                char = char.toUpperCase();\n            checksummed += char;\n        }\n        return add0x(checksummed);\n    },\n    verifyChecksum(address) {\n        const addr = strip0x(address);\n        if (addr.length !== 40)\n            throw new Error('Invalid address, must have 40 chars');\n        if (addr === addr.toLowerCase() || addr === addr.toUpperCase())\n            return true;\n        const hash = bytesToHex(keccak_256(addr.toLowerCase()));\n        for (let i = 0; i < 40; i++) {\n            // the nth letter should be uppercase if the nth digit of casemap is 1\n            const char = addr[i];\n            const nth = Number.parseInt(hash[i], 16);\n            if (nth > 7 && char.toUpperCase() !== char)\n                return false;\n            if (nth <= 7 && char.toLowerCase() !== char)\n                return false;\n        }\n        return true;\n    },\n};\nexport class Transaction {\n    constructor(data, chain, hardfork = Transaction.DEFAULT_HARDFORK, type) {\n        this.hardfork = hardfork;\n        let norm;\n        if (typeof data === 'string') {\n            norm = data;\n        }\n        else if (data instanceof Uint8Array) {\n            norm = bytesToHex(data);\n        }\n        else if (Array.isArray(data) || (typeof data === 'object' && data != null)) {\n            norm = rawToSerialized(data, chain, type);\n        }\n        else {\n            throw new TypeError('Expected valid serialized tx');\n        }\n        if (norm.length <= 6)\n            throw new Error('Invalid tx length');\n        this.hex = add0x(norm);\n        let txData;\n        const prevType = type;\n        if (this.hex.startsWith('0x01'))\n            [txData, type] = [add0x(this.hex.slice(4)), 'eip2930'];\n        else if (this.hex.startsWith('0x02'))\n            [txData, type] = [add0x(this.hex.slice(4)), 'eip1559'];\n        else\n            [txData, type] = [this.hex, 'legacy'];\n        if (prevType && prevType !== type)\n            throw new Error('Invalid transaction type');\n        this.type = type;\n        const ui8a = RLP.decode(txData);\n        this.raw = ui8a.reduce((res, value, i) => {\n            const name = TypeToFields[type][i];\n            if (!name)\n                return res;\n            res[name] = normalizeField(name, value);\n            return res;\n        }, {});\n        if (!this.raw.chainId) {\n            // Unsigned transaction with EIP-155\n            if (type === 'legacy' && !this.raw.r && !this.raw.s) {\n                this.raw.chainId = this.raw.v;\n                this.raw.v = '';\n            }\n        }\n        if (!this.raw.chainId) {\n            this.raw.chainId = normalizeField('chainId', CHAIN_TYPES[chain || Transaction.DEFAULT_CHAIN]);\n        }\n        this.isSigned = !!(this.raw.r && this.raw.r !== '0x');\n    }\n    isNew() {\n        return this.type === 'eip1559';\n    }\n    get bytes() {\n        return hexToBytes(this.hex);\n    }\n    equals(other) {\n        return this.getMessageToSign() === other.getMessageToSign();\n    }\n    get chain() {\n        for (let k in CHAIN_TYPES)\n            if (CHAIN_TYPES[k] === Number(this.raw.chainId))\n                return k;\n        return undefined;\n    }\n    get sender() {\n        const sender = this.recoverSenderPublicKey();\n        if (!sender)\n            throw new Error('Invalid signed transaction');\n        return Address.fromPublicKey(sender);\n    }\n    get gasPrice() {\n        if (this.isNew())\n            throw new Error('Field only available for \"legacy\" transactions');\n        return BigInt(this.raw.gasPrice);\n    }\n    // maxFeePerGas: Represents the maximum amount that a user is willing to pay for their tx (inclusive of baseFeePerGas and maxPriorityFeePerGas)\n    get maxFeePerGas() {\n        if (!this.isNew())\n            throw new Error('Field only available for \"eip1559\" transactions');\n        return BigInt(this.raw.maxFeePerGas);\n    }\n    get maxPriorityFeePerGas() {\n        if (!this.isNew())\n            throw new Error('Field only available for \"eip1559\" transactions');\n        return BigInt(this.raw.maxPriorityFeePerGas);\n    }\n    get gasLimit() {\n        return BigInt(this.raw.gasLimit);\n    }\n    // Amount in wei\n    get amount() {\n        return BigInt(this.raw.value);\n    }\n    // Total fee in wei\n    get fee() {\n        const price = this.isNew() ? this.maxFeePerGas : this.gasPrice;\n        return price * this.gasLimit;\n    }\n    // Amount + fee in wei\n    get upfrontCost() {\n        return this.amount + this.fee;\n    }\n    // Checksummed address\n    get to() {\n        return Address.checksum(this.raw.to);\n    }\n    // Nonce is a counter that represents a number of outgoing transactions on the acct\n    get nonce() {\n        return Number.parseInt(this.raw.nonce, 16) || 0;\n    }\n    supportsReplayProtection() {\n        const properBlock = !['chainstart', 'homestead', 'dao', 'tangerineWhistle'].includes(this.hardfork);\n        if (!this.isSigned)\n            return true; // Unsigned, supports EIP155\n        const v = Number(hexToNumber(this.raw.v));\n        const chainId = Number(this.raw.chainId);\n        const meetsConditions = v === chainId * 2 + 35 || v === chainId * 2 + 36;\n        return properBlock && meetsConditions;\n    }\n    getMessageToSign(signed = false) {\n        let values = TypeToFields[this.type].map((i) => this.raw[i]);\n        if (!signed) {\n            // TODO: merge with line #252 somehow? (same strip & EIP-155)\n            // Strip signature (last 3 values)\n            values = values.slice(0, -3);\n            // EIP-155\n            if (this.type === 'legacy' && this.supportsReplayProtection())\n                values.push(this.raw.chainId, '', '');\n        }\n        let encoded = RLP.encode(values);\n        if (this.type !== 'legacy')\n            encoded = new Uint8Array([TRANSACTION_TYPES[this.type], ...Array.from(encoded)]);\n        return bytesToHex(keccak_256(encoded));\n    }\n    // Used in block explorers etc\n    get hash() {\n        if (!this.isSigned)\n            throw new Error('Expected signed transaction');\n        return this.getMessageToSign(true);\n    }\n    sign(privateKey, extraEntropy = false) {\n        if (this.isSigned)\n            throw new Error('Expected unsigned transaction');\n        if (typeof privateKey === 'string')\n            privateKey = strip0x(privateKey);\n        const sig = secp.sign(this.getMessageToSign(), privateKey, { extraEntropy });\n        const rec = sig.recovery;\n        const chainId = Number(this.raw.chainId);\n        const vv = this.type === 'legacy' ? (chainId ? rec + (chainId * 2 + 35) : rec + 27) : rec;\n        const [v, r, s] = [vv, sig.r, sig.s].map(numberTo0xHex);\n        const signedRaw = this.type === 'legacy'\n            ? { ...this.raw, v, r, s }\n            : { ...cloneDeep(this.raw), yParity: v, r, s };\n        return new Transaction(signedRaw, this.chain, this.hardfork, this.type);\n    }\n    recoverSenderPublicKey() {\n        if (!this.isSigned)\n            throw new Error('Expected signed transaction: cannot recover sender of unsigned tx');\n        const v = Number(hexToNumber(this.type === 'legacy' ? this.raw.v : this.raw.yParity));\n        const chainId = Number(this.raw.chainId);\n        const recovery = this.type === 'legacy' ? (chainId ? v - (chainId * 2 + 35) : v - 27) : v;\n        const [r, s] = [this.raw.r, this.raw.s].map(hexToNumber);\n        const checkHighS = this.hardfork !== 'chainstart';\n        return secp.sigRecoverPub({ r, s, recovery }, this.getMessageToSign(), checkHighS);\n    }\n}\nTransaction.DEFAULT_HARDFORK = 'london';\nTransaction.DEFAULT_CHAIN = 'mainnet';\nTransaction.DEFAULT_TYPE = 'eip1559';\n",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"/*! noble-secp256k1 - MIT License (c) 2019 Paul Miller (paulmillr.com) */\nconst B256 = 2n ** 256n; // secp256k1 is short weierstrass curve\nconst P = B256 - 0x1000003d1n; // curve's field prime\nconst N = B256 - 0x14551231950b75fc4402da1732fc9bebfn; // curve (group) order\nconst Gx = 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798n; // base point x\nconst Gy = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8n; // base point y\nconst CURVE = { p: P, n: N, a: 0n, b: 7n, Gx, Gy }; // exported variables incl. a, b\nconst fLen = 32; // field / group byte length\nconst crv = (x) => mod(mod(x * x) * x + CURVE.b); // x³ + ax + b weierstrass formula; no a\nconst err = (m = '') => { throw new Error(m); }; // error helper, messes-up stack trace\nconst big = (n) => typeof n === 'bigint'; // is big integer\nconst str = (s) => typeof s === 'string'; // is string\nconst fe = (n) => big(n) && 0n < n && n < P; // is field element (invertible)\nconst ge = (n) => big(n) && 0n < n && n < N; // is group element\nconst au8 = (a, l) => // is Uint8Array (of specific length)\n !(a instanceof Uint8Array) || (typeof l === 'number' && l > 0 && a.length !== l) ?\n    err('Uint8Array expected') : a;\nconst u8n = (data) => new Uint8Array(data); // creates Uint8Array\nconst toU8 = (a, len) => au8(str(a) ? h2b(a) : u8n(a), len); // norm(hex/u8a) to u8a\nconst mod = (a, b = P) => { let r = a % b; return r >= 0n ? r : b + r; }; // mod division\nconst isPoint = (p) => (p instanceof Point ? p : err('Point expected')); // is 3d point\nlet Gpows = undefined; // precomputes for base point G\nclass Point {\n    constructor(px, py, pz) {\n        this.px = px;\n        this.py = py;\n        this.pz = pz;\n    } //3d=less inversions\n    static fromAffine(p) { return new Point(p.x, p.y, 1n); }\n    static fromHex(hex) {\n        hex = toU8(hex); // convert hex string to Uint8Array\n        let p = undefined;\n        const head = hex[0], tail = hex.subarray(1); // first byte is prefix, rest is data\n        const x = slcNum(tail, 0, fLen), len = hex.length; // next 32 bytes are x coordinate\n        if (len === 33 && [0x02, 0x03].includes(head)) { // compressed points: 33b, start\n            if (!fe(x))\n                err('Point hex invalid: x not FE'); // with byte 0x02 or 0x03. Check if 0<x<P\n            let y = sqrt(crv(x)); // x³ + ax + b is right side of equation\n            const isYOdd = (y & 1n) === 1n; // y² is equivalent left-side. Calculate y²:\n            const headOdd = (head & 1) === 1; // y = √y²; there are two solutions: y, -y\n            if (headOdd !== isYOdd)\n                y = mod(-y); // determine proper solution\n            p = new Point(x, y, 1n); // create point\n        } // Uncompressed points: 65b, start with 0x04\n        if (len === 65 && head === 0x04)\n            p = new Point(x, slcNum(tail, fLen, 2 * fLen), 1n);\n        return p ? p.ok() : err('Point is not on curve'); // Verify the result\n    }\n    static fromPrivateKey(k) { return G.mul(toPriv(k)); } // Create point from a private key.\n    get x() { return this.aff().x; } // .x, .y will call expensive toAffine:\n    get y() { return this.aff().y; } // should be used with care.\n    equals(other) {\n        const { px: X1, py: Y1, pz: Z1 } = this;\n        const { px: X2, py: Y2, pz: Z2 } = isPoint(other); // isPoint() checks class equality\n        const X1Z2 = mod(X1 * Z2), X2Z1 = mod(X2 * Z1);\n        const Y1Z2 = mod(Y1 * Z2), Y2Z1 = mod(Y2 * Z1);\n        return X1Z2 === X2Z1 && Y1Z2 === Y2Z1;\n    }\n    negate() { return new Point(this.px, mod(-this.py), this.pz); } // Flip point over y coord\n    double() { return this.add(this); } // Point doubling: P+P, complete formula.\n    add(other) {\n        const { px: X1, py: Y1, pz: Z1 } = this; // free formula from Renes-Costello-Batina\n        const { px: X2, py: Y2, pz: Z2 } = isPoint(other); // https://eprint.iacr.org/2015/1060, algo 1\n        const { a, b } = CURVE; // Cost: 12M + 0S + 3*a + 3*b3 + 23add\n        let X3 = 0n, Y3 = 0n, Z3 = 0n;\n        const b3 = mod(b * 3n);\n        let t0 = mod(X1 * X2), t1 = mod(Y1 * Y2), t2 = mod(Z1 * Z2), t3 = mod(X1 + Y1); // step 1\n        let t4 = mod(X2 + Y2); // step 5\n        t3 = mod(t3 * t4);\n        t4 = mod(t0 + t1);\n        t3 = mod(t3 - t4);\n        t4 = mod(X1 + Z1);\n        let t5 = mod(X2 + Z2); // step 10\n        t4 = mod(t4 * t5);\n        t5 = mod(t0 + t2);\n        t4 = mod(t4 - t5);\n        t5 = mod(Y1 + Z1);\n        X3 = mod(Y2 + Z2); // step 15\n        t5 = mod(t5 * X3);\n        X3 = mod(t1 + t2);\n        t5 = mod(t5 - X3);\n        Z3 = mod(a * t4);\n        X3 = mod(b3 * t2); // step 20\n        Z3 = mod(X3 + Z3);\n        X3 = mod(t1 - Z3);\n        Z3 = mod(t1 + Z3);\n        Y3 = mod(X3 * Z3);\n        t1 = mod(t0 + t0); // step 25\n        t1 = mod(t1 + t0);\n        t2 = mod(a * t2);\n        t4 = mod(b3 * t4);\n        t1 = mod(t1 + t2);\n        t2 = mod(t0 - t2); // step 30\n        t2 = mod(a * t2);\n        t4 = mod(t4 + t2);\n        t0 = mod(t1 * t4);\n        Y3 = mod(Y3 + t0);\n        t0 = mod(t5 * t4); // step 35\n        X3 = mod(t3 * X3);\n        X3 = mod(X3 - t0);\n        t0 = mod(t3 * t1);\n        Z3 = mod(t5 * Z3);\n        Z3 = mod(Z3 + t0); // step 40\n        return new Point(X3, Y3, Z3);\n    }\n    mul(n, safe = true) {\n        if (!safe && n === 0n)\n            return I; // in unsafe mode, allow zero\n        if (!ge(n))\n            err('invalid scalar'); // must be 0 < n < CURVE.n\n        if (this.equals(G))\n            return wNAF(n).p; // use precomputes for base point\n        let p = I, f = G; // init result point & fake point\n        for (let d = this; n > 0n; d = d.double(), n >>= 1n) { // double-and-add ladder\n            if (n & 1n)\n                p = p.add(d); // if bit is present, add to point\n            else if (safe)\n                f = f.add(d); // if not, add to fake for timing safety\n        }\n        return p;\n    }\n    mulAddQUns(R, u1, u2) {\n        return this.mul(u1, false).add(R.mul(u2, false)).ok(); // Unsafe: do NOT use for stuff related\n    } // to private keys. Doesn't use Shamir trick\n    toAffine() {\n        const { px: x, py: y, pz: z } = this; // (x, y, z) ∋ (x=x/z, y=y/z)\n        if (this.equals(I))\n            return { x: 0n, y: 0n }; // fast-path for zero point\n        if (z === 1n)\n            return { x, y }; // if z is 1, pass affine coordinates as-is\n        const iz = inv(z); // z^-1: invert z\n        if (mod(z * iz) !== 1n)\n            err('invalid inverse'); // (z * z^-1) must be 1, otherwise bad math\n        return { x: mod(x * iz), y: mod(y * iz) }; // x = x*z^-1; y = y*z^-1\n    }\n    assertValidity() {\n        const { x, y } = this.aff(); // convert to 2d xy affine point.\n        if (!fe(x) || !fe(y))\n            err('Point invalid: x or y'); // x and y must be in range 0 < n < P\n        return mod(y * y) === crv(x) ? // y² = x³ + ax + b, must be equal\n            this : err('Point invalid: not on curve');\n    }\n    multiply(n) { return this.mul(n); } // Aliases to compress code\n    aff() { return this.toAffine(); }\n    ok() { return this.assertValidity(); }\n    toHex(isCompressed = true) {\n        const { x, y } = this.aff(); // convert to 2d xy affine point\n        const head = isCompressed ? ((y & 1n) === 0n ? '02' : '03') : '04'; // 0x02, 0x03, 0x04 prefix\n        return head + n2h(x) + (isCompressed ? '' : n2h(y)); // prefix||x and ||y\n    }\n    toRawBytes(isCompressed = true) {\n        return h2b(this.toHex(isCompressed)); // re-use toHex(), convert hex to bytes\n    }\n}\nPoint.BASE = new Point(Gx, Gy, 1n); // Generator / base point\nPoint.ZERO = new Point(0n, 1n, 0n); // Identity / zero point\nconst { BASE: G, ZERO: I } = Point; // Generator, identity points\nconst padh = (n, pad) => n.toString(16).padStart(pad, '0');\nconst b2h = (b) => Array.from(b).map(e => padh(e, 2)).join(''); // bytes to hex\nconst h2b = (hex) => {\n    const l = hex.length; // error if not string,\n    if (!str(hex) || l % 2)\n        err('hex invalid 1'); // or has odd length like 3, 5.\n    const arr = u8n(l / 2); // create result array\n    for (let i = 0; i < arr.length; i++) {\n        const j = i * 2;\n        const h = hex.slice(j, j + 2); // hexByte. slice is faster than substr\n        const b = Number.parseInt(h, 16); // byte, created from string part\n        if (Number.isNaN(b) || b < 0)\n            err('hex invalid 2'); // byte must be valid 0 <= byte < 256\n        arr[i] = b;\n    }\n    return arr;\n};\nconst b2n = (b) => BigInt('0x' + (b2h(b) || '0')); // bytes to number\nconst slcNum = (b, from, to) => b2n(b.slice(from, to)); // slice bytes num\nconst n2b = (num) => {\n    return big(num) && num >= 0n && num < B256 ? h2b(padh(num, 2 * fLen)) : err('bigint expected');\n};\nconst n2h = (num) => b2h(n2b(num)); // number to 32b hex\nconst concatB = (...arrs) => {\n    const r = u8n(arrs.reduce((sum, a) => sum + au8(a).length, 0)); // create u8a of summed length\n    let pad = 0; // walk through each array,\n    arrs.forEach(a => { r.set(a, pad); pad += a.length; }); // ensure they have proper type\n    return r;\n};\nconst inv = (num, md = P) => {\n    if (num === 0n || md <= 0n)\n        err('no inverse n=' + num + ' mod=' + md); // no neg exponent for now\n    let a = mod(num, md), b = md, x = 0n, y = 1n, u = 1n, v = 0n;\n    while (a !== 0n) { // uses euclidean gcd algorithm\n        const q = b / a, r = b % a; // not constant-time\n        const m = x - u * q, n = y - v * q;\n        b = a, a = r, x = u, y = v, u = m, v = n;\n    }\n    return b === 1n ? mod(x, md) : err('no inverse'); // b is gcd at this point\n};\nconst sqrt = (n) => {\n    let r = 1n; // So, a special, fast case. Paper: \"Square Roots from 1;24,51,10 to Dan Shanks\".\n    for (let num = n, e = (P + 1n) / 4n; e > 0n; e >>= 1n) { // powMod: modular exponentiation.\n        if (e & 1n)\n            r = (r * num) % P; // Uses exponentiation by squaring.\n        num = (num * num) % P; // Not constant-time.\n    }\n    return mod(r * r) === n ? r : err('sqrt invalid'); // check if result is valid\n};\nconst toPriv = (p) => {\n    if (!big(p))\n        p = b2n(toU8(p, fLen)); // convert to bigint when bytes\n    return ge(p) ? p : err('private key out of range'); // check if bigint is in range\n};\nconst moreThanHalfN = (n) => n > (N >> 1n); // if a number is bigger than CURVE.n/2\nfunction getPublicKey(privKey, isCompressed = true) {\n    return Point.fromPrivateKey(privKey).toRawBytes(isCompressed); // 33b or 65b output\n}\nclass Signature {\n    constructor(r, s, recovery) {\n        this.r = r;\n        this.s = s;\n        this.recovery = recovery;\n        this.assertValidity(); // recovery bit is optional when\n    } // constructed outside.\n    static fromCompact(hex) {\n        hex = toU8(hex, 64); // compact repr is (32b r)||(32b s)\n        return new Signature(slcNum(hex, 0, fLen), slcNum(hex, fLen, 2 * fLen));\n    }\n    assertValidity() { return ge(this.r) && ge(this.s) ? this : err(); } // 0 < r or s < CURVE.n\n    addRecoveryBit(rec) { return new Signature(this.r, this.s, rec); }\n    hasHighS() { return moreThanHalfN(this.s); }\n    recoverPublicKey(msgh) {\n        const { r, s, recovery: rec } = this; // secg.org/sec1-v2.pdf 4.1.6\n        if (![0, 1, 2, 3].includes(rec))\n            err('recovery id invalid'); // check recovery id\n        const h = bits2int_modN(toU8(msgh, 32)); // Truncate hash\n        const radj = rec === 2 || rec === 3 ? r + N : r; // If rec was 2 or 3, q.x is bigger than n\n        if (radj >= P)\n            err('q.x invalid'); // ensure q.x is still a field element\n        const head = (rec & 1) === 0 ? '02' : '03'; // head is 0x02 or 0x03\n        const R = Point.fromHex(head + n2h(radj)); // concat head + hex repr of r\n        const ir = inv(radj, N); // r^-1\n        const u1 = mod(-h * ir, N); // -hr^-1\n        const u2 = mod(s * ir, N); // sr^-1\n        return G.mulAddQUns(R, u1, u2); // (sr^-1)R-(hr^-1)G = -(hr^-1)G + (sr^-1)\n    }\n    toCompactRawBytes() { return h2b(this.toCompactHex()); } // Uint8Array 64b compact repr\n    toCompactHex() { return n2h(this.r) + n2h(this.s); } // hex 64b compact repr\n}\nconst bits2int = (bytes) => {\n    const delta = bytes.length * 8 - 256; // RFC suggests optional truncating via bits2octets\n    const num = b2n(bytes); // FIPS 186-4 4.6 suggests the leftmost min(nBitLen, outLen) bits, which\n    return delta > 0 ? num >> BigInt(delta) : num; // matches bits2int. bits2int can produce res>N.\n};\nconst bits2int_modN = (bytes) => {\n    return mod(bits2int(bytes), N); // with 0: BAD for trunc as per RFC vectors\n};\nconst i2o = (num) => n2b(num); // int to octets\nconst cr = () => // We support: 1) browsers 2) node.js 19+ 3) deno, other envs with crypto\n typeof globalThis === 'object' && 'crypto' in globalThis ? globalThis.crypto : undefined;\nlet _hmacSync; // Can be redefined by use in utils; built-ins don't provide it\nconst optS = { lowS: true }; // opts for sign()\nconst optV = { lowS: true }; // standard opts for verify()\nfunction prepSig(msgh, priv, opts = optS) {\n    if (['der', 'recovered', 'canonical'].some(k => k in opts)) // Ban legacy options\n        err('sign() legacy options not supported');\n    let { lowS } = opts; // generates low-s sigs by default\n    if (lowS == null)\n        lowS = true; // RFC6979 3.2: we skip step A\n    const h1i = bits2int_modN(toU8(msgh)); // msg bigint\n    const h1o = i2o(h1i); // msg octets\n    const d = toPriv(priv); // validate private key, convert to bigint\n    const seed = [i2o(d), h1o]; // Step D of RFC6979 3.2\n    let ent = opts.extraEntropy; // RFC6979 3.6: additional k' (optional)\n    if (ent) { // K = HMAC_K(V || 0x00 || int2octets(x) || bits2octets(h1) || k')\n        if (ent === true)\n            ent = etc.randomBytes(fLen); // if true, use CSPRNG to generate data\n        const e = toU8(ent); // convert Hex|Bytes to Bytes\n        if (e.length !== fLen)\n            err(); // Expected 32 bytes of extra data\n        seed.push(e);\n    }\n    const m = h1i; // convert msg to bigint\n    const k2sig = (kBytes) => {\n        const k = bits2int(kBytes); // RFC6979 method.\n        if (!ge(k))\n            return; // Check 0 < k < CURVE.n\n        const ik = inv(k, N); // k^-1 mod n, NOT mod P\n        const q = G.mul(k).aff(); // q = Gk\n        const r = mod(q.x, N); // r = q.x mod n\n        if (r === 0n)\n            return; // r=0 invalid\n        const s = mod(ik * mod(m + mod(d * r, N), N), N); // s = k^-1(m + rd) mod n\n        if (s === 0n)\n            return; // s=0 invalid\n        let normS = s; // normalized S\n        let rec = (q.x === r ? 0 : 2) | Number(q.y & 1n); // recovery bit\n        if (lowS && moreThanHalfN(s)) { // if lowS was passed, ensure s is always\n            normS = mod(-s, N); // in the bottom half of CURVE.n\n            rec ^= 1;\n        }\n        return new Signature(r, normS, rec); // use normS, not s\n    };\n    return { seed: concatB(...seed), k2sig };\n}\nfunction hmacDrbg(asynchronous) {\n    let v = u8n(fLen); // Minimal non-full-spec HMAC-DRBG from NIST 800-90 for RFC6979 sigs.\n    let k = u8n(fLen); // Steps B, 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 = () => { v.fill(1); k.fill(0); i = 0; };\n    const _e = 'drbg: tried 1000 values';\n    if (asynchronous) { // asynchronous=true\n        const h = (...b) => etc.hmacSha256Async(k, v, ...b); // hmac(k)(v, ...values)\n        const reseed = async (seed = u8n()) => {\n            k = await h(u8n([0x00]), seed); // k = hmac(K || V || 0x00 || seed)\n            v = await h(); // v = hmac(K || V)\n            if (seed.length === 0)\n                return;\n            k = await h(u8n([0x01]), seed); // k = hmac(K || V || 0x01 || seed)\n            v = await h(); // v = hmac(K || V)\n        };\n        const gen = async () => {\n            if (i++ >= 1000)\n                err(_e);\n            v = await h(); // v = hmac(K || V)\n            return v;\n        };\n        return async (seed, pred) => {\n            reset(); // the returned fn, don't, it's: 1. slower (JIT). 2. unsafe (async race conditions)\n            await reseed(seed); // Steps D-G\n            let res = undefined; // Step H: grind until k is in [1..n-1]\n            while (!(res = pred(await gen())))\n                await reseed(); // test predicate until it returns ok\n            reset();\n            return res;\n        };\n    }\n    else {\n        const h = (...b) => {\n            const f = _hmacSync;\n            if (!f)\n                err('etc.hmacSha256Sync not set');\n            return f(k, v, ...b); // hmac(k)(v, ...values)\n        };\n        const reseed = (seed = u8n()) => {\n            k = h(u8n([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(u8n([0x01]), seed); // k = hmac(k || v || 0x01 || seed)\n            v = h(); // v = hmac(k || v)\n        };\n        const gen = () => {\n            if (i++ >= 1000)\n                err(_e);\n            v = h(); // v = hmac(k || v)\n            return v;\n        };\n        return (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(); // test predicate until it returns ok\n            reset();\n            return res;\n        };\n    }\n}\n// ECDSA signature generation. via secg.org/sec1-v2.pdf 4.1.2 + RFC6979 deterministic k\nasync function signAsync(msgh, priv, opts = optS) {\n    const { seed, k2sig } = prepSig(msgh, priv, opts); // Extract arguments for hmac-drbg\n    return hmacDrbg(true)(seed, k2sig); // Re-run hmac-drbg until k2sig returns ok\n}\nfunction sign(msgh, priv, opts = optS) {\n    const { seed, k2sig } = prepSig(msgh, priv, opts); // Extract arguments for hmac-drbg\n    return hmacDrbg(false)(seed, k2sig); // Re-run hmac-drbg until k2sig returns ok\n}\nfunction verify(sig, msgh, pub, opts = optV) {\n    let { lowS } = opts; // ECDSA signature verification\n    if (lowS == null)\n        lowS = true; // Default lowS=true\n    if ('strict' in opts)\n        err('verify() legacy options not supported'); // legacy param\n    let sig_, h, P; // secg.org/sec1-v2.pdf 4.1.4\n    const rs = sig && typeof sig === 'object' && 'r' in sig; // Previous ver supported DER sigs. We\n    if (!rs && (toU8(sig).length !== 2 * fLen)) // throw error when DER is suspected now.\n        err('signature must be 64 bytes');\n    try {\n        sig_ = rs ? new Signature(sig.r, sig.s).assertValidity() : Signature.fromCompact(sig);\n        h = bits2int_modN(toU8(msgh, fLen)); // Truncate hash\n        P = pub instanceof Point ? pub.ok() : Point.fromHex(pub); // Validate public key\n    }\n    catch (e) {\n        return false;\n    } // Check sig for validity in both cases\n    if (!sig_)\n        return false;\n    const { r, s } = sig_;\n    if (lowS && moreThanHalfN(s))\n        return false; // lowS bans sig.s >= CURVE.n/2\n    let R;\n    try {\n        const is = inv(s, N); // s^-1\n        const u1 = mod(h * is, N); // u1 = hs^-1 mod n\n        const u2 = mod(r * is, N); // u2 = rs^-1 mod n\n        R = G.mulAddQUns(P, u1, u2).aff(); // R = u1⋅G + u2⋅P\n    }\n    catch (error) {\n        return false;\n    }\n    if (!R)\n        return false; // stop if R is identity / zero point\n    const v = mod(R.x, N); // <== The weird ECDSA part. R.x must be in N's field, not P's\n    return v === r; // mod(R.x, n) == r\n}\nfunction getSharedSecret(privA, pubB, isCompressed = true) {\n    return Point.fromHex(pubB).mul(toPriv(privA)).toRawBytes(isCompressed); // ECDH\n}\nfunction hashToPrivateKey(hash) {\n    hash = toU8(hash); // produces private keys with modulo bias\n    const minLen = fLen + 8; // being neglible.\n    if (hash.length < minLen || hash.length > 1024)\n        err('expected proper params');\n    const num = mod(b2n(hash), N - 1n) + 1n; // takes at least n+8 bytes\n    return n2b(num);\n}\nconst etc = {\n    hexToBytes: h2b, bytesToHex: b2h,\n    concatBytes: concatB, bytesToNumberBE: b2n, numberToBytesBE: n2b,\n    mod, invert: inv,\n    hmacSha256Async: async (key, ...msgs) => {\n        const crypto = cr(); // HMAC-SHA256 async. No sync built-in!\n        if (!crypto)\n            return err('etc.hmacSha256Async not set'); // Uses webcrypto: native cryptography.\n        const s = crypto.subtle;\n        const k = await s.importKey('raw', key, { name: 'HMAC', hash: { name: 'SHA-256' } }, false, ['sign']);\n        return u8n(await s.sign('HMAC', k, concatB(...msgs)));\n    },\n    hmacSha256Sync: _hmacSync,\n    hashToPrivateKey,\n    randomBytes: (len) => {\n        const crypto = cr(); // Can be shimmed in node.js <= 18 to prevent error:\n        // import { webcrypto } from 'node:crypto';\n        // if (!globalThis.crypto) globalThis.crypto = webcrypto;\n        if (!crypto)\n            err('crypto.getRandomValues must be defined');\n        return crypto.getRandomValues(u8n(len));\n    },\n};\nconst utils = {\n    normPrivateKeyToScalar: toPriv,\n    isValidPrivateKey: (key) => { try {\n        return !!toPriv(key);\n    }\n    catch (e) {\n        return false;\n    } },\n    randomPrivateKey: () => hashToPrivateKey(etc.randomBytes(fLen + 8)),\n    precompute(w = 8, p = G) { p.multiply(3n); return p; }, // no-op\n};\nObject.defineProperties(etc, { hmacSha256Sync: {\n        configurable: false, get() { return _hmacSync; }, set(f) { if (!_hmacSync)\n            _hmacSync = f; },\n    } });\nconst W = 8; // Precomputes-related code. W = window size\nconst precompute = () => {\n    const points = []; // 10x sign(), 2x verify(). To achieve this,\n    const windows = 256 / W + 1; // app needs to spend 40ms+ to calculate\n    let p = G, b = p; // a lot of points related to base point G.\n    for (let w = 0; w < windows; w++) { // Points are stored in array and used\n        b = p; // any time Gx multiplication is done.\n        points.push(b); // They consume 16-32 MiB of RAM.\n        for (let i = 1; i < 2 ** (W - 1); i++) {\n            b = b.add(p);\n            points.push(b);\n        }\n        p = b.double(); // Precomputes don't speed-up getSharedKey,\n    } // which multiplies user point by scalar,\n    return points; // when precomputes are using base point\n};\nconst wNAF = (n) => {\n    // Compared to other point mult methods,\n    const comp = Gpows || (Gpows = precompute()); // stores 2x less points using subtraction\n    const neg = (cnd, p) => { let n = p.negate(); return cnd ? n : p; }; // negate\n    let p = I, f = G; // f must be G, or could become I in the end\n    const windows = 1 + 256 / W; // W=8 17 windows\n    const wsize = 2 ** (W - 1); // W=8 128 window size\n    const mask = BigInt(2 ** W - 1); // W=8 will create mask 0b11111111\n    const maxNum = 2 ** W; // W=8 256\n    const shiftBy = BigInt(W); // W=8 8\n    for (let w = 0; w < windows; w++) {\n        const off = w * wsize;\n        let wbits = Number(n & mask); // extract W bits.\n        n >>= shiftBy; // shift number by W bits.\n        if (wbits > wsize) {\n            wbits -= maxNum;\n            n += 1n;\n        } // split if bits > max: +224 => 256-32\n        const off1 = off, off2 = off + Math.abs(wbits) - 1; // offsets, evaluate both\n        const cnd1 = w % 2 !== 0, cnd2 = wbits < 0; // conditions, evaluate both\n        if (wbits === 0) {\n            f = f.add(neg(cnd1, comp[off1])); // bits are 0: add garbage to fake point\n        }\n        else { //          ^ can't add off2, off2 = I\n            p = p.add(neg(cnd2, comp[off2])); // bits are 1: add to result point\n        }\n    }\n    return { p, f }; // return both real and fake points for JIT\n}; // !! you can disable precomputes by commenting-out call of the wNAF() inside Point#mul()\nexport { getPublicKey, sign, signAsync, verify, CURVE, // Remove the export to easily use in REPL\ngetSharedSecret, etc, utils, Point as ProjectivePoint, Signature }; // envs like browser console\n",null,"import { getMinHashLength, mapHashToField } from './modular.js';\nimport { bitLen, bitGet, ensureBytes } from './utils.js';\n// prettier-ignore\nimport { createHasher } from './hash-to-curve.js';\nimport { weierstrassPoints, } from './weierstrass.js';\n// prettier-ignore\nconst _2n = BigInt(2), _3n = BigInt(3);\nexport function bls(CURVE) {\n    // Fields are specific for curve, so for now we'll need to pass them with opts\n    const { Fp, Fr, Fp2, Fp6, Fp12 } = CURVE.fields;\n    const BLS_X_LEN = bitLen(CURVE.params.x);\n    // Pre-compute coefficients for sparse multiplication\n    // Point addition and point double calculations is reused for coefficients\n    function calcPairingPrecomputes(p) {\n        const { x, y } = p;\n        // prettier-ignore\n        const Qx = x, Qy = y, Qz = Fp2.ONE;\n        // prettier-ignore\n        let Rx = Qx, Ry = Qy, Rz = Qz;\n        let ell_coeff = [];\n        for (let i = BLS_X_LEN - 2; i >= 0; i--) {\n            // Double\n            let t0 = Fp2.sqr(Ry); // Ry²\n            let t1 = Fp2.sqr(Rz); // Rz²\n            let t2 = Fp2.multiplyByB(Fp2.mul(t1, _3n)); // 3 * T1 * B\n            let t3 = Fp2.mul(t2, _3n); // 3 * T2\n            let t4 = Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(Ry, Rz)), t1), t0); // (Ry + Rz)² - T1 - T0\n            ell_coeff.push([\n                Fp2.sub(t2, t0), // T2 - T0\n                Fp2.mul(Fp2.sqr(Rx), _3n), // 3 * Rx²\n                Fp2.neg(t4), // -T4\n            ]);\n            Rx = Fp2.div(Fp2.mul(Fp2.mul(Fp2.sub(t0, t3), Rx), Ry), _2n); // ((T0 - T3) * Rx * Ry) / 2\n            Ry = Fp2.sub(Fp2.sqr(Fp2.div(Fp2.add(t0, t3), _2n)), Fp2.mul(Fp2.sqr(t2), _3n)); // ((T0 + T3) / 2)² - 3 * T2²\n            Rz = Fp2.mul(t0, t4); // T0 * T4\n            if (bitGet(CURVE.params.x, i)) {\n                // Addition\n                let t0 = Fp2.sub(Ry, Fp2.mul(Qy, Rz)); // Ry - Qy * Rz\n                let t1 = Fp2.sub(Rx, Fp2.mul(Qx, Rz)); // Rx - Qx * Rz\n                ell_coeff.push([\n                    Fp2.sub(Fp2.mul(t0, Qx), Fp2.mul(t1, Qy)), // T0 * Qx - T1 * Qy\n                    Fp2.neg(t0), // -T0\n                    t1, // T1\n                ]);\n                let t2 = Fp2.sqr(t1); // T1²\n                let t3 = Fp2.mul(t2, t1); // T2 * T1\n                let t4 = Fp2.mul(t2, Rx); // T2 * Rx\n                let t5 = Fp2.add(Fp2.sub(t3, Fp2.mul(t4, _2n)), Fp2.mul(Fp2.sqr(t0), Rz)); // T3 - 2 * T4 + T0² * Rz\n                Rx = Fp2.mul(t1, t5); // T1 * T5\n                Ry = Fp2.sub(Fp2.mul(Fp2.sub(t4, t5), t0), Fp2.mul(t3, Ry)); // (T4 - T5) * T0 - T3 * Ry\n                Rz = Fp2.mul(Rz, t3); // Rz * T3\n            }\n        }\n        return ell_coeff;\n    }\n    function millerLoop(ell, g1) {\n        const { x } = CURVE.params;\n        const Px = g1[0];\n        const Py = g1[1];\n        let f12 = Fp12.ONE;\n        for (let j = 0, i = BLS_X_LEN - 2; i >= 0; i--, j++) {\n            const E = ell[j];\n            f12 = Fp12.multiplyBy014(f12, E[0], Fp2.mul(E[1], Px), Fp2.mul(E[2], Py));\n            if (bitGet(x, i)) {\n                j += 1;\n                const F = ell[j];\n                f12 = Fp12.multiplyBy014(f12, F[0], Fp2.mul(F[1], Px), Fp2.mul(F[2], Py));\n            }\n            if (i !== 0)\n                f12 = Fp12.sqr(f12);\n        }\n        return Fp12.conjugate(f12);\n    }\n    const utils = {\n        randomPrivateKey: () => {\n            const length = getMinHashLength(Fr.ORDER);\n            return mapHashToField(CURVE.randomBytes(length), Fr.ORDER);\n        },\n        calcPairingPrecomputes,\n    };\n    // Point on G1 curve: (x, y)\n    const G1_ = weierstrassPoints({ n: Fr.ORDER, ...CURVE.G1 });\n    const G1 = Object.assign(G1_, createHasher(G1_.ProjectivePoint, CURVE.G1.mapToCurve, {\n        ...CURVE.htfDefaults,\n        ...CURVE.G1.htfDefaults,\n    }));\n    function pairingPrecomputes(point) {\n        const p = point;\n        if (p._PPRECOMPUTES)\n            return p._PPRECOMPUTES;\n        p._PPRECOMPUTES = calcPairingPrecomputes(point.toAffine());\n        return p._PPRECOMPUTES;\n    }\n    // TODO: export\n    // function clearPairingPrecomputes(point: G2) {\n    //   const p = point as G2 & withPairingPrecomputes;\n    //   p._PPRECOMPUTES = undefined;\n    // }\n    // Point on G2 curve (complex numbers): (x₁, x₂+i), (y₁, y₂+i)\n    const G2_ = weierstrassPoints({ n: Fr.ORDER, ...CURVE.G2 });\n    const G2 = Object.assign(G2_, createHasher(G2_.ProjectivePoint, CURVE.G2.mapToCurve, {\n        ...CURVE.htfDefaults,\n        ...CURVE.G2.htfDefaults,\n    }));\n    const { ShortSignature } = CURVE.G1;\n    const { Signature } = CURVE.G2;\n    // Calculates bilinear pairing\n    function pairing(Q, P, withFinalExponent = true) {\n        if (Q.equals(G1.ProjectivePoint.ZERO) || P.equals(G2.ProjectivePoint.ZERO))\n            throw new Error('pairing is not available for ZERO point');\n        Q.assertValidity();\n        P.assertValidity();\n        // Performance: 9ms for millerLoop and ~14ms for exp.\n        const Qa = Q.toAffine();\n        const looped = millerLoop(pairingPrecomputes(P), [Qa.x, Qa.y]);\n        return withFinalExponent ? Fp12.finalExponentiate(looped) : looped;\n    }\n    function normP1(point) {\n        return point instanceof G1.ProjectivePoint ? point : G1.ProjectivePoint.fromHex(point);\n    }\n    function normP1Hash(point, htfOpts) {\n        return point instanceof G1.ProjectivePoint\n            ? point\n            : G1.hashToCurve(ensureBytes('point', point), htfOpts);\n    }\n    function normP2(point) {\n        return point instanceof G2.ProjectivePoint ? point : Signature.fromHex(point);\n    }\n    function normP2Hash(point, htfOpts) {\n        return point instanceof G2.ProjectivePoint\n            ? point\n            : G2.hashToCurve(ensureBytes('point', point), htfOpts);\n    }\n    // Multiplies generator (G1) by private key.\n    // P = pk x G\n    function getPublicKey(privateKey) {\n        return G1.ProjectivePoint.fromPrivateKey(privateKey).toRawBytes(true);\n    }\n    // Multiplies generator (G2) by private key.\n    // P = pk x G\n    function getPublicKeyForShortSignatures(privateKey) {\n        return G2.ProjectivePoint.fromPrivateKey(privateKey).toRawBytes(true);\n    }\n    function sign(message, privateKey, htfOpts) {\n        const msgPoint = normP2Hash(message, htfOpts);\n        msgPoint.assertValidity();\n        const sigPoint = msgPoint.multiply(G1.normPrivateKeyToScalar(privateKey));\n        if (message instanceof G2.ProjectivePoint)\n            return sigPoint;\n        return Signature.toRawBytes(sigPoint);\n    }\n    function signShortSignature(message, privateKey, htfOpts) {\n        const msgPoint = normP1Hash(message, htfOpts);\n        msgPoint.assertValidity();\n        const sigPoint = msgPoint.multiply(G1.normPrivateKeyToScalar(privateKey));\n        if (message instanceof G1.ProjectivePoint)\n            return sigPoint;\n        return ShortSignature.toRawBytes(sigPoint);\n    }\n    // Checks if pairing of public key & hash is equal to pairing of generator & signature.\n    // e(P, H(m)) == e(G, S)\n    function verify(signature, message, publicKey, htfOpts) {\n        const P = normP1(publicKey);\n        const Hm = normP2Hash(message, htfOpts);\n        const G = G1.ProjectivePoint.BASE;\n        const S = normP2(signature);\n        // Instead of doing 2 exponentiations, we use property of billinear maps\n        // and do one exp after multiplying 2 points.\n        const ePHm = pairing(P.negate(), Hm, false);\n        const eGS = pairing(G, S, false);\n        const exp = Fp12.finalExponentiate(Fp12.mul(eGS, ePHm));\n        return Fp12.eql(exp, Fp12.ONE);\n    }\n    // Checks if pairing of public key & hash is equal to pairing of generator & signature.\n    // e(S, G) == e(H(m), P)\n    function verifyShortSignature(signature, message, publicKey, htfOpts) {\n        const P = normP2(publicKey);\n        const Hm = normP1Hash(message, htfOpts);\n        const G = G2.ProjectivePoint.BASE;\n        const S = normP1(signature);\n        // Instead of doing 2 exponentiations, we use property of billinear maps\n        // and do one exp after multiplying 2 points.\n        const eHmP = pairing(Hm, P, false);\n        const eSG = pairing(S, G.negate(), false);\n        const exp = Fp12.finalExponentiate(Fp12.mul(eSG, eHmP));\n        return Fp12.eql(exp, Fp12.ONE);\n    }\n    function aggregatePublicKeys(publicKeys) {\n        if (!publicKeys.length)\n            throw new Error('Expected non-empty array');\n        const agg = publicKeys.map(normP1).reduce((sum, p) => sum.add(p), G1.ProjectivePoint.ZERO);\n        const aggAffine = agg; //.toAffine();\n        if (publicKeys[0] instanceof G1.ProjectivePoint) {\n            aggAffine.assertValidity();\n            return aggAffine;\n        }\n        // toRawBytes ensures point validity\n        return aggAffine.toRawBytes(true);\n    }\n    function aggregateSignatures(signatures) {\n        if (!signatures.length)\n            throw new Error('Expected non-empty array');\n        const agg = signatures.map(normP2).reduce((sum, s) => sum.add(s), G2.ProjectivePoint.ZERO);\n        const aggAffine = agg; //.toAffine();\n        if (signatures[0] instanceof G2.ProjectivePoint) {\n            aggAffine.assertValidity();\n            return aggAffine;\n        }\n        return Signature.toRawBytes(aggAffine);\n    }\n    function aggregateShortSignatures(signatures) {\n        if (!signatures.length)\n            throw new Error('Expected non-empty array');\n        const agg = signatures.map(normP1).reduce((sum, s) => sum.add(s), G1.ProjectivePoint.ZERO);\n        const aggAffine = agg; //.toAffine();\n        if (signatures[0] instanceof G1.ProjectivePoint) {\n            aggAffine.assertValidity();\n            return aggAffine;\n        }\n        return ShortSignature.toRawBytes(aggAffine);\n    }\n    // https://ethresear.ch/t/fast-verification-of-multiple-bls-signatures/5407\n    // e(G, S) = e(G, SUM(n)(Si)) = MUL(n)(e(G, Si))\n    function verifyBatch(signature, messages, publicKeys, htfOpts) {\n        // @ts-ignore\n        // console.log('verifyBatch', bytesToHex(signature as any), messages, publicKeys.map(bytesToHex));\n        if (!messages.length)\n            throw new Error('Expected non-empty messages array');\n        if (publicKeys.length !== messages.length)\n            throw new Error('Pubkey count should equal msg count');\n        const sig = normP2(signature);\n        const nMessages = messages.map((i) => normP2Hash(i, htfOpts));\n        const nPublicKeys = publicKeys.map(normP1);\n        try {\n            const paired = [];\n            for (const message of new Set(nMessages)) {\n                const groupPublicKey = nMessages.reduce((groupPublicKey, subMessage, i) => subMessage === message ? groupPublicKey.add(nPublicKeys[i]) : groupPublicKey, G1.ProjectivePoint.ZERO);\n                // const msg = message instanceof PointG2 ? message : await PointG2.hashToCurve(message);\n                // Possible to batch pairing for same msg with different groupPublicKey here\n                paired.push(pairing(groupPublicKey, message, false));\n            }\n            paired.push(pairing(G1.ProjectivePoint.BASE.negate(), sig, false));\n            const product = paired.reduce((a, b) => Fp12.mul(a, b), Fp12.ONE);\n            const exp = Fp12.finalExponentiate(product);\n            return Fp12.eql(exp, Fp12.ONE);\n        }\n        catch {\n            return false;\n        }\n    }\n    G1.ProjectivePoint.BASE._setWindowSize(4);\n    return {\n        getPublicKey,\n        getPublicKeyForShortSignatures,\n        sign,\n        signShortSignature,\n        verify,\n        verifyBatch,\n        verifyShortSignature,\n        aggregatePublicKeys,\n        aggregateSignatures,\n        aggregateShortSignatures,\n        millerLoop,\n        pairing,\n        G1,\n        G2,\n        Signature,\n        ShortSignature,\n        fields: {\n            Fr,\n            Fp,\n            Fp2,\n            Fp6,\n            Fp12,\n        },\n        params: {\n            x: CURVE.params.x,\n            r: CURVE.params.r,\n            G1b: CURVE.G1.b,\n            G2b: CURVE.G2.b,\n        },\n        utils,\n    };\n}\n//# sourceMappingURL=bls.js.map","/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n// bls12-381 is pairing-friendly Barreto-Lynn-Scott elliptic curve construction allowing to:\n// - Construct zk-SNARKs at the 120-bit security\n// - Efficiently verify N aggregate signatures with 1 pairing and N ec additions:\n//   the Boneh-Lynn-Shacham signature scheme is orders of magnitude more efficient than Schnorr\n//\n// ### Summary\n// 1. BLS Relies on Bilinear Pairing (expensive)\n// 2. Private Keys: 32 bytes\n// 3. Public Keys: 48 bytes: 381 bit affine x coordinate, encoded into 48 big-endian bytes.\n// 4. Signatures: 96 bytes: two 381 bit integers (affine x coordinate), encoded into two 48 big-endian byte arrays.\n//     - The signature is a point on the G2 subgroup, which is defined over a finite field\n//     with elements twice as big as the G1 curve (G2 is over Fp2 rather than Fp. Fp2 is analogous to the complex numbers).\n// 5. The 12 stands for the Embedding degree.\n//\n// ### Formulas\n// - `P = pk x G` - public keys\n// - `S = pk x H(m)` - signing\n// - `e(P, H(m)) == e(G, S)` - verification using pairings\n// - `e(G, S) = e(G, SUM(n)(Si)) = MUL(n)(e(G, Si))` - signature aggregation\n//\n// ### Compatibility and notes\n// 1. It is compatible with Algorand, Chia, Dfinity, Ethereum, Filecoin, ZEC\n//    Filecoin uses little endian byte arrays for private keys - make sure to reverse byte order.\n// 2. Some projects use G2 for public keys and G1 for signatures. It's called \"short signature\"\n// 3. Curve security level is about 120 bits as per Barbulescu-Duquesne 2017\n//    https://hal.science/hal-01534101/file/main.pdf\n// 4. Compatible with specs:\n// [cfrg-pairing-friendly-curves-11](https://tools.ietf.org/html/draft-irtf-cfrg-pairing-friendly-curves-11),\n// [cfrg-bls-signature-05](https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-bls-signature-05),\n// [RFC 9380](https://www.rfc-editor.org/rfc/rfc9380).\nimport { sha256 } from '@noble/hashes/sha256';\nimport { randomBytes } from '@noble/hashes/utils';\nimport { bls } from './abstract/bls.js';\nimport * as mod from './abstract/modular.js';\nimport { concatBytes as concatB, ensureBytes, numberToBytesBE, bytesToNumberBE, bitLen, bitGet, bitMask, bytesToHex, } from './abstract/utils.js';\n// Types\nimport { mapToCurveSimpleSWU, } from './abstract/weierstrass.js';\nimport { isogenyMap } from './abstract/hash-to-curve.js';\n// Be friendly to bad ECMAScript parsers by not using bigint literals\n// prettier-ignore\nconst _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3), _4n = BigInt(4);\n// prettier-ignore\nconst _8n = BigInt(8), _16n = BigInt(16);\n// CURVE FIELDS\n// Finite field over p.\nconst Fp_raw = BigInt('0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab');\nconst Fp = mod.Field(Fp_raw);\n// Finite field over r.\n// This particular field is not used anywhere in bls12-381, but it is still useful.\nconst Fr = mod.Field(BigInt('0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001'));\nconst Fp2Add = ({ c0, c1 }, { c0: r0, c1: r1 }) => ({\n    c0: Fp.add(c0, r0),\n    c1: Fp.add(c1, r1),\n});\nconst Fp2Subtract = ({ c0, c1 }, { c0: r0, c1: r1 }) => ({\n    c0: Fp.sub(c0, r0),\n    c1: Fp.sub(c1, r1),\n});\nconst Fp2Multiply = ({ c0, c1 }, rhs) => {\n    if (typeof rhs === 'bigint')\n        return { c0: Fp.mul(c0, rhs), c1: Fp.mul(c1, rhs) };\n    // (a+bi)(c+di) = (ac−bd) + (ad+bc)i\n    const { c0: r0, c1: r1 } = rhs;\n    let t1 = Fp.mul(c0, r0); // c0 * o0\n    let t2 = Fp.mul(c1, r1); // c1 * o1\n    // (T1 - T2) + ((c0 + c1) * (r0 + r1) - (T1 + T2))*i\n    const o0 = Fp.sub(t1, t2);\n    const o1 = Fp.sub(Fp.mul(Fp.add(c0, c1), Fp.add(r0, r1)), Fp.add(t1, t2));\n    return { c0: o0, c1: o1 };\n};\nconst Fp2Square = ({ c0, c1 }) => {\n    const a = Fp.add(c0, c1);\n    const b = Fp.sub(c0, c1);\n    const c = Fp.add(c0, c0);\n    return { c0: Fp.mul(a, b), c1: Fp.mul(c, c1) };\n};\n// G2 is the order-q subgroup of E2(Fp²) : y² = x³+4(1+√−1),\n// where Fp2 is Fp[√−1]/(x2+1). #E2(Fp2 ) = h2q, where\n// G² - 1\n// h2q\n// NOTE: ORDER was wrong!\nconst FP2_ORDER = Fp_raw * Fp_raw;\nconst Fp2 = {\n    ORDER: FP2_ORDER,\n    BITS: bitLen(FP2_ORDER),\n    BYTES: Math.ceil(bitLen(FP2_ORDER) / 8),\n    MASK: bitMask(bitLen(FP2_ORDER)),\n    ZERO: { c0: Fp.ZERO, c1: Fp.ZERO },\n    ONE: { c0: Fp.ONE, c1: Fp.ZERO },\n    create: (num) => num,\n    isValid: ({ c0, c1 }) => typeof c0 === 'bigint' && typeof c1 === 'bigint',\n    is0: ({ c0, c1 }) => Fp.is0(c0) && Fp.is0(c1),\n    eql: ({ c0, c1 }, { c0: r0, c1: r1 }) => Fp.eql(c0, r0) && Fp.eql(c1, r1),\n    neg: ({ c0, c1 }) => ({ c0: Fp.neg(c0), c1: Fp.neg(c1) }),\n    pow: (num, power) => mod.FpPow(Fp2, num, power),\n    invertBatch: (nums) => mod.FpInvertBatch(Fp2, nums),\n    // Normalized\n    add: Fp2Add,\n    sub: Fp2Subtract,\n    mul: Fp2Multiply,\n    sqr: Fp2Square,\n    // NonNormalized stuff\n    addN: Fp2Add,\n    subN: Fp2Subtract,\n    mulN: Fp2Multiply,\n    sqrN: Fp2Square,\n    // Why inversion for bigint inside Fp instead of Fp2? it is even used in that context?\n    div: (lhs, rhs) => Fp2.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp2.inv(rhs)),\n    inv: ({ c0: a, c1: b }) => {\n        // We wish to find the multiplicative inverse of a nonzero\n        // element a + bu in Fp2. We leverage an identity\n        //\n        // (a + bu)(a - bu) = a² + b²\n        //\n        // which holds because u² = -1. This can be rewritten as\n        //\n        // (a + bu)(a - bu)/(a² + b²) = 1\n        //\n        // because a² + b² = 0 has no nonzero solutions for (a, b).\n        // This gives that (a - bu)/(a² + b²) is the inverse\n        // of (a + bu). Importantly, this can be computing using\n        // only a single inversion in Fp.\n        const factor = Fp.inv(Fp.create(a * a + b * b));\n        return { c0: Fp.mul(factor, Fp.create(a)), c1: Fp.mul(factor, Fp.create(-b)) };\n    },\n    sqrt: (num) => {\n        if (Fp2.eql(num, Fp2.ZERO))\n            return Fp2.ZERO; // Algo doesn't handles this case\n        // TODO: Optimize this line. It's extremely slow.\n        // Speeding this up would boost aggregateSignatures.\n        // https://eprint.iacr.org/2012/685.pdf applicable?\n        // https://github.com/zkcrypto/bls12_381/blob/080eaa74ec0e394377caa1ba302c8c121df08b07/src/fp2.rs#L250\n        // https://github.com/supranational/blst/blob/aae0c7d70b799ac269ff5edf29d8191dbd357876/src/exp2.c#L1\n        // Inspired by https://github.com/dalek-cryptography/curve25519-dalek/blob/17698df9d4c834204f83a3574143abacb4fc81a5/src/field.rs#L99\n        const candidateSqrt = Fp2.pow(num, (Fp2.ORDER + _8n) / _16n);\n        const check = Fp2.div(Fp2.sqr(candidateSqrt), num); // candidateSqrt.square().div(this);\n        const R = FP2_ROOTS_OF_UNITY;\n        const divisor = [R[0], R[2], R[4], R[6]].find((r) => Fp2.eql(r, check));\n        if (!divisor)\n            throw new Error('No root');\n        const index = R.indexOf(divisor);\n        const root = R[index / 2];\n        if (!root)\n            throw new Error('Invalid root');\n        const x1 = Fp2.div(candidateSqrt, root);\n        const x2 = Fp2.neg(x1);\n        const { re: re1, im: im1 } = Fp2.reim(x1);\n        const { re: re2, im: im2 } = Fp2.reim(x2);\n        if (im1 > im2 || (im1 === im2 && re1 > re2))\n            return x1;\n        return x2;\n    },\n    // Same as sgn0_m_eq_2 in RFC 9380\n    isOdd: (x) => {\n        const { re: x0, im: x1 } = Fp2.reim(x);\n        const sign_0 = x0 % _2n;\n        const zero_0 = x0 === _0n;\n        const sign_1 = x1 % _2n;\n        return BigInt(sign_0 || (zero_0 && sign_1)) == _1n;\n    },\n    // Bytes util\n    fromBytes(b) {\n        if (b.length !== Fp2.BYTES)\n            throw new Error(`fromBytes wrong length=${b.length}`);\n        return { c0: Fp.fromBytes(b.subarray(0, Fp.BYTES)), c1: Fp.fromBytes(b.subarray(Fp.BYTES)) };\n    },\n    toBytes: ({ c0, c1 }) => concatB(Fp.toBytes(c0), Fp.toBytes(c1)),\n    cmov: ({ c0, c1 }, { c0: r0, c1: r1 }, c) => ({\n        c0: Fp.cmov(c0, r0, c),\n        c1: Fp.cmov(c1, r1, c),\n    }),\n    // Specific utils\n    // toString() {\n    //   return `Fp2(${this.c0} + ${this.c1}×i)`;\n    // }\n    reim: ({ c0, c1 }) => ({ re: c0, im: c1 }),\n    // multiply by u + 1\n    mulByNonresidue: ({ c0, c1 }) => ({ c0: Fp.sub(c0, c1), c1: Fp.add(c0, c1) }),\n    multiplyByB: ({ c0, c1 }) => {\n        let t0 = Fp.mul(c0, _4n); // 4 * c0\n        let t1 = Fp.mul(c1, _4n); // 4 * c1\n        // (T0-T1) + (T0+T1)*i\n        return { c0: Fp.sub(t0, t1), c1: Fp.add(t0, t1) };\n    },\n    fromBigTuple: (tuple) => {\n        if (tuple.length !== 2)\n            throw new Error('Invalid tuple');\n        const fps = tuple.map((n) => Fp.create(n));\n        return { c0: fps[0], c1: fps[1] };\n    },\n    frobeniusMap: ({ c0, c1 }, power) => ({\n        c0,\n        c1: Fp.mul(c1, FP2_FROBENIUS_COEFFICIENTS[power % 2]),\n    }),\n};\n// Finite extension field over irreducible polynominal.\n// Fp(u) / (u² - β) where β = -1\nconst FP2_FROBENIUS_COEFFICIENTS = [\n    BigInt('0x1'),\n    BigInt('0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa'),\n].map((item) => Fp.create(item));\n// For Fp2 roots of unity.\nconst rv1 = BigInt('0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09');\n// const ev1 =\n//   BigInt('0x699be3b8c6870965e5bf892ad5d2cc7b0e85a117402dfd83b7f4a947e02d978498255a2aaec0ac627b5afbdf1bf1c90');\n// const ev2 =\n//   BigInt('0x8157cd83046453f5dd0972b6e3949e4288020b5b8a9cc99ca07e27089a2ce2436d965026adad3ef7baba37f2183e9b5');\n// const ev3 =\n//   BigInt('0xab1c2ffdd6c253ca155231eb3e71ba044fd562f6f72bc5bad5ec46a0b7a3b0247cf08ce6c6317f40edbc653a72dee17');\n// const ev4 =\n//   BigInt('0xaa404866706722864480885d68ad0ccac1967c7544b447873cc37e0181271e006df72162a3d3e0287bf597fbf7f8fc1');\n// Eighth roots of unity, used for computing square roots in Fp2.\n// To verify or re-calculate:\n// Array(8).fill(new Fp2([1n, 1n])).map((fp2, k) => fp2.pow(Fp2.ORDER * BigInt(k) / 8n))\nconst FP2_ROOTS_OF_UNITY = [\n    [_1n, _0n],\n    [rv1, -rv1],\n    [_0n, _1n],\n    [rv1, rv1],\n    [-_1n, _0n],\n    [-rv1, rv1],\n    [_0n, -_1n],\n    [-rv1, -rv1],\n].map((pair) => Fp2.fromBigTuple(pair));\nconst Fp6Add = ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) => ({\n    c0: Fp2.add(c0, r0),\n    c1: Fp2.add(c1, r1),\n    c2: Fp2.add(c2, r2),\n});\nconst Fp6Subtract = ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) => ({\n    c0: Fp2.sub(c0, r0),\n    c1: Fp2.sub(c1, r1),\n    c2: Fp2.sub(c2, r2),\n});\nconst Fp6Multiply = ({ c0, c1, c2 }, rhs) => {\n    if (typeof rhs === 'bigint') {\n        return {\n            c0: Fp2.mul(c0, rhs),\n            c1: Fp2.mul(c1, rhs),\n            c2: Fp2.mul(c2, rhs),\n        };\n    }\n    const { c0: r0, c1: r1, c2: r2 } = rhs;\n    const t0 = Fp2.mul(c0, r0); // c0 * o0\n    const t1 = Fp2.mul(c1, r1); // c1 * o1\n    const t2 = Fp2.mul(c2, r2); // c2 * o2\n    return {\n        // t0 + (c1 + c2) * (r1 * r2) - (T1 + T2) * (u + 1)\n        c0: Fp2.add(t0, Fp2.mulByNonresidue(Fp2.sub(Fp2.mul(Fp2.add(c1, c2), Fp2.add(r1, r2)), Fp2.add(t1, t2)))),\n        // (c0 + c1) * (r0 + r1) - (T0 + T1) + T2 * (u + 1)\n        c1: Fp2.add(Fp2.sub(Fp2.mul(Fp2.add(c0, c1), Fp2.add(r0, r1)), Fp2.add(t0, t1)), Fp2.mulByNonresidue(t2)),\n        // T1 + (c0 + c2) * (r0 + r2) - T0 + T2\n        c2: Fp2.sub(Fp2.add(t1, Fp2.mul(Fp2.add(c0, c2), Fp2.add(r0, r2))), Fp2.add(t0, t2)),\n    };\n};\nconst Fp6Square = ({ c0, c1, c2 }) => {\n    let t0 = Fp2.sqr(c0); // c0²\n    let t1 = Fp2.mul(Fp2.mul(c0, c1), _2n); // 2 * c0 * c1\n    let t3 = Fp2.mul(Fp2.mul(c1, c2), _2n); // 2 * c1 * c2\n    let t4 = Fp2.sqr(c2); // c2²\n    return {\n        c0: Fp2.add(Fp2.mulByNonresidue(t3), t0), // T3 * (u + 1) + T0\n        c1: Fp2.add(Fp2.mulByNonresidue(t4), t1), // T4 * (u + 1) + T1\n        // T1 + (c0 - c1 + c2)² + T3 - T0 - T4\n        c2: Fp2.sub(Fp2.sub(Fp2.add(Fp2.add(t1, Fp2.sqr(Fp2.add(Fp2.sub(c0, c1), c2))), t3), t0), t4),\n    };\n};\nconst Fp6 = {\n    ORDER: Fp2.ORDER, // TODO: unused, but need to verify\n    BITS: 3 * Fp2.BITS,\n    BYTES: 3 * Fp2.BYTES,\n    MASK: bitMask(3 * Fp2.BITS),\n    ZERO: { c0: Fp2.ZERO, c1: Fp2.ZERO, c2: Fp2.ZERO },\n    ONE: { c0: Fp2.ONE, c1: Fp2.ZERO, c2: Fp2.ZERO },\n    create: (num) => num,\n    isValid: ({ c0, c1, c2 }) => Fp2.isValid(c0) && Fp2.isValid(c1) && Fp2.isValid(c2),\n    is0: ({ c0, c1, c2 }) => Fp2.is0(c0) && Fp2.is0(c1) && Fp2.is0(c2),\n    neg: ({ c0, c1, c2 }) => ({ c0: Fp2.neg(c0), c1: Fp2.neg(c1), c2: Fp2.neg(c2) }),\n    eql: ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) => Fp2.eql(c0, r0) && Fp2.eql(c1, r1) && Fp2.eql(c2, r2),\n    sqrt: () => {\n        throw new Error('Not implemented');\n    },\n    // Do we need division by bigint at all? Should be done via order:\n    div: (lhs, rhs) => Fp6.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp6.inv(rhs)),\n    pow: (num, power) => mod.FpPow(Fp6, num, power),\n    invertBatch: (nums) => mod.FpInvertBatch(Fp6, nums),\n    // Normalized\n    add: Fp6Add,\n    sub: Fp6Subtract,\n    mul: Fp6Multiply,\n    sqr: Fp6Square,\n    // NonNormalized stuff\n    addN: Fp6Add,\n    subN: Fp6Subtract,\n    mulN: Fp6Multiply,\n    sqrN: Fp6Square,\n    inv: ({ c0, c1, c2 }) => {\n        let t0 = Fp2.sub(Fp2.sqr(c0), Fp2.mulByNonresidue(Fp2.mul(c2, c1))); // c0² - c2 * c1 * (u + 1)\n        let t1 = Fp2.sub(Fp2.mulByNonresidue(Fp2.sqr(c2)), Fp2.mul(c0, c1)); // c2² * (u + 1) - c0 * c1\n        let t2 = Fp2.sub(Fp2.sqr(c1), Fp2.mul(c0, c2)); // c1² - c0 * c2\n        // 1/(((c2 * T1 + c1 * T2) * v) + c0 * T0)\n        let t4 = Fp2.inv(Fp2.add(Fp2.mulByNonresidue(Fp2.add(Fp2.mul(c2, t1), Fp2.mul(c1, t2))), Fp2.mul(c0, t0)));\n        return { c0: Fp2.mul(t4, t0), c1: Fp2.mul(t4, t1), c2: Fp2.mul(t4, t2) };\n    },\n    // Bytes utils\n    fromBytes: (b) => {\n        if (b.length !== Fp6.BYTES)\n            throw new Error(`fromBytes wrong length=${b.length}`);\n        return {\n            c0: Fp2.fromBytes(b.subarray(0, Fp2.BYTES)),\n            c1: Fp2.fromBytes(b.subarray(Fp2.BYTES, 2 * Fp2.BYTES)),\n            c2: Fp2.fromBytes(b.subarray(2 * Fp2.BYTES)),\n        };\n    },\n    toBytes: ({ c0, c1, c2 }) => concatB(Fp2.toBytes(c0), Fp2.toBytes(c1), Fp2.toBytes(c2)),\n    cmov: ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }, c) => ({\n        c0: Fp2.cmov(c0, r0, c),\n        c1: Fp2.cmov(c1, r1, c),\n        c2: Fp2.cmov(c2, r2, c),\n    }),\n    // Utils\n    //   fromTriple(triple: [Fp2, Fp2, Fp2]) {\n    //     return new Fp6(...triple);\n    //   }\n    //   toString() {\n    //     return `Fp6(${this.c0} + ${this.c1} * v, ${this.c2} * v^2)`;\n    //   }\n    fromBigSix: (t) => {\n        if (!Array.isArray(t) || t.length !== 6)\n            throw new Error('Invalid Fp6 usage');\n        return {\n            c0: Fp2.fromBigTuple(t.slice(0, 2)),\n            c1: Fp2.fromBigTuple(t.slice(2, 4)),\n            c2: Fp2.fromBigTuple(t.slice(4, 6)),\n        };\n    },\n    frobeniusMap: ({ c0, c1, c2 }, power) => ({\n        c0: Fp2.frobeniusMap(c0, power),\n        c1: Fp2.mul(Fp2.frobeniusMap(c1, power), FP6_FROBENIUS_COEFFICIENTS_1[power % 6]),\n        c2: Fp2.mul(Fp2.frobeniusMap(c2, power), FP6_FROBENIUS_COEFFICIENTS_2[power % 6]),\n    }),\n    mulByNonresidue: ({ c0, c1, c2 }) => ({ c0: Fp2.mulByNonresidue(c2), c1: c0, c2: c1 }),\n    // Sparse multiplication\n    multiplyBy1: ({ c0, c1, c2 }, b1) => ({\n        c0: Fp2.mulByNonresidue(Fp2.mul(c2, b1)),\n        c1: Fp2.mul(c0, b1),\n        c2: Fp2.mul(c1, b1),\n    }),\n    // Sparse multiplication\n    multiplyBy01({ c0, c1, c2 }, b0, b1) {\n        let t0 = Fp2.mul(c0, b0); // c0 * b0\n        let t1 = Fp2.mul(c1, b1); // c1 * b1\n        return {\n            // ((c1 + c2) * b1 - T1) * (u + 1) + T0\n            c0: Fp2.add(Fp2.mulByNonresidue(Fp2.sub(Fp2.mul(Fp2.add(c1, c2), b1), t1)), t0),\n            // (b0 + b1) * (c0 + c1) - T0 - T1\n            c1: Fp2.sub(Fp2.sub(Fp2.mul(Fp2.add(b0, b1), Fp2.add(c0, c1)), t0), t1),\n            // (c0 + c2) * b0 - T0 + T1\n            c2: Fp2.add(Fp2.sub(Fp2.mul(Fp2.add(c0, c2), b0), t0), t1),\n        };\n    },\n    multiplyByFp2: ({ c0, c1, c2 }, rhs) => ({\n        c0: Fp2.mul(c0, rhs),\n        c1: Fp2.mul(c1, rhs),\n        c2: Fp2.mul(c2, rhs),\n    }),\n};\nconst FP6_FROBENIUS_COEFFICIENTS_1 = [\n    [BigInt('0x1'), BigInt('0x0')],\n    [\n        BigInt('0x0'),\n        BigInt('0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac'),\n    ],\n    [\n        BigInt('0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe'),\n        BigInt('0x0'),\n    ],\n    [BigInt('0x0'), BigInt('0x1')],\n    [\n        BigInt('0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac'),\n        BigInt('0x0'),\n    ],\n    [\n        BigInt('0x0'),\n        BigInt('0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe'),\n    ],\n].map((pair) => Fp2.fromBigTuple(pair));\nconst FP6_FROBENIUS_COEFFICIENTS_2 = [\n    [BigInt('0x1'), BigInt('0x0')],\n    [\n        BigInt('0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad'),\n        BigInt('0x0'),\n    ],\n    [\n        BigInt('0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac'),\n        BigInt('0x0'),\n    ],\n    [\n        BigInt('0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa'),\n        BigInt('0x0'),\n    ],\n    [\n        BigInt('0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe'),\n        BigInt('0x0'),\n    ],\n    [\n        BigInt('0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffeffff'),\n        BigInt('0x0'),\n    ],\n].map((pair) => Fp2.fromBigTuple(pair));\n// The BLS parameter x for BLS12-381\nconst BLS_X = BigInt('0xd201000000010000');\nconst BLS_X_LEN = bitLen(BLS_X);\nconst Fp12Add = ({ c0, c1 }, { c0: r0, c1: r1 }) => ({\n    c0: Fp6.add(c0, r0),\n    c1: Fp6.add(c1, r1),\n});\nconst Fp12Subtract = ({ c0, c1 }, { c0: r0, c1: r1 }) => ({\n    c0: Fp6.sub(c0, r0),\n    c1: Fp6.sub(c1, r1),\n});\nconst Fp12Multiply = ({ c0, c1 }, rhs) => {\n    if (typeof rhs === 'bigint')\n        return { c0: Fp6.mul(c0, rhs), c1: Fp6.mul(c1, rhs) };\n    let { c0: r0, c1: r1 } = rhs;\n    let t1 = Fp6.mul(c0, r0); // c0 * r0\n    let t2 = Fp6.mul(c1, r1); // c1 * r1\n    return {\n        c0: Fp6.add(t1, Fp6.mulByNonresidue(t2)), // T1 + T2 * v\n        // (c0 + c1) * (r0 + r1) - (T1 + T2)\n        c1: Fp6.sub(Fp6.mul(Fp6.add(c0, c1), Fp6.add(r0, r1)), Fp6.add(t1, t2)),\n    };\n};\nconst Fp12Square = ({ c0, c1 }) => {\n    let ab = Fp6.mul(c0, c1); // c0 * c1\n    return {\n        // (c1 * v + c0) * (c0 + c1) - AB - AB * v\n        c0: Fp6.sub(Fp6.sub(Fp6.mul(Fp6.add(Fp6.mulByNonresidue(c1), c0), Fp6.add(c0, c1)), ab), Fp6.mulByNonresidue(ab)),\n        c1: Fp6.add(ab, ab),\n    }; // AB + AB\n};\nfunction Fp4Square(a, b) {\n    const a2 = Fp2.sqr(a);\n    const b2 = Fp2.sqr(b);\n    return {\n        first: Fp2.add(Fp2.mulByNonresidue(b2), a2), // b² * Nonresidue + a²\n        second: Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(a, b)), a2), b2), // (a + b)² - a² - b²\n    };\n}\nconst Fp12 = {\n    ORDER: Fp2.ORDER, // TODO: unused, but need to verify\n    BITS: 2 * Fp2.BITS,\n    BYTES: 2 * Fp2.BYTES,\n    MASK: bitMask(2 * Fp2.BITS),\n    ZERO: { c0: Fp6.ZERO, c1: Fp6.ZERO },\n    ONE: { c0: Fp6.ONE, c1: Fp6.ZERO },\n    create: (num) => num,\n    isValid: ({ c0, c1 }) => Fp6.isValid(c0) && Fp6.isValid(c1),\n    is0: ({ c0, c1 }) => Fp6.is0(c0) && Fp6.is0(c1),\n    neg: ({ c0, c1 }) => ({ c0: Fp6.neg(c0), c1: Fp6.neg(c1) }),\n    eql: ({ c0, c1 }, { c0: r0, c1: r1 }) => Fp6.eql(c0, r0) && Fp6.eql(c1, r1),\n    sqrt: () => {\n        throw new Error('Not implemented');\n    },\n    inv: ({ c0, c1 }) => {\n        let t = Fp6.inv(Fp6.sub(Fp6.sqr(c0), Fp6.mulByNonresidue(Fp6.sqr(c1)))); // 1 / (c0² - c1² * v)\n        return { c0: Fp6.mul(c0, t), c1: Fp6.neg(Fp6.mul(c1, t)) }; // ((C0 * T) * T) + (-C1 * T) * w\n    },\n    div: (lhs, rhs) => Fp12.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp12.inv(rhs)),\n    pow: (num, power) => mod.FpPow(Fp12, num, power),\n    invertBatch: (nums) => mod.FpInvertBatch(Fp12, nums),\n    // Normalized\n    add: Fp12Add,\n    sub: Fp12Subtract,\n    mul: Fp12Multiply,\n    sqr: Fp12Square,\n    // NonNormalized stuff\n    addN: Fp12Add,\n    subN: Fp12Subtract,\n    mulN: Fp12Multiply,\n    sqrN: Fp12Square,\n    // Bytes utils\n    fromBytes: (b) => {\n        if (b.length !== Fp12.BYTES)\n            throw new Error(`fromBytes wrong length=${b.length}`);\n        return {\n            c0: Fp6.fromBytes(b.subarray(0, Fp6.BYTES)),\n            c1: Fp6.fromBytes(b.subarray(Fp6.BYTES)),\n        };\n    },\n    toBytes: ({ c0, c1 }) => concatB(Fp6.toBytes(c0), Fp6.toBytes(c1)),\n    cmov: ({ c0, c1 }, { c0: r0, c1: r1 }, c) => ({\n        c0: Fp6.cmov(c0, r0, c),\n        c1: Fp6.cmov(c1, r1, c),\n    }),\n    // Utils\n    // toString() {\n    //   return `Fp12(${this.c0} + ${this.c1} * w)`;\n    // },\n    // fromTuple(c: [Fp6, Fp6]) {\n    //   return new Fp12(...c);\n    // }\n    fromBigTwelve: (t) => ({\n        c0: Fp6.fromBigSix(t.slice(0, 6)),\n        c1: Fp6.fromBigSix(t.slice(6, 12)),\n    }),\n    // Raises to q**i -th power\n    frobeniusMap(lhs, power) {\n        const r0 = Fp6.frobeniusMap(lhs.c0, power);\n        const { c0, c1, c2 } = Fp6.frobeniusMap(lhs.c1, power);\n        const coeff = FP12_FROBENIUS_COEFFICIENTS[power % 12];\n        return {\n            c0: r0,\n            c1: Fp6.create({\n                c0: Fp2.mul(c0, coeff),\n                c1: Fp2.mul(c1, coeff),\n                c2: Fp2.mul(c2, coeff),\n            }),\n        };\n    },\n    // Sparse multiplication\n    multiplyBy014: ({ c0, c1 }, o0, o1, o4) => {\n        let t0 = Fp6.multiplyBy01(c0, o0, o1);\n        let t1 = Fp6.multiplyBy1(c1, o4);\n        return {\n            c0: Fp6.add(Fp6.mulByNonresidue(t1), t0), // T1 * v + T0\n            // (c1 + c0) * [o0, o1+o4] - T0 - T1\n            c1: Fp6.sub(Fp6.sub(Fp6.multiplyBy01(Fp6.add(c1, c0), o0, Fp2.add(o1, o4)), t0), t1),\n        };\n    },\n    multiplyByFp2: ({ c0, c1 }, rhs) => ({\n        c0: Fp6.multiplyByFp2(c0, rhs),\n        c1: Fp6.multiplyByFp2(c1, rhs),\n    }),\n    conjugate: ({ c0, c1 }) => ({ c0, c1: Fp6.neg(c1) }),\n    // A cyclotomic group is a subgroup of Fp^n defined by\n    //   GΦₙ(p) = {α ∈ Fpⁿ : α^Φₙ(p) = 1}\n    // The result of any pairing is in a cyclotomic subgroup\n    // https://eprint.iacr.org/2009/565.pdf\n    _cyclotomicSquare: ({ c0, c1 }) => {\n        const { c0: c0c0, c1: c0c1, c2: c0c2 } = c0;\n        const { c0: c1c0, c1: c1c1, c2: c1c2 } = c1;\n        const { first: t3, second: t4 } = Fp4Square(c0c0, c1c1);\n        const { first: t5, second: t6 } = Fp4Square(c1c0, c0c2);\n        const { first: t7, second: t8 } = Fp4Square(c0c1, c1c2);\n        let t9 = Fp2.mulByNonresidue(t8); // T8 * (u + 1)\n        return {\n            c0: Fp6.create({\n                c0: Fp2.add(Fp2.mul(Fp2.sub(t3, c0c0), _2n), t3), // 2 * (T3 - c0c0)  + T3\n                c1: Fp2.add(Fp2.mul(Fp2.sub(t5, c0c1), _2n), t5), // 2 * (T5 - c0c1)  + T5\n                c2: Fp2.add(Fp2.mul(Fp2.sub(t7, c0c2), _2n), t7),\n            }), // 2 * (T7 - c0c2)  + T7\n            c1: Fp6.create({\n                c0: Fp2.add(Fp2.mul(Fp2.add(t9, c1c0), _2n), t9), // 2 * (T9 + c1c0) + T9\n                c1: Fp2.add(Fp2.mul(Fp2.add(t4, c1c1), _2n), t4), // 2 * (T4 + c1c1) + T4\n                c2: Fp2.add(Fp2.mul(Fp2.add(t6, c1c2), _2n), t6),\n            }),\n        }; // 2 * (T6 + c1c2) + T6\n    },\n    _cyclotomicExp(num, n) {\n        let z = Fp12.ONE;\n        for (let i = BLS_X_LEN - 1; i >= 0; i--) {\n            z = Fp12._cyclotomicSquare(z);\n            if (bitGet(n, i))\n                z = Fp12.mul(z, num);\n        }\n        return z;\n    },\n    // https://eprint.iacr.org/2010/354.pdf\n    // https://eprint.iacr.org/2009/565.pdf\n    finalExponentiate: (num) => {\n        const x = BLS_X;\n        // this^(q⁶) / this\n        const t0 = Fp12.div(Fp12.frobeniusMap(num, 6), num);\n        // t0^(q²) * t0\n        const t1 = Fp12.mul(Fp12.frobeniusMap(t0, 2), t0);\n        const t2 = Fp12.conjugate(Fp12._cyclotomicExp(t1, x));\n        const t3 = Fp12.mul(Fp12.conjugate(Fp12._cyclotomicSquare(t1)), t2);\n        const t4 = Fp12.conjugate(Fp12._cyclotomicExp(t3, x));\n        const t5 = Fp12.conjugate(Fp12._cyclotomicExp(t4, x));\n        const t6 = Fp12.mul(Fp12.conjugate(Fp12._cyclotomicExp(t5, x)), Fp12._cyclotomicSquare(t2));\n        const t7 = Fp12.conjugate(Fp12._cyclotomicExp(t6, x));\n        const t2_t5_pow_q2 = Fp12.frobeniusMap(Fp12.mul(t2, t5), 2);\n        const t4_t1_pow_q3 = Fp12.frobeniusMap(Fp12.mul(t4, t1), 3);\n        const t6_t1c_pow_q1 = Fp12.frobeniusMap(Fp12.mul(t6, Fp12.conjugate(t1)), 1);\n        const t7_t3c_t1 = Fp12.mul(Fp12.mul(t7, Fp12.conjugate(t3)), t1);\n        // (t2 * t5)^(q²) * (t4 * t1)^(q³) * (t6 * t1.conj)^(q^1) * t7 * t3.conj * t1\n        return Fp12.mul(Fp12.mul(Fp12.mul(t2_t5_pow_q2, t4_t1_pow_q3), t6_t1c_pow_q1), t7_t3c_t1);\n    },\n};\nconst FP12_FROBENIUS_COEFFICIENTS = [\n    [BigInt('0x1'), BigInt('0x0')],\n    [\n        BigInt('0x1904d3bf02bb0667c231beb4202c0d1f0fd603fd3cbd5f4f7b2443d784bab9c4f67ea53d63e7813d8d0775ed92235fb8'),\n        BigInt('0x00fc3e2b36c4e03288e9e902231f9fb854a14787b6c7b36fec0c8ec971f63c5f282d5ac14d6c7ec22cf78a126ddc4af3'),\n    ],\n    [\n        BigInt('0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffeffff'),\n        BigInt('0x0'),\n    ],\n    [\n        BigInt('0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2'),\n        BigInt('0x06af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09'),\n    ],\n    [\n        BigInt('0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe'),\n        BigInt('0x0'),\n    ],\n    [\n        BigInt('0x144e4211384586c16bd3ad4afa99cc9170df3560e77982d0db45f3536814f0bd5871c1908bd478cd1ee605167ff82995'),\n        BigInt('0x05b2cfd9013a5fd8df47fa6b48b1e045f39816240c0b8fee8beadf4d8e9c0566c63a3e6e257f87329b18fae980078116'),\n    ],\n    [\n        BigInt('0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa'),\n        BigInt('0x0'),\n    ],\n    [\n        BigInt('0x00fc3e2b36c4e03288e9e902231f9fb854a14787b6c7b36fec0c8ec971f63c5f282d5ac14d6c7ec22cf78a126ddc4af3'),\n        BigInt('0x1904d3bf02bb0667c231beb4202c0d1f0fd603fd3cbd5f4f7b2443d784bab9c4f67ea53d63e7813d8d0775ed92235fb8'),\n    ],\n    [\n        BigInt('0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac'),\n        BigInt('0x0'),\n    ],\n    [\n        BigInt('0x06af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09'),\n        BigInt('0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2'),\n    ],\n    [\n        BigInt('0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad'),\n        BigInt('0x0'),\n    ],\n    [\n        BigInt('0x05b2cfd9013a5fd8df47fa6b48b1e045f39816240c0b8fee8beadf4d8e9c0566c63a3e6e257f87329b18fae980078116'),\n        BigInt('0x144e4211384586c16bd3ad4afa99cc9170df3560e77982d0db45f3536814f0bd5871c1908bd478cd1ee605167ff82995'),\n    ],\n].map((n) => Fp2.fromBigTuple(n));\n// END OF CURVE FIELDS\n// HashToCurve\n// 3-isogeny map from E' to E https://www.rfc-editor.org/rfc/rfc9380#appendix-E.3\nconst isogenyMapG2 = isogenyMap(Fp2, [\n    // xNum\n    [\n        [\n            '0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97d6',\n            '0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97d6',\n        ],\n        [\n            '0x0',\n            '0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71a',\n        ],\n        [\n            '0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71e',\n            '0x8ab05f8bdd54cde190937e76bc3e447cc27c3d6fbd7063fcd104635a790520c0a395554e5c6aaaa9354ffffffffe38d',\n        ],\n        [\n            '0x171d6541fa38ccfaed6dea691f5fb614cb14b4e7f4e810aa22d6108f142b85757098e38d0f671c7188e2aaaaaaaa5ed1',\n            '0x0',\n        ],\n    ],\n    // xDen\n    [\n        [\n            '0x0',\n            '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa63',\n        ],\n        [\n            '0xc',\n            '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa9f',\n        ],\n        ['0x1', '0x0'], // LAST 1\n    ],\n    // yNum\n    [\n        [\n            '0x1530477c7ab4113b59a4c18b076d11930f7da5d4a07f649bf54439d87d27e500fc8c25ebf8c92f6812cfc71c71c6d706',\n            '0x1530477c7ab4113b59a4c18b076d11930f7da5d4a07f649bf54439d87d27e500fc8c25ebf8c92f6812cfc71c71c6d706',\n        ],\n        [\n            '0x0',\n            '0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97be',\n        ],\n        [\n            '0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71c',\n            '0x8ab05f8bdd54cde190937e76bc3e447cc27c3d6fbd7063fcd104635a790520c0a395554e5c6aaaa9354ffffffffe38f',\n        ],\n        [\n            '0x124c9ad43b6cf79bfbf7043de3811ad0761b0f37a1e26286b0e977c69aa274524e79097a56dc4bd9e1b371c71c718b10',\n            '0x0',\n        ],\n    ],\n    // yDen\n    [\n        [\n            '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa8fb',\n            '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa8fb',\n        ],\n        [\n            '0x0',\n            '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa9d3',\n        ],\n        [\n            '0x12',\n            '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa99',\n        ],\n        ['0x1', '0x0'], // LAST 1\n    ],\n].map((i) => i.map((pair) => Fp2.fromBigTuple(pair.map(BigInt)))));\n// 11-isogeny map from E' to E\nconst isogenyMapG1 = isogenyMap(Fp, [\n    // xNum\n    [\n        '0x11a05f2b1e833340b809101dd99815856b303e88a2d7005ff2627b56cdb4e2c85610c2d5f2e62d6eaeac1662734649b7',\n        '0x17294ed3e943ab2f0588bab22147a81c7c17e75b2f6a8417f565e33c70d1e86b4838f2a6f318c356e834eef1b3cb83bb',\n        '0xd54005db97678ec1d1048c5d10a9a1bce032473295983e56878e501ec68e25c958c3e3d2a09729fe0179f9dac9edcb0',\n        '0x1778e7166fcc6db74e0609d307e55412d7f5e4656a8dbf25f1b33289f1b330835336e25ce3107193c5b388641d9b6861',\n        '0xe99726a3199f4436642b4b3e4118e5499db995a1257fb3f086eeb65982fac18985a286f301e77c451154ce9ac8895d9',\n        '0x1630c3250d7313ff01d1201bf7a74ab5db3cb17dd952799b9ed3ab9097e68f90a0870d2dcae73d19cd13c1c66f652983',\n        '0xd6ed6553fe44d296a3726c38ae652bfb11586264f0f8ce19008e218f9c86b2a8da25128c1052ecaddd7f225a139ed84',\n        '0x17b81e7701abdbe2e8743884d1117e53356de5ab275b4db1a682c62ef0f2753339b7c8f8c8f475af9ccb5618e3f0c88e',\n        '0x80d3cf1f9a78fc47b90b33563be990dc43b756ce79f5574a2c596c928c5d1de4fa295f296b74e956d71986a8497e317',\n        '0x169b1f8e1bcfa7c42e0c37515d138f22dd2ecb803a0c5c99676314baf4bb1b7fa3190b2edc0327797f241067be390c9e',\n        '0x10321da079ce07e272d8ec09d2565b0dfa7dccdde6787f96d50af36003b14866f69b771f8c285decca67df3f1605fb7b',\n        '0x6e08c248e260e70bd1e962381edee3d31d79d7e22c837bc23c0bf1bc24c6b68c24b1b80b64d391fa9c8ba2e8ba2d229',\n    ],\n    // xDen\n    [\n        '0x8ca8d548cff19ae18b2e62f4bd3fa6f01d5ef4ba35b48ba9c9588617fc8ac62b558d681be343df8993cf9fa40d21b1c',\n        '0x12561a5deb559c4348b4711298e536367041e8ca0cf0800c0126c2588c48bf5713daa8846cb026e9e5c8276ec82b3bff',\n        '0xb2962fe57a3225e8137e629bff2991f6f89416f5a718cd1fca64e00b11aceacd6a3d0967c94fedcfcc239ba5cb83e19',\n        '0x3425581a58ae2fec83aafef7c40eb545b08243f16b1655154cca8abc28d6fd04976d5243eecf5c4130de8938dc62cd8',\n        '0x13a8e162022914a80a6f1d5f43e7a07dffdfc759a12062bb8d6b44e833b306da9bd29ba81f35781d539d395b3532a21e',\n        '0xe7355f8e4e667b955390f7f0506c6e9395735e9ce9cad4d0a43bcef24b8982f7400d24bc4228f11c02df9a29f6304a5',\n        '0x772caacf16936190f3e0c63e0596721570f5799af53a1894e2e073062aede9cea73b3538f0de06cec2574496ee84a3a',\n        '0x14a7ac2a9d64a8b230b3f5b074cf01996e7f63c21bca68a81996e1cdf9822c580fa5b9489d11e2d311f7d99bbdcc5a5e',\n        '0xa10ecf6ada54f825e920b3dafc7a3cce07f8d1d7161366b74100da67f39883503826692abba43704776ec3a79a1d641',\n        '0x95fc13ab9e92ad4476d6e3eb3a56680f682b4ee96f7d03776df533978f31c1593174e4b4b7865002d6384d168ecdd0a',\n        '0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001', // LAST 1\n    ],\n    // yNum\n    [\n        '0x90d97c81ba24ee0259d1f094980dcfa11ad138e48a869522b52af6c956543d3cd0c7aee9b3ba3c2be9845719707bb33',\n        '0x134996a104ee5811d51036d776fb46831223e96c254f383d0f906343eb67ad34d6c56711962fa8bfe097e75a2e41c696',\n        '0xcc786baa966e66f4a384c86a3b49942552e2d658a31ce2c344be4b91400da7d26d521628b00523b8dfe240c72de1f6',\n        '0x1f86376e8981c217898751ad8746757d42aa7b90eeb791c09e4a3ec03251cf9de405aba9ec61deca6355c77b0e5f4cb',\n        '0x8cc03fdefe0ff135caf4fe2a21529c4195536fbe3ce50b879833fd221351adc2ee7f8dc099040a841b6daecf2e8fedb',\n        '0x16603fca40634b6a2211e11db8f0a6a074a7d0d4afadb7bd76505c3d3ad5544e203f6326c95a807299b23ab13633a5f0',\n        '0x4ab0b9bcfac1bbcb2c977d027796b3ce75bb8ca2be184cb5231413c4d634f3747a87ac2460f415ec961f8855fe9d6f2',\n        '0x987c8d5333ab86fde9926bd2ca6c674170a05bfe3bdd81ffd038da6c26c842642f64550fedfe935a15e4ca31870fb29',\n        '0x9fc4018bd96684be88c9e221e4da1bb8f3abd16679dc26c1e8b6e6a1f20cabe69d65201c78607a360370e577bdba587',\n        '0xe1bba7a1186bdb5223abde7ada14a23c42a0ca7915af6fe06985e7ed1e4d43b9b3f7055dd4eba6f2bafaaebca731c30',\n        '0x19713e47937cd1be0dfd0b8f1d43fb93cd2fcbcb6caf493fd1183e416389e61031bf3a5cce3fbafce813711ad011c132',\n        '0x18b46a908f36f6deb918c143fed2edcc523559b8aaf0c2462e6bfe7f911f643249d9cdf41b44d606ce07c8a4d0074d8e',\n        '0xb182cac101b9399d155096004f53f447aa7b12a3426b08ec02710e807b4633f06c851c1919211f20d4c04f00b971ef8',\n        '0x245a394ad1eca9b72fc00ae7be315dc757b3b080d4c158013e6632d3c40659cc6cf90ad1c232a6442d9d3f5db980133',\n        '0x5c129645e44cf1102a159f748c4a3fc5e673d81d7e86568d9ab0f5d396a7ce46ba1049b6579afb7866b1e715475224b',\n        '0x15e6be4e990f03ce4ea50b3b42df2eb5cb181d8f84965a3957add4fa95af01b2b665027efec01c7704b456be69c8b604',\n    ],\n    // yDen\n    [\n        '0x16112c4c3a9c98b252181140fad0eae9601a6de578980be6eec3232b5be72e7a07f3688ef60c206d01479253b03663c1',\n        '0x1962d75c2381201e1a0cbd6c43c348b885c84ff731c4d59ca4a10356f453e01f78a4260763529e3532f6102c2e49a03d',\n        '0x58df3306640da276faaae7d6e8eb15778c4855551ae7f310c35a5dd279cd2eca6757cd636f96f891e2538b53dbf67f2',\n        '0x16b7d288798e5395f20d23bf89edb4d1d115c5dbddbcd30e123da489e726af41727364f2c28297ada8d26d98445f5416',\n        '0xbe0e079545f43e4b00cc912f8228ddcc6d19c9f0f69bbb0542eda0fc9dec916a20b15dc0fd2ededda39142311a5001d',\n        '0x8d9e5297186db2d9fb266eaac783182b70152c65550d881c5ecd87b6f0f5a6449f38db9dfa9cce202c6477faaf9b7ac',\n        '0x166007c08a99db2fc3ba8734ace9824b5eecfdfa8d0cf8ef5dd365bc400a0051d5fa9c01a58b1fb93d1a1399126a775c',\n        '0x16a3ef08be3ea7ea03bcddfabba6ff6ee5a4375efa1f4fd7feb34fd206357132b920f5b00801dee460ee415a15812ed9',\n        '0x1866c8ed336c61231a1be54fd1d74cc4f9fb0ce4c6af5920abc5750c4bf39b4852cfe2f7bb9248836b233d9d55535d4a',\n        '0x167a55cda70a6e1cea820597d94a84903216f763e13d87bb5308592e7ea7d4fbc7385ea3d529b35e346ef48bb8913f55',\n        '0x4d2f259eea405bd48f010a01ad2911d9c6dd039bb61a6290e591b36e636a5c871a5c29f4f83060400f8b49cba8f6aa8',\n        '0xaccbb67481d033ff5852c1e48c50c477f94ff8aefce42d28c0f9a88cea7913516f968986f7ebbea9684b529e2561092',\n        '0xad6b9514c767fe3c3613144b45f1496543346d98adf02267d5ceef9a00d9b8693000763e3b90ac11e99b138573345cc',\n        '0x2660400eb2e4f3b628bdd0d53cd76f2bf565b94e72927c1cb748df27942480e420517bd8714cc80d1fadc1326ed06f7',\n        '0xe0fa1d816ddc03e6b24255e0d7819c171c40f65e273b853324efcd6356caa205ca2f570f13497804415473a1d634b8f',\n        '0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001', // LAST 1\n    ],\n].map((i) => i.map((j) => BigInt(j))));\n// SWU Map - Fp2 to G2': y² = x³ + 240i * x + 1012 + 1012i\nconst G2_SWU = mapToCurveSimpleSWU(Fp2, {\n    A: Fp2.create({ c0: Fp.create(_0n), c1: Fp.create(BigInt(240)) }), // A' = 240 * I\n    B: Fp2.create({ c0: Fp.create(BigInt(1012)), c1: Fp.create(BigInt(1012)) }), // B' = 1012 * (1 + I)\n    Z: Fp2.create({ c0: Fp.create(BigInt(-2)), c1: Fp.create(BigInt(-1)) }), // Z: -(2 + I)\n});\n// Optimized SWU Map - Fp to G1\nconst G1_SWU = mapToCurveSimpleSWU(Fp, {\n    A: Fp.create(BigInt('0x144698a3b8e9433d693a02c96d4982b0ea985383ee66a8d8e8981aefd881ac98936f8da0e0f97f5cf428082d584c1d')),\n    B: Fp.create(BigInt('0x12e2908d11688030018b12e8753eee3b2016c1f0f24f4070a0b9c14fcef35ef55a23215a316ceaa5d1cc48e98e172be0')),\n    Z: Fp.create(BigInt(11)),\n});\n// Endomorphisms (for fast cofactor clearing)\n// Ψ(P) endomorphism\nconst ut_root = Fp6.create({ c0: Fp2.ZERO, c1: Fp2.ONE, c2: Fp2.ZERO });\nconst wsq = Fp12.create({ c0: ut_root, c1: Fp6.ZERO });\nconst wcu = Fp12.create({ c0: Fp6.ZERO, c1: ut_root });\nconst [wsq_inv, wcu_inv] = Fp12.invertBatch([wsq, wcu]);\nfunction psi(x, y) {\n    // Untwist Fp2->Fp12 && frobenius(1) && twist back\n    const x2 = Fp12.mul(Fp12.frobeniusMap(Fp12.multiplyByFp2(wsq_inv, x), 1), wsq).c0.c0;\n    const y2 = Fp12.mul(Fp12.frobeniusMap(Fp12.multiplyByFp2(wcu_inv, y), 1), wcu).c0.c0;\n    return [x2, y2];\n}\n// Ψ endomorphism\nfunction G2psi(c, P) {\n    const affine = P.toAffine();\n    const p = psi(affine.x, affine.y);\n    return new c(p[0], p[1], Fp2.ONE);\n}\n// Ψ²(P) endomorphism\n// 1 / F2(2)^((p-1)/3) in GF(p²)\nconst PSI2_C1 = BigInt('0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac');\nfunction psi2(x, y) {\n    return [Fp2.mul(x, PSI2_C1), Fp2.neg(y)];\n}\nfunction G2psi2(c, P) {\n    const affine = P.toAffine();\n    const p = psi2(affine.x, affine.y);\n    return new c(p[0], p[1], Fp2.ONE);\n}\n// Default hash_to_field options are for hash to G2.\n//\n// Parameter definitions are in section 5.3 of the spec unless otherwise noted.\n// Parameter values come from section 8.8.2 of the spec.\n// https://www.rfc-editor.org/rfc/rfc9380#section-8.8.2\n//\n// Base field F is GF(p^m)\n// p = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab\n// m = 2 (or 1 for G1 see section 8.8.1)\n// k = 128\nconst htfDefaults = Object.freeze({\n    // DST: a domain separation tag\n    // defined in section 2.2.5\n    // Use utils.getDSTLabel(), utils.setDSTLabel(value)\n    DST: 'BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_NUL_',\n    encodeDST: 'BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_NUL_',\n    // p: the characteristic of F\n    //    where F is a finite field of characteristic p and order q = p^m\n    p: Fp.ORDER,\n    // m: the extension degree of F, m >= 1\n    //     where F is a finite field of characteristic p and order q = p^m\n    m: 2,\n    // k: the target security level for the suite in bits\n    // defined in section 5.1\n    k: 128,\n    // option to use a message that has already been processed by\n    // expand_message_xmd\n    expand: 'xmd',\n    // Hash functions for: expand_message_xmd is appropriate for use with a\n    // wide range of hash functions, including SHA-2, SHA-3, BLAKE2, and others.\n    // BBS+ uses blake2: https://github.com/hyperledger/aries-framework-go/issues/2247\n    hash: sha256,\n});\n// Encoding utils\n// Point on G1 curve: (x, y)\n// Compressed point of infinity\nconst COMPRESSED_ZERO = setMask(Fp.toBytes(_0n), { infinity: true, compressed: true }); // set compressed & point-at-infinity bits\nfunction parseMask(bytes) {\n    // Copy, so we can remove mask data. It will be removed also later, when Fp.create will call modulo.\n    bytes = bytes.slice();\n    const mask = bytes[0] & 224;\n    const compressed = !!((mask >> 7) & 1); // compression bit (0b1000_0000)\n    const infinity = !!((mask >> 6) & 1); // point at infinity bit (0b0100_0000)\n    const sort = !!((mask >> 5) & 1); // sort bit (0b0010_0000)\n    bytes[0] &= 31; // clear mask (zero first 3 bits)\n    return { compressed, infinity, sort, value: bytes };\n}\nfunction setMask(bytes, mask) {\n    if (bytes[0] & 224)\n        throw new Error('setMask: non-empty mask');\n    if (mask.compressed)\n        bytes[0] |= 128;\n    if (mask.infinity)\n        bytes[0] |= 64;\n    if (mask.sort)\n        bytes[0] |= 32;\n    return bytes;\n}\nfunction signatureG1ToRawBytes(point) {\n    point.assertValidity();\n    const isZero = point.equals(bls12_381.G1.ProjectivePoint.ZERO);\n    const { x, y } = point.toAffine();\n    if (isZero)\n        return COMPRESSED_ZERO.slice();\n    const P = Fp.ORDER;\n    const sort = Boolean((y * _2n) / P);\n    return setMask(numberToBytesBE(x, Fp.BYTES), { compressed: true, sort });\n}\nfunction signatureG2ToRawBytes(point) {\n    // NOTE: by some reasons it was missed in bls12-381, looks like bug\n    point.assertValidity();\n    const len = Fp.BYTES;\n    if (point.equals(bls12_381.G2.ProjectivePoint.ZERO))\n        return concatB(COMPRESSED_ZERO, numberToBytesBE(_0n, len));\n    const { x, y } = point.toAffine();\n    const { re: x0, im: x1 } = Fp2.reim(x);\n    const { re: y0, im: y1 } = Fp2.reim(y);\n    const tmp = y1 > _0n ? y1 * _2n : y0 * _2n;\n    const sort = Boolean((tmp / Fp.ORDER) & _1n);\n    const z2 = x0;\n    return concatB(setMask(numberToBytesBE(x1, len), { sort, compressed: true }), numberToBytesBE(z2, len));\n}\n// To verify curve parameters, see pairing-friendly-curves spec:\n// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-pairing-friendly-curves-11\n// Basic math is done over finite fields over p.\n// More complicated math is done over polynominal extension fields.\n// To simplify calculations in Fp12, we construct extension tower:\n// Fp₁₂ = Fp₆² => Fp₂³\n// Fp(u) / (u² - β) where β = -1\n// Fp₂(v) / (v³ - ξ) where ξ = u + 1\n// Fp₆(w) / (w² - γ) where γ = v\n// Here goes constants && point encoding format\nexport const bls12_381 = bls({\n    // Fields\n    fields: {\n        Fp,\n        Fp2,\n        Fp6,\n        Fp12,\n        Fr,\n    },\n    // G1 is the order-q subgroup of E1(Fp) : y² = x³ + 4, #E1(Fp) = h1q, where\n    // characteristic; z + (z⁴ - z² + 1)(z - 1)²/3\n    G1: {\n        Fp,\n        // cofactor; (z - 1)²/3\n        h: BigInt('0x396c8c005555e1568c00aaab0000aaab'),\n        // generator's coordinates\n        // x = 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507\n        // y = 1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569\n        Gx: BigInt('0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb'),\n        Gy: BigInt('0x08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1'),\n        a: Fp.ZERO,\n        b: _4n,\n        htfDefaults: { ...htfDefaults, m: 1, DST: 'BLS_SIG_BLS12381G1_XMD:SHA-256_SSWU_RO_NUL_' },\n        wrapPrivateKey: true,\n        allowInfinityPoint: true,\n        // Checks is the point resides in prime-order subgroup.\n        // point.isTorsionFree() should return true for valid points\n        // It returns false for shitty points.\n        // https://eprint.iacr.org/2021/1130.pdf\n        isTorsionFree: (c, point) => {\n            // φ endomorphism\n            const cubicRootOfUnityModP = BigInt('0x5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe');\n            const phi = new c(Fp.mul(point.px, cubicRootOfUnityModP), point.py, point.pz);\n            // todo: unroll\n            const xP = point.multiplyUnsafe(bls12_381.params.x).negate(); // [x]P\n            const u2P = xP.multiplyUnsafe(bls12_381.params.x); // [u2]P\n            return u2P.equals(phi);\n            // https://eprint.iacr.org/2019/814.pdf\n            // (z² − 1)/3\n            // const c1 = BigInt('0x396c8c005555e1560000000055555555');\n            // const P = this;\n            // const S = P.sigma();\n            // const Q = S.double();\n            // const S2 = S.sigma();\n            // // [(z² − 1)/3](2σ(P) − P − σ²(P)) − σ²(P) = O\n            // const left = Q.subtract(P).subtract(S2).multiplyUnsafe(c1);\n            // const C = left.subtract(S2);\n            // return C.isZero();\n        },\n        // Clear cofactor of G1\n        // https://eprint.iacr.org/2019/403\n        clearCofactor: (_c, point) => {\n            // return this.multiplyUnsafe(CURVE.h);\n            return point.multiplyUnsafe(bls12_381.params.x).add(point); // x*P + P\n        },\n        mapToCurve: (scalars) => {\n            const { x, y } = G1_SWU(Fp.create(scalars[0]));\n            return isogenyMapG1(x, y);\n        },\n        fromBytes: (bytes) => {\n            const { compressed, infinity, sort, value } = parseMask(bytes);\n            if (value.length === 48 && compressed) {\n                // TODO: Fp.bytes\n                const P = Fp.ORDER;\n                const compressedValue = bytesToNumberBE(value);\n                // Zero\n                const x = Fp.create(compressedValue & Fp.MASK);\n                if (infinity) {\n                    if (x !== _0n)\n                        throw new Error('G1: non-empty compressed point at infinity');\n                    return { x: _0n, y: _0n };\n                }\n                const right = Fp.add(Fp.pow(x, _3n), Fp.create(bls12_381.params.G1b)); // y² = x³ + b\n                let y = Fp.sqrt(right);\n                if (!y)\n                    throw new Error('Invalid compressed G1 point');\n                if ((y * _2n) / P !== BigInt(sort))\n                    y = Fp.neg(y);\n                return { x: Fp.create(x), y: Fp.create(y) };\n            }\n            else if (value.length === 96 && !compressed) {\n                // Check if the infinity flag is set\n                const x = bytesToNumberBE(value.subarray(0, Fp.BYTES));\n                const y = bytesToNumberBE(value.subarray(Fp.BYTES));\n                if (infinity) {\n                    if (x !== _0n || y !== _0n)\n                        throw new Error('G1: non-empty point at infinity');\n                    return bls12_381.G1.ProjectivePoint.ZERO.toAffine();\n                }\n                return { x: Fp.create(x), y: Fp.create(y) };\n            }\n            else {\n                throw new Error('Invalid point G1, expected 48/96 bytes');\n            }\n        },\n        toBytes: (c, point, isCompressed) => {\n            const isZero = point.equals(c.ZERO);\n            const { x, y } = point.toAffine();\n            if (isCompressed) {\n                if (isZero)\n                    return COMPRESSED_ZERO.slice();\n                const P = Fp.ORDER;\n                const sort = Boolean((y * _2n) / P);\n                return setMask(numberToBytesBE(x, Fp.BYTES), { compressed: true, sort });\n            }\n            else {\n                if (isZero) {\n                    // 2x PUBLIC_KEY_LENGTH\n                    const x = concatB(new Uint8Array([0x40]), new Uint8Array(2 * Fp.BYTES - 1));\n                    return x;\n                }\n                else {\n                    return concatB(numberToBytesBE(x, Fp.BYTES), numberToBytesBE(y, Fp.BYTES));\n                }\n            }\n        },\n        ShortSignature: {\n            fromHex(hex) {\n                const { infinity, sort, value } = parseMask(ensureBytes('signatureHex', hex, 48));\n                const P = Fp.ORDER;\n                const compressedValue = bytesToNumberBE(value);\n                // Zero\n                if (infinity)\n                    return bls12_381.G1.ProjectivePoint.ZERO;\n                const x = Fp.create(compressedValue & Fp.MASK);\n                const right = Fp.add(Fp.pow(x, _3n), Fp.create(bls12_381.params.G1b)); // y² = x³ + b\n                let y = Fp.sqrt(right);\n                if (!y)\n                    throw new Error('Invalid compressed G1 point');\n                const aflag = BigInt(sort);\n                if ((y * _2n) / P !== aflag)\n                    y = Fp.neg(y);\n                const point = bls12_381.G1.ProjectivePoint.fromAffine({ x, y });\n                point.assertValidity();\n                return point;\n            },\n            toRawBytes(point) {\n                return signatureG1ToRawBytes(point);\n            },\n            toHex(point) {\n                return bytesToHex(signatureG1ToRawBytes(point));\n            },\n        },\n    },\n    // G2 is the order-q subgroup of E2(Fp²) : y² = x³+4(1+√−1),\n    // where Fp2 is Fp[√−1]/(x2+1). #E2(Fp2 ) = h2q, where\n    // G² - 1\n    // h2q\n    G2: {\n        Fp: Fp2,\n        // cofactor\n        h: BigInt('0x5d543a95414e7f1091d50792876a202cd91de4547085abaa68a205b2e5a7ddfa628f1cb4d9e82ef21537e293a6691ae1616ec6e786f0c70cf1c38e31c7238e5'),\n        Gx: Fp2.fromBigTuple([\n            BigInt('0x024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8'),\n            BigInt('0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e'),\n        ]),\n        // y =\n        // 927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582,\n        // 1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905\n        Gy: Fp2.fromBigTuple([\n            BigInt('0x0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801'),\n            BigInt('0x0606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be'),\n        ]),\n        a: Fp2.ZERO,\n        b: Fp2.fromBigTuple([_4n, _4n]),\n        hEff: BigInt('0xbc69f08f2ee75b3584c6a0ea91b352888e2a8e9145ad7689986ff031508ffe1329c2f178731db956d82bf015d1212b02ec0ec69d7477c1ae954cbc06689f6a359894c0adebbf6b4e8020005aaa95551'),\n        htfDefaults: { ...htfDefaults },\n        wrapPrivateKey: true,\n        allowInfinityPoint: true,\n        mapToCurve: (scalars) => {\n            const { x, y } = G2_SWU(Fp2.fromBigTuple(scalars));\n            return isogenyMapG2(x, y);\n        },\n        // Checks is the point resides in prime-order subgroup.\n        // point.isTorsionFree() should return true for valid points\n        // It returns false for shitty points.\n        // https://eprint.iacr.org/2021/1130.pdf\n        isTorsionFree: (c, P) => {\n            return P.multiplyUnsafe(bls12_381.params.x).negate().equals(G2psi(c, P)); // ψ(P) == [u](P)\n            // Older version: https://eprint.iacr.org/2019/814.pdf\n            // Ψ²(P) => Ψ³(P) => [z]Ψ³(P) where z = -x => [z]Ψ³(P) - Ψ²(P) + P == O\n            // return P.psi2().psi().mulNegX().subtract(psi2).add(P).isZero();\n        },\n        // Maps the point into the prime-order subgroup G2.\n        // clear_cofactor_bls12381_g2 from cfrg-hash-to-curve-11\n        // https://eprint.iacr.org/2017/419.pdf\n        // prettier-ignore\n        clearCofactor: (c, P) => {\n            const x = bls12_381.params.x;\n            let t1 = P.multiplyUnsafe(x).negate(); // [-x]P\n            let t2 = G2psi(c, P); // Ψ(P)\n            let t3 = P.double(); // 2P\n            t3 = G2psi2(c, t3); // Ψ²(2P)\n            t3 = t3.subtract(t2); // Ψ²(2P) - Ψ(P)\n            t2 = t1.add(t2); // [-x]P + Ψ(P)\n            t2 = t2.multiplyUnsafe(x).negate(); // [x²]P - [x]Ψ(P)\n            t3 = t3.add(t2); // Ψ²(2P) - Ψ(P) + [x²]P - [x]Ψ(P)\n            t3 = t3.subtract(t1); // Ψ²(2P) - Ψ(P) + [x²]P - [x]Ψ(P) + [x]P\n            const Q = t3.subtract(P); // Ψ²(2P) - Ψ(P) + [x²]P - [x]Ψ(P) + [x]P - 1P\n            return Q; // [x²-x-1]P + [x-1]Ψ(P) + Ψ²(2P)\n        },\n        fromBytes: (bytes) => {\n            const { compressed, infinity, sort, value } = parseMask(bytes);\n            if ((!compressed && !infinity && sort) || // 00100000\n                (!compressed && infinity && sort) || // 01100000\n                (sort && infinity && compressed) // 11100000\n            ) {\n                throw new Error('Invalid encoding flag: ' + (bytes[0] & 224));\n            }\n            const L = Fp.BYTES;\n            const slc = (b, from, to) => bytesToNumberBE(b.slice(from, to));\n            if (value.length === 96 && compressed) {\n                const b = bls12_381.params.G2b;\n                const P = Fp.ORDER;\n                if (infinity) {\n                    // check that all bytes are 0\n                    if (value.reduce((p, c) => (p !== 0 ? c + 1 : c), 0) > 0) {\n                        throw new Error('Invalid compressed G2 point');\n                    }\n                    return { x: Fp2.ZERO, y: Fp2.ZERO };\n                }\n                const x_1 = slc(value, 0, L);\n                const x_0 = slc(value, L, 2 * L);\n                const x = Fp2.create({ c0: Fp.create(x_0), c1: Fp.create(x_1) });\n                const right = Fp2.add(Fp2.pow(x, _3n), b); // y² = x³ + 4 * (u+1) = x³ + b\n                let y = Fp2.sqrt(right);\n                const Y_bit = y.c1 === _0n ? (y.c0 * _2n) / P : (y.c1 * _2n) / P ? _1n : _0n;\n                y = sort && Y_bit > 0 ? y : Fp2.neg(y);\n                return { x, y };\n            }\n            else if (value.length === 192 && !compressed) {\n                if (infinity) {\n                    if (value.reduce((p, c) => (p !== 0 ? c + 1 : c), 0) > 0) {\n                        throw new Error('Invalid uncompressed G2 point');\n                    }\n                    return { x: Fp2.ZERO, y: Fp2.ZERO };\n                }\n                const x1 = slc(value, 0, L);\n                const x0 = slc(value, L, 2 * L);\n                const y1 = slc(value, 2 * L, 3 * L);\n                const y0 = slc(value, 3 * L, 4 * L);\n                return { x: Fp2.fromBigTuple([x0, x1]), y: Fp2.fromBigTuple([y0, y1]) };\n            }\n            else {\n                throw new Error('Invalid point G2, expected 96/192 bytes');\n            }\n        },\n        toBytes: (c, point, isCompressed) => {\n            const { BYTES: len, ORDER: P } = Fp;\n            const isZero = point.equals(c.ZERO);\n            const { x, y } = point.toAffine();\n            if (isCompressed) {\n                if (isZero)\n                    return concatB(COMPRESSED_ZERO, numberToBytesBE(_0n, len));\n                const flag = Boolean(y.c1 === _0n ? (y.c0 * _2n) / P : (y.c1 * _2n) / P);\n                return concatB(setMask(numberToBytesBE(x.c1, len), { compressed: true, sort: flag }), numberToBytesBE(x.c0, len));\n            }\n            else {\n                if (isZero)\n                    return concatB(new Uint8Array([0x40]), new Uint8Array(4 * len - 1)); // bytes[0] |= 1 << 6;\n                const { re: x0, im: x1 } = Fp2.reim(x);\n                const { re: y0, im: y1 } = Fp2.reim(y);\n                return concatB(numberToBytesBE(x1, len), numberToBytesBE(x0, len), numberToBytesBE(y1, len), numberToBytesBE(y0, len));\n            }\n        },\n        Signature: {\n            // TODO: Optimize, it's very slow because of sqrt.\n            fromHex(hex) {\n                const { infinity, sort, value } = parseMask(ensureBytes('signatureHex', hex));\n                const P = Fp.ORDER;\n                const half = hex.length / 2;\n                if (half !== 48 && half !== 96)\n                    throw new Error('Invalid compressed signature length, must be 96 or 192');\n                const z1 = bytesToNumberBE(value.slice(0, half));\n                const z2 = bytesToNumberBE(value.slice(half));\n                // Indicates the infinity point\n                if (infinity)\n                    return bls12_381.G2.ProjectivePoint.ZERO;\n                const x1 = Fp.create(z1 & Fp.MASK);\n                const x2 = Fp.create(z2);\n                const x = Fp2.create({ c0: x2, c1: x1 });\n                const y2 = Fp2.add(Fp2.pow(x, _3n), bls12_381.params.G2b); // y² = x³ + 4\n                // The slow part\n                let y = Fp2.sqrt(y2);\n                if (!y)\n                    throw new Error('Failed to find a square root');\n                // Choose the y whose leftmost bit of the imaginary part is equal to the a_flag1\n                // If y1 happens to be zero, then use the bit of y0\n                const { re: y0, im: y1 } = Fp2.reim(y);\n                const aflag1 = BigInt(sort);\n                const isGreater = y1 > _0n && (y1 * _2n) / P !== aflag1;\n                const isZero = y1 === _0n && (y0 * _2n) / P !== aflag1;\n                if (isGreater || isZero)\n                    y = Fp2.neg(y);\n                const point = bls12_381.G2.ProjectivePoint.fromAffine({ x, y });\n                point.assertValidity();\n                return point;\n            },\n            toRawBytes(point) {\n                return signatureG2ToRawBytes(point);\n            },\n            toHex(point) {\n                return bytesToHex(signatureG2ToRawBytes(point));\n            },\n        },\n    },\n    params: {\n        x: BLS_X, // The BLS parameter x for BLS12-381\n        r: Fr.ORDER, // order; z⁴ − z² + 1; CURVE.n from other curves\n    },\n    htfDefaults,\n    hash: sha256,\n    randomBytes,\n});\n//# 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