drand-client/build/cjs/index.cjs.map

A client to the drand randomness beacon network.

{
  "version": 3,
  "sources": ["../../node_modules/@noble/hashes/src/cryptoNode.ts", "../../node_modules/@noble/hashes/src/utils.ts", "../../node_modules/@noble/curves/src/abstract/utils.ts", "../../node_modules/@noble/curves/src/abstract/modular.ts", "../../node_modules/@noble/curves/src/abstract/hash-to-curve.ts", "../../node_modules/@noble/curves/src/abstract/curve.ts", "../../node_modules/@noble/curves/src/abstract/weierstrass.ts", "../../node_modules/@noble/curves/src/abstract/bls.ts", "../../node_modules/@noble/curves/src/abstract/tower.ts", "../../node_modules/@noble/hashes/src/_u64.ts", "../../node_modules/@noble/hashes/src/sha3.ts", "../../node_modules/@kevincharm/noble-bn254-drand/dist/src/bn254.js", "../../node_modules/@kevincharm/noble-bn254-drand/dist/src/index.js", "../../lib/index.ts", "../../lib/version.ts", "../../lib/util.ts", "../../lib/http-caching-chain.ts", "../../lib/http-chain-client.ts", "../../lib/speedtest.ts", "../../lib/fastest-node-client.ts", "../../lib/multi-beacon-node.ts", "../../node_modules/@noble/hashes/src/cryptoNode.ts", "../../node_modules/@noble/hashes/src/utils.ts", "../../node_modules/@noble/hashes/src/_md.ts", "../../node_modules/@noble/hashes/src/_u64.ts", "../../node_modules/@noble/hashes/src/sha2.ts", "../../node_modules/@noble/curves/src/abstract/utils.ts", "../../node_modules/@noble/curves/src/abstract/modular.ts", "../../node_modules/@noble/curves/src/abstract/hash-to-curve.ts", "../../node_modules/@noble/curves/src/abstract/curve.ts", "../../node_modules/@noble/curves/src/abstract/weierstrass.ts", "../../node_modules/@noble/curves/src/abstract/bls.ts", "../../node_modules/@noble/curves/src/abstract/tower.ts", "../../node_modules/@noble/curves/src/bls12-381.ts", "../../lib/beacon-verification.ts", "../../node_modules/@noble/hashes/src/sha3.ts", "../../lib/defaults.ts"],
  "sourcesContent": ["/**\n * Internal webcrypto alias.\n * We prefer WebCrypto aka globalThis.crypto, which exists in node.js 16+.\n * Falls back to Node.js built-in crypto for Node.js <=v14.\n * See utils.ts for details.\n * @module\n */\n// @ts-ignore\nimport * as nc from 'node:crypto';\nexport const crypto: any =\n  nc && typeof nc === 'object' && 'webcrypto' in nc\n    ? (nc.webcrypto as any)\n    : nc && typeof nc === 'object' && 'randomBytes' in nc\n      ? nc\n      : undefined;\n", "/**\n * Utilities for hex, bytes, CSPRNG.\n * @module\n */\n/*! noble-hashes - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n\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\n/** Checks if something is Uint8Array. Be careful: nodejs Buffer will return true. */\nexport function isBytes(a: unknown): a is Uint8Array {\n  return a instanceof Uint8Array || (ArrayBuffer.isView(a) && a.constructor.name === 'Uint8Array');\n}\n\n/** Asserts something is positive integer. */\nexport function anumber(n: number): void {\n  if (!Number.isSafeInteger(n) || n < 0) throw new Error('positive integer expected, got ' + n);\n}\n\n/** Asserts something is Uint8Array. */\nexport function abytes(b: Uint8Array | undefined, ...lengths: number[]): void {\n  if (!isBytes(b)) throw new Error('Uint8Array expected');\n  if (lengths.length > 0 && !lengths.includes(b.length))\n    throw new Error('Uint8Array expected of length ' + lengths + ', got length=' + b.length);\n}\n\n/** Asserts something is hash */\nexport function ahash(h: IHash): void {\n  if (typeof h !== 'function' || typeof h.create !== 'function')\n    throw new Error('Hash should be wrapped by utils.createHasher');\n  anumber(h.outputLen);\n  anumber(h.blockLen);\n}\n\n/** Asserts a hash instance has not been destroyed / finished */\nexport function aexists(instance: any, checkFinished = true): void {\n  if (instance.destroyed) throw new Error('Hash instance has been destroyed');\n  if (checkFinished && instance.finished) throw new Error('Hash#digest() has already been called');\n}\n\n/** Asserts output is properly-sized byte array */\nexport function aoutput(out: any, instance: any): void {\n  abytes(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}\n\n/** Generic type encompassing 8/16/32-byte arrays - but not 64-byte. */\n// prettier-ignore\nexport type TypedArray = Int8Array | Uint8ClampedArray | Uint8Array |\n  Uint16Array | Int16Array | Uint32Array | Int32Array;\n\n/** Cast u8 / u16 / u32 to u8. */\nexport function u8(arr: TypedArray): Uint8Array {\n  return new Uint8Array(arr.buffer, arr.byteOffset, arr.byteLength);\n}\n\n/** Cast u8 / u16 / u32 to u32. */\nexport function u32(arr: TypedArray): Uint32Array {\n  return new Uint32Array(arr.buffer, arr.byteOffset, Math.floor(arr.byteLength / 4));\n}\n\n/** Zeroize a byte array. Warning: JS provides no guarantees. */\nexport function clean(...arrays: TypedArray[]): void {\n  for (let i = 0; i < arrays.length; i++) {\n    arrays[i].fill(0);\n  }\n}\n\n/** Create DataView of an array for easy byte-level manipulation. */\nexport function createView(arr: TypedArray): DataView {\n  return new DataView(arr.buffer, arr.byteOffset, arr.byteLength);\n}\n\n/** The rotate right (circular right shift) operation for uint32 */\nexport function rotr(word: number, shift: number): number {\n  return (word << (32 - shift)) | (word >>> shift);\n}\n\n/** The rotate left (circular left shift) operation for uint32 */\nexport function rotl(word: number, shift: number): number {\n  return (word << shift) | ((word >>> (32 - shift)) >>> 0);\n}\n\n/** Is current platform little-endian? Most are. Big-Endian platform: IBM */\nexport const isLE: boolean = /* @__PURE__ */ (() =>\n  new Uint8Array(new Uint32Array([0x11223344]).buffer)[0] === 0x44)();\n\n/** The byte swap operation for uint32 */\nexport function byteSwap(word: number): number {\n  return (\n    ((word << 24) & 0xff000000) |\n    ((word << 8) & 0xff0000) |\n    ((word >>> 8) & 0xff00) |\n    ((word >>> 24) & 0xff)\n  );\n}\n/** Conditionally byte swap if on a big-endian platform */\nexport const swap8IfBE: (n: number) => number = isLE\n  ? (n: number) => n\n  : (n: number) => byteSwap(n);\n\n/** @deprecated */\nexport const byteSwapIfBE: typeof swap8IfBE = swap8IfBE;\n/** In place byte swap for Uint32Array */\nexport function byteSwap32(arr: Uint32Array): Uint32Array {\n  for (let i = 0; i < arr.length; i++) {\n    arr[i] = byteSwap(arr[i]);\n  }\n  return arr;\n}\n\nexport const swap32IfBE: (u: Uint32Array) => Uint32Array = isLE\n  ? (u: Uint32Array) => u\n  : byteSwap32;\n\n// Built-in hex conversion https://caniuse.com/mdn-javascript_builtins_uint8array_fromhex\nconst hasHexBuiltin: boolean = /* @__PURE__ */ (() =>\n  // @ts-ignore\n  typeof Uint8Array.from([]).toHex === 'function' && typeof Uint8Array.fromHex === 'function')();\n\n// Array where index 0xf0 (240) is mapped to string 'f0'\nconst hexes = /* @__PURE__ */ Array.from({ length: 256 }, (_, i) =>\n  i.toString(16).padStart(2, '0')\n);\n\n/**\n * Convert byte array to hex string. Uses built-in function, when available.\n * @example bytesToHex(Uint8Array.from([0xca, 0xfe, 0x01, 0x23])) // 'cafe0123'\n */\nexport function bytesToHex(bytes: Uint8Array): string {\n  abytes(bytes);\n  // @ts-ignore\n  if (hasHexBuiltin) return bytes.toHex();\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\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 } as const;\nfunction asciiToBase16(ch: number): number | undefined {\n  if (ch >= asciis._0 && ch <= asciis._9) return ch - asciis._0; // '2' => 50-48\n  if (ch >= asciis.A && ch <= asciis.F) return ch - (asciis.A - 10); // 'B' => 66-(65-10)\n  if (ch >= asciis.a && ch <= asciis.f) return ch - (asciis.a - 10); // 'b' => 98-(97-10)\n  return;\n}\n\n/**\n * Convert hex string to byte array. Uses built-in function, when available.\n * @example hexToBytes('cafe0123') // Uint8Array.from([0xca, 0xfe, 0x01, 0x23])\n */\nexport function hexToBytes(hex: string): Uint8Array {\n  if (typeof hex !== 'string') throw new Error('hex string expected, got ' + typeof hex);\n  // @ts-ignore\n  if (hasHexBuiltin) return Uint8Array.fromHex(hex);\n  const hl = hex.length;\n  const al = hl / 2;\n  if (hl % 2) throw new Error('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; // multiply first octet, e.g. 'a3' => 10*16+3 => 160 + 3 => 163\n  }\n  return array;\n}\n\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.\n */\nexport const nextTick = async (): Promise<void> => {};\n\n/** Returns control to thread each 'tick' ms to avoid blocking. */\nexport async function asyncLoop(\n  iters: number,\n  tick: number,\n  cb: (i: number) => void\n): Promise<void> {\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) continue;\n    await nextTick();\n    ts += diff;\n  }\n}\n\n// Global symbols, but ts doesn't see them: https://github.com/microsoft/TypeScript/issues/31535\ndeclare const TextEncoder: any;\ndeclare const TextDecoder: any;\n\n/**\n * Converts string to bytes using UTF8 encoding.\n * @example utf8ToBytes('abc') // Uint8Array.from([97, 98, 99])\n */\nexport function utf8ToBytes(str: string): Uint8Array {\n  if (typeof str !== 'string') throw new Error('string expected');\n  return new Uint8Array(new TextEncoder().encode(str)); // https://bugzil.la/1681809\n}\n\n/**\n * Converts bytes to string using UTF8 encoding.\n * @example bytesToUtf8(Uint8Array.from([97, 98, 99])) // 'abc'\n */\nexport function bytesToUtf8(bytes: Uint8Array): string {\n  return new TextDecoder().decode(bytes);\n}\n\n/** Accepted input of hash functions. Strings are converted to byte arrays. */\nexport type Input = string | Uint8Array;\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: Input): Uint8Array {\n  if (typeof data === 'string') data = utf8ToBytes(data);\n  abytes(data);\n  return data;\n}\n\n/** KDFs can accept string or Uint8Array for user convenience. */\nexport type KDFInput = string | Uint8Array;\n/**\n * Helper for KDFs: consumes uint8array or string.\n * When string is passed, does utf8 decoding, using TextDecoder.\n */\nexport function kdfInputToBytes(data: KDFInput): Uint8Array {\n  if (typeof data === 'string') data = utf8ToBytes(data);\n  abytes(data);\n  return data;\n}\n\n/** Copies several Uint8Arrays into one. */\nexport function concatBytes(...arrays: Uint8Array[]): Uint8Array {\n  let sum = 0;\n  for (let i = 0; i < arrays.length; i++) {\n    const a = arrays[i];\n    abytes(a);\n    sum += a.length;\n  }\n  const res = new Uint8Array(sum);\n  for (let i = 0, pad = 0; i < arrays.length; i++) {\n    const a = arrays[i];\n    res.set(a, pad);\n    pad += a.length;\n  }\n  return res;\n}\n\ntype EmptyObj = {};\nexport function checkOpts<T1 extends EmptyObj, T2 extends EmptyObj>(\n  defaults: T1,\n  opts?: T2\n): T1 & T2 {\n  if (opts !== undefined && {}.toString.call(opts) !== '[object Object]')\n    throw new Error('options should be object or undefined');\n  const merged = Object.assign(defaults, opts);\n  return merged as T1 & T2;\n}\n\n/** Hash interface. */\nexport type IHash = {\n  (data: Uint8Array): Uint8Array;\n  blockLen: number;\n  outputLen: number;\n  create: any;\n};\n\n/** For runtime check if class implements interface */\nexport abstract class Hash<T extends Hash<T>> {\n  abstract blockLen: number; // Bytes per block\n  abstract outputLen: number; // Bytes in output\n  abstract update(buf: Input): this;\n  // Writes digest into buf\n  abstract digestInto(buf: Uint8Array): void;\n  abstract digest(): Uint8Array;\n  /**\n   * Resets internal state. Makes Hash instance unusable.\n   * Reset is impossible for keyed hashes if key is consumed into state. If digest is not consumed\n   * by user, they will need to manually call `destroy()` when zeroing is necessary.\n   */\n  abstract destroy(): void;\n  /**\n   * Clones hash instance. Unsafe: doesn't check whether `to` is valid. Can be used as `clone()`\n   * when no options are passed.\n   * Reasons to use `_cloneInto` instead of clone: 1) performance 2) reuse instance => all internal\n   * buffers are overwritten => causes buffer overwrite which is used for digest in some cases.\n   * There are no guarantees for clean-up because it's impossible in JS.\n   */\n  abstract _cloneInto(to?: T): T;\n  // Safe version that clones internal state\n  abstract clone(): T;\n}\n\n/**\n * XOF: streaming API to read digest in chunks.\n * Same as 'squeeze' in keccak/k12 and 'seek' in blake3, but more generic name.\n * When hash used in XOF mode it is up to user to call '.destroy' afterwards, since we cannot\n * destroy state, next call can require more bytes.\n */\nexport type HashXOF<T extends Hash<T>> = Hash<T> & {\n  xof(bytes: number): Uint8Array; // Read 'bytes' bytes from digest stream\n  xofInto(buf: Uint8Array): Uint8Array; // read buf.length bytes from digest stream into buf\n};\n\n/** Hash function */\nexport type CHash = ReturnType<typeof createHasher>;\n/** Hash function with output */\nexport type CHashO = ReturnType<typeof createOptHasher>;\n/** XOF with output */\nexport type CHashXO = ReturnType<typeof createXOFer>;\n\n/** Wraps hash function, creating an interface on top of it */\nexport function createHasher<T extends Hash<T>>(\n  hashCons: () => Hash<T>\n): {\n  (msg: Input): Uint8Array;\n  outputLen: number;\n  blockLen: number;\n  create(): Hash<T>;\n} {\n  const hashC = (msg: Input): Uint8Array => 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}\n\nexport function createOptHasher<H extends Hash<H>, T extends Object>(\n  hashCons: (opts?: T) => Hash<H>\n): {\n  (msg: Input, opts?: T): Uint8Array;\n  outputLen: number;\n  blockLen: number;\n  create(opts?: T): Hash<H>;\n} {\n  const hashC = (msg: Input, opts?: T): Uint8Array => hashCons(opts).update(toBytes(msg)).digest();\n  const tmp = hashCons({} as T);\n  hashC.outputLen = tmp.outputLen;\n  hashC.blockLen = tmp.blockLen;\n  hashC.create = (opts?: T) => hashCons(opts);\n  return hashC;\n}\n\nexport function createXOFer<H extends HashXOF<H>, T extends Object>(\n  hashCons: (opts?: T) => HashXOF<H>\n): {\n  (msg: Input, opts?: T): Uint8Array;\n  outputLen: number;\n  blockLen: number;\n  create(opts?: T): HashXOF<H>;\n} {\n  const hashC = (msg: Input, opts?: T): Uint8Array => hashCons(opts).update(toBytes(msg)).digest();\n  const tmp = hashCons({} as T);\n  hashC.outputLen = tmp.outputLen;\n  hashC.blockLen = tmp.blockLen;\n  hashC.create = (opts?: T) => hashCons(opts);\n  return hashC;\n}\nexport const wrapConstructor: typeof createHasher = createHasher;\nexport const wrapConstructorWithOpts: typeof createOptHasher = createOptHasher;\nexport const wrapXOFConstructorWithOpts: typeof createXOFer = createXOFer;\n\n/** Cryptographically secure PRNG. Uses internal OS-level `crypto.getRandomValues`. */\nexport function randomBytes(bytesLength = 32): Uint8Array {\n  if (crypto && typeof crypto.getRandomValues === 'function') {\n    return crypto.getRandomValues(new Uint8Array(bytesLength));\n  }\n  // Legacy Node.js compatibility\n  if (crypto && typeof crypto.randomBytes === 'function') {\n    return Uint8Array.from(crypto.randomBytes(bytesLength));\n  }\n  throw new Error('crypto.getRandomValues must be defined');\n}\n", "/**\n * Hex, bytes and number utilities.\n * @module\n */\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n\n// 100 lines of code in the file are duplicated from noble-hashes (utils).\n// This is OK: `abstract` directory does not use noble-hashes.\n// User may opt-in into using different hashing library. This way, noble-hashes\n// won't be included into their bundle.\nconst _0n = /* @__PURE__ */ BigInt(0);\nconst _1n = /* @__PURE__ */ BigInt(1);\nexport type Hex = Uint8Array | string; // hex strings are accepted for simplicity\nexport type PrivKey = Hex | bigint; // bigints are accepted to ease learning curve\nexport type CHash = {\n  (message: Uint8Array | string): Uint8Array;\n  blockLen: number;\n  outputLen: number;\n  create(opts?: { dkLen?: number }): any; // For shake\n};\nexport type FHash = (message: Uint8Array | string) => Uint8Array;\n\nexport function isBytes(a: unknown): a is Uint8Array {\n  return a instanceof Uint8Array || (ArrayBuffer.isView(a) && a.constructor.name === 'Uint8Array');\n}\n\nexport function abytes(item: unknown): void {\n  if (!isBytes(item)) throw new Error('Uint8Array expected');\n}\n\nexport function abool(title: string, value: boolean): void {\n  if (typeof value !== 'boolean') throw new Error(title + ' boolean expected, got ' + value);\n}\n\n// Used in weierstrass, der\nexport function numberToHexUnpadded(num: number | bigint): string {\n  const hex = num.toString(16);\n  return hex.length & 1 ? '0' + hex : hex;\n}\n\nexport function hexToNumber(hex: string): bigint {\n  if (typeof hex !== 'string') throw new Error('hex string expected, got ' + typeof hex);\n  return hex === '' ? _0n : BigInt('0x' + hex); // Big Endian\n}\n\n// Built-in hex conversion https://caniuse.com/mdn-javascript_builtins_uint8array_fromhex\nconst hasHexBuiltin: boolean =\n  // @ts-ignore\n  typeof Uint8Array.from([]).toHex === 'function' && typeof Uint8Array.fromHex === 'function';\n\n// Array where index 0xf0 (240) is mapped to string 'f0'\nconst hexes = /* @__PURE__ */ Array.from({ length: 256 }, (_, i) =>\n  i.toString(16).padStart(2, '0')\n);\n\n/**\n * Convert byte array to hex string. Uses built-in function, when available.\n * @example bytesToHex(Uint8Array.from([0xca, 0xfe, 0x01, 0x23])) // 'cafe0123'\n */\nexport function bytesToHex(bytes: Uint8Array): string {\n  abytes(bytes);\n  // @ts-ignore\n  if (hasHexBuiltin) return bytes.toHex();\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\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 } as const;\nfunction asciiToBase16(ch: number): number | undefined {\n  if (ch >= asciis._0 && ch <= asciis._9) return ch - asciis._0; // '2' => 50-48\n  if (ch >= asciis.A && ch <= asciis.F) return ch - (asciis.A - 10); // 'B' => 66-(65-10)\n  if (ch >= asciis.a && ch <= asciis.f) return ch - (asciis.a - 10); // 'b' => 98-(97-10)\n  return;\n}\n\n/**\n * Convert hex string to byte array. Uses built-in function, when available.\n * @example hexToBytes('cafe0123') // Uint8Array.from([0xca, 0xfe, 0x01, 0x23])\n */\nexport function hexToBytes(hex: string): Uint8Array {\n  if (typeof hex !== 'string') throw new Error('hex string expected, got ' + typeof hex);\n  // @ts-ignore\n  if (hasHexBuiltin) return Uint8Array.fromHex(hex);\n  const hl = hex.length;\n  const al = hl / 2;\n  if (hl % 2) throw new Error('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; // multiply first octet, e.g. 'a3' => 10*16+3 => 160 + 3 => 163\n  }\n  return array;\n}\n\n// BE: Big Endian, LE: Little Endian\nexport function bytesToNumberBE(bytes: Uint8Array): bigint {\n  return hexToNumber(bytesToHex(bytes));\n}\nexport function bytesToNumberLE(bytes: Uint8Array): bigint {\n  abytes(bytes);\n  return hexToNumber(bytesToHex(Uint8Array.from(bytes).reverse()));\n}\n\nexport function numberToBytesBE(n: number | bigint, len: number): Uint8Array {\n  return hexToBytes(n.toString(16).padStart(len * 2, '0'));\n}\nexport function numberToBytesLE(n: number | bigint, len: number): Uint8Array {\n  return numberToBytesBE(n, len).reverse();\n}\n// Unpadded, rarely used\nexport function numberToVarBytesBE(n: number | bigint): Uint8Array {\n  return hexToBytes(numberToHexUnpadded(n));\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: string, hex: Hex, expectedLength?: number): Uint8Array {\n  let res: Uint8Array;\n  if (typeof hex === 'string') {\n    try {\n      res = hexToBytes(hex);\n    } catch (e) {\n      throw new Error(title + ' must be hex string or Uint8Array, cause: ' + e);\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  } 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 + ' of length ' + expectedLength + ' expected, got ' + len);\n  return res;\n}\n\n/**\n * Copies several Uint8Arrays into one.\n */\nexport function concatBytes(...arrays: Uint8Array[]): Uint8Array {\n  let sum = 0;\n  for (let i = 0; i < arrays.length; i++) {\n    const a = arrays[i];\n    abytes(a);\n    sum += a.length;\n  }\n  const res = new Uint8Array(sum);\n  for (let i = 0, pad = 0; i < arrays.length; i++) {\n    const a = arrays[i];\n    res.set(a, pad);\n    pad += a.length;\n  }\n  return res;\n}\n\n// Compares 2 u8a-s in kinda constant time\nexport function equalBytes(a: Uint8Array, b: Uint8Array): boolean {\n  if (a.length !== b.length) return false;\n  let diff = 0;\n  for (let i = 0; i < a.length; i++) diff |= a[i] ^ b[i];\n  return diff === 0;\n}\n\n// Global symbols in both browsers and Node.js since v11\n// See https://github.com/microsoft/TypeScript/issues/31535\ndeclare const TextEncoder: any;\n\n/**\n * @example utf8ToBytes('abc') // new Uint8Array([97, 98, 99])\n */\nexport function utf8ToBytes(str: string): Uint8Array {\n  if (typeof str !== 'string') throw new Error('string expected');\n  return new Uint8Array(new TextEncoder().encode(str)); // https://bugzil.la/1681809\n}\n\n// Is positive bigint\nconst isPosBig = (n: bigint) => typeof n === 'bigint' && _0n <= n;\n\nexport function inRange(n: bigint, min: bigint, max: bigint): boolean {\n  return isPosBig(n) && isPosBig(min) && isPosBig(max) && min <= n && n < max;\n}\n\n/**\n * Asserts min <= n < max. NOTE: It's < max and not <= max.\n * @example\n * aInRange('x', x, 1n, 256n); // would assume x is in (1n..255n)\n */\nexport function aInRange(title: string, n: bigint, min: bigint, max: bigint): void {\n  // Why min <= n < max and not a (min < n < max) OR b (min <= n <= max)?\n  // consider P=256n, min=0n, max=P\n  // - a for min=0 would require -1:          `inRange('x', x, -1n, P)`\n  // - b would commonly require subtraction:  `inRange('x', x, 0n, P - 1n)`\n  // - our way is the cleanest:               `inRange('x', x, 0n, P)\n  if (!inRange(n, min, max))\n    throw new Error('expected valid ' + title + ': ' + min + ' <= n < ' + max + ', got ' + n);\n}\n\n// Bit operations\n\n/**\n * Calculates amount of bits in a bigint.\n * Same as `n.toString(2).length`\n * TODO: merge with nLength in modular\n */\nexport function bitLen(n: bigint): number {\n  let len;\n  for (len = 0; n > _0n; n >>= _1n, len += 1);\n  return len;\n}\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: bigint, pos: number): bigint {\n  return (n >> BigInt(pos)) & _1n;\n}\n\n/**\n * Sets single bit at position.\n */\nexport function bitSet(n: bigint, pos: number, value: boolean): bigint {\n  return n | ((value ? _1n : _0n) << BigInt(pos));\n}\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: number): bigint => (_1n << BigInt(n)) - _1n;\n\n// DRBG\n\nconst u8n = (len: number) => new Uint8Array(len); // creates Uint8Array\nconst u8fr = (arr: ArrayLike<number>) => Uint8Array.from(arr); // another shortcut\ntype Pred<T> = (v: Uint8Array) => T | undefined;\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<T>(\n  hashLen: number,\n  qByteLen: number,\n  hmacFn: (key: Uint8Array, ...messages: Uint8Array[]) => Uint8Array\n): (seed: Uint8Array, predicate: Pred<T>) => T {\n  if (typeof hashLen !== 'number' || hashLen < 2) throw new Error('hashLen must be a number');\n  if (typeof qByteLen !== 'number' || qByteLen < 2) throw new Error('qByteLen must be a number');\n  if (typeof hmacFn !== 'function') 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: Uint8Array[]) => hmacFn(k, v, ...b); // hmac(k)(v, ...values)\n  const reseed = (seed = u8n(0)) => {\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) 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) throw new Error('drbg: tried 1000 values');\n    let len = 0;\n    const out: Uint8Array[] = [];\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: Uint8Array, pred: Pred<T>): T => {\n    reset();\n    reseed(seed); // Steps D-G\n    let res: T | undefined = undefined; // Step H: grind until k is in [1..n-1]\n    while (!(res = pred(gen()))) reseed();\n    reset();\n    return res;\n  };\n  return genUntil;\n}\n\n// Validating curves and fields\n\nconst validatorFns = {\n  bigint: (val: any): boolean => typeof val === 'bigint',\n  function: (val: any): boolean => typeof val === 'function',\n  boolean: (val: any): boolean => typeof val === 'boolean',\n  string: (val: any): boolean => typeof val === 'string',\n  stringOrUint8Array: (val: any): boolean => typeof val === 'string' || isBytes(val),\n  isSafeInteger: (val: any): boolean => Number.isSafeInteger(val),\n  array: (val: any): boolean => Array.isArray(val),\n  field: (val: any, object: any): any => (object as any).Fp.isValid(val),\n  hash: (val: any): boolean => typeof val === 'function' && Number.isSafeInteger(val.outputLen),\n} as const;\ntype Validator = keyof typeof validatorFns;\ntype ValMap<T extends Record<string, any>> = { [K in keyof T]?: Validator };\n// type Record<K extends string | number | symbol, T> = { [P in K]: T; }\n\nexport function validateObject<T extends Record<string, any>>(\n  object: T,\n  validators: ValMap<T>,\n  optValidators: ValMap<T> = {}\n): T {\n  const checkField = (fieldName: keyof T, type: Validator, isOptional: boolean) => {\n    const checkVal = validatorFns[type];\n    if (typeof checkVal !== 'function') throw new Error('invalid validator function');\n\n    const val = object[fieldName as keyof typeof object];\n    if (isOptional && val === undefined) return;\n    if (!checkVal(val, object)) {\n      throw new Error(\n        'param ' + String(fieldName) + ' is invalid. Expected ' + type + ', got ' + val\n      );\n    }\n  };\n  for (const [fieldName, type] of Object.entries(validators)) checkField(fieldName, type!, false);\n  for (const [fieldName, type] of Object.entries(optValidators)) checkField(fieldName, type!, true);\n  return object;\n}\n// validate type tests\n// const o: { a: number; b: number; c: number } = { a: 1, b: 5, c: 6 };\n// const z0 = validateObject(o, { a: 'isSafeInteger' }, { c: 'bigint' }); // Ok!\n// // Should fail type-check\n// const z1 = validateObject(o, { a: 'tmp' }, { c: 'zz' });\n// const z2 = validateObject(o, { a: 'isSafeInteger' }, { c: 'zz' });\n// const z3 = validateObject(o, { test: 'boolean', z: 'bug' });\n// const z4 = validateObject(o, { a: 'boolean', z: 'bug' });\n\n/**\n * throws not implemented error\n */\nexport const notImplemented = (): never => {\n  throw new Error('not implemented');\n};\n\n/**\n * Memoizes (caches) computation result.\n * Uses WeakMap: the value is going auto-cleaned by GC after last reference is removed.\n */\nexport function memoized<T extends object, R, O extends any[]>(\n  fn: (arg: T, ...args: O) => R\n): (arg: T, ...args: O) => R {\n  const map = new WeakMap<T, R>();\n  return (arg: T, ...args: O): R => {\n    const val = map.get(arg);\n    if (val !== undefined) return val;\n    const computed = fn(arg, ...args);\n    map.set(arg, computed);\n    return computed;\n  };\n}\n", "/**\n * Utils for modular division and finite fields.\n * A finite field over 11 is integer number operations `mod 11`.\n * There is no division: it is replaced by modular multiplicative inverse.\n * @module\n */\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\nimport { anumber } from '@noble/hashes/utils';\nimport {\n  bitMask,\n  bytesToNumberBE,\n  bytesToNumberLE,\n  ensureBytes,\n  numberToBytesBE,\n  numberToBytesLE,\n  validateObject,\n} from './utils.ts';\n\n// prettier-ignore\nconst _0n = BigInt(0), _1n = BigInt(1), _2n = /* @__PURE__ */ BigInt(2), _3n = /* @__PURE__ */ BigInt(3);\n// prettier-ignore\nconst _4n = /* @__PURE__ */ BigInt(4), _5n = /* @__PURE__ */ BigInt(5), _8n = /* @__PURE__ */ BigInt(8);\n// prettier-ignore\nconst _9n =/* @__PURE__ */ BigInt(9), _16n = /* @__PURE__ */ BigInt(16);\n\n// Calculates a modulo b\nexport function mod(a: bigint, b: bigint): bigint {\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 * TODO: remove.\n * @example\n * pow(2n, 6n, 11n) // 64n % 11n == 9n\n */\nexport function pow(num: bigint, power: bigint, modulo: bigint): bigint {\n  if (power < _0n) throw new Error('invalid exponent, negatives unsupported');\n  if (modulo <= _0n) throw new Error('invalid modulus');\n  if (modulo === _1n) return _0n;\n  let res = _1n;\n  while (power > _0n) {\n    if (power & _1n) res = (res * num) % modulo;\n    num = (num * num) % modulo;\n    power >>= _1n;\n  }\n  return res;\n}\n\n/** Does `x^(2^power)` mod p. `pow2(30, 4)` == `30^(2^4)` */\nexport function pow2(x: bigint, power: bigint, modulo: bigint): bigint {\n  let res = x;\n  while (power-- > _0n) {\n    res *= res;\n    res %= modulo;\n  }\n  return res;\n}\n\n/**\n * Inverses number over modulo.\n * Implemented using [Euclidean GCD](https://brilliant.org/wiki/extended-euclidean-algorithm/).\n */\nexport function invert(number: bigint, modulo: bigint): bigint {\n  if (number === _0n) throw new Error('invert: expected non-zero number');\n  if (modulo <= _0n) throw new Error('invert: expected positive modulus, got ' + modulo);\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) throw new Error('invert: does not exist');\n  return mod(x, modulo);\n}\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 * @param P field order\n * @returns function that takes field Fp (created from P) and number n\n */\nexport function tonelliShanks(P: bigint): <T>(Fp: IField<T>, n: T) => T {\n  // Do expensive precomputation step\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  let Q = P - _1n;\n  let S = 0;\n  while (Q % _2n === _0n) {\n    Q /= _2n;\n    S++;\n  }\n\n  // Step 2: Select a non-square z such that (z | p) \u2261 -1 and set c \u2261 zq\n  let Z = _2n;\n  const _Fp = Field(P);\n  while (Z < P && FpIsSquare(_Fp, Z)) {\n    if (Z++ > 1000) throw new Error('Cannot find square root: probably non-prime P');\n  }\n\n  // Fast-path\n  if (S === 1) {\n    const p1div4 = (P + _1n) / _4n;\n    return function tonelliFast<T>(Fp: IField<T>, n: T) {\n      const root = Fp.pow(n, p1div4);\n      if (!Fp.eql(Fp.sqr(root), 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<T>(Fp: IField<T>, n: T): T {\n    // Step 0: Check that n is indeed a square: (n | p) should not be \u2261 -1\n    if (!FpIsSquare(Fp, n)) throw new Error('Cannot find square root');\n    let r = S;\n    // TODO: test on Fp2 and others\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\n    while (!Fp.eql(b, Fp.ONE)) {\n      // (4. If t = 0, return r = 0)\n      // https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm\n      if (Fp.eql(b, Fp.ZERO)) return Fp.ZERO;\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)) 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,\n      // 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}\n\n/**\n * Square root for a finite field. It will try to check if optimizations are applicable and fall back to 4:\n *\n * 1. P \u2261 3 (mod 4)\n * 2. P \u2261 5 (mod 8)\n * 3. P \u2261 9 (mod 16)\n * 4. Tonelli-Shanks algorithm\n *\n * 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 */\nexport function FpSqrt(P: bigint): <T>(Fp: IField<T>, n: T) => T {\n  // P \u2261 3 (mod 4)\n  // \u221An = n^((P+1)/4)\n  if (P % _4n === _3n) {\n    // Not all roots possible!\n    // const ORDER =\n    //   0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaabn;\n    // const NUM = 72057594037927816n;\n    return function sqrt3mod4<T>(Fp: IField<T>, n: T) {\n      const p1div4 = (P + _1n) / _4n;\n      const root = Fp.pow(n, p1div4);\n      // Throw if root**2 != n\n      if (!Fp.eql(Fp.sqr(root), n)) throw new Error('Cannot find square root');\n      return root;\n    };\n  }\n\n  // Atkin algorithm for q \u2261 5 (mod 8), https://eprint.iacr.org/2012/685.pdf (page 10)\n  if (P % _8n === _5n) {\n    return function sqrt5mod8<T>(Fp: IField<T>, n: T) {\n      const n2 = Fp.mul(n, _2n);\n      const c1 = (P - _5n) / _8n;\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)) throw new Error('Cannot find square root');\n      return root;\n    };\n  }\n\n  // P \u2261 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\n// Little-endian check for first LE bit (last BE bit);\nexport const isNegativeLE = (num: bigint, modulo: bigint): boolean =>\n  (mod(num, modulo) & _1n) === _1n;\n\n/** Field is not always over prime: for example, Fp2 has ORDER(q)=p^m. */\nexport interface IField<T> {\n  ORDER: bigint;\n  isLE: boolean;\n  BYTES: number;\n  BITS: number;\n  MASK: bigint;\n  ZERO: T;\n  ONE: T;\n  // 1-arg\n  create: (num: T) => T;\n  isValid: (num: T) => boolean;\n  is0: (num: T) => boolean;\n  neg(num: T): T;\n  inv(num: T): T;\n  sqrt(num: T): T;\n  sqr(num: T): T;\n  // 2-args\n  eql(lhs: T, rhs: T): boolean;\n  add(lhs: T, rhs: T): T;\n  sub(lhs: T, rhs: T): T;\n  mul(lhs: T, rhs: T | bigint): T;\n  pow(lhs: T, power: bigint): T;\n  div(lhs: T, rhs: T | bigint): T;\n  // N for NonNormalized (for now)\n  addN(lhs: T, rhs: T): T;\n  subN(lhs: T, rhs: T): T;\n  mulN(lhs: T, rhs: T | bigint): T;\n  sqrN(num: T): T;\n\n  // Optional\n  // Should be same as sgn0 function in\n  // [RFC9380](https://www.rfc-editor.org/rfc/rfc9380#section-4.1).\n  // NOTE: sgn0 is 'negative in LE', which is same as odd. And negative in LE is kinda strange definition anyway.\n  isOdd?(num: T): boolean; // Odd instead of even since we have it for Fp2\n  // legendre?(num: T): T;\n  pow(lhs: T, power: bigint): T;\n  invertBatch: (lst: T[]) => T[];\n  toBytes(num: T): Uint8Array;\n  fromBytes(bytes: Uint8Array): T;\n  // If c is False, CMOV returns a, otherwise it returns b.\n  cmov(a: T, b: T, c: boolean): T;\n}\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] as const;\nexport function validateField<T>(field: IField<T>): IField<T> {\n  const initial = {\n    ORDER: 'bigint',\n    MASK: 'bigint',\n    BYTES: 'isSafeInteger',\n    BITS: 'isSafeInteger',\n  } as Record<string, string>;\n  const opts = FIELD_FIELDS.reduce((map, val: string) => {\n    map[val] = 'function';\n    return map;\n  }, initial);\n  return validateObject(field, opts);\n}\n\n// Generic field functions\n\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<T>(Fp: IField<T>, num: T, power: bigint): T {\n  if (power < _0n) throw new Error('invalid exponent, negatives unsupported');\n  if (power === _0n) return Fp.ONE;\n  if (power === _1n) return num;\n  // @ts-ignore\n  let p = Fp.ONE;\n  let d = num;\n  while (power > _0n) {\n    if (power & _1n) p = Fp.mul(p, d);\n    d = Fp.sqr(d);\n    power >>= _1n;\n  }\n  return p;\n}\n\n/**\n * Efficiently invert an array of Field elements.\n * Exception-free. Will return `undefined` for 0 elements.\n * @param passZero map 0 to 0 (instead of undefined)\n */\nexport function FpInvertBatch<T>(Fp: IField<T>, nums: T[], passZero = false): T[] {\n  const inverted = new Array(nums.length).fill(passZero ? Fp.ZERO : undefined);\n  // Walk from first to last, multiply them by each other MOD p\n  const multipliedAcc = nums.reduce((acc, num, i) => {\n    if (Fp.is0(num)) return acc;\n    inverted[i] = acc;\n    return Fp.mul(acc, num);\n  }, Fp.ONE);\n  // Invert last element\n  const invertedAcc = Fp.inv(multipliedAcc);\n  // Walk from last to first, multiply them by inverted each other MOD p\n  nums.reduceRight((acc, num, i) => {\n    if (Fp.is0(num)) return acc;\n    inverted[i] = Fp.mul(acc, inverted[i]);\n    return Fp.mul(acc, num);\n  }, invertedAcc);\n  return inverted;\n}\n\n// TODO: remove\nexport function FpDiv<T>(Fp: IField<T>, lhs: T, rhs: T | bigint): T {\n  return Fp.mul(lhs, typeof rhs === 'bigint' ? invert(rhs, Fp.ORDER) : Fp.inv(rhs));\n}\n\n/**\n * Legendre symbol.\n * Legendre constant is used to calculate Legendre symbol (a | p)\n * which denotes the value of a^((p-1)/2) (mod p)..\n *\n * * (a | p) \u2261 1    if a is a square (mod p), quadratic residue\n * * (a | p) \u2261 -1   if a is not a square (mod p), quadratic non residue\n * * (a | p) \u2261 0    if a \u2261 0 (mod p)\n */\nexport function FpLegendre<T>(Fp: IField<T>, n: T): number {\n  const legc = (Fp.ORDER - _1n) / _2n;\n  const powered = Fp.pow(n, legc);\n  const yes = Fp.eql(powered, Fp.ONE);\n  const zero = Fp.eql(powered, Fp.ZERO);\n  const no = Fp.eql(powered, Fp.neg(Fp.ONE));\n  if (!yes && !zero && !no) throw new Error('Cannot find square root: probably non-prime P');\n  return yes ? 1 : zero ? 0 : -1;\n}\n\n// This function returns True whenever the value x is a square in the field F.\nexport function FpIsSquare<T>(Fp: IField<T>, n: T): boolean {\n  const l = FpLegendre(Fp, n);\n  return l === 0 || l === 1;\n}\n\n// CURVE.n lengths\nexport function nLength(\n  n: bigint,\n  nBitLength?: number\n): {\n  nBitLength: number;\n  nByteLength: number;\n} {\n  // Bit size, byte size of CURVE.n\n  if (nBitLength !== undefined) anumber(nBitLength);\n  const _nBitLength = nBitLength !== undefined ? nBitLength : n.toString(2).length;\n  const nByteLength = Math.ceil(_nBitLength / 8);\n  return { nBitLength: _nBitLength, nByteLength };\n}\n\ntype FpField = IField<bigint> & Required<Pick<IField<bigint>, 'isOdd'>>;\n/**\n * Initializes a finite field over prime.\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 * Fragile: always run a benchmark on a change.\n * Security note: operations don't check 'isValid' for all elements for performance reasons,\n * it is caller responsibility to check this.\n * This is low-level code, please make sure you know what you're doing.\n * @param ORDER prime positive bigint\n * @param bitLen how many bits the field consumes\n * @param isLE (def: false) if encoding / decoding should be in little-endian\n * @param redef optional faster redefinitions of sqrt and other methods\n */\nexport function Field(\n  ORDER: bigint,\n  bitLen?: number,\n  isLE = false,\n  redef: Partial<IField<bigint>> = {}\n): Readonly<FpField> {\n  if (ORDER <= _0n) throw new Error('invalid field: expected ORDER > 0, got ' + ORDER);\n  const { nBitLength: BITS, nByteLength: BYTES } = nLength(ORDER, bitLen);\n  if (BYTES > 2048) throw new Error('invalid field: expected ORDER of <= 2048 bytes');\n  let sqrtP: ReturnType<typeof FpSqrt>; // cached sqrtP\n  const f: Readonly<FpField> = Object.freeze({\n    ORDER,\n    isLE,\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\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\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\n    inv: (num) => invert(num, ORDER),\n    sqrt:\n      redef.sqrt ||\n      ((n) => {\n        if (!sqrtP) sqrtP = FpSqrt(ORDER);\n        return sqrtP(f, n);\n      }),\n    toBytes: (num) => (isLE ? numberToBytesLE(num, BYTES) : numberToBytesBE(num, BYTES)),\n    fromBytes: (bytes) => {\n      if (bytes.length !== BYTES)\n        throw new Error('Field.fromBytes: expected ' + BYTES + ' bytes, got ' + bytes.length);\n      return isLE ? bytesToNumberLE(bytes) : bytesToNumberBE(bytes);\n    },\n    // TODO: we don't need it here, move out to separate fn\n    invertBatch: (lst) => FpInvertBatch(f, lst),\n    // We can't move this out because Fp6, Fp12 implement it\n    // and it's unclear what to return in there.\n    cmov: (a, b, c) => (c ? b : a),\n  } as FpField);\n  return Object.freeze(f);\n}\n\nexport function FpSqrtOdd<T>(Fp: IField<T>, elm: T): T {\n  if (!Fp.isOdd) throw new Error(\"Field doesn't have isOdd\");\n  const root = Fp.sqrt(elm);\n  return Fp.isOdd(root) ? root : Fp.neg(root);\n}\n\nexport function FpSqrtEven<T>(Fp: IField<T>, elm: T): T {\n  if (!Fp.isOdd) 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/**\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(\n  hash: string | Uint8Array,\n  groupOrder: bigint,\n  isLE = false\n): bigint {\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(\n      'hashToPrivateScalar: expected ' + minLen + '-1024 bytes of input, got ' + hashLen\n    );\n  const num = isLE ? bytesToNumberLE(hash) : bytesToNumberBE(hash);\n  return mod(num, groupOrder - _1n) + _1n;\n}\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: bigint): number {\n  if (typeof fieldOrder !== 'bigint') throw new Error('field order must be bigint');\n  const bitLength = fieldOrder.toString(2).length;\n  return Math.ceil(bitLength / 8);\n}\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: bigint): number {\n  const length = getFieldBytesLength(fieldOrder);\n  return length + Math.ceil(length / 2);\n}\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.