/*! noble-secp256k1 - MIT License (c) 2019 Paul Miller (paulmillr.com) */
/**
 * 5KB JS implementation of secp256k1 ECDSA / Schnorr signatures & ECDH.
 * Compliant with RFC6979 & BIP340.
 * @module
 */
/**
 * Curve params from SEC 2 v2 §2.4.1.
 * secp256k1 is a short Weierstrass / Koblitz curve with equation
 * `y² == x³ + ax + b`.
 * * P = `2n**256n - 2n**32n - 977n` // field over which calculations are done
 * * N = `2n**256n - 0x14551231950b75fc4402da1732fc9bebfn` // group order, amount of curve points
 * * h = `1n` // cofactor
 * * a = `0n` // equation param
 * * b = `7n` // equation param
 * * Gx, Gy are coordinates of Generator / base point
 */
const freeze = Object.freeze;
const P = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2fn;
const N = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141n;
const Gx = 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798n;
const Gy = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8n;
// Mirror noble-curves: Point.CURVE() returns shared params, but those params must stay frozen so
// callers cannot mutate them out from under the arithmetic constants captured below.
const secp256k1_CURVE: WeierstrassOpts<bigint> = freeze({
  p: P,
  n: N,
  h: 1n,
  a: 0n,
  b: 7n,
  Gx,
  Gy,
});

// 32-byte field / scalar width, and the SHA-256 / HMAC-DRBG output width used
// by the RFC6979 paths here.
const L = 32;
/** Alias to Uint8Array. */
export type Bytes = Uint8Array;

// ## TS compatibility types
// -------------------------
// Type-level only: nothing here survives compilation. Skip to "End of TS
// compatibility types" for the actual crypto code.
/**
 * Uint8Array API type helpers for old + new TypeScript.
 *
 * TS 5.6 has `Uint8Array`, while TS 5.9+ made it generic `Uint8Array<ArrayBuffer>`.
 * We can't use specific return type, because TS 5.6 will error.
 * We can't use generic return type, because most TS 5.9 software will expect specific type.
 *
 * Maps typed-array input leaves to broad forms.
 * These are compatibility adapters, not ownership guarantees.
 *
 * - `TArg` keeps byte inputs broad.
 * - `TRet` marks byte outputs for TS 5.6 and TS 5.9+ compatibility.
 */
export type TypedArg<T> = T extends BigInt64Array
  ? BigInt64Array
  : T extends BigUint64Array
    ? BigUint64Array
    : T extends Float32Array
      ? Float32Array
      : T extends Float64Array
        ? Float64Array
        : T extends Int16Array
          ? Int16Array
          : T extends Int32Array
            ? Int32Array
            : T extends Int8Array
              ? Int8Array
              : T extends Uint16Array
                ? Uint16Array
                : T extends Uint32Array
                  ? Uint32Array
                  : T extends Uint8ClampedArray
                    ? Uint8ClampedArray
                    : T extends Uint8Array
                      ? Uint8Array
                      : never;
/** Maps typed-array output leaves to narrow TS-compatible forms. */
export type TypedRet<T> = T extends BigInt64Array
  ? ReturnType<typeof BigInt64Array.of>
  : T extends BigUint64Array
    ? ReturnType<typeof BigUint64Array.of>
    : T extends Float32Array
      ? ReturnType<typeof Float32Array.of>
      : T extends Float64Array
        ? ReturnType<typeof Float64Array.of>
        : T extends Int16Array
          ? ReturnType<typeof Int16Array.of>
          : T extends Int32Array
            ? ReturnType<typeof Int32Array.of>
            : T extends Int8Array
              ? ReturnType<typeof Int8Array.of>
              : T extends Uint16Array
                ? ReturnType<typeof Uint16Array.of>
                : T extends Uint32Array
                  ? ReturnType<typeof Uint32Array.of>
                  : T extends Uint8ClampedArray
                    ? ReturnType<typeof Uint8ClampedArray.of>
                    : T extends Uint8Array
                      ? ReturnType<typeof Uint8Array.of>
                      : never;
/** Recursively adapts byte-carrying API input types. See {@link TypedArg}. */
export type TArg<T> =
  | T
  | ([TypedArg<T>] extends [never]
      ? T extends (...args: infer A) => infer R
        ? ((...args: { [K in keyof A]: TRet<A[K]> }) => TArg<R>) & {
            [K in keyof T]: T[K] extends (...args: any) => any ? T[K] : TArg<T[K]>;
          }
        : T extends [infer A, ...infer R]
          ? [TArg<A>, ...{ [K in keyof R]: TArg<R[K]> }]
          : T extends readonly [infer A, ...infer R]
            ? readonly [TArg<A>, ...{ [K in keyof R]: TArg<R[K]> }]
            : T extends (infer A)[]
              ? TArg<A>[]
              : T extends readonly (infer A)[]
                ? readonly TArg<A>[]
                : T extends Promise<infer A>
                  ? Promise<TArg<A>>
                  : T extends object
                    ? { [K in keyof T]: TArg<T[K]> }
                    : T
      : TypedArg<T>);
/** Recursively adapts byte-carrying API output types. See {@link TypedArg}. */
export type TRet<T> = T extends unknown
  ? T &
      ([TypedRet<T>] extends [never]
        ? T extends (...args: infer A) => infer R
          ? ((...args: { [K in keyof A]: TArg<A[K]> }) => TRet<R>) & {
              [K in keyof T]: T[K] extends (...args: any) => any ? T[K] : TRet<T[K]>;
            }
          : T extends [infer A, ...infer R]
            ? [TRet<A>, ...{ [K in keyof R]: TRet<R[K]> }]
            : T extends readonly [infer A, ...infer R]
              ? readonly [TRet<A>, ...{ [K in keyof R]: TRet<R[K]> }]
              : T extends (infer A)[]
                ? TRet<A>[]
                : T extends readonly (infer A)[]
                  ? readonly TRet<A>[]
                  : T extends Promise<infer A>
                    ? Promise<TRet<A>>
                    : T extends object
                      ? { [K in keyof T]: TRet<T[K]> }
                      : T
        : TypedRet<T>)
  : never;
// ## End of TS compatibility types
// --------------------------------

/** Signature instance, which allows recovering pubkey from it. */
export type RecoveredSignature = Signature & { recovery: number };
/** Weierstrass elliptic curve options. */
export type WeierstrassOpts<T> = Readonly<{
  p: bigint;
  n: bigint;
  h: bigint;
  a: T;
  b: T;
  Gx: T;
  Gy: T;
}>;

// Helpers and Precomputes sections are reused between libraries

// ## Helpers
// ----------
/** Checks if something is Uint8Array. Be careful: nodejs Buffer will return true. */
const isBytes = (a: unknown): a is Uint8Array => {
  // Plain `instanceof Uint8Array` is too strict for some Buffer / proxy / cross-realm cases.
  // The fallback still requires a real ArrayBuffer view, so plain
  // JSON-deserialized `{ constructor: ... }` spoofing is rejected, and
  // `BYTES_PER_ELEMENT === 1` keeps the fallback on byte-oriented views.
  return (
    a instanceof Uint8Array ||
    (ArrayBuffer.isView(a) &&
      a.constructor.name === 'Uint8Array' &&
      (a as Uint8Array).BYTES_PER_ELEMENT === 1)
  );
};
/** Asserts something is Uint8Array. */
const abytes = (value: TArg<Uint8Array>, length?: number, title: string = ''): TRet<Uint8Array> => {
  // Success path first: this runs at the start of every update() / digestInto(), and the
  // common `abytes(data)` form must not pay for length handling it does not use.
  if (isBytes(value) && (length === undefined || value.length === length))
    return value as TRet<Uint8Array>;
  // Error path: recompute freely to build the exact message.
  const bytes = isBytes(value);
  const ofLen = length !== undefined ? ` of length ${length}` : '';
  const got = bytes ? `length=${value.length}` : `type=${typeof value}`;
  const message = (title ? `"${title}" ` : '') + 'expected Uint8Array' + ofLen + ', got ' + got;
  if (!bytes) throw new TypeError(message);
  throw new RangeError(message);
};
// Signing can retain the message across hash callbacks / awaits, and Schnorr hashes it more than
// once. Take one owned snapshot so caller mutation cannot change the signing transcript.
// cloneBytes expects an already-validated view; snapshotBytes validates, then copies.
const cloneBytes = (value: Uint8Array): TRet<Uint8Array> => Uint8Array.from(value);
const snapshotBytes = (value: TArg<Uint8Array>, title: string, length?: number): TRet<Uint8Array> =>
  cloneBytes(abytes(value, length, title));
// Callers keep values non-negative and within the requested width; padStart() won't truncate over-wide inputs.
const padh = (n: number | bigint, pad: number) => n.toString(16).padStart(pad, '0');
/** Convert byte array to hex string. */
const bytesToHex = (bytes: TArg<Uint8Array>): string => {
  let hex = '';
  for (const byte of abytes(bytes)) hex += padh(byte, 2);
  return hex;
};
/** Convert hex string to byte array. */
const hexToBytes = (hex: string): TRet<Uint8Array> => {
  const e = 'hex invalid'; // Strict ASCII hex only, with one generic error for parse failures.
  if (typeof hex !== 'string') throw new TypeError(e);
  if (hex.length % 2 || !/^[\da-f]*$/i.test(hex)) throw new RangeError(e);
  const array = new Uint8Array(hex.length / 2);
  for (let ai = 0, hi = 0; ai < array.length; ai++, hi += 2) {
    const n1 = hex.charCodeAt(hi);
    const n2 = hex.charCodeAt(hi + 1);
    // Regex guarantees ASCII. For 0..9/A..F/a..f, this maps char codes to 0..15.
    array[ai] = ((n1 & 15) + (n1 >> 6) * 9) * 16 + (n2 & 15) + (n2 >> 6) * 9;
  }
  return array as TRet<Uint8Array>;
};
declare const globalThis: Record<string, any> | undefined; // Typescript symbol present in browsers
// WebCrypto is available in all modern environments
const subtle = () => {
  const s = globalThis?.crypto?.subtle;
  if (s) return s;
  throw new Error('crypto.subtle must be defined, consider polyfill');
};
/** Copies several Uint8Arrays into one. */
const concatBytes = (...arrays: TArg<Uint8Array[]>): TRet<Uint8Array> => {
  let sum = 0;
  for (const a of arrays) sum += abytes(a).length;
  const res = new Uint8Array(sum);
  let pad = 0;
  for (const a of arrays) {
    res.set(a, pad);
    pad += a.length;
  }
  return res;
};
/**
 * WebCrypto OS-level CSPRNG (random number generator).
 * Will throw when not available; large-request ceilings are delegated to getRandomValues().
 */
const randomBytes = (len: number = L): TRet<Uint8Array> => {
  const c = globalThis?.crypto;
  if (typeof c?.getRandomValues !== 'function')
    throw new Error('crypto.getRandomValues must be defined, consider polyfill');
  return c.getRandomValues(new Uint8Array(len)) as TRet<Uint8Array>;
};
const big = BigInt;
const arange = (n: bigint, min: bigint, max: bigint, msg = 'bad number: out of range'): bigint => {
  if (typeof n !== 'bigint') throw new TypeError(msg);
  if (min <= n && n < max) return n;
  throw new RangeError(msg);
};
/** Canonical modular reduction. Callers must provide a positive modulus. */
const M = (a: bigint, b: bigint = P) => ((a %= b) >= 0n ? a : b + a);
const modN = (a: bigint) => M(a, N);
/** Modular inversion using extended euclidean GCD. Variable-time (non-CT). */
const invert = (number: bigint, modulo: bigint): bigint => {
  if (number === 0n) throw new Error('invert: expected non-zero number');
  // modulo = 1 is the zero ring: gcd(x, 1) = 1 makes the loop below "succeed" and return the
  // useless inverse 0. Reject it.
  if (modulo <= 1n) throw new Error('invert: expected modulus > 1, got ' + modulo);
  // This is variable-time: the loop count depends on `number`.
  let a = M(number, modulo);
  let b = modulo;
  // Only the Bézout coefficient of `number` (x/u chain) is tracked; the coefficient of `modulo`
  // never affects the output, so it is not computed.
  // prettier-ignore
  let x = 0n, u = 1n;
  while (a !== 0n) {
    const q = b / a;
    const r = b - a * q;
    const m = x - u * q;
    // prettier-ignore
    b = a, a = r, x = u, u = m;
  }
  const gcd = b;
  if (gcd !== 1n) throw new Error('invert: does not exist');
  return M(x, modulo);
};
const _hash = (name: string) => {
  // @ts-ignore
  const fn = hashes[name];
  if (typeof fn !== 'function') throw new Error('hashes.' + name + ' not set');
  return fn;
};
// All exported provider slots are caller-configurable and may be unset or return arbitrary values,
// so wrapper helpers must enforce the exact 32-byte digest contract instead of trusting providers.
const callHash = (name: string, a: TArg<Uint8Array>, b?: TArg<Uint8Array>): TRet<Uint8Array> =>
  abytes(_hash(name)(a, b), L, 'digest');
const callHashAsync = async (
  name: string,
  a: TArg<Uint8Array>,
  b?: TArg<Uint8Array>
): Promise<TRet<Uint8Array>> => abytes(await _hash(name)(a, b), L, 'digest');
/**
 * SHA-256 helper used by the synchronous API.
 * @param msg - message bytes to hash
 * @returns 32-byte SHA-256 digest.
 * @example
 * Hash message bytes after wiring the synchronous SHA-256 implementation.
 * ```ts
 * import * as secp from '@noble/secp256k1';
 * import { sha256 } from '@noble/hashes/sha2.js';
 * secp.hashes.sha256 = sha256;
 * const digest = secp.hash(new Uint8Array([1, 2, 3]));
 * ```
 */
// Public helper validates the message boundary explicitly; the configured provider is still looked
// up dynamically and its output is checked with `gh(...)`.
const hash = (msg: TArg<Uint8Array>): TRet<Uint8Array> =>
  callHash('sha256', abytes(msg, undefined, 'message'));
// also rejects structurally similar Point values from other realms / bundled copies
const apoint = (p: unknown) => {
  if (p instanceof Point) return p;
  throw new TypeError('Point expected');
};
/** Point in 2d xy affine coordinates. */
export type AffinePoint = {
  /** Affine x coordinate. */
  x: bigint;
  /** Affine y coordinate. */
  y: bigint;
};
// ## End of Helpers
// -----------------

const E_BADPOINT = 'bad point: not on curve';
/**
 * secp256k1 formula. Koblitz curves are subclass of weierstrass curves with a=0,
 * making it x³+b; callers validate x first.
 */
const koblitz = (x: bigint) => M(M(x * x) * x + 7n);
/** assert is element of field mod P (incl. 0 for projective infinity coordinates) */
const FpIsValid = (n: bigint) => arange(n, 0n, P);
/** assert is element of field mod P (excl. 0 where current callers need a non-zero coordinate) */
const FpIsValidNot0 = (n: bigint) => arange(n, 1n, P);
/** assert is element of field mod N (excl. 0), matching the shared BIP340 scalar-failure rule used here.
 * There is deliberately no FnIsValid: no caller accepts the scalar 0. */
const FnIsValidNot0 = (n: bigint) => arange(n, 1n, N);
// Shared parity primitive for BIP340 even-y checks and SEC 1 compressed prefixes.
const isEven = (y: bigint) => !(y & 1n);
/** SEC 1 compressed-prefix helper. Parity only: callers validate y before asking for the prefix byte. */
const getPrefix = (y: bigint) => Uint8Array.of(isEven(y) ? 0x02 : 0x03);
/** lift_x from BIP340 returns the unique point with x and an even square root of x³+7.
 * SEC 1 callers still negate it for the odd-prefix branch. */
const lift_x = (x: bigint) => {
  // Let c = x³ + 7 mod p. Fail if x ≥ p. (also fail if x < 1)
  const c = koblitz(FpIsValidNot0(x));
  // r = √c candidate
  // r = c^((p+1)/4) mod p
  // This formula works for fields p = 3 mod 4 -- a special, fast case.
  // Paper: "Square Roots from 1;24,51,10 to Dan Shanks".
  let r = 1n;
  for (let num = c, e = (P + 1n) / 4n; e > 0n; e >>= 1n) {
    // powMod: modular exponentiation.
    if (e & 1n) r = (r * num) % P; // Uses exponentiation by squaring.
    num = (num * num) % P; // Not constant-time.
  }
  if (M(r * r) !== c) throw new Error('sqrt invalid'); // check if result is valid
  return new Point(x, isEven(r) ? r : M(-r), 1n);
};
/**
 * Point in 3d xyz projective coordinates. 3d takes less inversions than 2d.
 * @param X - X coordinate.
 * @param Y - Y coordinate.
 * @param Z - projective Z coordinate.
 * @example
 * Do point arithmetic with the base point and encode the result as hex.
 * ```ts
 * import { Point } from '@noble/secp256k1';
 * const hex = Point.BASE.double().toHex();
 * ```
 */
class Point {
  static BASE: Point;
  static ZERO: Point;
  readonly X: bigint;
  readonly Y: bigint;
  readonly Z: bigint;
  constructor(X: bigint, Y: bigint, Z: bigint) {
    this.X = FpIsValid(X);
    this.Y = FpIsValidNot0(Y); // Y can't be 0 in Projective
    this.Z = FpIsValid(Z);
    freeze(this);
  }
  /** Returns the shared curve metadata object by reference.
   * It is readonly only at type level, and mutating it won't retarget arithmetic,
   * which already uses module-load snapshots. */
  static CURVE(): WeierstrassOpts<bigint> {
    return secp256k1_CURVE;
  }
  /** Create 3d xyz point from 2d xy. (0, 0) => (0, 1, 0), not (0, 0, 1) */
  static fromAffine(ap: AffinePoint): Point {
    const { x, y } = ap;
    return x === 0n && y === 0n ? I : new Point(x, y, 1n);
  }
  /** Convert Uint8Array or hex string to Point. */
  static fromBytes(bytes: TArg<Uint8Array>): Point {
    abytes(bytes);
    const length = bytes.length;
    const head = bytes[0];
    const x = sliceBytesNumBE(bytes, 1, 33);
    // SEC 1 defines the rare infinity encoding 0x00, but SEC 1 public-key validation rejects
    // infinity. We keep 0x00 rejected here because this parser is reused by verify(), ECDH,
    // and public-key validation helpers, so strict handling applies to all callers by default.
    // Local secp256k1 crosstests show OpenSSL raw point codecs accept 0x00 too.
    // Parse and validate SEC 1 compressed/uncompressed encodings before returning.
    try {
      if (length === 33 && (head === 0x02 || head === 0x03)) {
        // Equation is y² == x³ + ax + b. We calculate y from x.
        // lift_x() returns the even point; SEC 1 0x03 still needs the odd point.
        const p = lift_x(x);
        return head === 0x03 ? p.negate() : p;
      }
      // Uncompressed 65-byte point, 0x04 prefix
      if (length === 65 && head === 0x04)
        return new Point(x, sliceBytesNumBE(bytes, 33, 65), 1n).assertValidity();
    } catch (error) {
      // Out-of-range coordinates and non-residue x report the same error as wrong
      // prefixes / off-curve points, instead of generic range-check messages.
      throw new Error(E_BADPOINT);
    }
    throw new Error(E_BADPOINT);
  }
  static fromHex(hex: string): Point {
    return Point.fromBytes(hexToBytes(hex));
  }
  get x(): bigint {
    return this.toAffine().x;
  }
  get y(): bigint {
    return this.toAffine().y;
  }
  /** Equality check: compare points P&Q. */
  equals(other: Point): boolean {
    const { X: X1, Y: Y1, Z: Z1 } = this;
    const { X: X2, Y: Y2, Z: Z2 } = apoint(other); // checks class equality
    return M(X1 * Z2) === M(X2 * Z1) && M(Y1 * Z2) === M(Y2 * Z1);
  }
  is0(): boolean {
    return this.Z === 0n;
  }
  /** Flip point over y coordinate. */
  negate(): Point {
    return new Point(this.X, M(-this.Y), this.Z);
  }
  /** Point doubling: P+P, complete formula. */
  double(): Point {
    return this.add(this);
  }
  /**
   * Point addition: P+Q, complete, exception-free formula
   * (Renes-Costello-Batina, algo 1 of [2015/1060](https://eprint.iacr.org/2015/1060)).
   * Cost: `12M + 0S + 3*a + 3*b3 + 23add`.
   */
  // prettier-ignore
  add(other: Point): Point {
    const { X: X1, Y: Y1, Z: Z1 } = this;
    const { X: X2, Y: Y2, Z: Z2 } = apoint(other);
    const a = 0n;
    const b = 7n;
    let X3 = 0n, Y3 = 0n, Z3 = 0n;
    const b3 = M(b * 3n);
    let t0 = M(X1 * X2), t1 = M(Y1 * Y2), t2 = M(Z1 * Z2), t3 = M(X1 + Y1); // step 1
    let t4 = M(X2 + Y2); // step 5
    t3 = M(t3 * t4); t4 = M(t0 + t1); t3 = M(t3 - t4); t4 = M(X1 + Z1);
    let t5 = M(X2 + Z2); // step 10
    t4 = M(t4 * t5); t5 = M(t0 + t2); t4 = M(t4 - t5); t5 = M(Y1 + Z1);
    X3 = M(Y2 + Z2); // step 15
    t5 = M(t5 * X3); X3 = M(t1 + t2); t5 = M(t5 - X3); Z3 = M(a * t4);
    X3 = M(b3 * t2); // step 20
    Z3 = M(X3 + Z3); X3 = M(t1 - Z3); Z3 = M(t1 + Z3); Y3 = M(X3 * Z3);
    t1 = M(t0 + t0); // step 25
    t1 = M(t1 + t0); t2 = M(a * t2); t4 = M(b3 * t4); t1 = M(t1 + t2);
    t2 = M(t0 - t2); // step 30
    t2 = M(a * t2); t4 = M(t4 + t2); t0 = M(t1 * t4); Y3 = M(Y3 + t0);
    t0 = M(t5 * t4); // step 35
    X3 = M(t3 * X3); X3 = M(X3 - t0); t0 = M(t3 * t1); Z3 = M(t5 * Z3);
    Z3 = M(Z3 + t0); // step 40
    return new Point(X3, Y3, Z3);
  }
  subtract(other: Point): Point {
    return this.add(apoint(other).negate());
  }
  /**
   * Point-by-scalar multiplication. Scalar must be in range 1 <= n < CURVE.n.
   * Uses {@link wNAF} for base point.
   * Uses fake point to mitigate leakage shape in JS, not as a hard constant-time guarantee.
   * @param n scalar by which point is multiplied
   * @param safe safe mode guards against timing attacks; unsafe mode is faster
   */
  multiply(n: bigint, safe = true): Point {
    // Unsafe internal callers may legitimately need 0*P = O during double-scalar multiplication.
    if (!safe && n === 0n) return I;
    FnIsValidNot0(n);
    if (n === 1n) return this;
    if (this.equals(G)) return wNAF(n).p;
    // init result point & fake point
    let p = I;
    let f = G;
    let d: Point = this;
    // Safe mode always runs 256 iterations so ladder length can't leak the scalar's
    // leading zero bits; unsafe mode stops at the top set bit for speed.
    for (let i = 0; safe ? i < 256 : n > 0n; i++) {
      // if bit is present, add to point
      // if not present, add to fake, for timing safety
      if (n & 1n) p = p.add(d);
      else if (safe) f = f.add(d);
      d = d.double();
      n >>= 1n;
    }
    return p;
  }
  multiplyUnsafe(scalar: bigint): Point {
    return this.multiply(scalar, false);
  }
  /** Convert point to 2d xy affine point. (X, Y, Z) ∋ (x=X/Z, y=Y/Z) */
  toAffine(): AffinePoint {
    const { X: x, Y: y, Z: z } = this;
    // fast-paths for ZERO point OR Z=1
    if (z === 0n) return { x: 0n, y: 0n };
    if (z === 1n) return { x, y };
    const iz = invert(z, P);
    // (Z * Z^-1) must be 1, otherwise bad math
    if (M(z * iz) !== 1n) throw new Error('inverse invalid');
    // x = X*Z^-1; y = Y*Z^-1
    return { x: M(x * iz), y: M(y * iz) };
  }
  /** Checks if the point is valid and on-curve. */
  assertValidity(): Point {
    const { x, y } = this.toAffine(); // convert to 2d xy affine point.
    FpIsValidNot0(x); // must be in range 1 <= x,y < P
    FpIsValidNot0(y);
    // y² == x³ + ax + b, equation sides must be equal
    if (M(y * y) !== koblitz(x)) throw new Error(E_BADPOINT);
    return this;
  }
  /** Converts point to 33/65-byte Uint8Array. */
  toBytes(isCompressed = true): TRet<Uint8Array> {
    // Same policy as fromBytes(): SEC 1 has the rare infinity encoding 0x00, but we keep ZERO
    // out of this byte surface because callers treat these encodings as public keys by default.
    const { x, y } = this.assertValidity().toAffine();
    const x32b = numTo32b(x);
    if (isCompressed) return concatBytes(getPrefix(y), x32b);
    return concatBytes(Uint8Array.of(0x04), x32b, numTo32b(y));
  }

  toHex(isCompressed?: boolean): string {
    return bytesToHex(this.toBytes(isCompressed));
  }
}
/** Generator / base point */
const G: Point = new Point(Gx, Gy, 1n);
/** Identity / zero point */
const I: Point = new Point(0n, 1n, 0n);
// Static aliases
Point.BASE = G;
Point.ZERO = I;
/** `Q = u1⋅G + u2⋅R`. Verifies Q is not ZERO. Unsafe: non-CT. */
const doubleScalarMulUns = (R: Point, u1: bigint, u2: bigint): Point => {
  return G.multiply(u1, false).add(R.multiply(u2, false)).assertValidity();
};
// Inherits byte validation from bytesToHex(); the || '0' fallback keeps empty input mapped to 0n.
const bytesToNumBE = (b: TArg<Uint8Array>): bigint => big('0x' + (bytesToHex(b) || '0'));
// Callers provide monotone slice bounds; subarray() would otherwise clamp or reinterpret them silently.
const sliceBytesNumBE = (b: TArg<Uint8Array>, from: number, to: number) =>
  bytesToNumBE(b.subarray(from, to));
/** Generic 32-byte big-endian encoder. Must be 0 <= num < 2²⁵⁶; call sites need not be field/scalar elements. */
const numTo32b = (num: bigint): TRet<Uint8Array> =>
  hexToBytes(padh(arange(num, 0n, 2n ** 256n), L * 2)); // L*2 = 64 hex chars for a zero-padded 32-byte value
/** Normalize private key to scalar (bigint). Verifies scalar is in range 1 <= d < N. */
const secretKeyToScalar = (secretKey: TArg<Uint8Array>): bigint => {
  const num = bytesToNumBE(abytes(secretKey, L, 'secret key'));
  return arange(num, 1n, N, 'invalid secret key: outside of range');
};
/** For signature malleability, checks the strict upper-half predicate s > floor(N/2). */
const highS = (n: bigint): boolean => n > N >> 1n;
// Recovery id of an affine nonce point: bit 0 is y parity, bit 1 is x = r + n.
const getRecoveryBit = (x: bigint, y: bigint, r: bigint): number =>
  (x === r ? 0 : 2) | Number(y & 1n);
/**
 * Creates a SEC 1 public key from a 32-byte private key.
 * @param privKey - 32-byte secret key.
 * @param isCompressed - return 33-byte compressed SEC 1 encoding when `true`, otherwise 65-byte uncompressed.
 * @returns serialized secp256k1 public key in SEC 1 encoding.
 * @example
 * Derive the serialized public key for a secp256k1 secret key.
 * ```ts
 * import * as secp from '@noble/secp256k1';
 * const secretKey = secp.utils.randomSecretKey();
 * const publicKey = secp.getPublicKey(secretKey);
 * ```
 */
const getPublicKey = (privKey: TArg<Uint8Array>, isCompressed = true): TRet<Uint8Array> => {
  return G.multiply(secretKeyToScalar(privKey)).toBytes(isCompressed);
};

const isValidSecretKey = (secretKey: TArg<Uint8Array>): boolean => {
  try {
    return !!secretKeyToScalar(secretKey);
  } catch (error) {
    return false;
  }
};
const isValidPublicKey = (publicKey: TArg<Uint8Array>, isCompressed?: boolean): boolean => {
  try {
    const l = publicKey.length;
    if (isCompressed === true && l !== 33) return false;
    if (isCompressed === false && l !== 65) return false;
    return !!Point.fromBytes(publicKey);
  } catch (error) {
    return false;
  }
};

const assertRecoveryBit = (recovery?: number): number => {
  if (recovery != null && [0, 1, 2, 3].includes(recovery)) return recovery;
  throw new Error('invalid recovery id');
};
const assertSigFormat = (format?: ECDSASignatureFormat) => {
  if (format === 'der')
    throw new Error('Signature format "der" is not supported: switch to noble-curves');
  if (format != null && format !== SIG_COMPACT && format !== SIG_RECOVERED)
    throw new Error('Signature format must be one of: compact, recovered, der');
};
const assertSigLength = (
  sig: TArg<Uint8Array>,
  format: ECDSASignatureFormat = SIG_COMPACT
): TRet<Uint8Array> => {
  assertSigFormat(format);
  const bytes = abytes(sig, undefined, 'signature');
  const len = 64 + Number(format === SIG_RECOVERED);
  if (bytes.length !== len)
    throw new Error(`Signature format "${format}" expects Uint8Array with length ${len}`);
  return bytes;
};
/**
 * ECDSA Signature class. Supports only compact 64-byte representation, not DER.
 * @param r - signature `r` scalar.
 * @param s - signature `s` scalar.
 * @param recovery - optional recovery id.
 * @example
 * Build a recovered-format signature object and serialize it.
 * ```ts
 * import { Signature } from '@noble/secp256k1';
 * const bytes = new Signature(1n, 2n, 0).toBytes('recovered');
 * ```
 */
class Signature {
  readonly r: bigint;
  readonly s: bigint;
  readonly recovery?: number;
  constructor(r: bigint, s: bigint, recovery?: number) {
    this.r = FnIsValidNot0(r); // 1 <= r < N
    this.s = FnIsValidNot0(s); // 1 <= s < N
    // Keep recovered Signature objects internally consistent across all construction paths.
    if (recovery != null) this.recovery = assertRecoveryBit(recovery);
    freeze(this);
  }
  static fromBytes(b: TArg<Uint8Array>, format: ECDSASignatureFormat = SIG_COMPACT): Signature {
    b = assertSigLength(b, format);
    let rec: number | undefined;
    if (format === SIG_RECOVERED) {
      rec = b[0];
      b = b.subarray(1);
    }
    const r = sliceBytesNumBE(b, 0, L);
    const s = sliceBytesNumBE(b, L, 64);
    return new Signature(r, s, rec);
  }
  addRecoveryBit(bit: number): RecoveredSignature {
    return new Signature(this.r, this.s, bit) as RecoveredSignature;
  }
  hasHighS(): boolean {
    return highS(this.s);
  }
  toBytes(format: ECDSASignatureFormat = SIG_COMPACT): TRet<Uint8Array> {
    // Standalone noble-secp256k1 does not implement DER; reject here so direct Signature users
    // don't silently get compact bytes for an unsupported format.
    assertSigFormat(format);
    const { r, s, recovery } = this;
    const res = concatBytes(numTo32b(r), numTo32b(s));
    if (format === SIG_RECOVERED) {
      return concatBytes(Uint8Array.of(assertRecoveryBit(recovery)), res);
    }
    return res;
  }
}

/**
 * RFC6979: ensure ECDSA msg is X bytes, convert to BigInt.
 * RFC 6979 §2.3.2 says bits2int keeps the leftmost qlen bits and discards the rest.
 * FIPS 186-4 4.6 gives the same leftmost-bit truncation rule. bits2int can produce res>N.
 */
// The 8 KiB cap is only a local DoS guard. Longer ordinary prehashes must still follow
// RFC 6979 §2.3.2 truncation instead of being rejected just because blen > qlen.
const MAX_PREHASHED_BYTES = 8192;
const E_MSGBIG = 'input is too large';
const oversizedMsg = (bytes: TArg<Uint8Array>, prehash?: boolean): boolean =>
  !prehash && bytes.length > MAX_PREHASHED_BYTES;
const bits2int = (bytes: TArg<Uint8Array>): bigint => {
  if (oversizedMsg(bytes)) throw new Error(E_MSGBIG);
  const delta = bytes.length * 8 - 256;
  const num = bytesToNumBE(bytes);
  return delta > 0 ? num >> big(delta) : num;
};
/** int2octets can't be used; pads small msgs with 0: BAD for truncation as per RFC vectors */
const bits2int_modN = (bytes: TArg<Uint8Array>): bigint => modN(bits2int(abytes(bytes)));
// Async entry points snapshot the message before their first await. An oversized prehash is
// rejected before the copy, so an attacker-controlled view is never cloned just to fail in
// bits2int().
const snapshotMsg = (message: TArg<Uint8Array>, prehash?: boolean): TRet<Uint8Array> => {
  const view = abytes(message, undefined, 'message');
  if (oversizedMsg(view, prehash)) throw new Error(E_MSGBIG);
  return cloneBytes(view);
};
/**
 * Option to enable hedged signatures with improved security.
 *
 * * Randomly generated k is bad, because broken CSPRNG would leak private keys.
 * * Deterministic k (RFC6979) is better; but is suspectible to fault attacks.
 *
 * We allow using technique described in RFC6979 3.6: additional k', a.k.a. adding randomness
 * to deterministic sig. If CSPRNG is broken & randomness is weak, it would STILL be as secure
 * as ordinary sig without ExtraEntropy.
 *
 * * `true` means "fetch data, from CSPRNG, incorporate it into k generation"
 * * `false` means "disable extra entropy, use purely deterministic k"
 * * `Uint8Array` passed means "incorporate following data into k generation"
 *
 * See {@link https://paulmillr.com/posts/deterministic-signatures/ | Deterministic signatures}.
 */
export type ECDSAExtraEntropy = boolean | Uint8Array;
const SIG_COMPACT = 'compact';
const SIG_RECOVERED = 'recovered';
/**
 * - `compact` is the default format
 * - `recovered` is the same as compact, but with an extra byte indicating recovery byte
 * - `der` is not supported; it is included only so unsupported requests can be rejected consistently.
 *   Switch to noble-curves if you need der.
 */
export type ECDSASignatureFormat = 'compact' | 'recovered' | 'der';
/**
 * - `prehash`: (default: true) indicates whether to do sha256(message).
 *   When a custom hash is used, it must be set to `false`.
 */
export type ECDSARecoverOpts = {
  /** Set to `false` when the message is already hashed with a custom digest. */
  prehash?: boolean;
  /** Set to `false` to return a 65-byte uncompressed public key instead of the 33-byte default. */
  isCompressed?: boolean;
};
/**
 * - `prehash`: (default: true) indicates whether to do sha256(message).
 *   When a custom hash is used, it must be set to `false`.
 * - `lowS`: (default: true) prohibits signatures in the strict upper half (`sig.s > floor(CURVE.n / 2n)`).
 *   Compatible with BTC/ETH. Setting `lowS: false` allows to create malleable signatures,
 *   which is default openssl behavior.
 *   Non-malleable signatures can still be successfully verified in openssl.
 * - `format`: (default: 'compact') 'compact' or 'recovered' with recovery byte
 */
export type ECDSAVerifyOpts = {
  /** Set to `false` when the message is already hashed with a custom digest. */
  prehash?: boolean;
  /** Set to `false` to accept high-S signatures instead of enforcing canonical low-S ones. */
  lowS?: boolean;
  /** Signature encoding accepted by the verifier. */
  format?: ECDSASignatureFormat;
};
/**
 * - `prehash`: (default: true) indicates whether to do sha256(message).
 *   When a custom hash is used, it must be set to `false`.
 * - `lowS`: (default: true) prohibits signatures in the strict upper half (`sig.s > floor(CURVE.n / 2n)`).
 *   Compatible with BTC/ETH. Setting `lowS: false` allows to create malleable signatures,
 *   which is default openssl behavior.
 *   Non-malleable signatures can still be successfully verified in openssl.
 * - `format`: (default: 'compact') 'compact' or 'recovered' with recovery byte
 * - `extraEntropy`: (default: false) creates sigs with increased security, see {@link ECDSAExtraEntropy}
 */
export type ECDSASignOpts = {
  /** Set to `false` when the message is already hashed with a custom digest. */
  prehash?: boolean;
  /** Set to `false` to allow high-S signatures instead of normalizing to low-S form. */
  lowS?: boolean;
  /** Signature encoding produced by the signer. */
  format?: ECDSASignatureFormat;
  /** Extra entropy mixed into RFC6979 nonce generation for hedged signatures. */
  extraEntropy?: ECDSAExtraEntropy;
};

const _sha = 'SHA-256';
/**
 * Hash implementations used by the synchronous and async ECDSA / Schnorr helpers.
 * All slots are configurable API surface; wrapper helpers revalidate that SHA-256 and HMAC-SHA256
 * providers still return exact 32-byte Uint8Array digests.
 * @example
 * Provide sync hash helpers before calling the synchronous signing API.
 * ```ts
 * import * as secp from '@noble/secp256k1';
 * import { hmac } from '@noble/hashes/hmac.js';
 * import { sha256 } from '@noble/hashes/sha2.js';
 * secp.hashes.sha256 = sha256;
 * secp.hashes.hmacSha256 = (key, msg) => hmac(sha256, key, msg);
 * const secretKey = secp.utils.randomSecretKey();
 * const sig = secp.sign(new Uint8Array([1, 2, 3]), secretKey);
 * ```
 */
const hashes = {
  hmacSha256Async: async (
    key: TArg<Uint8Array>,
    message: TArg<Uint8Array>
  ): Promise<TRet<Uint8Array>> => {
    const s = subtle();
    const k = await s.importKey('raw', key, { name: 'HMAC', hash: _sha }, false, ['sign']);
    return new Uint8Array(await s.sign('HMAC', k, message)) as TRet<Uint8Array>;
  },
  hmacSha256: undefined as
    undefined | ((key: TArg<Uint8Array>, message: TArg<Uint8Array>) => TRet<Uint8Array>),
  sha256Async: async (msg: TArg<Uint8Array>): Promise<TRet<Uint8Array>> =>
    new Uint8Array(await subtle().digest(_sha, msg)) as TRet<Uint8Array>,
  sha256: undefined as undefined | ((message: TArg<Uint8Array>) => TRet<Uint8Array>),
};

// prehash=false means the caller already supplies the digest bytes
// used by sign/verify/recover, and this helper returns the same reference unchanged.
const prepMsg = (
  msg: TArg<Uint8Array>,
  prehash: boolean,
  async_: boolean
): TRet<Uint8Array | Promise<Uint8Array>> => {
  const message = abytes(msg, undefined, 'message');
  if (!prehash) return message;
  return async_ ? callHashAsync('sha256Async', message) : callHash('sha256', message);
};

type Pred<T> = (v: Uint8Array) => T | undefined;
type ECDSAOpts = readonly [
  boolean, // lowS
  boolean, // prehash
  ECDSASignatureFormat,
  ECDSAExtraEntropy | undefined,
];
const NULL = /* @__PURE__ */ new Uint8Array(0);
const byte0 = /* @__PURE__ */ Uint8Array.of(0x00);
const byte1 = /* @__PURE__ */ Uint8Array.of(0x01);
const _drbgErr = 'drbg: tried max amount of iterations';
// HMAC-DRBG from NIST 800-90. Minimal, non-full-spec - used for RFC6979 signatures.
const hmacDrbg = <T>(seed: Uint8Array, pred: Pred<T>): T => {
  let v = new Uint8Array(L); // Steps B, C of RFC6979 3.2: set hashLen
  let k = new Uint8Array(L); // In our case, it's always equal to L
  let i = 0; // Iterations counter, will throw when over max
  const reset = () => {
    v.fill(1);
    k.fill(0);
  };
  // h = hmac(k || v || ...). The configured provider is still checked on every call because the
  // exported slot can be replaced or unset at runtime.
  const h = (...b: Uint8Array[]) => callHash('hmacSha256', k, concatBytes(v, ...b));
  const reseed = (seed: Uint8Array = NULL) => {
    // HMAC-DRBG reseed() function. Steps D-G
    k = h(byte0, seed); // k = hmac(k || v || 0x00 || seed)
    v = h(); // v = hmac(k || v)
    if (seed.length === 0) return;
    k = h(byte1, seed); // k = hmac(k || v || 0x01 || seed)
    v = h(); // v = hmac(k || v)
  };
  // HMAC-DRBG generate() function
  const gen = () => {
    if (i++ >= 1000) throw new Error(_drbgErr);
    v = h(); // v = hmac(k || v)
    return v; // One block is enough here because secp256k1 qlen and SHA-256 hlen are both 32 bytes.
  };
  reset();
  reseed(seed); // Steps D-G
  let res: T | undefined = undefined; // Step H: grind until k is in [1..n-1]
  // `pred` receives the live V buffer from gen(); it must treat that input as read-only and
  // return independent bytes, because reset() scrubs the DRBG state before hmacDrbg returns.
  while (!(res = pred(gen()))) reseed(); // test predicate until it returns ok
  reset();
  return res!;
};

// Identical to hmacDrbg, but async: uses built-in WebCrypto
const hmacDrbgAsync = async <T>(seed: Uint8Array, pred: Pred<T>): Promise<T> => {
  let v = new Uint8Array(L); // Steps B, C of RFC6979 3.2: set hashLen
  let k = new Uint8Array(L); // In our case, it's always equal to L
  let i = 0; // Iterations counter, will throw when over max
  const reset = () => {
    v.fill(1);
    k.fill(0);
  };
  // h = hmac(k || v || ...). Async provider lookup still goes through `callHash(...)` because the
  // exported slot can be replaced or unset at runtime.
  const h = (...b: Uint8Array[]) => callHashAsync('hmacSha256Async', k, concatBytes(v, ...b));
  const reseed = async (seed: Uint8Array = NULL) => {
    // HMAC-DRBG reseed() function. Steps D-G
    k = await h(byte0, seed); // k = hmac(k || v || 0x00 || seed)
    v = await h(); // v = hmac(k || v)
    if (seed.length === 0) return;
    k = await h(byte1, seed); // k = hmac(k || v || 0x01 || seed)
    v = await h(); // v = hmac(k || v)
  };
  // HMAC-DRBG generate() function
  const gen = async () => {
    if (i++ >= 1000) throw new Error(_drbgErr);
    v = await h(); // v = hmac(k || v)
    return v; // Same one-block shortcut: secp256k1 qlen and SHA-256 hlen are both 32 bytes here.
  };
  reset();
  await reseed(seed); // Steps D-G
  let res: T | undefined = undefined; // Step H: grind until k is in [1..n-1]
  // Same contract as sync hmacDrbg(): pred sees the live V buffer and must not mutate or return it.
  while (!(res = pred(await gen()))) await reseed(); // test predicate until it returns ok
  reset();
  return res!;
};

// RFC6979 signature generation, preparation step.
// Follows [SEC1](https://secg.org/sec1-v2.pdf) 4.1.3 & RFC6979.
const _sign = <T>(
  messageHash: Uint8Array,
  secretKey: Uint8Array,
  opts: ECDSAOpts,
  drbg: (seed: Uint8Array, pred: Pred<TRet<Uint8Array>>) => T
): T => {
  const [lowS, , format, extraEntropy] = opts; // generates low-s sigs by default
  // RFC6979 3.2: we skip step A
  const h1i = bits2int_modN(messageHash); // msg bigint
  const d = secretKeyToScalar(secretKey); // validate private key, convert to bigint
  const seedArgs: Uint8Array[] = [numTo32b(d), numTo32b(h1i)]; // Step D of RFC6979 3.2
  /** RFC6979 3.6: additional k' (optional). See {@link ECDSAExtraEntropy}. */
  if (extraEntropy != null && extraEntropy !== false) {
    // K = HMAC_K(V || 0x00 || int2octets(x) || bits2octets(h1) || k')
    // gen random bytes OR pass as-is
    seedArgs.push(
      abytes(extraEntropy === true ? randomBytes(L) : extraEntropy, undefined, 'extraEntropy')
    );
  }
  // Converts signature params into point w r/s, checks result for validity.
  // To transform k => Signature:
  // q = k⋅G
  // r = q.x mod n
  // s = k^-1(m + rd) mod n
  // Can use scalar blinding b^-1(bm + bdr) where b ∈ [1,q−1] according to
  // https://tches.iacr.org/index.php/TCHES/article/view/7337/6509. We've decided against it:
  // a) dependency on CSPRNG b) 15% slowdown c) doesn't really help since bigints are not CT
  const k2sig = (kBytes: Uint8Array): TRet<Uint8Array> | undefined => {
    // RFC 6979 Section 3.2, step 3: k = bits2int(T)
    // Important: all mod() calls here must be done over N
    const k = bits2int(kBytes);
    if (!(1n <= k && k < N)) return; // Valid scalars (including k) must be in 1..N-1
    const ik = invert(k, N); // k^-1 mod n
    const q = G.multiply(k).toAffine(); // q = k⋅G
    const r = modN(q.x); // r = q.x mod n
    // RFC 6979 §2.4 step 3 / §3.4 only spell out retry for r = 0.
    // FIPS 186-5 §6.4.1 step 11 says deterministic ECDSA should fail on r = 0 or s = 0, but
    // that restart-from-scratch note does not apply here: hmacDrbg() keeps advancing through one
    // RFC6979 stream until k2sig() accepts a candidate, instead of restarting from the same seed.
    if (r === 0n) return;
    const s = modN(ik * (h1i + r * d)); // s = k^-1(m + rd) mod n
    if (s === 0n) return;
    let recovery = getRecoveryBit(q.x, q.y, r); // recovery bit (2 or 3, when q.x > n)
    let normS = s; // normalized S
    if (lowS && highS(s)) {
      // if lowS was passed, ensure s is always
      normS = N - s; // in the bottom half of CURVE.n
      recovery ^= 1;
    }
    const sig = new Signature(r, normS, recovery) as RecoveredSignature; // use normS, not s
    return sig.toBytes(format);
  };
  return drbg(concatBytes(...seedArgs), k2sig);
};

// Follows [SEC1](https://secg.org/sec1-v2.pdf) 4.1.4.
const _verify = (
  sig: TArg<Uint8Array>,
  messageHash: TArg<Uint8Array>,
  publicKey: TArg<Uint8Array>,
  opts: ECDSAOpts
) => {
  const [lowS, , format] = opts;
  if (sig instanceof Signature) throw new Error('Signature must be in Uint8Array, use .toBytes()');
  // Deliberately outside the try: wrong-length / wrongly-typed inputs are caller bugs which
  // throw loudly, while only well-formed signatures failing crypto checks return false.
  assertSigLength(sig, format);
  abytes(publicKey, undefined, 'publicKey');
  try {
    const { r, s, recovery } = Signature.fromBytes(sig, format);
    const h = bits2int_modN(messageHash); // Truncate hash
    const Q = Point.fromBytes(publicKey); // Validate public key. Q, not P: P is the field prime
    if (lowS && highS(s)) return false; // lowS bans sig.s >= CURVE.n/2
    const is = invert(s, N); // s^-1
    // R = u1⋅G + u2⋅Q with u1 = hs^-1, u2 = rs^-1. Identity throws inside doubleScalarMulUns.
    const { x, y } = doubleScalarMulUns(Q, modN(h * is), modN(r * is)).toAffine();
    if (modN(x) !== r) return false; // Reduce R.x in N's field, not P's.
    // The recovery byte is part of the recovered signature and must describe this exact R.
    return format !== SIG_RECOVERED || recovery === getRecoveryBit(x, y, r);
  } catch (error) {
    return false;
  }
};

// `own` snapshots extraEntropy bytes, for async paths that must not see caller mutation.
const setDefaults = (opts: TArg<ECDSASignOpts>, own = false): ECDSAOpts => {
  const e = opts.extraEntropy;
  return [
    opts.lowS ?? true,
    opts.prehash ?? true,
    opts.format ?? SIG_COMPACT,
    own && e != null && typeof e !== 'boolean' ? snapshotBytes(e, 'extraEntropy') : e,
  ];
};

/**
 * Sign a message using secp256k1. Sync: uses `hashes.sha256` and `hashes.hmacSha256`.
 * Prehashes message with sha256, disable using `prehash: false`.
 * @param message - message bytes to sign.
 * @param secretKey - 32-byte secret key.
 * @param opts - See {@link ECDSASignOpts} for details. Enabling {@link ECDSAExtraEntropy} improves security.
 * @returns ECDSA signature encoded according to `opts.format`.
 * @example
 * Sign a message using secp256k1.
 * ```ts
 * import * as secp from '@noble/secp256k1';
 * import { hmac } from '@noble/hashes/hmac.js';
 * import { sha256 } from '@noble/hashes/sha2.js';
 * secp.hashes.sha256 = sha256;
 * secp.hashes.hmacSha256 = (key, msg) => hmac(sha256, key, msg);
 * const secretKey = secp.utils.randomSecretKey();
 * const msg = new TextEncoder().encode('hello noble');
 * secp.sign(msg, secretKey);
 * secp.sign(msg, secretKey, { extraEntropy: true });
 * secp.sign(msg, secretKey, { format: 'recovered' });
 * ```
 */
const sign = (
  message: TArg<Uint8Array>,
  secretKey: TArg<Uint8Array>,
  opts: TArg<ECDSASignOpts> = {}
): TRet<Uint8Array> => {
  const o = setDefaults(opts);
  assertSigFormat(o[2]);
  const msg = prepMsg(message, o[1], false) as Uint8Array;
  return _sign<TRet<Uint8Array>>(msg, secretKey, o, hmacDrbg);
};

/**
 * Sign a message using secp256k1. Async: uses built-in WebCrypto hashes.
 * Prehashes message with sha256, disable using `prehash: false`.
 * @param message - message bytes to sign.
 * @param secretKey - 32-byte secret key.
 * @param opts - See {@link ECDSASignOpts} for details. Enabling {@link ECDSAExtraEntropy} improves security.
 * @returns ECDSA signature encoded according to `opts.format`.
 * @example
 * Sign a message using secp256k1 with the async WebCrypto path.
 * ```ts
 * import * as secp from '@noble/secp256k1';
 * import { keccak_256 } from '@noble/hashes/sha3.js';
 * const secretKey = secp.utils.randomSecretKey();
 * const msg = new TextEncoder().encode('hello noble');
 * await secp.signAsync(msg, secretKey);
 * await secp.signAsync(keccak_256(msg), secretKey, { prehash: false });
 * await secp.signAsync(msg, secretKey, { extraEntropy: true });
 * await secp.signAsync(msg, secretKey, { format: 'recovered' });
 * ```
 */
const signAsync = async (
  message: TArg<Uint8Array>,
  secretKey: TArg<Uint8Array>,
  opts: TArg<ECDSASignOpts> = {}
): Promise<TRet<Uint8Array>> => {
  const o = setDefaults(opts, true);
  assertSigFormat(o[2]);
  const msgBytes = snapshotMsg(message, o[1]);
  const secretBytes = snapshotBytes(secretKey, 'secret key', L);
  const msg = (await prepMsg(msgBytes, o[1], true)) as Uint8Array;
  return _sign<Promise<TRet<Uint8Array>>>(msg, secretBytes, o, hmacDrbgAsync);
};

/**
 * Verify a signature using secp256k1. Sync: uses `hashes.sha256` and `hashes.hmacSha256`.
 * @param signature - default is 64-byte `compact` format; also see {@link ECDSASignatureFormat}.
 * @param message - message which was signed. Keep in mind `prehash` from opts.
 * @param publicKey - public key that should verify the signature.
 * @param opts - See {@link ECDSAVerifyOpts} for details.
 * @returns `true` when the signature is valid. Malformed inputs — wrong signature length for
 * the chosen format, non-Uint8Array arguments, unsupported format — throw instead of
 * returning `false`. This is intentional, so caller bugs fail loudly; only well-formed
 * signatures failing cryptographic checks return `false`.
 * @example
 * Verify a signature using secp256k1.
 * ```ts
 * import * as secp from '@noble/secp256k1';
 * import { hmac } from '@noble/hashes/hmac.js';
 * import { sha256 } from '@noble/hashes/sha2.js';
 * import { keccak_256 } from '@noble/hashes/sha3.js';
 * secp.hashes.sha256 = sha256;
 * secp.hashes.hmacSha256 = (key, msg) => hmac(sha256, key, msg);
 * const secretKey = secp.utils.randomSecretKey();
 * const msg = new TextEncoder().encode('hello noble');
 * const publicKey = secp.getPublicKey(secretKey);
 * const sig = secp.sign(msg, secretKey);
 * const sigr = secp.sign(msg, secretKey, { format: 'recovered' });
 * secp.verify(sig, msg, publicKey);
 * secp.verify(sig, keccak_256(msg), publicKey, { prehash: false });
 * secp.verify(sig, msg, publicKey, { lowS: false });
 * secp.verify(sigr, msg, publicKey, { format: 'recovered' });
 * ```
 */
const verify = (
  signature: TArg<Uint8Array>,
  message: TArg<Uint8Array>,
  publicKey: TArg<Uint8Array>,
  opts: TArg<ECDSAVerifyOpts> = {}
): boolean => {
  const o = setDefaults(opts);
  const msg = prepMsg(message, o[1], false) as Uint8Array;
  return _verify(signature, msg, publicKey, o);
};

/**
 * Verify a signature using secp256k1. Async: uses built-in WebCrypto hashes.
 * @param sig - default is 64-byte `compact` format; also see {@link ECDSASignatureFormat}.
 * @param message - message which was signed. Keep in mind `prehash` from opts.
 * @param publicKey - public key that should verify the signature.
 * @param opts - See {@link ECDSAVerifyOpts} for details.
 * @returns `true` when the signature is valid. Malformed inputs — wrong signature length for
 * the chosen format, non-Uint8Array arguments, unsupported format — reject instead of
 * resolving `false`. This is intentional, so caller bugs fail loudly; only well-formed
 * signatures failing cryptographic checks resolve to `false`.
 * @example
 * Verify a signature using secp256k1 with the async WebCrypto path.
 * ```ts
 * import * as secp from '@noble/secp256k1';
 * import { keccak_256 } from '@noble/hashes/sha3.js';
 * const secretKey = secp.utils.randomSecretKey();
 * const msg = new TextEncoder().encode('hello noble');
 * const publicKey = secp.getPublicKey(secretKey);
 * const sig = await secp.signAsync(msg, secretKey);
 * const sigr = await secp.signAsync(msg, secretKey, { format: 'recovered' });
 * await secp.verifyAsync(sig, msg, publicKey);
 * await secp.verifyAsync(sigr, msg, publicKey, { format: 'recovered' });
 * await secp.verifyAsync(sig, keccak_256(msg), publicKey, { prehash: false });
 * ```
 */
const verifyAsync = async (
  sig: TArg<Uint8Array>,
  message: TArg<Uint8Array>,
  publicKey: TArg<Uint8Array>,
  opts: TArg<ECDSAVerifyOpts> = {}
): Promise<boolean> => {
  const o = setDefaults(opts);
  const sigView = assertSigLength(sig, o[2]);
  const msgView = abytes(message, undefined, 'message');
  const publicKeyView = abytes(publicKey, undefined, 'publicKey');
  // Reject bounded malformed inputs before copying attacker-controlled views. This also avoids
  // copying a prehashed message that bits2int() would reject immediately.
  if (oversizedMsg(msgView, o[1]) || (publicKeyView.length !== 33 && publicKeyView.length !== 65))
    return false;
  const sigBytes = cloneBytes(sigView);
  const msgBytes = cloneBytes(msgView);
  const publicKeyBytes = cloneBytes(publicKeyView);
  const msg = (await prepMsg(msgBytes, o[1], true)) as Uint8Array;
  return _verify(sigBytes, msg, publicKeyBytes, o);
};

const _recover = (
  signature: TArg<Uint8Array>,
  messageHash: TArg<Uint8Array>,
  isCompressed: boolean
): TRet<Uint8Array> => {
  const { r, s, recovery: rec } = Signature.fromBytes(signature, 'recovered');
  // 0 or 1 recovery id determines sign of "y" coordinate.
  // 2 or 3 means q.x was >N.
  const recovery = assertRecoveryBit(rec);
  // SEC 1 recovery derives e through the same truncation path as verification, so prehash:false
  // must accept long digests here too instead of hard-requiring 32-byte SHA-256 input.
  const h = bits2int_modN(messageHash); // Truncate hash; prepMsg() already validated it.
  const radj = recovery > 1 ? r + N : r;
  FpIsValidNot0(radj); // ensure q.x is still a field element
  const ir = invert(radj, N); // r^-1
  // Recovery bit and R.y share parity: even bit => 0x02, odd => 0x03.
  const R = Point.fromBytes(concatBytes(getPrefix(big(recovery)), numTo32b(radj)));
  // (sr^-1)R-(hr^-1)G = -(hr^-1)G + (sr^-1)R
  return doubleScalarMulUns(R, modN(-h * ir), modN(s * ir)).toBytes(isCompressed);
};

/**
 * ECDSA public key recovery. Requires msg hash and recovery id.
 * Follows {@link https://secg.org/sec1-v2.pdf | SEC1} 4.1.6.
 * @param signature - recovered-format signature from `sign(..., { format: 'recovered' })`.
 * @param message - signed message bytes.
 * @param opts - See {@link ECDSARecoverOpts} for details.
 * @returns recovered public key bytes, compressed by default.
 * @example
 * Recover a secp256k1 public key from a recovered-format signature.
 * ```ts
 * import * as secp from '@noble/secp256k1';
 * import { hmac } from '@noble/hashes/hmac.js';
 * import { sha256 } from '@noble/hashes/sha2.js';
 * secp.hashes.sha256 = sha256;
 * secp.hashes.hmacSha256 = (key, msg) => hmac(sha256, key, msg);
 * const secretKey = secp.utils.randomSecretKey();
 * const message = new Uint8Array([1, 2, 3]);
 * const sig = secp.sign(message, secretKey, { format: 'recovered' });
 * secp.recoverPublicKey(sig, message);
 * ```
 */
const recoverPublicKey = (
  signature: TArg<Uint8Array>,
  message: TArg<Uint8Array>,
  opts: TArg<ECDSARecoverOpts> = {}
): TRet<Uint8Array> => {
  const msg = prepMsg(message, setDefaults(opts)[1], false) as Uint8Array;
  return _recover(signature, msg, opts.isCompressed ?? true);
};

/**
 * Async ECDSA public key recovery. Requires msg hash and recovery id.
 * @param signature - recovered-format signature from `signAsync(..., { format: 'recovered' })`.
 * @param message - signed message bytes.
 * @param opts - See {@link ECDSARecoverOpts} for details.
 * @returns recovered public key bytes, compressed by default.
 * @example
 * Recover a secp256k1 public key from a recovered-format signature with the async API.
 * ```ts
 * import * as secp from '@noble/secp256k1';
 * const secretKey = secp.utils.randomSecretKey();
 * const message = new Uint8Array([1, 2, 3]);
 * const sig = await secp.signAsync(message, secretKey, { format: 'recovered' });
 * await secp.recoverPublicKeyAsync(sig, message);
 * ```
 */
const recoverPublicKeyAsync = async (
  signature: TArg<Uint8Array>,
  message: TArg<Uint8Array>,
  opts: TArg<ECDSARecoverOpts> = {}
): Promise<TRet<Uint8Array>> => {
  const prehash = setDefaults(opts)[1];
  const sigBytes = cloneBytes(assertSigLength(signature, SIG_RECOVERED));
  const msgBytes = snapshotMsg(message, prehash);
  const isCompressed = opts.isCompressed ?? true;
  const msg = (await prepMsg(msgBytes, prehash, true)) as Uint8Array;
  return _recover(sigBytes, msg, isCompressed);
};

/**
 * Elliptic Curve Diffie-Hellman (ECDH) on secp256k1.
 * Result is **NOT hashed** and returns the serialized shared point (compressed by default),
 * not the SEC 1 x-only primitive `z = x_P`.
 * secp256k1 has cofactor `h = 1`, so there is no separate cofactor-ECDH distinction here.
 * @param secretKeyA - local 32-byte secret key.
 * @param publicKeyB - peer public key.
 * @param isCompressed - return 33-byte compressed output when `true`.
 * @returns shared secret point bytes.
 * @example
 * Derive a shared secp256k1 secret with ECDH.
 * ```ts
 * import * as secp from '@noble/secp256k1';
 * const alice = secp.utils.randomSecretKey();
 * const bob = secp.utils.randomSecretKey();
 * const shared = secp.getSharedSecret(alice, secp.getPublicKey(bob));
 * ```
 */
const getSharedSecret = (
  secretKeyA: TArg<Uint8Array>,
  publicKeyB: TArg<Uint8Array>,
  isCompressed = true
): TRet<Uint8Array> => {
  return Point.fromBytes(publicKeyB).multiply(secretKeyToScalar(secretKeyA)).toBytes(isCompressed);
};

// FIPS 186-5 Appendix A.4.1 style key generation reduces a wide random integer mod (n - 1) and adds 1.
// The 48-byte minimum keeps the secp256k1 bias bound below the appendix's epsilon <= 2^-64 target.
const randomSecretKey = (seed?: TArg<Uint8Array>): TRet<Uint8Array> => {
  seed = seed === undefined ? randomBytes(48) : seed;
  abytes(seed);
  // Keep the public range text aligned with the enforced 48-byte FIPS floor.
  if (seed.length < 48 || seed.length > 1024) throw new RangeError('expected 48-1024b');
  const num = M(bytesToNumBE(seed), N - 1n);
  return numTo32b(num + 1n);
};

type KeysSecPub = { secretKey: Uint8Array; publicKey: Uint8Array };
type KeygenFn = (seed?: TArg<Uint8Array>) => TRet<KeysSecPub>;
const createKeygen =
  (getPublicKey: (secretKey: Uint8Array) => Uint8Array) =>
  (seed?: TArg<Uint8Array>): TRet<KeysSecPub> => {
    const secretKey = randomSecretKey(seed);
    return { secretKey, publicKey: getPublicKey(secretKey) } as TRet<KeysSecPub>;
  };
/**
 * Generates a secp256k1 keypair.
 * @param seed - optional entropy seed.
 * @returns keypair with `secretKey` and `publicKey`.
 * @example
 * Generate a secp256k1 keypair for sync signing.
 * ```ts
 * import * as secp from '@noble/secp256k1';
 * import { hmac } from '@noble/hashes/hmac.js';
 * import { sha256 } from '@noble/hashes/sha2.js';
 * secp.hashes.sha256 = sha256;
 * secp.hashes.hmacSha256 = (key, msg) => hmac(sha256, key, msg);
 * const { secretKey, publicKey } = secp.keygen();
 * ```
 */
const keygen: KeygenFn = /* @__PURE__ */ createKeygen(getPublicKey);

/**
 * Math, hex, byte helpers. Not in `utils` because utils share API with noble-curves.
 * @example
 * Convert bytes to a hex string with the low-level helper namespace.
 * ```ts
 * import { etc } from '@noble/secp256k1';
 * const hex = etc.bytesToHex(new Uint8Array([1, 2, 3]));
 * ```
 */
const etc: {
  hexToBytes: (hex: string) => TRet<Uint8Array>;
  bytesToHex: (bytes: TArg<Uint8Array>) => string;
  concatBytes: (...arrs: TArg<Uint8Array[]>) => TRet<Uint8Array>;
  bytesToNumberBE: (a: TArg<Uint8Array>) => bigint;
  numberToBytesBE: (n: bigint) => TRet<Uint8Array>;
  mod: (a: bigint, md?: bigint) => bigint;
  invert: typeof invert;
  randomBytes: (len?: number) => TRet<Uint8Array>;
  secretKeyToScalar: typeof secretKeyToScalar;
  abytes: typeof abytes;
} = /* @__PURE__ */ freeze({
  hexToBytes,
  bytesToHex,
  concatBytes,
  bytesToNumberBE: bytesToNumBE,
  numberToBytesBE: numTo32b,
  mod: M,
  invert,
  randomBytes,
  secretKeyToScalar,
  abytes,
});

/**
 * Curve-specific key utilities.
 * @example
 * Generate a fresh secret key and derive its public key.
 * ```ts
 * import * as secp from '@noble/secp256k1';
 * const secretKey = secp.utils.randomSecretKey();
 * const publicKey = secp.getPublicKey(secretKey);
 * ```
 */
const utils: {
  isValidSecretKey: typeof isValidSecretKey;
  isValidPublicKey: typeof isValidPublicKey;
  randomSecretKey: typeof randomSecretKey;
} = /* @__PURE__ */ freeze({
  isValidSecretKey,
  isValidPublicKey,
  randomSecretKey,
});

// Schnorr signatures are superior to ECDSA from above. Below is Schnorr-specific BIP0340 code.
// https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki
// Internal BIP340 tag names are ASCII-only here, so charCodeAt() is enough; this is not a general UTF-8 encoder.
const getTag = (tag: string): TRet<Uint8Array> =>
  Uint8Array.from('BIP0340/' + tag, (c) => c.charCodeAt(0)) as TRet<Uint8Array>;
// Both SHA-256 provider slots are configurable, so tag hashing still goes through the checked
// wrappers even though the built-in defaults are deterministic and the tag bytes are ASCII-only.
const taggedHash = (tag: string, ...messages: TArg<Uint8Array[]>): TRet<Uint8Array> => {
  const tagH = callHash('sha256', getTag(tag));
  return callHash('sha256', concatBytes(tagH, tagH, ...messages));
};
// Async twin of taggedHash with the same checked provider boundary.
const taggedHashAsync = (tag: string, ...messages: TArg<Uint8Array[]>): Promise<TRet<Uint8Array>> =>
  callHashAsync('sha256Async', getTag(tag)).then((tagH) =>
    callHashAsync('sha256Async', concatBytes(tagH, tagH, ...messages))
  );

// BIP340 PubKey(sk) = bytes(d'⋅G), where bytes(P) is bytes(x(P)); signing also normalizes
// d to the equivalent scalar whose point has even y so the x-only public key stays canonical.
const extpubSchnorr = (priv: TArg<Uint8Array>) => {
  const d_ = secretKeyToScalar(priv);
  const p = G.multiply(d_); // P = d'⋅G; 0 < d' < n check is done inside
  const { x, y } = p.assertValidity().toAffine(); // validate Point is not at infinity
  const d = isEven(y) ? d_ : modN(-d_);
  const px = numTo32b(x);
  return { d, px };
};

const bytesModN = (bytes: TArg<Uint8Array>) => modN(bytesToNumBE(bytes));
const challenge = (...args: TArg<Uint8Array[]>): bigint =>
  bytesModN(taggedHash('challenge', ...args));
const challengeAsync = async (...args: TArg<Uint8Array[]>): Promise<bigint> =>
  bytesModN(await taggedHashAsync('challenge', ...args));

/** Schnorr public key is just `x` coordinate of Point as per BIP340. */
const pubSchnorr = (secretKey: TArg<Uint8Array>): TRet<Uint8Array> => {
  return extpubSchnorr(secretKey).px; // d'=int(sk). Fail if d'=0 or d'≥n. Ret bytes(d'⋅G)
};

const keygenSchnorr: KeygenFn = /* @__PURE__ */ createKeygen(pubSchnorr);

// Common preparation fn for both sync and async signing
const prepSigSchnorr = (
  message: TArg<Uint8Array>,
  secretKey: TArg<Uint8Array>,
  auxRand: TArg<Uint8Array>
) => {
  const m = snapshotBytes(message, 'message');
  const { px, d } = extpubSchnorr(secretKey);
  return { m, px, d, a: abytes(auxRand, L) };
};

const extractK = (rand: TArg<Uint8Array>): TRet<{ rx: Uint8Array; k: bigint }> => {
  const k_ = bytesModN(rand); // Let k' = int(rand) mod n
  if (k_ === 0n) throw new Error('sign failed: k is zero'); // Fail if k' = 0.
  const { px, d } = extpubSchnorr(numTo32b(k_)); // Let R = k'⋅G.
  return { rx: px, k: d } as TRet<{ rx: Uint8Array; k: bigint }>;
};

// Common signature creation helper
const createSigSchnorr = (
  k: bigint,
  px: TArg<Uint8Array>,
  e: bigint,
  d: bigint
): TRet<Uint8Array> => {
  return concatBytes(px, numTo32b(modN(k + e * d)));
};

const E_INVSIG = 'invalid signature produced';
/**
 * Creates Schnorr signature as per BIP340. Verifies itself before returning anything.
 * auxRand is optional and defaults to fresh 32-byte randomness; it is not the sole source of
 * k generation, so bad CSPRNG won't be the only entropy source.
 */
const signSchnorr = (
  message: TArg<Uint8Array>,
  secretKey: TArg<Uint8Array>,
  auxRand: TArg<Uint8Array> = randomBytes(L)
): TRet<Uint8Array> => {
  const { m, px, d, a } = prepSigSchnorr(message, secretKey, auxRand);
  // Let t be the byte-wise xor of bytes(d) and hash/aux(a)
  const t = numTo32b(d ^ bytesToNumBE(taggedHash('aux', a)));
  // Let rand = hash/nonce(t || bytes(P) || m)
  const { rx, k } = extractK(taggedHash('nonce', t, px, m));
  // Let e = int(hash/challenge(bytes(R) || bytes(P) || m)) mod n.
  const sig = createSigSchnorr(k, rx, challenge(rx, px, m), d);
  // If Verify(bytes(P), m, sig) (see below) returns failure, abort
  if (!verifySchnorr(sig, m, px)) throw new Error(E_INVSIG);
  return sig;
};

const signSchnorrAsync = async (
  message: TArg<Uint8Array>,
  secretKey: TArg<Uint8Array>,
  auxRand: TArg<Uint8Array> = randomBytes(L)
): Promise<TRet<Uint8Array>> => {
  const { m, px, d, a } = prepSigSchnorr(message, secretKey, auxRand);
  // Let t be the byte-wise xor of bytes(d) and hash/aux(a)
  const t = numTo32b(d ^ bytesToNumBE(await taggedHashAsync('aux', a)));
  // Let rand = hash/nonce(t || bytes(P) || m)
  const { rx, k } = extractK(await taggedHashAsync('nonce', t, px, m));
  // Let e = int(hash/challenge(bytes(R) || bytes(P) || m)) mod n.
  const sig = createSigSchnorr(k, rx, await challengeAsync(rx, px, m), d);
  // If Verify(bytes(P), m, sig) (see below) returns failure, abort
  if (!(await verifySchnorrAsync(sig, m, px))) throw new Error(E_INVSIG);
  return sig;
};

type MaybePromise<T> = T | Promise<T>;
const callSyncAsyncFn = <T, O>(res: MaybePromise<T>, later: (res2: T) => O) => {
  return res instanceof Promise ? res.then(later) : later(res);
};

const _verifSchnorr = (
  signature: TArg<Uint8Array>,
  message: TArg<Uint8Array>,
  publicKey: TArg<Uint8Array>,
  challengeFn: (...args: Uint8Array[]) => MaybePromise<bigint>
): MaybePromise<boolean> => {
  const sig = abytes(signature, 64, 'signature');
  const msg = abytes(message, undefined, 'message');
  const pub = abytes(publicKey, L, 'publicKey');
  let P_: Point;
  let r: bigint;
  let s: bigint;
  let chalInput: Uint8Array; // challenge preimage bytes(r) || bytes(P) || m
  try {
    // lift_x from BIP340. Convert 32-byte x coordinate to elliptic curve point.
    // Fail if x ≥ p. Let c = x³ + 7 mod p.
    const x = bytesToNumBE(pub);
    P_ = lift_x(x); // lift_x returns the validated even-y point required by BIP340.
    // P = lift_x(int(pk)); fail if that fails
    r = FpIsValidNot0(sliceBytesNumBE(sig, 0, L)); // Let r = int(sig[0:32]); fail if r ≥ p.
    // Let s = int(sig[32:64]); fail if s ≥ n.
    // Stricter than BIP-340/libsecp256k1, which only reject s >= n. Honest signing reaches
    // s = 0 only with negligible probability (k + e*d ≡ 0 mod n), so treat zero-s inputs as
    // crafted edge cases and fail closed instead of carrying that extra verification surface.
    s = FnIsValidNot0(sliceBytesNumBE(sig, L, 64));
    // lift_x validated x < P, so the 32-byte input encoding equals bytes(P.x) exactly.
    chalInput = concatBytes(numTo32b(r), pub, msg);
  } catch (error) {
    return false;
  }
  // Hash-provider errors (unset hashes.sha256, missing crypto.subtle, bad provider digests)
  // stay outside the catch above: backend misconfiguration is not an "invalid signature"
  // result, so it throws / rejects instead of becoming false.
  // int(challenge(bytes(r)||bytes(P)||m))%n
  return callSyncAsyncFn(challengeFn(chalInput), (e) => {
    try {
      const { x, y } = doubleScalarMulUns(P_, s, modN(-e)).toAffine(); // R = s⋅G - e⋅P
      if (!isEven(y) || x !== r) return false; // -eP == (n-e)P
      return true; // Fail if is_infinite(R) / not has_even_y(R) / x(R) ≠ r.
    } catch (error) {
      return false; // is_infinite(R) throws inside doubleScalarMulUns
    }
  });
};

/** Verifies Schnorr signature. Invalid points, scalars and failed curve checks return false;
 * hash-backend misconfiguration (e.g. unset hashes.sha256) throws instead, since it is a
 * runtime/backend error, not an "invalid signature" result. */
const verifySchnorr = (s: TArg<Uint8Array>, m: TArg<Uint8Array>, p: TArg<Uint8Array>): boolean =>
  _verifSchnorr(s, m, p, challenge) as boolean;
/** Async Schnorr verification. Curve/encoding failures after the initial byte checks still
 * become false, but async backend failures reject the promise. Missing crypto.subtle is a
 * runtime/backend error, not an "invalid signature" result, so we surface it instead of
 * turning it into false. */
const verifySchnorrAsync = async (
  s: TArg<Uint8Array>,
  m: TArg<Uint8Array>,
  p: TArg<Uint8Array>
): Promise<boolean> => _verifSchnorr(s, m, p, challengeAsync) as Promise<boolean>;

/**
 * BIP340 Schnorr helpers over secp256k1.
 * @example
 * Sign and verify a BIP340 Schnorr signature.
 * ```ts
 * import * as secp from '@noble/secp256k1';
 * import { sha256 } from '@noble/hashes/sha2.js';
 * secp.hashes.sha256 = sha256;
 * const secretKey = secp.utils.randomSecretKey();
 * const message = new Uint8Array([1, 2, 3]);
 * const sig = secp.schnorr.sign(message, secretKey);
 * const publicKey = secp.schnorr.getPublicKey(secretKey);
 * const isValid = secp.schnorr.verify(sig, message, publicKey);
 * ```
 */
const schnorr: {
  keygen: typeof keygenSchnorr;
  getPublicKey: typeof pubSchnorr;
  sign: typeof signSchnorr;
  verify: typeof verifySchnorr;
  signAsync: typeof signSchnorrAsync;
  verifyAsync: typeof verifySchnorrAsync;
} = /* @__PURE__ */ freeze({
  keygen: keygenSchnorr,
  getPublicKey: pubSchnorr,
  sign: signSchnorr,
  verify: verifySchnorr,
  signAsync: signSchnorrAsync,
  verifyAsync: verifySchnorrAsync,
});

// ## Precomputes
// --------------

const precompute = () => {
  const points: Point[] = [];
  let p = G;
  let b = p;
  for (let w = 0; w < 33; w++) {
    b = p;
    points.push(b);
    for (let i = 1; i < 128; i++) {
      b = b.add(p);
      points.push(b);
    } // i=1, bc we skip 0
    p = b.double();
  }
  return points;
};
let Gpows: Point[] | undefined = undefined; // precomputes for base point G
// Branch-shaped negate helper for wNAF; not a hard constant-time primitive in JavaScript.
const ctneg = (cnd: boolean, p: Point) => {
  const n = p.negate();
  return cnd ? n : p;
};

/**
 * Precomputes give 12x faster getPublicKey(), 10x sign(), 2x verify() by
 * caching multiples of G (base point). Cache is stored in 32MB of RAM.
 * Any time `G.multiply` is done, precomputes are used.
 * Not used for getSharedSecret, which instead multiplies random pubkey `P.multiply`.
 *
 * w-ary non-adjacent form (wNAF) precomputation method is 10% slower than windowed method,
 * but takes 2x less RAM. RAM reduction is possible by utilizing `.subtract`.
 *
 * !! Precomputes can be disabled by commenting-out call of the wNAF() inside Point#multiply().
 */
const wNAF = (n: bigint): { p: Point; f: Point } => {
  const comp = Gpows || (Gpows = precompute());
  let p = I;
  let f = G; // f must be G, or could become I in the end
  for (let w = 0; w < 33; w++) {
    let wbits = Number(n & 255n); // extract W=8 bits.
    n >>= 8n; // shift number by W=8 bits.
    // We use negative indexes to reduce size of precomputed table by 2x.
    // Instead of needing precomputes 0..256, we only calculate them for 0..128.
    // If an index > 128 is found, we do (256-index) - where 256 is next window.
    // Naive: index +127 => 127, +224 => 224
    // Optimized: index +127 => 127, +224 => 256-32
    if (wbits > 128) {
      wbits -= 256;
      n += 1n;
    }
    const off = w * 128;
    const offP = off + Math.abs(wbits) - 1;
    const isOddW = w % 2 !== 0; // conditions, evaluate both; alternates fake-add sign per window
    const isNeg = wbits < 0;
    if (wbits === 0) {
      // off == I: can't add it. Add the first point in this window to the fake accumulator.
      f = f.add(ctneg(isOddW, comp[off])); // bits are 0: add garbage to fake point
    } else {
      p = p.add(ctneg(isNeg, comp[offP])); // bits are 1: add to result point
    }
  }
  if (n !== 0n) throw new Error('invalid wnaf');
  return { p, f }; // return both real and fake points for JIT/leakage-shape symmetry
};

/** Test-only surface for shared noble test suites. Not part of the public API. */
export const __TEST: TRet<{
  lift_x: (x: bigint) => Point;
  extractK: (rand: TArg<Uint8Array>) => TRet<{ rx: Uint8Array; k: bigint }>;
}> = /* @__PURE__ */ freeze({
  // Shared tests expect the BIP340 helper to expose the canonical even-y point, not just the root.
  lift_x: lift_x as (x: bigint) => TRet<Point>,
  extractK: extractK as (rand: TArg<Uint8Array>) => TRet<{ rx: Uint8Array; k: bigint }>,
});

// !! Remove the export below to easily use in REPL / browser console
export {
  etc,
  getPublicKey,
  getSharedSecret,
  hash,
  hashes,
  keygen,
  Point,
  recoverPublicKey,
  recoverPublicKeyAsync,
  schnorr,
  sign,
  signAsync,
  Signature,
  utils,
  verify,
  verifyAsync,
};