export declare function mod(a: bigint, b: bigint): bigint;
/**
 * Efficiently raise num to power and do modular division.
 * Unsafe in some contexts: uses ladder, so can expose bigint bits.
 * @example
 * pow(2n, 6n, 11n) // 64n % 11n == 9n
 */
export declare function pow(num: bigint, power: bigint, modulo: bigint): bigint;
export declare function pow2(x: bigint, power: bigint, modulo: bigint): bigint;
export declare function invert(number: bigint, modulo: bigint): bigint;
/**
 * Tonelli-Shanks square root search algorithm.
 * 1. https://eprint.iacr.org/2012/685.pdf (page 12)
 * 2. Square Roots from 1; 24, 51, 10 to Dan Shanks
 * Will start an infinite loop if field order P is not prime.
 * @param P field order
 * @returns function that takes field Fp (created from P) and number n
 */
export declare function tonelliShanks(P: bigint): <T>(Fp: IField<T>, n: T) => T;
export declare function FpSqrt(P: bigint): <T>(Fp: IField<T>, n: T) => T;
export declare const isNegativeLE: (num: bigint, modulo: bigint) => boolean;
export interface IField<T> {
    ORDER: bigint;
    BYTES: number;
    BITS: number;
    MASK: bigint;
    ZERO: T;
    ONE: T;
    create: (num: T) => T;
    isValid: (num: T) => boolean;
    is0: (num: T) => boolean;
    neg(num: T): T;
    inv(num: T): T;
    sqrt(num: T): T;
    sqr(num: T): T;
    eql(lhs: T, rhs: T): boolean;
    add(lhs: T, rhs: T): T;
    sub(lhs: T, rhs: T): T;
    mul(lhs: T, rhs: T | bigint): T;
    pow(lhs: T, power: bigint): T;
    div(lhs: T, rhs: T | bigint): T;
    addN(lhs: T, rhs: T): T;
    subN(lhs: T, rhs: T): T;
    mulN(lhs: T, rhs: T | bigint): T;
    sqrN(num: T): T;
    isOdd?(num: T): boolean;
    pow(lhs: T, power: bigint): T;
    invertBatch: (lst: T[]) => T[];
    toBytes(num: T): Uint8Array;
    fromBytes(bytes: Uint8Array): T;
    cmov(a: T, b: T, c: boolean): T;
}
export declare function validateField<T>(field: IField<T>): IField<T>;
/**
 * Same as `pow` but for Fp: non-constant-time.
 * Unsafe in some contexts: uses ladder, so can expose bigint bits.
 */
export declare function FpPow<T>(f: IField<T>, num: T, power: bigint): T;
/**
 * Efficiently invert an array of Field elements.
 * `inv(0)` will return `undefined` here: make sure to throw an error.
 */
export declare function FpInvertBatch<T>(f: IField<T>, nums: T[]): T[];
export declare function FpDiv<T>(f: IField<T>, lhs: T, rhs: T | bigint): T;
export declare function FpIsSquare<T>(f: IField<T>): (x: T) => boolean;
export declare function nLength(n: bigint, nBitLength?: number): {
    nBitLength: number;
    nByteLength: number;
};
type FpField = IField<bigint> & Required<Pick<IField<bigint>, 'isOdd'>>;
/**
 * Initializes a finite field over prime. **Non-primes are not supported.**
 * Do not init in loop: slow. Very fragile: always run a benchmark on a change.
 * Major performance optimizations:
 * * a) denormalized operations like mulN instead of mul
 * * b) same object shape: never add or remove keys
 * * c) Object.freeze
 * @param ORDER prime positive bigint
 * @param bitLen how many bits the field consumes
 * @param isLE (def: false) if encoding / decoding should be in little-endian
 * @param redef optional faster redefinitions of sqrt and other methods
 */
export declare function Field(ORDER: bigint, bitLen?: number, isLE?: boolean, redef?: Partial<IField<bigint>>): Readonly<FpField>;
export declare function FpSqrtOdd<T>(Fp: IField<T>, elm: T): T;
export declare function FpSqrtEven<T>(Fp: IField<T>, elm: T): T;
/**
 * "Constant-time" private key generation utility.
 * Same as mapKeyToField, but accepts less bytes (40 instead of 48 for 32-byte field).
 * Which makes it slightly more biased, less secure.
 * @deprecated use mapKeyToField instead
 */
export declare function hashToPrivateScalar(hash: string | Uint8Array, groupOrder: bigint, isLE?: boolean): bigint;
/**
 * Returns total number of bytes consumed by the field element.
 * For example, 32 bytes for usual 256-bit weierstrass curve.
 * @param fieldOrder number of field elements, usually CURVE.n
 * @returns byte length of field
 */
export declare function getFieldBytesLength(fieldOrder: bigint): number;
/**
 * Returns minimal amount of bytes that can be safely reduced
 * by field order.
 * Should be 2^-128 for 128-bit curve such as P256.
 * @param fieldOrder number of field elements, usually CURVE.n
 * @returns byte length of target hash
 */
export declare function getMinHashLength(fieldOrder: bigint): number;
/**
 * "Constant-time" private key generation utility.
 * Can take (n + n/2) or more bytes of uniform input e.g. from CSPRNG or KDF
 * and convert them into private scalar, with the modulo bias being negligible.
 * Needs at least 48 bytes of input for 32-byte private key.
 * https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
 * FIPS 186-5, A.2 https://csrc.nist.gov/publications/detail/fips/186/5/final
 * RFC 9380, https://www.rfc-editor.org/rfc/rfc9380#section-5
 * @param hash hash output from SHA3 or a similar function
 * @param groupOrder size of subgroup - (e.g. secp256k1.CURVE.n)
 * @param isLE interpret hash bytes as LE num
 * @returns valid private scalar
 */
export declare function mapHashToField(key: Uint8Array, fieldOrder: bigint, isLE?: boolean): Uint8Array;
export {};
//# sourceMappingURL=modular.d.ts.map