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/// <reference types="node" />
/**
* Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
*
* @param a
*
* @returns The absolute value of a
*/
declare function abs(a: number | bigint): number | bigint;
/**
* Returns the (minimum) length of a number expressed in bits.
*
* @param a
* @returns The bit length
*/
declare function bitLength(a: number | bigint): number;
/**
* Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime (no two divisors share a common factor other than 1). Provided that n_i are pairwise coprime, and a_i any integers, this function returns a solution for the following system of equations:
x ≡ a_1 mod n_1
x ≡ a_2 mod n_2
⋮
x ≡ a_k mod n_k
*
* @param remainders the array of remainders a_i. For example [17n, 243n, 344n]
* @param modulos the array of modulos n_i. For example [769n, 2017n, 47701n]
* @param modulo the product of all modulos. Provided here just to save some operations if it is already known
* @returns x
*/
declare function crt(remainders: bigint[], modulos: bigint[], modulo?: bigint): bigint;
interface Egcd {
g: bigint;
x: bigint;
y: bigint;
}
/**
* An iterative implementation of the extended euclidean algorithm or extended greatest common divisor algorithm.
* Take positive integers a, b as input, and return a triple (g, x, y), such that ax + by = g = gcd(a, b).
*
* @param a
* @param b
*
* @throws {@link RangeError} if a or b are <= 0
*
* @returns A triple (g, x, y), such that ax + by = g = gcd(a, b).
*/
declare function eGcd(a: number | bigint, b: number | bigint): Egcd;
/**
* Greatest common divisor of two integers based on the iterative binary algorithm.
*
* @param a
* @param b
*
* @returns The greatest common divisor of a and b
*/
declare function gcd(a: number | bigint, b: number | bigint): bigint;
/**
* The least common multiple computed as abs(a*b)/gcd(a,b)
* @param a
* @param b
*
* @returns The least common multiple of a and b
*/
declare function lcm(a: number | bigint, b: number | bigint): bigint;
/**
* Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<b
*
* @param a
* @param b
*
* @returns Maximum of numbers a and b
*/
declare function max(a: number | bigint, b: number | bigint): number | bigint;
/**
* Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<b
*
* @param a
* @param b
*
* @returns Minimum of numbers a and b
*/
declare function min(a: number | bigint, b: number | bigint): number | bigint;
/**
* Modular addition of (a_1 + ... + a_r) mod n
* @param addends an array of the numbers a_i to add. For example [3, 12353251235n, 1243, -12341232545990n]
* @param n the modulo
* @returns The smallest positive integer that is congruent with (a_1 + ... + a_r) mod n
*/
declare function modAdd(addends: Array<number | bigint>, n: number | bigint): bigint;
/**
* Modular inverse.
*
* @param a The number to find an inverse for
* @param n The modulo
*
* @throws {@link RangeError} if a does not have inverse modulo n
*
* @returns The inverse modulo n
*/
declare function modInv(a: number | bigint, n: number | bigint): bigint;
/**
* Modular addition of (a_1 * ... * a_r) mod n
* @param factors an array of the numbers a_i to multiply. For example [3, 12353251235n, 1243, -12341232545990n]
* @param n the modulo
* @returns The smallest positive integer that is congruent with (a_1 * ... * a_r) mod n
*/
declare function modMultiply(factors: Array<number | bigint>, n: number | bigint): bigint;
type PrimePower = [number | bigint, number | bigint];
type PrimeFactor = number | bigint | PrimePower;
/**
* Modular exponentiation b**e mod n. Currently using the right-to-left binary method if the prime factorization is not provided, or the chinese remainder theorem otherwise.
*
* @param b base
* @param e exponent
* @param n modulo
* @param primeFactorization an array of the prime factors, for example [5n, 5n, 13n, 27n], or prime powers as [p, k], for instance [[5, 2], [13, 1], [27, 1]]. If the prime factorization is provided the chinese remainder theorem is used to greatly speed up the exponentiation.
*
* @throws {@link RangeError} if n <= 0
*
* @returns b**e mod n
*/
declare function modPow(b: number | bigint, e: number | bigint, n: number | bigint, primeFactorization?: PrimeFactor[]): bigint;
type PrimeFactorization = Array<[bigint, bigint]>;
/**
* A function that computes the Euler's totien function of a number n, whose prime power factorization is known
*
* @param primeFactorization an array of arrays containing the prime power factorization of a number n. For example, for n = (p1**k1)*(p2**k2)*...*(pr**kr), one should provide [[p1, k1], [p2, k2], ... , [pr, kr]]
* @returns phi((p1**k1)*(p2**k2)*...*(pr**kr))
*/
declare function phi(primeFactorization: PrimeFactorization): bigint;
/**
* Finds the smallest positive element that is congruent to a in modulo n
*
* @remarks
* a and b must be the same type, either number or bigint
*
* @param a - An integer
* @param n - The modulo
*
* @throws {@link RangeError} if n <= 0
*
* @returns A bigint with the smallest positive representation of a modulo n
*/
declare function toZn(a: number | bigint, n: number | bigint): bigint;
/**
* The test first tries if any of the first 250 small primes are a factor of the input number and then passes several
* iterations of Miller-Rabin Probabilistic Primality Test (FIPS 186-4 C.3.1)
*
* @param w - A positive integer to be tested for primality
* @param iterations - The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3 of FIPS 186-4
* @param disableWorkers - Disable the use of workers for the primality test
*
* @throws {@link RangeError} if w<0
*
* @returns A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
*/
declare function isProbablyPrime(w: number | bigint, iterations?: number, disableWorkers?: boolean): Promise<boolean>;
/**
* A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
* The browser version uses web workers to parallelise prime look up. Therefore, it does not lock the UI
* main process, and it can be much faster (if several cores or cpu are available).
* The node version can also use worker_threads if they are available (enabled by default with Node 11 and
* and can be enabled at runtime executing node --experimental-worker with node >=10.5.0).
*
* @param bitLength - The required bit length for the generated prime
* @param iterations - The number of iterations for the Miller-Rabin Probabilistic Primality Test
*
* @throws {@link RangeError} if bitLength < 1
*
* @returns A promise that resolves to a bigint probable prime of bitLength bits.
*/
declare function prime(bitLength: number, iterations?: number): Promise<bigint>;
/**
* A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
* The sync version is NOT RECOMMENDED since it won't use workers and thus it'll be slower and may freeze thw window in browser's javascript. Please consider using prime() instead.
*
* @param bitLength - The required bit length for the generated prime
* @param iterations - The number of iterations for the Miller-Rabin Probabilistic Primality Test
*
* @throws {@link RangeError} if bitLength < 1
*
* @returns A bigint probable prime of bitLength bits.
*/
declare function primeSync(bitLength: number, iterations?: number): bigint;
/**
* Returns a cryptographically secure random integer between [min,max].
* @param max Returned value will be <= max
* @param min Returned value will be >= min
*
* @throws {@link RangeError} if max <= min
*
* @returns A cryptographically secure random bigint between [min,max]
*/
declare function randBetween(max: bigint, min?: bigint): bigint;
/**
* Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
*
* @param bitLength - The desired number of random bits
* @param forceLength - Set to true if you want to force the output to have a specific bit length. It basically forces the msb to be 1
*
* @throws {@link RangeError} if bitLength < 1
*
* @returns A Promise that resolves to a UInt8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bits
*/
declare function randBits(bitLength: number, forceLength?: boolean): Promise<Uint8Array | Buffer>;
/**
* Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
* @param bitLength - The desired number of random bits
* @param forceLength - Set to true if you want to force the output to have a specific bit length. It basically forces the msb to be 1
*
* @throws {@link RangeError} if bitLength < 1
*
* @returns A Uint8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bits
*/
declare function randBitsSync(bitLength: number, forceLength?: boolean): Uint8Array | Buffer;
/**
* Secure random bytes for both node and browsers. Node version uses crypto.randomBytes() and browser one self.crypto.getRandomValues()
*
* @param byteLength - The desired number of random bytes
* @param forceLength - Set to true if you want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
*
* @throws {@link RangeError} if byteLength < 1
*
* @returns A promise that resolves to a UInt8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bytes
*/
declare function randBytes(byteLength: number, forceLength?: boolean): Promise<Uint8Array | Buffer>;
/**
* Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
* This is the synchronous version, consider using the asynchronous one for improved efficiency.
*
* @param byteLength - The desired number of random bytes
* @param forceLength - Set to true if you want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
*
* @throws {@link RangeError} if byteLength < 1
*
* @returns A UInt8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bytes
*/
declare function randBytesSync(byteLength: number, forceLength?: boolean): Uint8Array | Buffer;
export { Egcd, PrimeFactor, PrimeFactorization, PrimePower, abs, bitLength, crt, eGcd, gcd, isProbablyPrime, lcm, max, min, modAdd, modInv, modMultiply, modPow, phi, prime, primeSync, randBetween, randBits, randBitsSync, randBytes, randBytesSync, toZn };
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