179 lines
7.7 KiB
TypeScript
179 lines
7.7 KiB
TypeScript
/**
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* A triple (g, x, y), such that ax + by = g = gcd(a, b).
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*/
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export type egcdReturn = {
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g: bigint;
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x: bigint;
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y: bigint;
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};
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/**
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* Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
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*
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* @param {number|bigint} a
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*
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* @returns {bigint} the absolute value of a
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*/
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export function abs(a: number | bigint): bigint;
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/**
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* Returns the bitlength of a number
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*
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* @param {number|bigint} a
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* @returns {number} - the bit length
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*/
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export function bitLength(a: number | bigint): number;
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/**
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* @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b).
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* @property {bigint} g
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* @property {bigint} x
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* @property {bigint} y
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*/
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/**
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* An iterative implementation of the extended euclidean algorithm or extended greatest common divisor algorithm.
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* Take positive integers a, b as input, and return a triple (g, x, y), such that ax + by = g = gcd(a, b).
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*
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* @param {number|bigint} a
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* @param {number|bigint} b
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*
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* @returns {egcdReturn} A triple (g, x, y), such that ax + by = g = gcd(a, b).
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*/
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export function eGcd(a: number | bigint, b: number | bigint): egcdReturn;
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/**
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* Greatest-common divisor of two integers based on the iterative binary algorithm.
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*
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* @param {number|bigint} a
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* @param {number|bigint} b
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*
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* @returns {bigint} The greatest common divisor of a and b
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*/
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export function gcd(a: number | bigint, b: number | bigint): bigint;
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/**
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* The test first tries if any of the first 250 small primes are a factor of the input number and then passes several
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* iterations of Miller-Rabin Probabilistic Primality Test (FIPS 186-4 C.3.1)
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*
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* @param {number | bigint} w An integer to be tested for primality
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* @param {number} [iterations = 16] The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3
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*
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* @returns {Promise<boolean>} A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
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*/
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export function isProbablyPrime(w: number | bigint, iterations?: number): Promise<boolean>;
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/**
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* The least common multiple computed as abs(a*b)/gcd(a,b)
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* @param {number|bigint} a
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* @param {number|bigint} b
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*
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* @returns {bigint} The least common multiple of a and b
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*/
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export function lcm(a: number | bigint, b: number | bigint): bigint;
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/**
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* Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b
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*
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* @param {number|bigint} a
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* @param {number|bigint} b
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*
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* @returns {bigint} maximum of numbers a and b
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*/
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export function max(a: number | bigint, b: number | bigint): bigint;
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/**
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* Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b
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*
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* @param {number|bigint} a
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* @param {number|bigint} b
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*
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* @returns {bigint} minimum of numbers a and b
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*/
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export function min(a: number | bigint, b: number | bigint): bigint;
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/**
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* Modular inverse.
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*
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* @param {number|bigint} a The number to find an inverse for
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* @param {number|bigint} n The modulo
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*
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* @returns {bigint} the inverse modulo n or NaN if it does not exist
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*/
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export function modInv(a: number | bigint, n: number | bigint): bigint;
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/**
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* Modular exponentiation b**e mod n. Currently using the right-to-left binary method
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*
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* @param {number|bigint} b base
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* @param {number|bigint} e exponent
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* @param {number|bigint} n modulo
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*
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* @returns {bigint} b**e mod n
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*/
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export function modPow(b: number | bigint, e: number | bigint, n: number | bigint): bigint;
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/**
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* A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
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* The browser version uses web workers to parallelise prime look up. Therefore, it does not lock the UI
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* main process, and it can be much faster (if several cores or cpu are available).
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* The node version can also use worker_threads if they are available (enabled by default with Node 11 and
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* and can be enabled at runtime executing node --experimental-worker with node >=10.5.0).
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*
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* @param {number} bitLength The required bit length for the generated prime
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* @param {number} [iterations = 16] The number of iterations for the Miller-Rabin Probabilistic Primality Test
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*
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* @returns {Promise<bigint>} A promise that resolves to a bigint probable prime of bitLength bits.
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*/
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export function prime(bitLength: number, iterations?: number): Promise<bigint>;
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/**
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* A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
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* 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.
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*
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* @param {number} bitLength The required bit length for the generated prime
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* @param {number} [iterations = 16] The number of iterations for the Miller-Rabin Probabilistic Primality Test
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*
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* @returns {bigint} A bigint probable prime of bitLength bits.
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*/
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export function primeSync(bitLength: number, iterations?: number): bigint;
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/**
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* Returns a cryptographically secure random integer between [min,max]
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* @param {bigint} max Returned value will be <= max
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* @param {bigint} [min = BigInt(1)] Returned value will be >= min
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*
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* @returns {bigint} A cryptographically secure random bigint between [min,max]
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*/
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export function randBetween(max: bigint, min?: bigint): bigint;
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/**
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* Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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*
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* @param {number} bitLength The desired number of random bits
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* @param {boolean} [forceLength = false] If we want to force the output to have a specific bit length. It basically forces the msb to be 1
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*
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* @returns {Promise<Buffer | Uint8Array>} A Promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bits
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*/
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export function randBits(bitLength: number, forceLength?: boolean): Promise<Uint8Array | Buffer>;
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/**
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* Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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*
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* @param {number} bitLength The desired number of random bits
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* @param {boolean} [forceLength = false] If we want to force the output to have a specific bit length. It basically forces the msb to be 1
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*
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* @returns {Buffer | Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bits
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*/
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export function randBitsSync(bitLength: number, forceLength?: boolean): Uint8Array | Buffer;
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/**
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* Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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*
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* @param {number} byteLength The desired number of random bytes
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* @param {boolean} [forceLength = false] If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
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*
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* @returns {Promise<Buffer | Uint8Array>} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
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*/
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export function randBytes(byteLength: number, forceLength?: boolean): Promise<Uint8Array | Buffer>;
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/**
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* Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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*
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* @param {number} byteLength The desired number of random bytes
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* @param {boolean} [forceLength = false] If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
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*
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* @returns {Buffer | Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
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*/
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export function randBytesSync(byteLength: number, forceLength?: boolean): Uint8Array | Buffer;
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/**
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* Finds the smallest positive element that is congruent to a in modulo n
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* @param {number|bigint} a An integer
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* @param {number|bigint} n The modulo
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*
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* @returns {bigint} The smallest positive representation of a in modulo n
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*/
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export function toZn(a: number | bigint, n: number | bigint): bigint;
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