LumeWeb
/
bigint-crypto-utils
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
bigint-crypto-utils/docs/API.md

14 KiB
Raw Blame History

bigint-crypto-utils - v3.2.2

Table of contents

Interfaces

Type Aliases

Functions

Type Aliases

PrimeFactor

Ƭ PrimeFactor: number | bigint | PrimePower

PrimeFactorization

Ƭ PrimeFactorization: [bigint, bigint][]

PrimePower

Ƭ PrimePower: [number | bigint, number | bigint]

Functions

abs

▸ abs(a): number | bigint

Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0

Parameters

Name Type
a number | bigint

Returns

number | bigint

The absolute value of a

bitLength

▸ bitLength(a): number

Returns the (minimum) length of a number expressed in bits.

Parameters

Name Type
a number | bigint

Returns

number

The bit length

crt

▸ crt(remainders, modulos, modulo?): bigint

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

Parameters

Name Type Description
remainders bigint[] the array of remainders a_i. For example [17n, 243n, 344n]
modulos bigint[] the array of modulos n_i. For example [769n, 2017n, 47701n]
modulo? bigint the product of all modulos. Provided here just to save some operations if it is already known

Returns

bigint

x

eGcd

▸ eGcd(a, b): Egcd

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).

Throws

RangeError if a or b are <= 0

Parameters

Name Type
a number | bigint
b number | bigint

Returns

Egcd

A triple (g, x, y), such that ax + by = g = gcd(a, b).

gcd

▸ gcd(a, b): bigint

Greatest common divisor of two integers based on the iterative binary algorithm.

Parameters

Name Type
a number | bigint
b number | bigint

Returns

bigint

The greatest common divisor of a and b

isProbablyPrime

▸ isProbablyPrime(w, iterations?, disableWorkers?): Promise<boolean>

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)

Throws

RangeError if w<0

Parameters

Name Type Default value Description
w number | bigint undefined A positive integer to be tested for primality
iterations number 16 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
disableWorkers boolean false Disable the use of workers for the primality test

Returns

Promise<boolean>

A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)

lcm

▸ lcm(a, b): bigint

The least common multiple computed as abs(a*b)/gcd(a,b)

Parameters

Name Type
a number | bigint
b number | bigint

Returns

bigint

The least common multiple of a and b

max

▸ max(a, b): number | bigint

Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<b

Parameters

Name Type
a number | bigint
b number | bigint

Returns

number | bigint

Maximum of numbers a and b

min

▸ min(a, b): number | bigint

Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<b

Parameters

Name Type
a number | bigint
b number | bigint

Returns

number | bigint

Minimum of numbers a and b

modAdd

▸ modAdd(addends, n): bigint

Modular addition of (a_1 + ... + a_r) mod n

Parameters

Name Type Description
addends (number | bigint)[] an array of the numbers a_i to add. For example [3, 12353251235n, 1243, -12341232545990n]
n number | bigint the modulo

Returns

bigint

The smallest positive integer that is congruent with (a_1 + ... + a_r) mod n

modInv

▸ modInv(a, n): bigint

Modular inverse.

Throws

RangeError if a does not have inverse modulo n

Parameters

Name Type Description
a number | bigint The number to find an inverse for
n number | bigint The modulo

Returns

bigint

The inverse modulo n

modMultiply

▸ modMultiply(factors, n): bigint

Modular addition of (a_1 * ... * a_r) mod n *

Parameters

Name Type Description
factors (number | bigint)[] an array of the numbers a_i to multiply. For example [3, 12353251235n, 1243, -12341232545990n] *
n number | bigint the modulo *

Returns

bigint

The smallest positive integer that is congruent with (a_1 * ... * a_r) mod n

modPow

▸ modPow(b, e, n, primeFactorization?): bigint

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.

Throws

RangeError if n <= 0

Parameters

Name Type Description
b number | bigint base
e number | bigint exponent
n number | bigint modulo
primeFactorization? PrimeFactor[] 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.

Returns

bigint

b**e mod n

phi

▸ phi(primeFactorization): bigint

A function that computes the Euler's totien function of a number n, whose prime power factorization is known

Parameters

Name Type Description
primeFactorization PrimeFactorization an array of arrays containing the prime power factorization of a number n. For example, for n = (p1k1)*(p2k2)...(pr**kr), one should provide p1, k1], [p2, k2], ... , [pr, kr

Returns

bigint

phi((p1k1)*(p2k2)...(pr**kr))

prime

▸ prime(bitLength, iterations?): Promise<bigint>

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).

Throws

RangeError if bitLength < 1

Parameters

Name Type Default value Description
bitLength number undefined The required bit length for the generated prime
iterations number 16 The number of iterations for the Miller-Rabin Probabilistic Primality Test

Returns

Promise<bigint>

A promise that resolves to a bigint probable prime of bitLength bits.

primeSync

▸ primeSync(bitLength, iterations?): 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.

Throws

RangeError if bitLength < 1

Parameters

Name Type Default value Description
bitLength number undefined The required bit length for the generated prime
iterations number 16 The number of iterations for the Miller-Rabin Probabilistic Primality Test

Returns

bigint

A bigint probable prime of bitLength bits.

randBetween

▸ randBetween(max, min?): bigint

Returns a cryptographically secure random integer between [min,max].

Throws

RangeError if max <= min

Parameters

Name Type Description
max bigint Returned value will be <= max
min bigint Returned value will be >= min

Returns

bigint

A cryptographically secure random bigint between [min,max]

randBits

▸ randBits(bitLength, forceLength?): Promise<Uint8Array | Buffer>

Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()

Throws

RangeError if bitLength < 1

Parameters

Name Type Default value Description
bitLength number undefined The desired number of random bits
forceLength boolean false Set to true if you want to force the output to have a specific bit length. It basically forces the msb to be 1

Returns

Promise<Uint8Array | Buffer>

A Promise that resolves to a UInt8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bits

randBitsSync

▸ randBitsSync(bitLength, forceLength?): Uint8Array | Buffer

Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()

Throws

RangeError if bitLength < 1

Parameters

Name Type Default value Description
bitLength number undefined The desired number of random bits
forceLength boolean false Set to true if you want to force the output to have a specific bit length. It basically forces the msb to be 1

Returns

Uint8Array | Buffer

A Uint8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bits

randBytes

▸ randBytes(byteLength, forceLength?): Promise<Uint8Array | Buffer>

Secure random bytes for both node and browsers. Node version uses crypto.randomBytes() and browser one self.crypto.getRandomValues()

Throws

RangeError if byteLength < 1

Parameters

Name Type Default value Description
byteLength number undefined The desired number of random bytes
forceLength boolean false 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

Returns

Promise<Uint8Array | Buffer>

A promise that resolves to a UInt8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bytes

randBytesSync

▸ randBytesSync(byteLength, forceLength?): 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.

Throws

RangeError if byteLength < 1

Parameters

Name Type Default value Description
byteLength number undefined The desired number of random bytes
forceLength boolean false 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

Returns

Uint8Array | Buffer

A UInt8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bytes

toZn

▸ toZn(a, n): 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

Throws

RangeError if n <= 0

Parameters

Name Type Description
a number | bigint An integer
n number | bigint The modulo

Returns

bigint

A bigint with the smallest positive representation of a modulo n