ntaff/Quick_Maths

Maths stuff, including cryptographic attacks implementations, and others useful algorithms

Quick_Maths

This repository contain some mathematicals implementations :

The repo now contain the following dir/files :

Python

0. lib/*.py : Contains various functions

1. Primality.py: Contains primality stuff

   • fermat_witness(n) Check if n is composite, if yes, then return a fermat_witness (see this article)
   • miller_rabin_primtest(n,k) Miller-Rabin primality test
   • prime_in_range(a,b) Find a prime number in a given range (a --> b)
   • is_prime(number) Check if 'number' is prime
   • getprime(nbits) Generate a prime number that can be stored in 'nbits' bits.
   • safe_prime(a,b) Find a safe prime number in a given range [a; b[
   • eratosthene() Yields the sequence of prime numbers via the Sieve of Eratosthene
   • sumPrimes(n) Return the sum of the first n primes
   • chinese_remainder(n, a) : Chinese remainder theorem
   • isCircularPrime(n) Return true if n is a circular prime
   • rsa_attack_small_primes(pathpubkey, outputname) Crack a RSA private key if one of n factor is < 1e9
   • rsa_pollard_attack(pathpubkey, outputname) Crack a RSA private key if one of n factor is < 1e14

2. Arithmetic.py.py: Contains arithmetic stuff

   • gcd(p, q) Return the greatest common divisor of p and q
   • extd_pgcd(a, b) Compute extended gcd of two integers (Extended Euclidean algorithm)
   • linear_congruence(a, b, n) Resolve linear congruence equations
   • fib(n) Return the nth-digit Fibonacci number
   • recfibo(n) Return the nth-digit Fibonacci number (recursive way)

Caml

1. Primality.ml: Contains primality stuff

C

1. Primality.c: Contains primality stuff

Elixir

1. Primality.exs: Contains primality stuff

   • PrimeFinder(n) Return the n-th prime number

2. Number.exs: Contains primality stuff

   • pandigital_product() Sum all products whose multiplicand/multiplier/product identity can be written as a 1...9 pandigital.

   TODO : Add links lol