Cryptanalysis of RSA: Integer Prime Factorization Using Genetic Algorithms

Abstract

In recent years, researchers have been exploring alternative methods to solving Integer Prime Factorization, the decomposition of an integer into its prime factors. This has direct application to cryptanalysis of RSA, as one means of breaking such a cryptosystem requires factorization of a large number that is the product of two prime numbers. This paper applies three different genetic algorithms to solve this issue, utilizing mathematical knowledge concerning distribution of primes to improve the algorithms. The best of the three genetic algorithms has a chromosome that represents m in the equation prime = 6 m ± 1, and is able to factor a number of up to 22 decimal digits. This is a significantly larger number than the largest factored by comparable methods in earlier work. This leads to the conclusion that approaches such as genetic algorithms are a promising avenue of research into the problem of integer factorization.