Integer Factorization Implementations

One difficult problem of mathematics that forms the basics of some public key cryptography systems like RSA, is finding factors of big numbers. To solve this problem, many factorization algorithms have been offered with different complexities. Many attempts have been made today to implement these factorization algorithms. And these implementations are different from various aspects. Each of these factorization algorithms is efficient for numbers with a specific size. These algorithms can be compared with regard to time and memory complexity. In this paper, some of these implementations are studied and compared and consequently the most appropriate one will be introduced.