Speeding Up Fermat’s Factoring Method using Precomputation

The security of many public-key cryptosystems and protocols relies on the difficulty factoring a large positive integer n into prime factors. Fermat method is core some modern important factorization methods, such as quadratic sieve number field methods. It factors composite n=pq in polynomial time if difference between equal to ∆=p-q≤n^(0.25) , where p>q. execution increases rapidly ∆ increases. One improvements based studying possible values (n mod 20). In this paper, we introduce an efficient algorithm factorize 20) precomputation strategy. experimental results, different sizes ∆, demonstrate that our proposed faster than previous by at least 48%.