MFFV2 and MNQSV2: Improved Factorization Algorithms

We propose a method to decrease processing time for two factorization algorithms. One is Modified Fermat Factorization Version 2 (MFFV2) modified from Modified Fermat Factorization (MFF). The other is Modified Non - sieving Quadratic Sieve Version 2 (MNQSV2) modified from Modified Non - Sieving Quadratic Sieve (MNQS). A key concept of this method is to decrease processing time to compute an integer´s square root. This method can be used with all factorization algorithms which the modulus is written as the difference of squares. The experiments showed that the speed of MFFV2 increases when compares with MFF and the speed of MNQSV2 increases when compares with MNQS. In addition, if two primes´ differences are small, the factorization speed of MNQSV2 is faster than the factorization speed of MFFV2.