A new modified integer factorization algorithm using integer modulo 20´s technique

The aim of this paper is to propose a new modified integer factorization algorithm, is called Modified Fermat Factorization Version 4 (MFFV4), in order to speed up the computation time for breaking RSA that the security is based on integer factorization problem. MFFV4 is improved from Modified Fermat Factorization Version 3 (MFFV3) that can factor the modulus faster than Modified Fermat Factorization Version 2 (MFFV2) and Modified Fermat Factorization (MFF). MFFV3 will avoid some computations to find the difference between two integers whenever we can analyze that the square root of the result is certainly not an integer. Avoiding some computations of MFFV3 can be done by using Difference´ s Least Significant Digit Table (DLSDT) in order to analyze the least significant digit of integer. However, MFFV4 can decrease more iterations of the computation than MFFV3. The key of MFFV4 is to analyze the result of the integer modulo 20 which may be a perfect square before making decision to find all digits of this integer. We propose Y2MOD20, which is the information table to analyze the result of integer modulo 20 that is used in Fermat Factorization problem. The experimental results show that the computation time of MFFV4 is reduced in comparison with MFFV3 for all possible values of the modulus.