The κ-Fermat's Integer Factorization Algorithm

It is very difficult problem to factorize composite number. Integer factorization algorithms, for the most part, find () that is congruence of squares ((mode )) with using factoring(factor base, B) and get the result, , with taking the greatest common divisor of Euclid based on the formula . The efficiency of these algorithms hangs on finding (). Fermat's algorithm that is base of congruence of squares finds . This paper proposes the method to find , (). It is supposed =0 or 5 to be surely, and b is a double number. First, the proposed method decides by getting kn that satisfies and about . Second, it decides that satisfies . Third, it figures out () from about as deciding that is in . The proposed algorithm is much more effective in comparison with the conventional Fermat algorithm.