Abstract
It is very difficult to factorize composite number, to integer factorization, p and q that is almost similar length of digits. Integer factorization algorithms, for the most part, find () that is congruence of squares ( (mod )) 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 () and deciding factor base, B. This paper proposes a efficient algorithm. The proposed algorithm extracts B from integer factorization with 3 digits prime numbers of and decides f, the combination of B. And then it obtains (this is, , ) from integer factorization of and gets , ={1,3,7,9}. Our algorithm is much more effective in comparison with the conventional Fermat algorithm that sequentially finds .
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