Prime factorization using square root approximation

Abstract

Many cryptosystems are based on the factorization of large integers. The complexity of this type of factorization is still an advantage for data security developers and a challenge for both mathematicians and cryptanalysts. The security of RSA relies on the difficulty of factoring large integers. The factorization was studied earlier by old civilizations like the Greek, but their methods were extended after the emergence of computers. The paradox of RSA is that, in order to make RSA more efficient, we use a modulus n = p q , which is as small as possible. On the other hand, it is sufficient to factor n in order to decrypt the encrypted messages. In this paper, we propose a new factorization method based on the square root approximation. This method allows in reducing the search for candidate prime factors of a given integer by approximating each prime factor before considering it as a candidate.