Large semi-primes factorization with its implications to RSA cryptosystems

Abstract

RSA’s strong cryptosystem works on the principle that there are no trivial solutions to integer factorization. Furthermore, factorization of very large semi-primes cannot be done in polynomial time when it comes to the processing power of classical computers. In this paper, we present the analysis of Fermat’s last theorem and Arnold’s theorem. Also highlighted are new techniques such as Arnold’s digitized summation technique and a top-to-bottom or bottom-to-top approach to search for the prime factors. These two drastically reduce the time taken to factorize large semi-primes, as is the case in the Rivest, Shamir, and Adleman cryptosystem.