Factoring With Two Large Primes

The study of integer factoring algorithms and the design of faster factoring algorithms is a subject of great importance in cryptology (cf. [1]), and a constant concern for cryptographers. In this paper we present a new technique that proved to be extremely useful, not only to achieve a considerable speed-up of an older and widely studied factoring algorithm, but also, and more importantly, to make practical application of a new factoring algorithm feasible. While this first application does not pose serious threats to factorization-based cryptosystems, the consequences of the second application could be very encouraging (from the cryptanalysts point of view).