How to factor N1 and N2 when p1 = p 2 mod 2t

Abstract

Let N1 = p1q1 and N2 = p 2q2 be two different RSA moduli. Suppose that p 1 = p2 mod 2t for some t, and q1 and q2 are α bit primes. Then May and Ritzenhofen showed that N1 and N2 can be factored in quadratic time if t ≥ 2α + 3. In this paper, we improve this lower bound on t. Namely we prove that N1 and N2 can be factored in quadratic time if t ≥ 2α + 1. Further our simulation result shows that our bound is tight as far as the factoring method of May and Ritzenhofen is used. © 2013 Springer-Verlag.