On the improvement attack upon some variants of RSA cryptosystem via the continued fractions method

Abstract

Let N=pq be an RSA modulus where p and q are primes not necessarily of the same bit size. Previous cryptanalysis results on the difficulty of factoring the public modulus N=pq deployed on variants of RSA cryptosystem are revisited. Each of these variants share a common key relation utilizing the modified Euler quotient (p2-1)(q2-1), given by the key relation ed-k(p2-1)(q2-1)=1 where e and d are the public and private keys respectively. By conducting continuous midpoint subdivision analysis upon an interval containing (p2-1)(q2-1) together with continued fractions on the key relation, we increase the security bound for d exponentially.