Exploiting the Security of RSA Variant’s Generalized Key Equations

Abstract

The security of RSA cryptosystem and its variants rely on the intractability of integer factorization problem. Series of attacks have been reported to exploit the cryptosystem leading to polynomial time factorization of the composite integer   into its prime factors  and . This paper presents two cryptanalysis attacks on the prime power modulus as one of the RSA variants with moduli  where generalized key equations of the form and  can be exploited and factored simultaneously using simultaneous Diophantine approximation method and lattice basis reduction technique.  The paper also gives numerical examples to demonstrate how the attacks work. 

Key-words: RSA Modulus, Key equations, Exploiting, Attacks, Simultaneous Diophantine