Exploiting the security of RSA variant’s generalized key equations
Saidu Isah Abubakar, Zaid Ibrahim, Sadiq Shehu, Ahmad Rufai · Caliphate Journal of Science and Technology · 2025
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 p and q. This paper presents two cryptanalysis attacks on the prime power modulus as one of the RSA variants with moduli Ni = pi2qi2 where generalized key equations of the form eid - kiφ(Ni)=1 and eidi - kφ(Ni) = 1 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.