Enhancing Private Key Cryptosystems: A Secure Approach with Pairwise Coprime Moduli

In our previous work, “Enhancing Communication Security: A Private Key Cryptosystem Employing the CRT,” we developed a private key encryption scheme using distinct prime moduli. While primes offer structured mathematical properties, their identification for large numbers is computationally demanding. In this work, we extend our approach by replacing prime moduli with pairwise co-prime integers, eliminating the need for primality testing and simplifying key selection. This extension not only avoids the complexity of choosing large primes but also enhances security by allowing greater flexibility in modulus selection, as any set of pairwise coprime integers can be used. Unlike factorization-dependent cryptosystems, our scheme ensures that neither the individual moduli nor their product is exposed, rendering standard factorizationbased attacks ineffective. We analyze the theoretical foundation, security implications, and computational efficiency of this modified scheme, demonstrating its advantages for secure communication.