Deterministic Rabin Cryptosystem Using Cubic Congruence and Chinese Remainder Theorem

Abstract

The Rabin Cryptosystem is a public-key cryptosystem known for providing security levels comparable to RSA but with reduced computational overhead. Despite these advantages, it has not been widely adopted for practical use due to its lack of a deterministic nature. This paper addresses this limitation by introducing a new Deterministic Rabin Cryptosystem (DRCS). The DRCS framework includes processes for key generation, encryption, and decryption, leveraging the concept of cubic congruence and the Chinese Remainder Theorem to ensure the decryption process is unambiguous and deterministic. This design not only retains the computational efficiency of the original Rabin Cryptosystem but also enhances its security. Our comparative analysis shows that the DRCS achieves similar performance to the traditional Rabin system in terms of computational overhead. While the encryption process in DRCS is less demanding, its decryption process is more complex, and overall, it maintains a polynomial time complexity. Furthermore, a detailed security analysis indicates that the DRCS is significantly harder to factorize compared to previous models, underscoring its improved security features.