Variants of RSA and Rabin Cryptosystems modulo p^rq^s

Cryptography is the technique to protect sensitive information from unauthorized persons by encryption. Cryptographers have invented various systems of cryptography to make it befitting. In the age of modern science, the use of mathematical theories has added a new dimension to cryptography. Prime factorization-based cryptography is widely used and effective. In 1977, Rivest, Shamir, and Adlerman proposed the first practical public key cryptosystem based on the prime factorization of large numbers known as the RSA cryptosystem. Later in 1979, Michael Oser Rabin developed a technique based on prime-factorization known as Rabin Cryptosystem. Several variants of these systems have been developed further by many famous mathematicians and computer scientists, aiming to increase security, reduce cost, time, and memory usage, and enhance overall performance. Tsuyoshi Takagi and Hugh C. Williams proposed such two famous variants. In this paper, we have first analyzed the traditional cryptosystems and existing variants. Identifying the security strength and field of improvement of these systems and their variants, we have proposed two new variants. The encryption-decryption techniques are described by employing them in several applications. The effectiveness of the proposed variants is demonstrated by a comparative analysis of these variants with others. Numerical experiments show that the proposed Rabin’s variant performs almost the same as the base algorithm. However, the proposed variant of RSA algorithm reduces computational time significantly, approximately 91% reduction from traditional RSA and 90% reduction from multi-prime RSA. J. Bangladesh Math. Soc. 44.2 (2024) 01–16