TY  - JOUR
T1  - Enhancing the Efficiency and Security of The Rabin Public-Key Cryptosystem Using Gaussian Integers
AU  - Awad, Yahia
AU  - Chehade, Haissam
AU  - Hindi, Ramiz
PY  - 2025
DA  - August
Y2  - 2025
DO  - 10.55549/epstem.1753690
JF  - The Eurasia Proceedings of Science Technology Engineering and Mathematics
JO  - EPSTEM
PB  - ISRES Publishing
WT  - DergiPark
SN  - 2602-3199
SP  - 107
EP  - 119
VL  - 34
LA  - en
AB  - The Rabin public-key cryptosystem is renowned for its provable security, making it one of the most extensively studied cryptographic schemes. Initially defined over the ring of integers, it has been extended to polynomial rings over finite fields. This work introduces a novel generalization of the Rabin cryptosystem to the domain of Gaussian integers Z[i], incorporating novel arithmetic operations and modifications tailored to this framework. We develop comprehensive encryption and decryption algorithms, supplemented by illustrative examples that clarify these adaptations. A comparative analysis between the classical Rabin scheme and its Gaussian integer extension reveals significant differences in security and computational complexity, demonstrating that the extended scheme significantly enhances resilience against attacks, particularly by mitigating decryption ambiguity and brute-force complexity. Empirical results, supported by computational experiments and graphical analysis, show that the time required for potential attacks increases substantially when transitioning from natural integers to Gaussian integers, a consequence of the richer algebraic structure of Z[i], which imposes additional computational challenges for adversaries. By leveraging these properties, the modified Rabin cryptosystem offers a robust defense against common cryptanalytic techniques, positioning it as a promising alternative for secure communication. This work not only lays the foundation for further exploration of public-key cryptography in alternative algebraic domains but also opens new avenues for both theoretical research and practical applications.
KW  - Rabin cryptosystem
KW  - Gaussian integers
KW  - Cryptographic security
KW  - Algebraic Coding Theory
CR  - Awad, Y., Chehade, H., & Hindi. R. (2025). Enhancing the efficiency and security of the rabin public-key
cryptosystem in the domain of Gaussian ıntegers. The Eurasia Proceedings of Science, Technology, Engineering
and Mathematics (EPSTEM), 34, 107-119.
UR  - https://doi.org/10.55549/epstem.1753690
L1  - https://dergipark.org.tr/en/download/article-file/5102726
ER  -