Enhancing the Efficiency and Security of The Rabin Public-Key Cryptosystem Using Gaussian Integers

Yahia Awad; Haissam Chehade; Ramiz Hindi

doi:10.55549/epstem.1753690

Enhancing the Efficiency and Security of The Rabin Public-Key Cryptosystem Using Gaussian Integers

Abstract

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.

Keywords

References

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.

Details

Primary Language

English

Subjects

Statistics (Other)

Journal Section

Conference Paper

Authors

Yahia Awad This is me
Lebanon

Haissam Chehade This is me
Lebanon

Ramiz Hindi This is me
Lebanon

Early Pub Date

August 1, 2025

Publication Date

August 1, 2025

Submission Date

February 25, 2025

Acceptance Date

April 2, 2025

Published in Issue

Year 2025 Volume: 34

DOI

https://doi.org/10.55549/epstem.1753690

IZ

https://izlik.org/JA37LX24CZ

Cite

RIS / Bibtex

APA

Awad, Y., Chehade, H., & Hindi, R. (2025). Enhancing the Efficiency and Security of The Rabin Public-Key Cryptosystem Using Gaussian Integers. The Eurasia Proceedings of Science Technology Engineering and Mathematics, 34, 107-119. https://doi.org/10.55549/epstem.1753690

AMA

1.Awad Y, Chehade H, Hindi R. Enhancing the Efficiency and Security of The Rabin Public-Key Cryptosystem Using Gaussian Integers. EPSTEM. 2025;34:107-119. doi:10.55549/epstem.1753690

Chicago

Awad, Yahia, Haissam Chehade, and Ramiz Hindi. 2025. “Enhancing the Efficiency and Security of The Rabin Public-Key Cryptosystem Using Gaussian Integers”. The Eurasia Proceedings of Science Technology Engineering and Mathematics 34 (August): 107-19. https://doi.org/10.55549/epstem.1753690.

EndNote

Awad Y, Chehade H, Hindi R (August 1, 2025) Enhancing the Efficiency and Security of The Rabin Public-Key Cryptosystem Using Gaussian Integers. The Eurasia Proceedings of Science Technology Engineering and Mathematics 34 107–119.

IEEE

[1]Y. Awad, H. Chehade, and R. Hindi, “Enhancing the Efficiency and Security of The Rabin Public-Key Cryptosystem Using Gaussian Integers”, EPSTEM, vol. 34, pp. 107–119, Aug. 2025, doi: 10.55549/epstem.1753690.

ISNAD

Awad, Yahia - Chehade, Haissam - Hindi, Ramiz. “Enhancing the Efficiency and Security of The Rabin Public-Key Cryptosystem Using Gaussian Integers”. The Eurasia Proceedings of Science Technology Engineering and Mathematics 34 (August 1, 2025): 107-119. https://doi.org/10.55549/epstem.1753690.

JAMA

1.Awad Y, Chehade H, Hindi R. Enhancing the Efficiency and Security of The Rabin Public-Key Cryptosystem Using Gaussian Integers. EPSTEM. 2025;34:107–119.

MLA

Awad, Yahia, et al. “Enhancing the Efficiency and Security of The Rabin Public-Key Cryptosystem Using Gaussian Integers”. The Eurasia Proceedings of Science Technology Engineering and Mathematics, vol. 34, Aug. 2025, pp. 107-19, doi:10.55549/epstem.1753690.

Vancouver

1.Yahia Awad, Haissam Chehade, Ramiz Hindi. Enhancing the Efficiency and Security of The Rabin Public-Key Cryptosystem Using Gaussian Integers. EPSTEM. 2025 Aug. 1;34:107-19. doi:10.55549/epstem.1753690