An Improved Hybrid Encryption Scheme Based on the Sequence of Reduced Residue Systems

The rapid growth of digital communication has created an urgent demand for advanced cryptographic techniques that ensure both security and efficiency. As reliance on digital platforms increases, so does the risk of cyber threats and data breaches. Robust cryptography is, therefore, essential to protect sensitive information and maintain trust in digital transactions. This research proposes an improved composed hybrid cryptosystem that integrates Transposition, Caesar, and Hill ciphers, followed sequentially by RSA encryption. The study examines how a hybrid of four ciphers can be attacked when treated as a composite function. To further enhance security, a sequence of Reduced Residue System (RRS) values was introduced to replace ASCII characters after the third cipher (Hill cipher), adding an additional layer of residue-based encryption before the final RSA stage. The findings demonstrate that the improved hybrid cryptosystem significantly enhances data security and key generation efficiency, adding a new level of complexity that makes it more challenging for attackers to guess or compute decryption keys.

Hybrid, Encryption, Decryption

1. Ariffin, S., Wijonarko, D., Suwarno, & Kristianto, E. S. (2024). Application of unimodular Hill cipher and RSA methods to text encryption algorithms using Python. Journal of Computer Science, 20(5), 548–563. https://doi.org/10.3844/jcssp.2024.548.563 [Google Scholar] [Crossref]

2. ASCII Table. (2024). Google Search. https://www.google.com/search?q=ascii+table&client=ms-opera-mini-android&channel=new&tpsf=opiminienpf [Google Scholar] [Crossref]

3. Hardy, G. H., & Wright, E. M. (2008). An introduction to the theory of numbers (6th ed.). Oxford University Press. [Google Scholar] [Crossref]

4. Hassan, A., Garko, A., Sani, S., Abdullahi, U., & Sahalu, S. (2023). Combined techniques of Hill cipher and transposition cipher. Journal of Mathematics Letters, 1(1), 57–64. https://www.scipublications.com/journal/index.php/jml/article/view/822 [Google Scholar] [Crossref]

5. Ibrahim, A. A., Muhammad, A. H., Shehu, S., Abubakar, T. U., Zaid, I., & Bello, U. (2021). Cryptanalysis on RSA using decryption exponent. IOSR Journal of Mathematics (IOSR-JM), 17(5), 1–8. [Google Scholar] [Crossref]

6. Khan, H. K., Pradhan, R., & Chandavarkar, B. R. (2021). Hybrid cryptography for cloud computing. In 2nd International Conference for Emerging Technology (INCET) (pp. 1–5). https://doi.org/10.1109/INCET51464.2021.9456210 [Google Scholar] [Crossref]

7. Manna, S., Prajapati, M., Sett, A., Banerjee, J., and S. Dutta, (2017). Design and implementation of a two-layered hybrid cryptosystem. Third International Conference on Research in Computational Intelligence and Communication Networks (ICRCICN), 327–331, DOI: 10.1109/ICRCICN.2017.8234529 [Google Scholar] [Crossref]

8. Prakash, K., Saeed, Q. Y. A., Rajan, J., Mohammad, H., & Ahmed, A. S. M. (2023). A hybrid encryption system for communication and financial transactions using RSA and a novel symmetric key algorithm. Bulletin of Electrical Engineering and Informatics, 12(2), 1148–1158. https://doi.org/10.11591/eei.v12i2.4967 [Google Scholar] [Crossref]

9. Rosen, K. H. (2011). Elementary number theory and its applications (6th ed.). Addison-Wesley Publishing Company, Pearson. [Google Scholar] [Crossref]

10. Rufa’i, A., Balarabe, A. T., Muazu, I., & Sirajo, M. (2020). Formulation of an improved hybrid cipher system. International Journal of Innovative Science and Research Technology, 5(12). [Google Scholar] [Crossref]

11. Saja, M. S., Zaynab, A. A., & Jaafer, A. H. (2023). Proposed hybrid cryptosystems based on modifications of Playfair cipher and RSA cryptosystem. Baghdad Science Journal. https://doi.org/10.21123/bsj.2023.8361 [Google Scholar] [Crossref]

12. Shehu, S., Abdullahi, H., Ibrahim, A. A., & Ahmad, R. (2023). Breaking modulus of the form N =p^r q^s with improved polynomial attacks. Journal of Advances in Mathematics and Computer Science, 38(8), 33–46. https://doi.org/10.9734/JAMCS/2023/v38i81788 [Google Scholar] [Crossref]

13. Suhasini, C. A., & Bushra, S. N. (2021). Securing of cloud data with duplex data encryption algorithm. In 5th International Conference on Computing Methodologies and Communication 252–256. https://doi.org/10.1109/ICCMC51019.2021.9418247 [Google Scholar] [Crossref]

14. Susmitha, C., Kumar, S. K., & Bulla, S. (2023). Hybrid cryptography for secure file storage. In 7th International Conference on Computing Methodologies and Communication (ICCMC). https://doi.org/10.1109/ICCMC56507.2023.10084073. [Google Scholar] [Crossref]

15. Yao, F. and Su, J., (2021). Hybrid Encryption Scheme for Hospital Financial Data Based on Noekeon Algorithm. Security and Communication Network. DOI: 10.1155/2021/7578752. [Google Scholar] [Crossref]

• Interplay of Students’ Emotional Intelligence and Attitude toward Mathematics on Performance in Grade 10 Algebra
• Numerical Simulation of Fitzhugh-Nagumo Dynamics Using a Finite Difference-Based Method of Lines
• Fixed Point Theorem in Controlled Metric Spaces
• Usage of Moving Average to Heart Rate, Blood Pressure and Blood Sugar
• Exploring Algebraic Topology and Homotopy Theory: Methods, Empirical Data, and Numerical Examples