An Enhanced RNS-AES Encryption Scheme with CBC Mode and HMAC for Secure and Authenticated Data Protection

  • Stephen Akobre Department of Cyber Security and Computer Engineering Technology, C. K. Tedam University of Technology & Applied Sciences, Navrongo, Ghana
  • Japheth Kodua Wiredu Department of Computer Science, Regentropfen University College, Bolgatanga, Ghana
  • Mohammed Ibrahim Daabo Department of Computer Science, C. K. Tedam University of Technology & Applied Sciences, Navrongo, Ghana
  • Moses Apambila Agebure Department of Computer Science, C. K. Tedam University of Technology & Applied Sciences, Navrongo, Ghana
Keywords: residue number system, advanced encryption standard, cipher block chaining mode, hash based message authentication code, Chinese remainder theorem

Abstract

Modern cryptographic systems in cloud and IoT environments must balance strong security with real-time performance, yet existing methods often require trade-offs that sacrifice speed for security or introduce latency through conservative designs. This paper presents RNS-AES-CBC-HMAC, a hybrid framework that integrates Residue Number System (RNS) arithmetic with AES-256 and HMAC-SHA256 to deliver both performance and robust security. Using a balanced modulus set $\{2^n - 1,\, 2^n,\, 2^n + 1\}$ for constant-time, carry-free arithmetic mitigates side-channel risks, while AES-256 in Cipher Block Chaining (CBC) mode ensures confidentiality and HMAC-SHA256 provides message integrity with minimal overhead. Implemented in Python 3.10 with PyCryptodome 3.18.0 and tested on an AMD Ryzen~5~2500U, the framework achieved encryption/decryption latencies of $55$--$593\,\mu\text{s}$ for 4--15 character payloads, representing 99\% improvement over previous RNS-based hybrids. It scales linearly in time and memory $\mathcal{O}(n)$, consumes only $21\,\text{KB}$, and produces ciphertext entropy of $7.999\,\text{bits/byte}$, surpassing NIST SP~800-22 standards. This dual-layer architecture effectively counters both passive and active threats, making it suitable for low-latency IoT edge devices and high-throughput cloud systems, merging theoretical number systems with practical cryptography for real-world deployment.

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Published
2025-10-05
How to Cite
Akobre, S., Wiredu, J. K., Daabo, M. I., & Agebure, M. A. (2025). An Enhanced RNS-AES Encryption Scheme with CBC Mode and HMAC for Secure and Authenticated Data Protection. Earthline Journal of Mathematical Sciences, 15(6), 1091-1112. https://doi.org/10.34198/ejms.15625.10911112
Section
Articles