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

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 \2ⁿ - 1,\, 2ⁿ,\, 2ⁿ + 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\, for 4--15 character payloads, representing 99% improvement over previous RNS-based hybrids. It scales linearly in time and memory O(n), consumes only 21\,KB, and produces ciphertext entropy of 7.999\,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.