A Systematic Review of Modular Exponentiation Acceleration for Smart Card Security: Methods, Architectures, and Future Research Directions

Abstract

Modular exponentiation is a fundamental operation underlying public-key cryptographic algorithms such as RSA, Diffie–Hellman, and certain implementations of Elliptic Curve Cryptography (ECC). In resource-constrained smart card environments, achieving efficient and secure execution of this operation is critical due to limitations in memory, power, and computational capacity. This systematic review analyzes advancements in modular exponentiation acceleration techniques based on 30 peer-reviewed studies selected through structured criteria. The findings categorize approaches into algorithmic optimizations, hardware-based acceleration, security-focused techniques, hybrid methods, and emerging AI-driven strategies. Hardware solutions offer significant performance gains through parallelism, while algorithmic methods reduce computational complexity in software implementations. However, side-channel attacks—such as timing and power analysis—remain a major concern, necessitating countermeasures like masking and constant-time execution, often at the cost of added overhead. Hybrid approaches emerge as the most effective, balancing performance and security. The review also highlights key trade-offs and identifies research gaps, including limited real-world validation and lack of unified optimization frameworks, emphasizing the need for adaptive, efficient, and secure future solutions.