Efficient Fine-Grained LuT-Based Optimization of AES MixColumns and InvMixColumns for FPGA Implementation

This paper presents fine-grained Field Programmable Gate Arrays (FPGA) architectures for the Advanced Encryption Standard (AES) MixColumns and InvMixColumns transformations, targeting improved performance and resource utilization. The proposed method reformulates these operations as boolean functions directly mapped onto FPGA Lookup-Table (LuT) primitives, replacing conventional xor-based arithmetic with memory-level computation. A custom MATLAB-R2019a-based pre-synthesis optimization algorithm performs algebraic simplification and shared subexpression extraction at the polynomial level of Galois Field $GF\left(2^8\right)$, reducing redundant logic memory. This architecture, LuT-level optimization minimizes the delay of the complex InvMixColumns stage and narrows the delay gap between encryption (1.305 ns) and decryption (1.854 ns), resulting in a more balanced and power-efficient AES pipeline. Hardware implementation on a Xilinx Virtex-5 FPGA confirms the efficiency of the design, demonstrating competitive performance compared to state-of-the-art FPGA realizations. Its fast performance and minimal hardware requirements make it well suited for real-time secure communication systems and embedded platforms with limited resources that need reliable bidirectional data processing.