Construction of Optimum Composite Field Architecture for Compact High-Throughput AES S-Boxes

In this work, we derive three novel composite field arithmetic (CFA) Advanced Encryption Standard (AES) S-boxes of the field GF(((2²)²)²). The best construction is selected after a sequence of algorithmic and architectural optimization processes. Furthermore, for each composite field constructions, there exists eight possible isomorphic mappings. Therefore, after the exploitation of a new common subexpression elimination algorithm, the isomorphic mapping that results in the minimal implementation area cost is chosen. High throughput hardware implementations of our proposed CFA AES S-boxes are reported towards the end of this paper. Through the exploitation of both algebraic normal form and seven stages fine-grained pipelining, our best case achieves a throughput 3.49 Gbps on a Cyclone II EP2C5T144C6 field-programmable gate array.