The design method of compact composite field aes S-box based on AND-XOR array structure

Among different implementations of Advanced Encryption Standard (AES) S-box, the implementations based on composite field arithmetic (CFA) technologies have the smallest size. In this paper, multiplication inverse over GF(2⁸) in AES S-boxes is mapped into GF((2⁴)²). To further optimize the multiplication inverse over GF((2⁴)²), the multiplications and multiplicative inverses over GF(2⁴) are constructed with AND-XOR-array structures. The hardware complexities analysis shows that AND-XOR-array structure has smaller area and shorter critical path. To find the optimal structures of composite field GF((2⁴)²) for S-box, the hardware complexities of total 768 different composite field S-box structures are analyzed. Compared with the previous works, the designs proposed in this work achieve the shortest critical path delay, and the area cost of them is smaller than most of the works.