The memory-less method of generating multiplicative inverse values for S-box in AES algorithm

The substitution box (S-box) component is the heart of the advanced encryption standard (AES) algorithm. The S-box values are generated from the multiplicative inverse of Galois finite field GF(2⁸) with an affine transform. There are many techniques of gaining the multiplicative inverse values were proposed. Most of the hardware implementations of S-box were using look-up tables (LUTs) (memory-based) to store the values which employ the largest area in design. In this paper, a software method of producing the multiplicative inverse values, which is the generator of S-box values and the possibilities of implementing the methods in hardware applications will be discussed. The method is using the log and antilog values. The method is modified to create a memory-less value generator in AES hardware-based implementation. The implementation is proposed to embed on limited memory, small-sized FPGA.