Biblio

In this paper, we propose a very fast, yet compact, AES S-box, by applying two techniques to a composite field \$GF((2ˆ4)ˆ2)\$ fast AES S-box. The composite field fast S-box has three main components, namely the input transformation matrix, the inversion circuit, and the output transformation matrix. The core inversion circuit computes the multiplicative inverse over the composite field \$GF((2ˆ4)ˆ2)\$ and consists of three arithmetic blocks over subfield \$GF(2ˆ4)\$, namely exponentiation, subfield inverter, and output multipliers. For the first technique, we consider multiplication of the input of the composite field fast S-box by 255 nonzero 8-bit binary field elements. The multiplication constant increases the variety of the input and output transformation matrices of the S-box by a factor of 255, hence increasing the search space of the logic minimization algorithm correspondingly. For the second technique, we reduce the delay of the composite field fast S-box, by combining the output multipliers and the output transformation matrix. Moreover, we modify the architecture of the input transformation matrix and re-design the exponentiation block and the subfield inverter for lower delay and area. We find that 8 unique binary transformation matrices could be used to change from the binary field \$GF(2ˆ8)\$ to the composite field \$GF((2ˆ4)ˆ2)\$ at the input of the composite field S-box. We use Matla \$\textbackslashtextbackslashmathbfb\$ ® to derive all \$(255\textbackslashtextbackslashtimes 8=2040)\$ new input transformation matrices. We search the matrices for the fastest and lowest complexity implementation and the minimal one is selected for the proposed fast S-box. The proposed fast S-box is 24% faster (with 5% increase in area) than the composite field fast design and 10% faster (with about 1% increase in area) than the fastest S-box available in the literature, to the best of our knowledge.