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An Optimized Real Time Generation of S-Box Inverses Using Arithmetic Modulo Powers of Two

Summary This paper proposes generation of entries of the S-Box using arithmetic modulo powers of two. The approach saves storage space and makes real time computations of the entries feasible. The inverse function used in the process is based on arithmetic modulo a power of two. The platform proposed for this project is modulo “2 n ” arithmetic which builds upon the hypothesis that the set of odd residues of “2 n ” forms a mathematical field. A first round optimization cuts the amount of required storage space by half. A second demonstrates that all entries of the S-Box could be derived from any of the remaining rows after the first round is completed; hence only a single row needs to be stored. For real time regeneration of the S-Box, each of the single row entries is unpacked into two digits. One array stores the most significant digits and other stores the least. The goal of this paper is therefore twofold: to enable real time computation of entries of the S-Box and to reduce the amount of stored information. The latter is small enough to reduce vulnerability and large enough to form a basis that enables real time generation of the complete S-Box.