Improved Algoritms in Parallel Evaluation of Large Cryptographic S-Box

Abstract: Nowadays computational complexity of fast walsh hadamard transform and nonlinearity for Boolean functions and large substitution boxes is a major challenge of modern cryptography research on strengthening encryption schemes against linear and differential attacks. Time and memory complexities of the best existing algorithm for computing fast walsh hadamard transform and non linearity for n x m substitution boxes (n >= 16;m >= 16) is O(2^n+m). This paper proposes three new acceleration methods that improve the computation time for parallelized walsh matrix up to 39 folds and the computation time for non linearity degree up to 563 folds, defining and accessing walsh matrix transpose, and incorporating an important part of computation process of non linearity in the computation algorithm of walsh matrix. The validity of the proposed algorithms is verified by means of simulation and experimentation and the overall analysis of resource consumption of proposed algorithms was compared with previous ones.