  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.
