In the evaluation of the randomness of an S-box, measures of resistance to higher order cryptanalysis, interpolation cryptanalysis, partitioning cryptanalysis and differential-linear cryptanalysis and necessary conditions for those measures to have resistance to each cryptanalysis are set, then for functions as candidates for the S-box, it is evaluated whether one or all of the conditions are satisfied, and those of the candidate functions for which one or all of the conditions are satisfied are selected as required. It is also possible to further evaluate the resistance of such selected functions to at least one of differential cryptanalysis and linear cryptanalysis and select those of the candidate functions which are resistant to at least one of the cryptanalyses as required.