Addendum to Classification of All t-Resilient Boolean Functions with t + 4 Variables

Abstract

In ToSC 2023(3), Rasoolzadeh presented an algorithm for classifying (n−m)-resilient Boolean functions with n variables, up to extended variable-permutation equivalence, for a small given positive integer m and any positive integer n with n ≥ m. By applying this algorithm along with several speed-up techniques, he classified n-variable (n − 4)-resilient Boolean functions up to equivalence for any n ≥ 4. However, for m = 5, due to the large number of representative functions, he was unable to classify n-variable (n − 5)-resilient Boolean functions for n > 6. In this work, we apply this algorithm together with a technique to restrict the ANF degree to classify quadratic and cubic (n − 5)-resilient Boolean functions with n variables, up to the same equivalence. We show that there are only 131 quadratic representative functions for any n ≥ 8. Additionally, we show that there are 359 078 cubic representative functions for any n ≥ 14.

Keywords

• correlation immunity
• resilient functions
• Boolean functions