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

Abstract

We apply Siegenthaler’s construction, along with several techniques, to classify all (n−4)-resilient Boolean functions with n variables, for all values of n ≥ 4, up to the extended variable-permutation equivalence. We show that, up to this equivalence, there are only 761 functions for any n larger than or equal to 10, and for smaller values of n, i.e., for n increasing from 4 to 9, there are 58, 256, 578, 720, 754, and 760 functions, respectively. Furthermore, we classify all 1-resilient 6-variable Boolean functions and show that there are 1 035 596 784 such functions up to the extended variable-permutation equivalence.

Keywords

• correlation immunity
• resilient functions
• Boolean functions