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

Authors

  • Shahram Rasoolzadeh Radboud University, Nijmegen, The Netherlands

DOI:

https://doi.org/10.46586/tosc.v2023.i3.213-226

Keywords:

correlation immunity, resilient functions, Boolean functions

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.

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Published

2023-09-19

Issue

Section

Articles

How to Cite

Classification of All t-Resilient Boolean Functions with t + 4 Variables. (2023). IACR Transactions on Symmetric Cryptology, 2023(3), 213-226. https://doi.org/10.46586/tosc.v2023.i3.213-226