CryptoDB
Addendum to Classification of All t-Resilient Boolean Functions with t + 4 Variables: Classification of Quadratic and Cubic t-Resilient Boolean Functions with t + 5 Variables
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| 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. |
BibTeX
@article{tosc-2024-34495,
title={Addendum to Classification of All t-Resilient Boolean Functions with t + 4 Variables: Classification of Quadratic and Cubic t-Resilient Boolean Functions with t + 5 Variables},
journal={IACR Transactions on Symmetric Cryptology},
publisher={Ruhr-Universität Bochum},
volume={2024},
pages={298-301},
url={https://tosc.iacr.org/index.php/ToSC/article/view/11818},
doi={10.46586/tosc.v2024.i3.298-301},
author={Shahram Rasoolzadeh},
year=2024
}