Classification of All t-Resilient Boolean Functions with t + 4 Variables
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...
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| Format: | Article |
| Language: | English |
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Ruhr-Universität Bochum
2023-09-01
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| Series: | IACR Transactions on Symmetric Cryptology |
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| Online Access: | https://tosc.iacr.org/index.php/ToSC/article/view/11189 |
| Summary: | 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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| ISSN: | 2519-173X |