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 |
| _version_ | 1827814055314718720 |
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| author | Shahram Rasoolzadeh |
| author_facet | Shahram Rasoolzadeh |
| author_sort | Shahram Rasoolzadeh |
| collection | DOAJ |
| description |
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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| first_indexed | 2024-03-11T23:40:21Z |
| format | Article |
| id | doaj.art-e5ad7a1d4903407dbca7f138aa7edaac |
| institution | Directory Open Access Journal |
| issn | 2519-173X |
| language | English |
| last_indexed | 2024-03-11T23:40:21Z |
| publishDate | 2023-09-01 |
| publisher | Ruhr-Universität Bochum |
| record_format | Article |
| series | IACR Transactions on Symmetric Cryptology |
| spelling | doaj.art-e5ad7a1d4903407dbca7f138aa7edaac2023-09-19T16:03:49ZengRuhr-Universität BochumIACR Transactions on Symmetric Cryptology2519-173X2023-09-012023310.46586/tosc.v2023.i3.213-226Classification of All t-Resilient Boolean Functions with t + 4 VariablesShahram Rasoolzadeh0Radboud University, Nijmegen, The Netherlands 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. https://tosc.iacr.org/index.php/ToSC/article/view/11189correlation immunityresilient functionsBoolean functions |
| spellingShingle | Shahram Rasoolzadeh Classification of All t-Resilient Boolean Functions with t + 4 Variables IACR Transactions on Symmetric Cryptology correlation immunity resilient functions Boolean functions |
| title | Classification of All t-Resilient Boolean Functions with t + 4 Variables |
| title_full | Classification of All t-Resilient Boolean Functions with t + 4 Variables |
| title_fullStr | Classification of All t-Resilient Boolean Functions with t + 4 Variables |
| title_full_unstemmed | Classification of All t-Resilient Boolean Functions with t + 4 Variables |
| title_short | Classification of All t-Resilient Boolean Functions with t + 4 Variables |
| title_sort | classification of all t resilient boolean functions with t 4 variables |
| topic | correlation immunity resilient functions Boolean functions |
| url | https://tosc.iacr.org/index.php/ToSC/article/view/11189 |
| work_keys_str_mv | AT shahramrasoolzadeh classificationofalltresilientbooleanfunctionswitht4variables |