Algorithm for Generating S-Boxes with Prescribed Differential Properties
Cryptographic S-boxes are vectorial Boolean functions that must fulfill strict criteria to provide security for cryptographic algorithms. There are several existing methods for generating strong cryptographic S-boxes, including stochastic search algorithms. These search algorithms typically generate...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Algorithms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1999-4893/16/3/157 |
| _version_ | 1797613908337360896 |
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| author | Stanislav Marochok Pavol Zajac |
| author_facet | Stanislav Marochok Pavol Zajac |
| author_sort | Stanislav Marochok |
| collection | DOAJ |
| description | Cryptographic S-boxes are vectorial Boolean functions that must fulfill strict criteria to provide security for cryptographic algorithms. There are several existing methods for generating strong cryptographic S-boxes, including stochastic search algorithms. These search algorithms typically generate random candidate Boolean functions (or permutations) that are improved during the search by examining the search space in a specific way. Here, we introduce a new type of stochastic algorithm for generating cryptographic S-boxes. We do not generate and then improve the Boolean function; instead, we build the vector of values incrementally. New values are obtained by randomized search driven by restrictions on the differential spectrum of the generated S-box. In this article, we formulate two new algorithms based on this new approach and study the better one in greater detail. We prove the correctness of the proposed algorithm and evaluate its complexity. The final part contains an experimental evaluation of the method. We show that the algorithm generates S-boxes with better properties than a random search. We believe that our approach can be extended in the future by adopting more advanced stochastic search methods. |
| first_indexed | 2024-03-11T07:02:18Z |
| format | Article |
| id | doaj.art-2e9a37a73deb4190ad8b9b3ff542a7b6 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-11T07:02:18Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-2e9a37a73deb4190ad8b9b3ff542a7b62023-11-17T09:09:22ZengMDPI AGAlgorithms1999-48932023-03-0116315710.3390/a16030157Algorithm for Generating S-Boxes with Prescribed Differential PropertiesStanislav Marochok0Pavol Zajac1Department of Computer Science and Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Ilkovičova 3, 812 19 Bratislava, SlovakiaDepartment of Computer Science and Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Ilkovičova 3, 812 19 Bratislava, SlovakiaCryptographic S-boxes are vectorial Boolean functions that must fulfill strict criteria to provide security for cryptographic algorithms. There are several existing methods for generating strong cryptographic S-boxes, including stochastic search algorithms. These search algorithms typically generate random candidate Boolean functions (or permutations) that are improved during the search by examining the search space in a specific way. Here, we introduce a new type of stochastic algorithm for generating cryptographic S-boxes. We do not generate and then improve the Boolean function; instead, we build the vector of values incrementally. New values are obtained by randomized search driven by restrictions on the differential spectrum of the generated S-box. In this article, we formulate two new algorithms based on this new approach and study the better one in greater detail. We prove the correctness of the proposed algorithm and evaluate its complexity. The final part contains an experimental evaluation of the method. We show that the algorithm generates S-boxes with better properties than a random search. We believe that our approach can be extended in the future by adopting more advanced stochastic search methods.https://www.mdpi.com/1999-4893/16/3/157S-boxdifferential spectrumsearch algorithmstochastic search |
| spellingShingle | Stanislav Marochok Pavol Zajac Algorithm for Generating S-Boxes with Prescribed Differential Properties Algorithms S-box differential spectrum search algorithm stochastic search |
| title | Algorithm for Generating S-Boxes with Prescribed Differential Properties |
| title_full | Algorithm for Generating S-Boxes with Prescribed Differential Properties |
| title_fullStr | Algorithm for Generating S-Boxes with Prescribed Differential Properties |
| title_full_unstemmed | Algorithm for Generating S-Boxes with Prescribed Differential Properties |
| title_short | Algorithm for Generating S-Boxes with Prescribed Differential Properties |
| title_sort | algorithm for generating s boxes with prescribed differential properties |
| topic | S-box differential spectrum search algorithm stochastic search |
| url | https://www.mdpi.com/1999-4893/16/3/157 |
| work_keys_str_mv | AT stanislavmarochok algorithmforgeneratingsboxeswithprescribeddifferentialproperties AT pavolzajac algorithmforgeneratingsboxeswithprescribeddifferentialproperties |