Further constructions of bent functions and their duals
Abstract In 2012, Carlet et al. developed two secondary constructions of bent functions (Advances in Mathematics of Communications, 6: 305‐314) and proposed some applications for their constructions. However, the duals of bent functions in their constructions were not presented. In order to find mor...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Online Access: | https://doi.org/10.1049/ise2.12006 |
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| author | Yanjun Li Jie Peng Chik How Tan Haibin Kan Lijing Zheng |
| author_facet | Yanjun Li Jie Peng Chik How Tan Haibin Kan Lijing Zheng |
| author_sort | Yanjun Li |
| collection | DOAJ |
| description | Abstract In 2012, Carlet et al. developed two secondary constructions of bent functions (Advances in Mathematics of Communications, 6: 305‐314) and proposed some applications for their constructions. However, the duals of bent functions in their constructions were not presented. In order to find more general applications to these constructions and obtain new classes of bent functions, an open problem was proposed by Carlet in 2014. Hence, in this study, a class of PS vectorial bent functions for answering that open problem, which also addresses another open problem on vectorial bent functions proposed by Mesnager in 2014, is constructed. In addition, a new secondary construction of bent functions that generalises one of Carlet et al.'s constructions in 2012 is presented. Based on that, two new classes of bent functions were obtained and their duals were presented explicitly. In particular, some self‐dual bent functions are constructed. Moreover, it can be proved that our bent functions can be EA‐inequivalent to those constructed by Carlet et al. in 2012. |
| format | Article |
| id | doaj-art-5fa25daebf344797850a5c6144c89d7b |
| institution | Kabale University |
| issn | 1751-8709 1751-8717 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | IET Information Security |
| spelling | doaj-art-5fa25daebf344797850a5c6144c89d7b2025-02-03T06:47:25ZengWileyIET Information Security1751-87091751-87172021-01-01151879710.1049/ise2.12006Further constructions of bent functions and their dualsYanjun Li0Jie Peng1Chik How Tan2Haibin Kan3Lijing Zheng4Mathematics and Science College, Shanghai Normal University Shanghai ChinaMathematics and Science College, Shanghai Normal University Shanghai ChinaTemasek Laboratories, National University of Singapore Singapore SingaporeShanghai Key Laboratory of Intelligent Information Processing, School of Computer Sciences Fudan University Shanghai ChinaSchool of Mathematics and Physics University of South China Hengyang Hunan ChinaAbstract In 2012, Carlet et al. developed two secondary constructions of bent functions (Advances in Mathematics of Communications, 6: 305‐314) and proposed some applications for their constructions. However, the duals of bent functions in their constructions were not presented. In order to find more general applications to these constructions and obtain new classes of bent functions, an open problem was proposed by Carlet in 2014. Hence, in this study, a class of PS vectorial bent functions for answering that open problem, which also addresses another open problem on vectorial bent functions proposed by Mesnager in 2014, is constructed. In addition, a new secondary construction of bent functions that generalises one of Carlet et al.'s constructions in 2012 is presented. Based on that, two new classes of bent functions were obtained and their duals were presented explicitly. In particular, some self‐dual bent functions are constructed. Moreover, it can be proved that our bent functions can be EA‐inequivalent to those constructed by Carlet et al. in 2012.https://doi.org/10.1049/ise2.12006Boolean functions |
| spellingShingle | Yanjun Li Jie Peng Chik How Tan Haibin Kan Lijing Zheng Further constructions of bent functions and their duals IET Information Security Boolean functions |
| title | Further constructions of bent functions and their duals |
| title_full | Further constructions of bent functions and their duals |
| title_fullStr | Further constructions of bent functions and their duals |
| title_full_unstemmed | Further constructions of bent functions and their duals |
| title_short | Further constructions of bent functions and their duals |
| title_sort | further constructions of bent functions and their duals |
| topic | Boolean functions |
| url | https://doi.org/10.1049/ise2.12006 |
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