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On constructions of bent, semi-bent and five valued spectrum functions from old bent functions
On construction of bent functions involving symmetric functions and their duals
| 1. | Department of Mathematics, University of Paris Ⅷ and Paris ⅩⅢ and Télécom ParisTech, LAGA, UMR 7539, CNRS, Sorbonne Paris Cité |
| 2. | School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China |
| 3. | State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an 710071, China |
In this paper, we firstly compute the dual functions of elementary symmetric bent functions. Next, we derive a new secondary construction of bent functions (given with their dual functions) involving symmetric bent functions, leading to a generalization of the well-know Rothaus' construction.
References:
| [1] |
C. Carlet, Boolean functions for cryptography and error correcting codes, in Boolean Models
and Methods in Mathematics, Computer Science, and Engineering (eds. Y. Crama and P.
Hammer), Cambridge Univ. Press, 2010,257-397.
doi: 10.1017/CBO9780511780448. |
| [2] |
C. Carlet and S. Mesnager,
Four decades of research on bent functions, Des. Codes Crypt., 78 (2016), 5-50.
doi: 10.1007/s10623-015-0145-8. |
| [3] |
S. Mesnager, Bent Functions: Fundamentals and Results, Springer-Verlag, 2016.
doi: 10.1007/978-3-319-32595-8.
|
| [4] |
O. S. Rothaus,
On "bent" functions, J. Combin. Theory Ser. A, 20 (1976), 300-305.
|
| [5] |
S. Mesnager and F. Zhang,
On constructions of bent, semi-bent and five valued spectrum functions from old bent functions, Adv. Math. Commun., 11 (2017), 339-345.
|
show all references
References:
| [1] |
C. Carlet, Boolean functions for cryptography and error correcting codes, in Boolean Models
and Methods in Mathematics, Computer Science, and Engineering (eds. Y. Crama and P.
Hammer), Cambridge Univ. Press, 2010,257-397.
doi: 10.1017/CBO9780511780448. |
| [2] |
C. Carlet and S. Mesnager,
Four decades of research on bent functions, Des. Codes Crypt., 78 (2016), 5-50.
doi: 10.1007/s10623-015-0145-8. |
| [3] |
S. Mesnager, Bent Functions: Fundamentals and Results, Springer-Verlag, 2016.
doi: 10.1007/978-3-319-32595-8.
|
| [4] |
O. S. Rothaus,
On "bent" functions, J. Combin. Theory Ser. A, 20 (1976), 300-305.
|
| [5] |
S. Mesnager and F. Zhang,
On constructions of bent, semi-bent and five valued spectrum functions from old bent functions, Adv. Math. Commun., 11 (2017), 339-345.
|
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