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May  2017, 11(2): 347-352. doi: 10.3934/amc.2017027

On construction of bent functions involving symmetric functions and their duals

Sihem Mesnager 1, , Fengrong Zhang 2,3,, and  Yong Zhou 2,

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

* Corresponding author

Received  February 2016 Revised  March 2016 Published  May 2017

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.

Keywords: Boolean functions, symmetric functions, bent functions, dual functions, stream cipher.
Mathematics Subject Classification: 06E30, 94A60.
Citation: Sihem Mesnager, Fengrong Zhang, Yong Zhou. On construction of bent functions involving symmetric functions and their duals. Advances in Mathematics of Communications, 2017, 11 (2) : 347-352. doi: 10.3934/amc.2017027
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.  Google Scholar

[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.  Google Scholar

[3] S. Mesnager, Bent Functions: Fundamentals and Results, Springer-Verlag, 2016.  doi: 10.1007/978-3-319-32595-8.  Google Scholar
[4]

O. S. Rothaus, On "bent" functions, J. Combin. Theory Ser. A, 20 (1976), 300-305.   Google Scholar

[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.   Google Scholar

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.  Google Scholar

[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.  Google Scholar

[3] S. Mesnager, Bent Functions: Fundamentals and Results, Springer-Verlag, 2016.  doi: 10.1007/978-3-319-32595-8.  Google Scholar
[4]

O. S. Rothaus, On "bent" functions, J. Combin. Theory Ser. A, 20 (1976), 300-305.   Google Scholar

[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.   Google Scholar

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