American Institute of Mathematical Sciences

Advanced
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

[1]

Ayça Çeşmelioǧlu, Wilfried Meidl, Alexander Pott. On the dual of (non)-weakly regular bent functions and self-dual bent functions. Advances in Mathematics of Communications, 2013, 7 (4) : 425-440. doi: 10.3934/amc.2013.7.425
[2]

Constanza Riera, Pantelimon Stănică. Landscape Boolean functions. Advances in Mathematics of Communications, 2019, 13 (4) : 613-627. doi: 10.3934/amc.2019038
[3]

SelÇuk Kavut, Seher Tutdere. Highly nonlinear (vectorial) Boolean functions that are symmetric under some permutations. Advances in Mathematics of Communications, 2020, 14 (1) : 127-136. doi: 10.3934/amc.2020010
[4]

Sihong Su. A new construction of rotation symmetric bent functions with maximal algebraic degree. Advances in Mathematics of Communications, 2019, 13 (2) : 253-265. doi: 10.3934/amc.2019017
[5]

Wenying Zhang, Zhaohui Xing, Keqin Feng. A construction of bent functions with optimal algebraic degree and large symmetric group. Advances in Mathematics of Communications, 2020, 14 (1) : 23-33. doi: 10.3934/amc.2020003
[6]

Claude Carlet, Serge Feukoua. Three basic questions on Boolean functions. Advances in Mathematics of Communications, 2017, 11 (4) : 837-855. doi: 10.3934/amc.2017061
[7]

Sihem Mesnager, Gérard Cohen. Fast algebraic immunity of Boolean functions. Advances in Mathematics of Communications, 2017, 11 (2) : 373-377. doi: 10.3934/amc.2017031
[8]

Claude Carlet, Khoongming Khoo, Chu-Wee Lim, Chuan-Wen Loe. On an improved correlation analysis of stream ciphers using multi-output Boolean functions and the related generalized notion of nonlinearity. Advances in Mathematics of Communications, 2008, 2 (2) : 201-221. doi: 10.3934/amc.2008.2.201
[9]

Claude Carlet, Fengrong Zhang, Yupu Hu. Secondary constructions of bent functions and their enforcement. Advances in Mathematics of Communications, 2012, 6 (3) : 305-314. doi: 10.3934/amc.2012.6.305
[10]

Jacques Wolfmann. Special bent and near-bent functions. Advances in Mathematics of Communications, 2014, 8 (1) : 21-33. doi: 10.3934/amc.2014.8.21
[11]

Jyrki Lahtonen, Gary McGuire, Harold N. Ward. Gold and Kasami-Welch functions, quadratic forms, and bent functions. Advances in Mathematics of Communications, 2007, 1 (2) : 243-250. doi: 10.3934/amc.2007.1.243
[12]

Kanat Abdukhalikov, Sihem Mesnager. Explicit constructions of bent functions from pseudo-planar functions. Advances in Mathematics of Communications, 2017, 11 (2) : 293-299. doi: 10.3934/amc.2017021
[13]

Sihem Mesnager, Fengrong Zhang. On constructions of bent, semi-bent and five valued spectrum functions from old bent functions. Advances in Mathematics of Communications, 2017, 11 (2) : 339-345. doi: 10.3934/amc.2017026
[14]

Jian Liu, Sihem Mesnager, Lusheng Chen. Variation on correlation immune Boolean and vectorial functions. Advances in Mathematics of Communications, 2016, 10 (4) : 895-919. doi: 10.3934/amc.2016048
[15]

Samir Hodžić, Enes Pasalic. Generalized bent functions -sufficient conditions and related constructions. Advances in Mathematics of Communications, 2017, 11 (3) : 549-566. doi: 10.3934/amc.2017043
[16]

Claude Carlet, Juan Carlos Ku-Cauich, Horacio Tapia-Recillas. Bent functions on a Galois ring and systematic authentication codes. Advances in Mathematics of Communications, 2012, 6 (2) : 249-258. doi: 10.3934/amc.2012.6.249
[17]

Ayça Çeşmelioğlu, Wilfried Meidl. Bent and vectorial bent functions, partial difference sets, and strongly regular graphs. Advances in Mathematics of Communications, 2018, 12 (4) : 691-705. doi: 10.3934/amc.2018041
[18]

Joan-Josep Climent, Francisco J. García, Verónica Requena. On the construction of bent functions of $n+2$ variables from bent functions of $n$ variables. Advances in Mathematics of Communications, 2008, 2 (4) : 421-431. doi: 10.3934/amc.2008.2.421
[19]

Leon Ehrenpreis. Special functions. Inverse Problems & Imaging, 2010, 4 (4) : 639-647. doi: 10.3934/ipi.2010.4.639
[20]

Yu Zhou. On the distribution of auto-correlation value of balanced Boolean functions. Advances in Mathematics of Communications, 2013, 7 (3) : 335-347. doi: 10.3934/amc.2013.7.335

2018 Impact Factor: 0.879

Tools

Metrics

  • PDF downloads (19)
  • HTML views (7)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences