The Bent and Hyper-Bent Properties of a Class of Boolean Functions
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32797
The Bent and Hyper-Bent Properties of a Class of Boolean Functions

Authors: Yu Lou, Chunming Tang, Yanfeng Qi, Maozhi Xu

Abstract:

This paper considers the bent and hyper-bent properties of a class of Boolean functions. For one case, we present a detailed description for them to be hyper-bent functions, and give a necessary condition for them to be bent functions for another case.

Keywords: Boolean functions, bent functions, hyper-bent functions, character sums.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1337399

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1186

References:


[1] C. Tang, Y. Qi, M. Xu, B. Wang and Y. Yang, A new class of hyper-bent Boolean functions in binomial forms, http://eprintweb.org/S/article/cs/1112.0062.
[2] A. Canteaut, P. Charpin and G. Kyureghyan, A new class of monomial bent functions, Finite Fields Applicat., vol. 14, no. 1, pp 221-241, 2008.
[3] H. Dobbertin and G. Leander, A survey of some recent results on bent functions, in T. Helleseth et al. (eds.) Sequences and Their Applications, LNCS 3486, pp. 1-29, Springer, Heidelberg, 2004.
[4] P. Charpin and G. Gong , Hyperbent functions, Kloosterman sums and Dickson polynomials, IEEE Trans. Inf. Theory, vol. 9, no. 54, pp 4230-4238, 2008.
[5] G. Lachaud and J. Wolfmann, The weights of the orthogonal of the extended quadratic binary Goppa codes, IEEE Trans. Inform. Theory, 36, pp. 686-692, 1990.
[6] S. Mesnager, A new class of bent boolean functions in polynomial forms, in Proc. Int. Workshop on Coding and Cryptography, WCC 2009, 2009, pp. 5-18.
[7] S. Mesnager, A new class of bent and hyper-bent boolean functions in polynomial forms, Des. Codes Cryptography, 59(1-3), 265-279, 2011
[8] S. Mesnager, A new family of hyper-bent Boolean functions in polynomial form, IMACC 2009, LNCS 5921, pp 402-417, 2009.
[9] O. Rothaus, On bent functions, J. Combin. Theory, ser. A, vol. 20, pp. 300-305, 1976.
[10] A. Youssef and G. Gong, Hyper-bent functions, in Advances in Crypology-Eurocrypt‘01, LNCS, pp. 406-419, 2001.
[11] M. Le, On the number of solutions of the generalized Ramanujan-Nagell equation x2−D = 2n+2, ACTA ARITHMETICA, LX.2, pp. 149-167, 1991.