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In this paper we study the lower bounds of second-order nonlinearities of bent functions in the class D_0 constructed by modifying certain cubicMaiorana-McFarland (MMF) type bent functions. We also obtain improvements on existing results on second-order nonlinearities of some cubic MMF type bent functions having no affine derivative.
Wydawca
Czasopismo
Rocznik
Tom
Strony
271--285
Opis fizyczny
Bibliogr. 14 poz., tab.
Twórcy
autor
autor
- Department of Mathematics Indian Institute of Technology Roorkee Roorkee 247667 India, gsugata@gmail.com
Bibliografia
- [1] C. Bracken, E. Byrne, N. Markin and Gary MacGuire, Determining the Nonlinearity a New Family of APN Functions, AAECC, LNCS 4851, Springer, 2007, pp. 72-79.
- [2] A. Canteaut, P. Charpin and G. M. Kyureghyan, A new class of monomial bent functions, Finite Fields and their Applications 14 (2008) 221-241.
- [3] C. Carlet, Two new classes of bent functions, in Proc. EUROCRYPT '93, LNCS vol. 765, Springer, 1994, pp. 77-101.
- [4] C. Carlet, The complexity of Boolean functions from cryptographic viewpoint, Proc. Dagstuhl Seminar Complexity of Boolean Functions, 2006, pp. 15
- [5] C. Carlet, Recursive lower bounds on the nonlinearity profile of Boolean functions and their applications, IEEE Trans. Inform. Theory 54 (3) (2008) 1262-1272.
- [6] G. Cohen, I. Honkala, S. Litsyn and A. Lobstein, Covering Codes, North- Holland, 1997.
- [7] N. Courtois, Higher order correlation attacks, XL algorithm and cryptanalysis of Toyocrypt, in: Proceedings of the ICISC'02, LNCS, vol. 2587, Springer, 2002, pp. 182-199.
- [8] R. Fourquet and C. Tavernier, An improved list decoding algorithm for the second-order Reed Muller codes and its applications, Designs Codes and Cryptography 49 (2008) 323-340.
- [9] J. Golić, Fast low order approximation of cryptographic functions, in: Proceedings of the EUROCRYPT'96, LNCS, vol. 1996, Springer, 1996, pp. 268-282.
- [10] S. Gangopadhyay, S. Sarkar and R. Telang, On the lower bounds of the second-order nonlinearities of some Boolean functions, Information Sciences 180 (2010) 266-273.
- [11] F. J. MacWilliams and N. J. A. Sloane, The theory of error correcting codes, North-Holland, Amsterdam, 1977.
- [12] O. S. Rothaus, On bent functions, Journal of Combinatorial Theory, Series A, 20 (1976), 300-305.
- [13] S. Sarkar and S. Gangopadhyay, On the Second Order Nonlinearity of a Cubic Maiorana-McFarland Bent Function, Finite Fields and their Applications, Fq 9, Dublin, Ireland, July 13-17, 2009.
- [14] G. Sun and C. Wu, The lower bounds on the second-order nonlinearity of three classes of Boolean functions with high nonlinearity, Information Sciences 179 (3) (2009) 267-278.
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Bibliografia
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bwmeta1.element.baztech-article-BUS8-0024-0018