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Journal of Multimedia Processing and Technologies

Constructing Bent Functions for Cryptography with Binary Functions

Milos Radmanovic
Faculty of Electronic Engineering & Aleksandra Medvedeva 14, 18000 Nis, Serbia

Abstract: We in this paper deal with Bent functions which are essential for cryptographic binary functions. These functions make very small subset of the total number of bent functions, especially for large number of variables. We do not find any formal method for construction of bent functions. Hence the methods for construction of bent functions are obtained by using the discovery of bent functions within a group of functions. For experimenting the bentness across a group of functions, even for small numbers of variables, requires a lot of processing time. We in this work introduced an efficient method for bentness testing of binary functions using statistical analysis of binary functions. The standard method for bentness testing is based on the usage of the fast Walsh transform calculations. This method uses conditional testing of the initial set of particular Walsh coefficients. In the current work, the selection of coefficients for conditional testing is determined using statistical analysis of binary functions.

Keywords: Cryptography, Binary Function, Bent, Walsh Transform, Statistical Method Constructing Bent Functions for Cryptography with Binary Functions

DOI:https://doi.org/10.6025/jmpt/2020/11/3/95-101

Full_Text PDF 947 KB Download: 421 times

References:

[1] Tokareva, N. (2015). Bent Functions, Results and Applications to Cryptography, Academic Press, 2015.
[2] Mesnager, S. (2016). Bent Functions, Fundamentals and Results. Springer International Publishing.
[3] Seberry, J., Zhang, X. (1994). Constructions of bent functions from two known bent functions, Australasian Journal of Combinatorics. vol. 9, p. 21-34.
[4] Langevin, P., Leander, G. (2011). Counting all bent functions in dimensions eight 99270589265934370305785861242880, Designs, Codes and Cryptography vol. 59, p. 193-201.
[5] Grocholewska-Czurylo, A., Stoklosa, J. (2002). Generating bent functions, Proc. Advanced Computer Systems Eighth International Conference, ACS2001, p. 361-370. Springer US, Mielno, Poland.
[6] Thornton, M. A., Drechsler, R., Miller, D. M. (2001). Spectral Techniques in VLSI CAD, Springer.
[7] Radmanovic, M., Stankovic, R. (2016). Random generation of bent functions on multicore CPU platform. Proc. ICEST 2016, p. 239-242. Ohrid, Macedonia.
[8] Radmanovic, M. (2016). Efficient random generation of bent functions using GPU platform, Proc. 12th Int. Workshop on Boolean Problems, IWSBP2016, p. 167-173. Freiberg, Germany.

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