NDLI: Cubic Monomial Bent Functions: A Subclass of $\mathcal{M}$

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Kyureghyan, Gohar M. Charpin, Pascale
Copyright Year	2008
Abstract	Based on a computer search, Anne Canteaut conjectured that the exponent $2^{2r}+2^r+1$ in ${\bf F}_{2^{6r}}$ and the exponent $(2^{r}+1)^2$ in ${\bf F}_{2^{4r}}$ yield bent monomial functions. These conjectures are proved in [A. Canteaut, P. Charpin, and G. Kyureghyan, A new class of monomial bent functions, in Proceedings of the 2006 IEEE International Symposium on Information Theory, (ISIT 06 Seattle), IEEE Press, Piscataway, NJ, 2006, pp. 903906] and [N. G. Leander, IEEE Trans. Inform. Theory, 52 (2006), pp. 738743]. Both exponents are of binary weight 3 and define functions from the MaioranaMcFarland class $\mathcal{M}$ of bent functions to the subfield. In this paper we show that these are the only such exponents. Our proof is based on the classification of the permutation binomials $X^{2^k+2}+ \nu X$ of finite fields of even characteristics. We also extend the result of Leander, determining all bent monomial functions with the exponent $(2^{r}+1)^2$.
Starting Page	650
Ending Page	665
Page Count	16
File Format	PDF
ISSN	08954801
DOI	10.1137/060677768
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	2
Volume Number	22
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2008-03-28
Access Restriction	Subscribed
Subject Keyword	MaioranaMcFarland family of bent functions General Algebraic coding theory; cryptography Polynomials monomial Boolean function permutation polynomial cubic bent function
Content Type	Text
Resource Type	Article
Subject	Mathematics

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