On the affine equivalence relation between two classes of Boolean functions with optimal algebraic immunity

Authors:
Huajin Chen;Tian Tian;Wenfeng Qi
Affiliations:
Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, China 450002;Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, China 450002;Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, China 450002
Venue:
Designs, Codes and Cryptography
Year:
2013

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Abstract

Recently, two classes of Boolean functions with optimal algebraic immunity have been proposed by Carlet et al. and Wang et al., respectively. Although it appears that their methods are very different, it is proved in this paper that the two classes of Boolean functions are in fact affine equivalent. Moreover, the number of affine equivalence classes of these functions is also studied.