On the Nonlinearity and Affine Equivalence Classes of C-F Functions

Lei SUN  Fangwei FU  Xuang GUANG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E99-A   No.6   pp.1251-1254
Publication Date: 2016/06/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E99.A.1251
Type of Manuscript: LETTER
Category: Cryptography and Information Security
Keyword: 
Boolean functions,  algebraic attacks,  algebraic immunity,  affine equivalence,  

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Summary: 
Since 2008, three different classes of Boolean functions with optimal algebraic immunity have been proposed by Carlet and Feng [2], Wang et al.[8] and Chen et al.[3]. We call them C-F functions, W-P-K-X functions and C-T-Q functions for short. In this paper, we propose three affine equivalent classes of Boolean functions containing C-F functions, W-P-K-X functions and C-T-Q functions as a subclass, respectively. Based on the affine equivalence relation, we construct more classes of Boolean functions with optimal algebraic immunity. Moreover, we deduce a new lower bound on the nonlinearity of C-F functions, which is better than all the known ones.