For Full-Text PDF, please login, if you are a member of IEICE,|
or go to Pay Per View on menu list, if you are a nonmember of IEICE.
On the Nonlinearity and Affine Equivalence Classes of C-F Functions
Lei SUN Fangwei FU Xuang GUANG
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2016/06/01
Online ISSN: 1745-1337
Type of Manuscript: LETTER
Category: Cryptography and Information Security
Boolean functions, algebraic attacks, algebraic immunity, affine equivalence,
Full Text: PDF>>
Since 2008, three different classes of Boolean functions with optimal algebraic immunity have been proposed by Carlet and Feng , Wang et al. and Chen et al.. 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.