Boolean functions optimizing most of the cryptographic criteria

Authors:
Ziran Tu;Yingpu Deng
Affiliations:
Faculty of Science, Henan University of Science and Technology, Luoyang 471003, People's Republic of China;Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
Venue:
Discrete Applied Mathematics
Year:
2012

Citing 18
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Note: Balanced Boolean functions with optimum algebraic degree, optimum algebraic immunity and very high nonlinearity

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Abstract

In this paper, we construct a class of 2k-variable Boolean functions which have optimal algebraic degree, very high nonlinearity, optimal algebraic immunity, and are 1-resilient. These properties are unconditional except the algebraic immunity property, which is optimal under some unproven assumptions. However, since the assumptions are verified to be true for k@?29, so these functions have optimal algebraic immunity at least for k@?29.