On Symmetric Boolean Functions With High Algebraic Immunity on Even Number of Variables

In this paper, we put forward an efficient method to study the symmetric Boolean functions with high algebraic immunity on even number of variables. We obtain some powerful necessary conditions for symmetric Boolean functions to achieve high algebraic immunity by studying the weight support of some...

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Bibliographic Details
Published in:IEEE transactions on information theory 2011-10, Vol.57 (10), p.7205-7220
Main Authors: Peng, Jie, Wu, Quanshui, Kan, Haibin
Format: Article
Language:English
Subjects:
Algebra
Algebraic attack
algebraic degree
algebraic immunity
Applied sciences
Artificial intelligence
Boolean functions
Correlation
Correlation analysis
Cryptography
Education
Exact sciences and technology
Hamming weight
Information theory
Information, signal and communications theory
Measurement
nonlinearity
Optimization algorithms
Signal and communications theory
stream cipher
symmetric Boolean function
Telecommunications and information theory
Variables
weight support
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Summary:In this paper, we put forward an efficient method to study the symmetric Boolean functions with high algebraic immunity on even number of variables. We obtain some powerful necessary conditions for symmetric Boolean functions to achieve high algebraic immunity by studying the weight support of some specific types of Boolean functions of low degrees. With these results, we prove that the algebraic immunity of a large class of symmetric correlation immune Boolean functions, namely the symmetric palindromic functions, is not high. Besides, we construct all symmetric Boolean functions with maximum algebraic immunity and give a description for those with submaximum algebraic immunity. We also determine the Hamming weight, degrees and nonlinearity of the symmetric Boolean functions with maximum algebraic immunity.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2011.2132113