On the Nonlinearity and Correlation Immunity of Two Classes of Boolean Functions
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Shaoyu Du,Meicheng Liu,Yin Zhang,Dongdai Lin. On the Nonlinearity and Correlation Immunity of Two Classes of Boolean Functions. International Journal of Software and Informatics, 2014,8(2):177~192
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Fund:Funding by the National 973 Program of China under Grant 2011CB302400, the National Basic Research of China under Grant 2013CB338002, the National Natural Science Foundation of China under Grant 61303258, the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant XDA06010701, and SKLOIS Research Project under Grant 2014-ZD-04.
Abstract:Recently, Liu et al. have proved a class of 2k-variable Boolean functions to have optimal algebraic immunity and good immunity to fast algebraic attacks. In this paper, we proceed to study those functions in aspect of correlation immunity and nonlinearity and through restrictions to those functions we propose two sub-classes of 2k-variable Boolean functions with good cryptographic properties. To the best of our knowledge, this is the first time whole classes of Boolean functions with high nonlinearity, 1-correlation immunity and good immunity against FAA can be found.
keywords:cryptography  Boolean functions  nonlinearity  correlation immunity  resiliency  algebraic immunity
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