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Sen-Shan Pan, Xiao-Tong Fu, Wei-Guo Zhang. Construction of 1-Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity[J]. Journal of Computer Science and Technology, 2011, 26(2): 269-275. DOI: 10.1007/s11390-011-1129-4
Citation: Sen-Shan Pan, Xiao-Tong Fu, Wei-Guo Zhang. Construction of 1-Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity[J]. Journal of Computer Science and Technology, 2011, 26(2): 269-275. DOI: 10.1007/s11390-011-1129-4

Construction of 1-Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity

  • This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in associative classes. For some n, a part of 1-resilient functions with maximum algebraic immunity constructed in the paper can achieve almost optimal nonlinearity. Apart from their high nonlinearity, the functions reach Siegenthaler's upper bound of algebraic degree. Also a class of 1-resilient functions on any number n > 2 of variables with at least sub-optimal algebraic immunity is provided.
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