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

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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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Author information

Correspondence to Sen-Shan Pan.

Additional information

This work is supported by the National Natural Science Foundations of China under Grant Nos. 60903200, 61003299.

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Pan, S., Fu, X. & Zhang, W. Construction of 1-Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity. J. Comput. Sci. Technol. 26, 269–275 (2011). https://doi.org/10.1007/s11390-011-9433-6

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  • stream ciphers
  • Boolean functions
  • 1-resilient
  • algebraic immunity
  • algebraic degree