Balanced Boolean Functions with (Almost) Optimal Algebraic Immunity and Very High Nonlinearity

  title={Balanced Boolean Functions with (Almost) Optimal Algebraic Immunity and Very High Nonlinearity},
  author={Xiaohu Tang and Deng Tang and Xiangyong Zeng and Lei Hu},
  journal={IACR Cryptology ePrint Archive},
In this paper, we present a class of 2k-variable balanced Boolean functions and a class of 2k-variable 1-resilient Boolean functions for an integer k ≥ 2, which both have the maximal algebraic degree and very high nonlinearity. Based on a newly proposed conjecture by Tu and Deng, it is shown that the proposed balanced Boolean functions have optimal algebraic immunity and the 1-resilient Boolean functions have almost optimal algebraic immunity. Among all the known results of balanced Boolean… CONTINUE READING
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