Paper 2011/549

1-Resilient Boolean Function with Optimal Algebraic Immunity

Qingfang Jin, Zhuojun Liu, and Baofeng Wu


In this paper, We propose a class of 2k-variable Boolean functions, which have optimal algebraic degree, high nonlinearity, and are 1-resilient. These functions have optimal algebraic immunity when k > 2 and u = -2^l; 0 =< l < k. Based on a general combinatorial conjecture, algebraic immunity of these functions is optimal when k > 2 and u = 2^l; 0 =< l < k. If the general combinatorial conjecture and a new assumption are both true, algebraic immunity of our functions is also optimal when k > 2, otherwise u.

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Published elsewhere. Unknown where it was published
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qfjin @ amss ac cn
2011-10-11: received
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      author = {Qingfang Jin and Zhuojun Liu and Baofeng Wu},
      title = {1-Resilient Boolean Function with Optimal Algebraic Immunity},
      howpublished = {Cryptology ePrint Archive, Paper 2011/549},
      year = {2011},
      note = {\url{}},
      url = {}
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