Construction and Analysis of Boolean Functions of 2t+1 Variables with Maximum Algebraic Immunity

  • Na Li
  • Wen-Feng Qi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4284)


In this paper, we study the construction of (2t+1)-variable Boolean functions with maximum algebraic immunity, and we also analyze some other cryptographic properties of this kind of functions, such as nonlinearity, resilience. We first identify several classes of this kind of functions. Further, some necessary conditions of this kind of functions which also have higher nonlinearity are obtained. In this way, a modified construction method is proposed to possibly obtain (2t+1)-variable Boolean functions which have maximum algebraic immunity and higher nonlinearity, and a class of such functions is also obtained. Finally, we present a sufficient and necessary condition of (2t+1)-variable Boolean functions with maximum algebraic immunity which are also 1-resilient.


Algebraic attack algebraic immunity Boolean functions balancedness nonlinearity resilience 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Na Li
    • 1
  • Wen-Feng Qi
    • 1
  1. 1.Department of Applied MathematicsZhengzhou Information, Engineering UniversityZhengzhouChina

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