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Efficient Computation of Algebraic Immunity of Symmetric Boolean Functions

  • Feng Liu
  • Keqin Feng
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4484)

Abstract

The computation on algebraic immunity (AI) of symmetric boolean functions includes: determining the AI of a given symmetric function and searching all symmetric functions with AI = d or AI ≥ d, where \(d\leq \left\lceil\frac{n}{2}\right\rceil\). In this paper we firstly showed a necessary and sufficient condition of AI of symmetric boolean functions and then proposed several efficient algorithms on computation of algebraic immunity of symmetric boolean functions. By these algorithms we could assess the vulnerability of symmetric boolean functions against algebraic/fast algebraic attacks efficiently, and find all symmetric functions having a given algebraic immunity AI n (f) = d, for some 0 ≤ d ≤ n.

Keywords

symmetric boolean function algebraic immunity cryptography 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Feng Liu
    • 1
  • Keqin Feng
    • 1
  1. 1.Department of Mathematical Sciences, Tsinghua University, Beijing 100084China

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