On the Algebraic Normal Form and Walsh Spectrum of Symmetric Functions over Finite Rings

  • Boris Batteux
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7369)


A function over finite rings is a function from a ring \(E_{q}^{n}\) to a ring E r , where E k is ℤ /k ℤ. These functions are well used in cryptography: cipher design, hash function design and in theoretical computer science. In this paper, we are especially interested in symmetric functions. We give practical ways of computing their ANF and their Walsh Spectrum in \(\mathcal{O}\left({ n+q-1 \choose q-1 }^2\right)\) using linear algebra. Thus, we achieve a better complexity both in time and memory than the fast Fourier transform which is in \(\mathcal{O}\left( q^nn\log(q) \right)\).


Boolean Function Symmetric Function Symmetry Class Gray Code Algebraic Degree 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Boris Batteux
    • 1
  1. 1.CASSIDIAN, Cyber SecurityFrance

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