Abstract
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 \(\mathcal{O}\left( q^nn\log(q) \right)\).
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Batteux, B. (2012). On the Algebraic Normal Form and Walsh Spectrum of Symmetric Functions over Finite Rings. In: Özbudak, F., Rodríguez-Henríquez, F. (eds) Arithmetic of Finite Fields. WAIFI 2012. Lecture Notes in Computer Science, vol 7369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31662-3_7
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DOI: https://doi.org/10.1007/978-3-642-31662-3_7
Publisher Name: Springer, Berlin, Heidelberg
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