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Vectorial Functions and Covering Sequences

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Finite Fields and Applications (Fq 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2948))

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Abstract

The design of large classes of highly nonlinear resilient vectorial functions (mappings from \(\mathbb{F}^n_2\) into \(\mathbb{F}^m_2\), also called S-boxes) is needed for iterated block ciphers and for pseudo-random generators with multiple output. In this paper, we recall the diverse known constructions of such S-boxes, and we show that those which provide good candidate functions are, in fact, all in the same class. This class corresponds to a generalization of a well known construction due to Maiorana and Mac- Farland. We study in detail this construction and we specify it to obtain good S-boxes. In a second part, we generalize to S-boxes the notion of covering sequence. We show that this generalization has the same properties as for Boolean functions, and that it has nice additional properties of stability. We study how this notion can be used to design attacks, and we explain why some functions, including the elements of the new class, cannot be involved in the construction of iterated block ciphers.

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Author information

Authors and Affiliations

  1. Claude Carlet, INRIA, projet CODES, BP 105, 78153, Le Chesnay Cedex, France

    Claude Carlet

  2. GREYC-Caen and University of Paris 8,  

    Claude Carlet

  3. Laboratoire de Recherche en Informatique, INRIA Projet CODES and University of Paris 11, 15 rue Georges Clemenceau, 91405, Orsay Cedex, France

    Emmanuel Prouff

Authors
  1. Claude Carlet
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  2. Emmanuel Prouff
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Editor information

Editors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, 16802, PA, USA

    Gary L. Mullen

  2. University Paul Sabatier, AAECC/IRIT, 118 route de Narbonne, 31300, Toulouse cedex, France

    Alain Poli

  3. Sabancı University - FENS, Orhanli - Tuzla, 34956, Istanbul, Turkey

    Henning Stichtenoth

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Carlet, C., Prouff, E. (2004). Vectorial Functions and Covering Sequences. In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds) Finite Fields and Applications. Fq 2003. Lecture Notes in Computer Science, vol 2948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24633-6_17

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  • DOI: https://doi.org/10.1007/978-3-540-24633-6_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21324-6

  • Online ISBN: 978-3-540-24633-6

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