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On Known and New Differentially Uniform Functions

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Book cover Information Security and Privacy (ACISP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6812))

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Abstract

We give a survey on the constructions of APN and differentially 4-uniform functions suitable for designing S-boxes for block ciphers. We recall why the search for more of such functions is necessary. We propose a way of designing functions which can possibly be APN or differentially 4-uniform and be bijective. We illustrate it with an example of a differentially 4-uniform (n,n)-permutation for n odd, based on the power function x 3 over the second order Galois extension of \({\Bbb F}_{2^{n+1}}\), and related to the Dickson polynomial D 3 over this field. These permutations have optimal algebraic degree and their nonlinearity happens to be rather good (but worse than that of the multiplicative inverse functions).

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Author information

Authors and Affiliations

  1. LAGA, Universities of Paris 8 and Paris 13 and CNRS, France

    Claude Carlet

  2. Dept. of Math, Univ. of Paris 8, 2 rue de la liberté, 93526, Saint-Denis Cedex, France

    Claude Carlet

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  1. Claude Carlet
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Software Engineering, The University of Melbourne, 3010, Victoria, Australia

    Udaya Parampalli

  2. Qualcomm Incorporated, Suite 301, Level 3, 77 King Street, NSW 2000, Sydney, Australia

    Philip Hawkes

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Carlet, C. (2011). On Known and New Differentially Uniform Functions. In: Parampalli, U., Hawkes, P. (eds) Information Security and Privacy. ACISP 2011. Lecture Notes in Computer Science, vol 6812. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22497-3_1

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  • DOI: https://doi.org/10.1007/978-3-642-22497-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22496-6

  • Online ISBN: 978-3-642-22497-3

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