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International Conference on Cryptology and Information Security in Latin America

LATINCRYPT 2012: Progress in Cryptology – LATINCRYPT 2012 pp 18–36Cite as

Semi-bent Functions with Multiple Trace Terms and Hyperelliptic Curves

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7533))

Abstract

Semi-bent functions with even number of variables are a class of important Boolean functions whose Hadamard transform takes three values. Semi-bent functions have been extensively studied due to their applications in cryptography and coding theory. In this paper we are interested in the property of semi-bentness of Boolean functions defined on the Galois field \({\mathbb F}_2^n\) (n even) with multiple trace terms obtained via Niho functions and two Dillon-like functions (the first one has been studied by the author and the second one has been studied very recently by Wang et al. using an approach introduced by the author). We subsequently give a connection between the property of semi-bentness and the number of rational points on some associated hyperelliptic curves. We use the hyperelliptic curve formalism to reduce the computational complexity in order to provide an efficient test of semi-bentness leading to substantial practical gain thanks to the current implementation of point counting over hyperelliptic curves.

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Author information

Authors and Affiliations

  1. LAGA (Laboratoire Analyse, Géometrie et Applications), UMR 7539, CNRS, Department of Mathematics, University of Paris XIII and University of Paris VIII, 2 rue de la liberté, 93526, Saint-Denis Cedex, France

    Sihem Mesnager

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  1. Sihem Mesnager
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Editors and Affiliations

  1. Department of Computer Science, University of Chile, Blanco Encalada 2120, Tercer Piso, Santiago, Chile

    Alejandro Hevia

  2. IBM Research - Zürich, Säumerstrasse 4, 8803, Rüschlikon, Switzerland

    Gregory Neven

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Mesnager, S. (2012). Semi-bent Functions with Multiple Trace Terms and Hyperelliptic Curves. In: Hevia, A., Neven, G. (eds) Progress in Cryptology – LATINCRYPT 2012. LATINCRYPT 2012. Lecture Notes in Computer Science, vol 7533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33481-8_2

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  • DOI: https://doi.org/10.1007/978-3-642-33481-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33480-1

  • Online ISBN: 978-3-642-33481-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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