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Generalised Jacobians in Cryptography and Coding Theory

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Arithmetic of Finite Fields (WAIFI 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7369))

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Abstract

The use of generalised Jacobians in discrete logarithm based cryptosystems has so far been rather limited since they offer no advantage over traditional discrete logarithm based systems. In this paper we continue the search for possible applications in two directions.

Firstly, we investigate pairings on generalised Jacobians and show that these are insecure. Secondly, generalising and extending prior work, we show how the discrete logarithm problem in generalised Jacobians can be reduced to the minimal non zero weight word and maximum likelihood decoding problems in generalised algebraic geometric codes.

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Author information

Authors and Affiliations

  1. Carl-von-Ossietzky Universität Oldenburg, Germany

    Florian Hess

Authors
  1. Florian Hess
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Editor information

Editors and Affiliations

  1. Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey

    Ferruh Özbudak

  2. Computer Science Section, CINVESTAV, Mexico DF, Mexico

    Francisco Rodríguez-Henríquez

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Hess, F. (2012). Generalised Jacobians in Cryptography and Coding Theory. 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_1

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  • DOI: https://doi.org/10.1007/978-3-642-31662-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31661-6

  • Online ISBN: 978-3-642-31662-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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