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Primality Proving with Elliptic Curves

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Theorem Proving in Higher Order Logics (TPHOLs 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4732))

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Abstract

Elliptic curves are fascinating mathematical objects. In this paper, we present the way they have been represented inside the Coq system, and how we have proved that the classical composition law on the points is internal and gives them a group structure. We then describe how having elliptic curves inside a prover makes it possible to derive a checker for proving the primality of natural numbers.

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Authors and Affiliations

  1. INRIA, France

    Laurent Théry & Guillaume Hanrot

Authors
  1. Laurent Théry
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  2. Guillaume Hanrot
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Klaus Schneider Jens Brandt

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Théry, L., Hanrot, G. (2007). Primality Proving with Elliptic Curves. In: Schneider, K., Brandt, J. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2007. Lecture Notes in Computer Science, vol 4732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74591-4_24

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  • DOI: https://doi.org/10.1007/978-3-540-74591-4_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74590-7

  • Online ISBN: 978-3-540-74591-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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