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A Formal Library for Elliptic Curves in the Coq Proof Assistant

  • Evmorfia-Iro Bartzia
  • Pierre-Yves Strub
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8558)

Abstract

A preliminary step towards the verification of elliptic curve cryptographic algorithms is the development of formal libraries with the corresponding mathematical theory. In this paper we present a formalization of elliptic curves theory, in the SSReflect extension of the Coq proof assistant. Our central contribution is a library containing many of the objects and core properties related to elliptic curve theory. We demonstrate the applicability of our library by formally proving a non-trivial property of elliptic curves: the existence of an isomorphism between a curve and its Picard group of divisors.

Keywords

Elliptic Curve Elliptic Curf Ring Quotient Elliptic Curve Cryptography Picard Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Evmorfia-Iro Bartzia
    • 1
  • Pierre-Yves Strub
    • 2
  1. 1.INRIA Paris-RocquencourtFrance
  2. 2.IMDEA Software InstituteSpain

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