8485 articles  [version française]

inria-00138382, version 2

Primality Proving with Elliptic Curves

Laurent Théry () a, 1, Guillaume Hanrot () a, 2

TPHOL 2007 4732 (2007) 319-333

Abstract: Elliptic curves are fascinating mathematical objects. In this paper, we present the way they have been represented inside the {\sc 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.

  • a –  INRIA
  • 1:  MARELLE (INRIA Sophia Antipolis)
  • INRIA
  • 2:  CACAO (INRIA Lorraine - LORIA)
  • CNRS : UMR7503 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
  • Domain : Computer Science/Cryptography and Security
    Computer Science/Logic in Computer Science
  • Internal note : RR-6155
  • Available versions :  v1 (2007-03-26) v2 (2007-04-09)
 
  • inria-00138382, version 2
  • http://hal.inria.fr/inria-00138382
  • oai:hal.inria.fr:inria-00138382
  • From: Guillaume Hanrot <>
  • Submitted on: Monday, 9 April 2007 07:50:19
  • Updated on: Wednesday, 10 October 2007 17:30:03