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Primality Proving with Elliptic Curves

Laurent Théry 1 Guillaume Hanrot 2
1 MARELLE - Mathematical, Reasoning and Software
CRISAM - Inria Sophia Antipolis - Méditerranée
2 CACAO - Curves, Algebra, Computer Arithmetic, and so On
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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.
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Contributor : Guillaume Hanrot Connect in order to contact the contributor
Submitted on : Monday, March 26, 2007 - 10:42:07 AM
Last modification on : Friday, February 26, 2021 - 3:28:08 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 10:10:24 PM


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  • HAL Id : inria-00138382, version 1



Laurent Théry, Guillaume Hanrot. Primality Proving with Elliptic Curves. [Research Report] RR-6155, 2007. ⟨inria-00138382v1⟩



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