%0 Conference Proceedings %T Primality Proving with Elliptic Curves %+ Mathematical, Reasoning and Software (MARELLE) %+ Curves, Algebra, Computer Arithmetic, and so On (CACAO) %A Théry, Laurent %A Hanrot, Guillaume %< avec comité de lecture %Z RR-6155 %B TPHOL 2007 %C Kaiserslautern, Germany %Y Klaus Schneider and Jens Brandt %I Springer-Verlag %3 LNCS %V 4732 %P 319-333 %8 2007-09 %D 2007 %Z Computer Science [cs]/Cryptography and Security [cs.CR] %Z Computer Science [cs]/Logic in Computer Science [cs.LO]Conference papers %X 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. %G English %2 https://inria.hal.science/inria-00138382v2/document %2 https://inria.hal.science/inria-00138382v2/file/paper.pdf %L inria-00138382 %U https://inria.hal.science/inria-00138382 %~ CNRS %~ INRIA %~ INPL %~ INRIA-SOPHIA %~ IRISA %~ INRIASO %~ INRIA_TEST %~ INRIA-LORRAINE %~ LORIA2 %~ HERVETHERY %~ INRIA-NANCY-GRAND-EST %~ TESTALAIN1 %~ UNIV-LORRAINE %~ INRIA2 %~ LORIA %~ UR1-MATH-STIC %~ UR1-UFR-ISTIC %~ INRIA-300009 %~ UR1-MATH-NUM