Primality Proving with Elliptic Curves.

Authors :: Hutchison, David
Kanade, Takeo
Kittler, Josef
Kleinberg, Jon M.
Mattern, Friedemann
Mitchell, John C.
Naor, Moni
Nierstrasz, Oscar
Pandu Rangan, C.
Steffen, Bernhard
Sudan, Madhu
Terzopoulos, Demetri
Tygar, Doug
Vardi, Moshe Y.
Weikum, Gerhard
Schneider, Klaus
Brandt, Jens
Théry, Laurent
Hanrot, Guillaume
Source :: Theorem Proving in Higher Order Logics (9783540745907); 2007, p319-333, 15p
Publication Year :: 2007
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. [ABSTRACT FROM AUTHOR]