Primality Proving with Elliptic Curves
نویسندگان
چکیده
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. Key-words: elliptic curve, formalising mathematics, primality proving Prouver la primalité avec des courbes elliptiques Résumé : Les courbes elliptiques sont des objets mathématiques fascinants. Dans ce travail, nous présentons la façon dont elles ont été représentées dans le système COQ, et comment nous avons prouvé le fait que la loi de composition classique est bien interne et munit l’ensemble des points de la courbe d’une structure de groupe. Nous décrivons alors comment cela permet d’obtenir un vérificateur permettant de prouver la primalité de nombres naturels. Mots-clés : courbe elliptique, formalisation des mathématiques, preuves de primalité Primality Proving with Elliptic Curves 3
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