• Citer

On the quaternion l-isogeny path problem

par Kohel, David;Lauter, Kristin;Petit, Christophe ;Tignol, Jean Pierre
Référence LMS journal of computation and mathematics, 17, page (418-432)
Publication Publié, 2014-07

Article révisé par les pairs

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

Let O be a maximal order in a definite quaternion algebra over ℚ of prime discriminant p, and l a small prime. We describe a probabilistic algorithm which, for a given left O-ideal, computes a representative in its left ideal class of l-power norm. In practice the algorithm is efficient and, subject to heuristics on expected distributions of primes, runs in expected polynomial time. This solves the underlying problem for a quaternion analog of the Charles-Goren-Lauter hash function, and has security implications for the original CGL construction in terms of supersingular elliptic curves.