LLL on the average - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2006

LLL on the average

Résumé

Despite their popularity, lattice reduction algorithms remain mysterious in many ways. It has been widely reported that they behave much more nicely than what was expected from the worst-case proved bounds, both in terms of the running time and the output quality. In this article, we investigate this puzzling statement by trying to model the average case of lattice reduction algorithms, starting with the celebrated Lenstra-Lenstra-Lovász algorithm (L3). We discuss what is meant by lattice reduction on the average, and we present extensive experiments on the average case behavior of L3, in order to give a clearer picture of the differences/similarities between the average and worst cases. Our work is intended to clarify the practical behavior of L3 and to raise theoretical questions on its average behavior.

Dates et versions

hal-00107309 , version 1 (18-10-2006)

Identifiants

Citer

Phong Nguyen, Damien Stehle. LLL on the average. Proceedings of the 7th International Symposium on Algorithmic Number Theory, ANTS-VII., 2006, Berlin, Germany. pp.238-256, ⟨10.1007/11792086_18⟩. ⟨hal-00107309⟩
162 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More