Hybrid approach for solving multivariate systems over finite fields - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Mathematical Cryptology Année : 2010

Hybrid approach for solving multivariate systems over finite fields

Luk Bettale
  • Fonction : Auteur
  • PersonId : 966118
Jean-Charles Faugère
Ludovic Perret
  • Fonction : Auteur
  • PersonId : 935330
  • IdRef : 123278864

Résumé

In this paper, we present an improved approach to solve multivariate systems over finite fields. Our approach is a tradeoff between exhaustive search and Gröbner bases techniques. We give theoretical evidences that our method brings a significant improvement in a very large context and we clearly define its limitations. The efficiency depends on the choice of the tradeoff. Our analysis gives an explicit way to choose the best tradeoff as well as an approximation. From our analysis, we present a new general algorithm to solve multivariate polynomial systems. Our theoretical results are experimentally supported by successful cryptanalysis of several multivariate schemes (TRMS, UOV, . . . ). As a proof of concept, we were able to break the proposed parameters assumed to be secure until now. Parameters that resists to our method are also explicitly given. Our work permits to refine the parameters to be chosen for multivariate schemes.

Dates et versions

hal-01148127 , version 1 (04-05-2015)

Identifiants

Citer

Luk Bettale, Jean-Charles Faugère, Ludovic Perret. Hybrid approach for solving multivariate systems over finite fields. Journal of Mathematical Cryptology, 2010, 3 (3), pp.177--197. ⟨10.1515/jmc.2009.009⟩. ⟨hal-01148127⟩
179 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More