An $L (1/3)$ Discrete Logarithm Algorithm for Low Degree Curves - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Journal of Cryptology Année : 2011

An $L (1/3)$ Discrete Logarithm Algorithm for Low Degree Curves

Résumé

We present an algorithm for solving the discrete logarithm problem in Jacobians of families of plane curves whose degrees in $X$ and $Y$ are low with respect to their genera. The finite base fields $\FF_q$ are arbitrary, but their sizes should not grow too fast compared to the genus. For such families, the group structure and discrete logarithms can be computed in subexponential time of $L_{q^g}(1/3, O(1))$. The runtime bounds rely on heuristics similar to the ones used in the number field sieve or the function field sieve.
Fichier principal
Vignette du fichier
L13.pdf (224.64 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

inria-00383941 , version 1 (13-05-2009)
inria-00383941 , version 2 (20-12-2009)

Identifiants

Citer

Andreas Enge, Pierrick Gaudry, Emmanuel Thomé. An $L (1/3)$ Discrete Logarithm Algorithm for Low Degree Curves. Journal of Cryptology, 2011, 24, pp.24-41. ⟨10.1007/s00145-010-9057-y⟩. ⟨inria-00383941v2⟩
481 Consultations
317 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More