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
Pré-Publication, Document De Travail Année : 2009

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 (207.63 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

  • HAL Id : inria-00383941 , version 1
  • ARXIV : 0905.2177

Citer

Andreas Enge, Pierrick Gaudry, Emmanuel Thomé. An $L (1/3)$ Discrete Logarithm Algorithm for Low Degree Curves. 2009. ⟨inria-00383941v1⟩
479 Consultations
316 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More