Anzeige
Erschienen in:
2005 | OriginalPaper | Buchkapitel
On the Discrete Logarithm Problem on Algebraic Tori
verfasst von : R. Granger, F. Vercauteren
Erschienen in: Advances in Cryptology – CRYPTO 2005
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Using a recent idea of Gaudry and exploiting rational representations of algebraic tori, we present an index calculus type algorithm for solving the discrete logarithm problem that works directly in these groups. Using a prototype implementation, we obtain practical upper bounds for the difficulty of solving the DLP in the tori
$T_2(\mathbb{F}_{p^m})$
and
$T_6(\mathbb{F}_{p^m})$
for various
p
and
m
. Our results do not affect the security of the cryptosystems LUC, XTR, or CEILIDH over prime fields. However, the practical efficiency of our method against other methods needs further examining, for certain choices of
p
and
m
in regions of cryptographic interest.