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Title: On the discrete logarithm problem on algebraic tori
Authors: Granger, R ×
Vercauteren, Fr├ęderik #
Issue Date: 2005
Publisher: Springer
Series Title: Lecture Notes in Computer Science vol:3621 pages:66-85
Conference: CRYPTO 2005 date:August 14-18, 2005
Abstract: 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(F(p)m) and T-6(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.
URI: 
ISSN: 0302-9743
Publication status: published
KU Leuven publication type: IT
Appears in Collections:ESAT - STADIUS, Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics
× corresponding author
# (joint) last author

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