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On the Discrete Logarithm Problem on Algebraic Tori

Granger, Robert and Vercauteren, F. (2005) On the Discrete Logarithm Problem on Algebraic Tori In: The 25th Annual International Cryptology Conference - Advances in Cryptology (CRYPTO 2005), 14-18 Aug 2005, Santa Barbara, California, USA.

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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 T2(Fpm) and T6(Fpm) 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.

Item Type: Conference or Workshop Item (Conference Paper)
Divisions : Faculty of Engineering and Physical Sciences > Computing Science
Authors :
Vercauteren, F.
Date : 2005
DOI : 10.1007/11535218_5
Copyright Disclaimer : © Springer-Verlag Berlin Heidelberg 2005
Uncontrolled Keywords : Discrete Logarithm; Discrete Logarithm Problem; Compression Factor; Cyclotomic Polynomial; Cryptology ePrint Archive
Depositing User : Clive Harris
Date Deposited : 08 Feb 2019 09:00
Last Modified : 08 Feb 2019 09:00

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