Overall Objectives
Research Program
Application Domains
Highlights of the Year
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
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Section: New Results

Discrete Logarithm Record Computation in Extension Fields

Participants : Laurent Grémy, Aurore Guillevic, Emmanuel Thomé.

Together with F. Morain from the GRACE team, we reached new record sizes for the discrete logarithm problems over non-prime finite fields of small extension degrees [19], [8]. Assessing the hardness of the discrete logarithm problem in such fields is highly relevant to the security of cryptographic pairings. Our computations are not terribly large computations compared to other record-size computations for integer factoring or discrete logarithm over prime fields, but on the other hand more novelty is present in these contexts: use of automorphisms, higher degree sieving, for example.

Further research in this direction is needed, especially regarding the effectiveness of the variants of the “tower” number field sieve variants.

Furthermore, A. Guillevic and L. Grémy have gathered in a database all published records of discrete logarithm computations in all kinds of finite fields. The database is hosted on gitlab and is open to external contributions. A web interface for browsing the database is available at