Section: New Results
Discrete logarithm in finite fields of small extension degree
Participant : Pierrick Gaudry [contact] .
Together with Razvan Barbulescu (CNRS, IMJ-PRG), Aurore Guillevic and François Morain (Grace project-team), we investigated the discrete logarithm problem in the case of finite fields of the form , where is a small integer. We proposed in a preprint — a part of which was accepted to Eurocrypt 2015 — various theoretical and practical improvements [25] :
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better (heuristic) asymptotic complexity in the case where , and
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use of algebraic number theory to show that in some cases we can skip the Schirokauer maps.
We have adapted Cado-nfs in order to perform a record computation in a field of the form , where has 180 digits. To our knowledge, this is the first time that the number field sieve algorithm is used in practice for record-size computations in this type of fields.