Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algorithmic aspects of elliptic bases in finite field discrete logarithm
  algorithms   Elliptic bases, introduced by Couveignes and Lercier in 2009, give an elegant
way of representing finite field extensions. A natural question which seems to
have been considered independently by several groups is to use this
representation as a starting point for small characteristic finite field
discrete logarithm algorithms. This idea has been recently proposed by two
groups working on it, in order to achieve provable quasi-polynomial time for
discrete logarithms in small characteristic finite fields. In this paper, we
don't try to achieve a provable algorithm but, instead, investigate the
practicality of heuristic algorithms based on elliptic bases. Our key idea, is
to use a different model of the elliptic curve used for the elliptic basis that
allows for a relatively simple adaptation of the techniques used with former
Frobenius representation algorithms. We haven't performed any record
computation with this new method but our experiments with the field F 3 1345
indicate that switching to elliptic representations might be possible with
performances comparable to the current best practical methods.

34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc