Anzeige
Erschienen in:
2013 | OriginalPaper | Buchkapitel
On the Function Field Sieve and the Impact of Higher Splitting Probabilities
Application to Discrete Logarithms in and
verfasst von : Faruk Göloğlu, Robert Granger, Gary McGuire, Jens Zumbrägel
Erschienen in: Advances in Cryptology – CRYPTO 2013
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
In this paper we propose a binary field variant of the Joux-Lercier medium-sized Function Field Sieve, which results not only in complexities as low as
$L_{q^n}(1/3,(4/9)^{1/3})$
for computing arbitrary logarithms, but also in an heuristic
polynomial time
algorithm for finding the discrete logarithms of degree one and two elements when the field has a subfield of an appropriate size. To illustrate the efficiency of the method, we have successfully solved the DLP in the finite fields with 2
1971
and 2
3164
elements, setting a record for binary fields.