Advertisement
Published in:
2014 | OriginalPaper | Chapter
A Heuristic Quasi-Polynomial Algorithm for Discrete Logarithm in Finite Fields of Small Characteristic
Authors : Razvan Barbulescu, Pierrick Gaudry, Antoine Joux, Emmanuel Thomé
Published in: Advances in Cryptology – EUROCRYPT 2014
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
The difficulty of computing discrete logarithms in fields
$\mathbb{F}_{q^k}$
depends on the relative sizes of
k
and
q
. Until recently all the cases had a sub-exponential complexity of type
L
(1/3), similar to the factorization problem. In 2013, Joux designed a new algorithm with a complexity of
L
(1/4 +
ε
) in small characteristic. In the same spirit, we propose in this article another heuristic algorithm that provides a quasi-polynomial complexity when
q
is of size at most comparable with
k
. By quasi-polynomial, we mean a runtime of
n
O
(log
n
)
where
n
is the bit-size of the input. For larger values of
q
that stay below the limit
$L_{q^k}(1/3)$
, our algorithm loses its quasi-polynomial nature, but still surpasses the Function Field Sieve. Complexity results in this article rely on heuristics which have been checked experimentally.