On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}{2^{1971}}$ and $\mathbb{F}{2^{3164}}$
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.
2013
Lecture Notes in Computer Science; 8043
109
128
Best Paper Award (by unanimous decision of the Program Committee)
REVIEWED
OTHER
| Event name | Event place | Event date |
Santa Barbara, CA, USA | August 18-22, 2013 | |