Section: New Results

Computation of Discrete Logarithms in $\mathrm{GF}\left({\mathbf{2}}^{\mathbf{809}}\right)$

Participants : Razvan Barbulescu, Cyril Bouvier, Jérémie Detrey, Pierrick Gaudry, Hamza Jeljeli, Emmanuel Thomé [contact] , Marion Videau, Paul Zimmermann.

In the context of the CATREL ANR project, most team members contributed to the achievement of a new record computation for discrete logarithms in $\mathrm{GF}\left(2^{809}\right)$, with the Function Field Sieve (FFS) algorithm. This is, to date, the largest computation in a binary field of prime extension degree. Beyond the experimental data and the improvements related to “what it takes” to beat such a record, this work provides very useful basis information towards the assessment of the cut-off with the novel quasi-polynomial algorithm discussed below.

This work has been reported in the article [15] , accepted for publication in the conference PKC 2014 (Public Key Cryptography). It was the occasion to illustrate several contributions of members of the teams to various phases of the algorithm: Răzvan Bărbulescu [21] analyzed the polynomial selection step for FFS; Jérémie Detrey, Pierrick Gaudry and Marion Videau [17] improved the practical implementation of the relation collection; Cyril Bouvier [23] studied the filtering step; and Hamza Jeljeli [28] proposed to use the Residue Number System representation for the linear algebra step on GPU and CPU.