## Section: New Results

### Number Field Sieve-related results

Participants : Pierrick Gaudry, Alexander Kruppa, Emmanuel Thomé, Paul Zimmermann.

The team has been involved in the factorization of RSA-768, a 768-bit integer. With the usage of Grid'5000 computers in “besteffort” mode, we have obtained more than 40% of a total of 64 billion relations in the first phase (sieving). Some experiments were done together with an internship, Cyril Bouvier, for the filtering phase. The linear algebra phase is expected to finish by the end of 2009, or at the turn of the year. The linear algebra phase is considerably more challenging than the sieving phase in terms of program distribution. The block Wiedemann algorithm, which is being used for this computation, makes it possible to distribute the computation somewhat. Using Grid'5000 computers, we have been able to participate to a large extent to the linear algebra computation. The work on RSA-768 is expected to yield several forthcoming papers describing the many facets of the experiment.

Antoine Joux, Reynald Lercier, David Naccache and Emmanuel Thomé extended their work on oracle-assisted modular e -th root computation to an attack on the so-called static Diffie-Hellmann problem [10] . A revised version of this work has been accepted and presented at the 12th IMA workshop on cryptography and coding.