Section: New Results

Collecting Relation for the Number Field Sieve in Medium Characteristic

Participants : Pierrick Gaudry, Laurent Grémy [contact] , Marion Videau.

We study the relation collection of NFS in medium characteristic, especially in $GF\left(p^6\right)$ [4]. We compare different polynomial selections that affect drastically the relation collection step, by giving the explicit formula in 3 dimensions of two functions to select the best polynomials. For the relation collection, we design new sieve algorithms in 3 dimensions and do the practical comparison of the different polynomial selections for different $p$. Finally, we perform the relation collection step for a field of 389 bits in 800 days, the largest computed relation collection in this type of field.