On the use of the lattice sieve in the 3D NFS

An adaptation of the Number Field Sieve (NFS) algorithm to solve a discrete logarithm problem in degree 6 finite fields (DLP6) requires a modified sieving procedure to find smooth elements of the three dimensional sieve space. In our successful solution [P. Zajac: Discrete Logarithms and Degree Six NumbereField Sieve: A practical Approach. VDM Verlag Dr. M¨uller, Saarbr¨ucken, 2009] we have used a modified line sieving to process a box-shaped region using a large factor base. In this contribution, we compare the results with an alternative approach based on the lattice sieving, which was used in most of the classical factorization and DLP record solutions. Results indicate that this approach does not scale to the 3D-case, making DLP6 more difficult in practice than comparable classical DLP cases.