On the use of the lattice sieve in the 3D NFS
Abstract
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 [12] 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 lattice sieving, which was used in most
of the classical factorization and DL record solutions. Results indicate
that this approach does not work well in the 3D-case, making DLP6
more difficult in practice than a comparable classical DLP cases.
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 [12] 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 lattice sieving, which was used in most
of the classical factorization and DL record solutions. Results indicate
that this approach does not work well in the 3D-case, making DLP6
more difficult in practice than a comparable classical DLP cases.
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PDFDOI: https://doi.org/10.2478/tatra.v45i0.59