In: Tatra Mountains Mathematical Publications, vol. 45, no. 1
Pavol Zajac
Detaily:
Rok, strany: 2010, 161 - 172
Kľúčové slová:
algebraic numbers, number field sieve, lattice sieve.
O článku:
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: \textit{Discrete Logarithms
and Degree Six Numbere Field 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.
Ako citovať:
ISO 690:
Zajac, P. 2010. On the use of the lattice sieve in the 3D NFS. In Tatra Mountains Mathematical Publications, vol. 45, no.1, pp. 161-172. 1210-3195.
APA:
Zajac, P. (2010). On the use of the lattice sieve in the 3D NFS. Tatra Mountains Mathematical Publications, 45(1), 161-172. 1210-3195.