This file explains how to use the FFS possibilities of CADO-NFS. It is
possible to deal with finite fields of one of the two following forms:
- finite fields of characteristic 2
- finite fields of characteristic 3
There is no general script for FFS. We describe here the sequence of
steps to be performed. It is assumed that the user has some background
knowledge on the algorithm.
Notation:
p, n: we want to compute dlog in GF(p^n), with p=2 or p=3.
You should first compile the FFS-related binaries. Visit the ffs/
subdirectory, copy Makefile.local.example to Makefile.local and edit it
to configure according to what you want; then type 'make'.
- polynomial selection:
Nothing automatic. There are some tools in the polyselect subdirectory.
The code presently assumes that curves with only one place at infinity
are chosen.
- relation collection:
Create a parameter file, imitating the ones in the ffs/params/
directory.
Then run
ffs/f2/makefb
or
ffs/f3/makefb
depending whether you are in characteristic 2 or 3. From now on, we assume
characteristic 2.
Computing relations is done with
ffs/f2/sieve
You'll have to deal by yourself with the special-q ranges, and so on.
- freerels/filtering
The script ffs/filter/filter.sh is available for doing all this step.
(like for NFS-DL, bad ideals must be taken care of in a way or antoher,
and it is up to you; nothing automatic yet). No Schirokauer maps are
needed here.
- Linear algebra:
Exactly the same as for NFS-DL.
Have a look at the ouput and log files of "./factor.sh p -dlp" and try
to imitate.
- Reconstruct dlogs of fb elements
The same as for NFS-DL, again.
- Individual logarithms
Nothing automatic. Use ffs/descent_init and ffs/sieve to do the
descent.