[Cado-nfs-discuss] Using cado-nfs to DLP a p270

Pierrick Gaudry pierrick.gaudry at loria.fr
Sat Jun 10 08:53:58 CEST 2017

Dear Peter,

CADO-NFS solves the DLP with an unknown generator (unknown even to the
programmer: this is a specificity of the algorithm we use). 

But this is not a problem: you can compute the log of Y, the log of G and
then divide mod ell to get the log of Y in base G (just like with
classical logarithms). Once the precomputation is done, computing one
more log for the same group is very cheap.

The option -gfpext is not at all for the generator. This is an
experimental feature to deal with groups of the form GF(p^2). You can
forget it.

Oh, and it seems that you have put your target for ell, while ell should
be the factor of p-1 modulo which you want to solve the discrete log. In
your case, my guess is that this is (p-1)/2, but I can't tell for sure.

And a final remark: the current largest DLP computation publicly
announced was for a 232-digits prime p. CADO-NFS is currently completely
unable to deal with 270-digits DLPs. And you would need dozen of
thousands of cores for a couple of years anyway...


On Sat, Jun 10, 2017 at 10:25:02AM +1200, Peter Lambrechtsen wrote:
> I'm not 100% sure if I am doing the right thing so I thought I would ask
> here to confirm.
> I'm looking to factor a p270 with a fixed generator.
> P 12824716....
> G 2
> Y 8990799.....
> So if I was going to set this up in cado-nfs I would need to do the
> following
> under the parameters/dlp directory copy params.p2dd20 to params.p2dd270
> Then the command line I would use would be:
> ./cado-nfs.py 12824716...  -dlp -ell 8990799..  -gfpext 2
> And see if any primes come out of factoring the prime and then sieve the
> ell.
> Or am I misunderstanding how I would achieve this as I am not sure how I
> would setup the hints if I wasn't using the gfpext = 2 which is the
> generator value.
> Cheers
> Peter

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