Skip to Content.
Sympa Menu

cado-nfs - Re: [cado-nfs] Cado-nfs Fails in Sqrt

Subject: Discussion related to cado-nfs

List archive

Re: [cado-nfs] Cado-nfs Fails in Sqrt


Chronological Thread 
    < Chronological >      < Thread >
  • From: Pierrick Gaudry <pierrick.gaudry@loria.fr>
  • To: Paul Zimmermann <Paul.Zimmermann@inria.fr>
  • Cc: "Thomas D. Dean" <tomdean@wavecable.com>, cado-nfs@inria.fr
  • Subject: Re: [cado-nfs] Cado-nfs Fails in Sqrt
  • Date: Thu, 21 Apr 2022 14:10:10 +0200
  • Authentication-results: mail2-relais-roc.national.inria.fr; dkim=none (message not signed) header.i=none
> After investigating with Pierrick Gaudry, it appears (in one run when he was
> able to reproduce the issue) that the two smallest factors 7901783 and
> 30578437
> do appear *both* in gcd(R-A,N) and gcd(R+A,N) for all dependencies that
> we've
> checked, where R and A are the rational and algebraic square roots.

In fact, these factors are so small that they belong to the factor base.
I can not make an opinion whether this can produce strange behaviours
regarding the probability that a dependency can separate them.
Theoretical considerations meet practical implementation details, here.

This is definitely a very atypical input for NFS.

Regards,
Pierrick

Archive powered by MHonArc 2.6.19+.

Top of Page