[Cado-nfs-discuss] (no subject)

Zimmermann Paul Paul.Zimmermann at inria.fr
Sat Sep 13 09:01:47 CEST 2014

       Hi John,

> From: John Waltos <jwaltos at hotmail.com>
> Date: Sat, 13 Sep 2014 04:21:05 +0000
> I will be setting up factorizations within CADO 2.1 to obtain polynomials. The values I intend to use are from 230 digits to a top end of 600 digits. I’ll be using a 6 core computer running Mageia 4.1 with 64 G RAM and about 800G of space.
> I would greatly appreciate any points on how to amend the parameter files as they cap out at 220 digits. Any pointers to a paper (s) directly addressing this would help also.
> Using GGNFS on Windows 7 last year, I was able to obtain a polynomial for a 298 digit factorization without any tweaks. It’s not pretty but is posted on the Mersenne forum.
> Thank you for any assistance. 
> Very nice work!

what you are looking from is at the frontier of what we know. There was only
one factorization of 230 digits or more so far, namely RSA768.

For numbers in the 230-270 digit range, I would suggest using the following
parameters (adapted from params.c220):

tasks.polyselect.degree = 6
tasks.polyselect.P = 10000000   # maybe try 20M or 50M too
tasks.polyselect.admax = 1e8
tasks.polyselect.incr = 60
tasks.polyselect.nq = 46656     # this is 6^6
tasks.polyselect.nrkeep = 2000

You should adjust admax so that the total search takes at least 40 cpu years
(which was what we used for RSA768).

Note that even if you find a good polynomial, performing a full factorization
of a 230-digit number is a highly non-trivial task, and CADO-NFS 2.1 might not
be ready for that. Don't even dream about 600 digits.

Also note that recent results might give better polynomials [1].

Best regards,
Paul Zimmermann

[1] http://www.loria.fr/~zimmerma/papers/sopt-20140905.pdf

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