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[cado-nfs] solving DLP in GF(p) with ell^2 divides p-1 using CADO-NFS


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  • From: T iffany <bcjzyyyhtw@outlook.com>
  • To: "cado-nfs@inria.fr" <cado-nfs@inria.fr>
  • Subject: [cado-nfs] solving DLP in GF(p) with ell^2 divides p-1 using CADO-NFS
  • Date: Fri, 18 Apr 2025 04:54:31 +0000
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Hi,
I am currently working on solving a discrete logarithm problem in the finite field GF(p), where the prime p satisfies the relation p−1=16q^2 with q also being prime. the command I use is:
  • [https://file+.vscode-resource.vscode-cdn.net/d%3A/CTF_challs/pytools/useful%20tools/cado-nfs.py]./cado-nfs.py -dlp -ell 10939385599812931291 target=1520104544106795253621809691052117121393 1914722516822312424274313822430190826897
And here target satisfy target^q=1 (mod p). When I attempt to solve this DLP using CADO-NFS, the result I obtain is 0:
  • Info:root: logbase = 1445716020256136655461963773328391563938
  • Info:root: target = 1520104544106795253621809691052117121393
  • Info:root: log(target) = 0 mod ell
 After researching this issue, I came across a similar question raised in the mailing list archives from August 2019 "[Cado-nfs-discuss] DLP in GF(p) turns out to be 0".
I would like to ask:
  1. Was the issue mentioned in that discussion eventually resolved?
  2. If so, is there a specific way to configure or use CADO-NFS to correctly handle such a case?
Any guidance or suggestions would be greatly appreciated. Thank you very much for your time and for your work on this great tool.
Best regards,
Tiffany




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