Remarks on the NFS complexity

Pavol Zajac

Paper 2008/064

Remarks on the NFS complexity

Pavol Zajac

Abstract

In this contribution we investigate practical issues with implementing the NFS algorithm to solve the DLP arising in XTR-based cryptosystems. We can transform original XTR-DLP to a DLP instance in $F_{p^{6}},$ where $p$ is a medium sized prime. Unfortunately, for practical ranges of $p,$ the optimal degree of NFS polynomial is less than the required degree 6. This leads to a problem to find enough smooth equations during the sieve stage of the NFS algorithm. We discuss several techniques that can increase the NFS output, i.e. the number of equations produced during the sieve, without increasing the smoothness bound.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Submitted to: TATRA MOUNTAINS Mathematical Publications
Keywords: cryptanalysis discrete logarithm problem number field sieve
Contact author(s): pavol zajac @ stuba sk
History: 2008-02-11: received
Short URL: https://ia.cr/2008/064
License: CC BY

BibTeX

@misc{cryptoeprint:2008/064,
      author = {Pavol Zajac},
      title = {Remarks on the {NFS} complexity},
      howpublished = {Cryptology {ePrint} Archive, Paper 2008/064},
      year = {2008},
      url = {https://eprint.iacr.org/2008/064}
}