A Note on the Behaviour of the NFS in the Medium Prime Case: Smoothness of Norms

Provided by: Shanghai Institute of Applied Physics, Chinese Academy of Sciences
Topic: Security
Format: PDF
During an ongoing examination of the behavior, in practice, of the Number Field Sieve (NFS) in the medium prime case the authors have noticed numerous interesting patterns. In this paper they present findings on run-time observations of an aspect of the sieving stage. The contributions of these observations to the computational mathematics community are twofold: firstly, they bring them a step closer to understanding the true practical effectiveness of the algorithm and secondly, they enabled the development of a test for the effectiveness of the polynomials used in the NFS.

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