The Multiple Number Field Sieve for Medium and High Characteristic Finite Fields

@article{Barbulescu2014TheMN,
  title={The Multiple Number Field Sieve for Medium and High Characteristic Finite Fields},
  author={Razvan Barbulescu and C{\'e}cile Pierrot},
  journal={IACR Cryptology ePrint Archive},
  year={2014},
  volume={2014},
  pages={147}
}
In this paper, we study the discrete logarithm problem in medium and high characteristic finite fields. We propose a variant of the Number Field Sieve (NFS) based on numerous number fields. Our improved algorithm computes discrete logarithms in Fpn for the whole range of applicability of NFS and lowers the asymptotic complexity from Lpn(1/3, (128/9)1/3) to Lpn(1/3, (213/36)1/3) in the medium characteristic case, and from Lpn(1/3, (64/9)1/3) to Lpn(1/3, ((92 + 26 √ 13)/27))1/3) in the high… CONTINUE READING