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={R. Barbulescu and C. Pierrot},
  journal={IACR Cryptol. ePrint Arch.},
  year={2014},
  volume={2014},
  pages={147}
}
  • R. Barbulescu, C. Pierrot
  • Published 2014
  • Mathematics, Computer Science, Physics
  • IACR Cryptol. ePrint Arch.
  • 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 $\mathbb{F}_{p^n}$ for the whole range of applicability of NFS and lowers the asymptotic complexity from $L_{p^n}(1/3,(128/9)^{1/3})$ to $L_{p^n}(1/3,(2^{13}/3^6)^{1/3})$ in the medium characteristic case, and from $L_{p^n}(1/3,(64/9)^{1/3})$ to $L_{p^n… CONTINUE READING

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