# 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}
}
• 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