Welcome to the resource topic for 2014/147
Title:
The Multiple Number Field Sieve for Medium and High Characteristic > Finite Fields
Authors: Razvan Barbulescu, Cécile Pierrot
Abstract: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}(1/3,((92 + 26\sqrt{13})/27))^{1/3}) in the high characteristic case. Version 2 contains an erratum.
ePrint: https://eprint.iacr.org/2014/147
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