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Paper 2014/147
The Multiple Number Field Sieve for Medium and High Characteristic Finite Fields
Razvan Barbulescu and 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.
Metadata
- Available format(s)
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- discrete logarithm problem
- Contact author(s)
- razvan barbulescu @ inria fr
- History
- 2015-10-19: revised
- 2014-02-27: received
- See all versions
- Short URL
- https://ia.cr/2014/147
- License
-
CC BY