Paper 2013/582 Original: eprint.iacr.org/2013/582 ↗
The Special Number Field Sieve in $\F _{p^{n}}$, Application to Pairing-Friendly Constructions
Abstract
In this paper, we study the discrete logarithm problem in finite fields related to pairing-based curves. We start with a precise analysis of the state-of-the-art algorithms for computing discrete logarithms that are suitable for finite fields related to pairing-friendly constructions. To improve upon these algorithms, we extend the Special Number Field Sieve to compute discrete logarithms in $\F_{p^{n}}$, where $p$ has an adequate sparse representation. Our improved algorithm works for the whole range of applicability of the Number Field Sieve.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2013-09-14: last updated
- 2013-09-14: published
- Short URL
- https://ia.cr/2013/582
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2013/582,
author = {Antoine Joux and Cécile Pierrot},
title = {The Special Number Field Sieve in $\F _{p^{n}}$, Application to Pairing-Friendly Constructions},
howpublished = {Cryptology {ePrint} Archive, Paper 2013/582},
year = {2013},
url = {https://eprint.iacr.org/2013/582}
}