The Special Number Field Sieve in $\F _{p^{n}}$, Application to Pairing-Friendly Constructions

Antoine Joux; Cécile Pierrot

Paper 2013/582

The Special Number Field Sieve in $\F _{p^{n}}$, Application to Pairing-Friendly Constructions

Antoine Joux and Cécile Pierrot

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. MINOR revision.
Keywords: Discrete logarithms SNFS pairing-based
Contact author(s): Antoine Joux @ m4x org
History: 2013-09-14: received
Short URL: https://ia.cr/2013/582
License: CC BY

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}
}