Index calculus in the trace zero variety

Elisa Gorla; Maike Massierer

Paper 2014/318

Index calculus in the trace zero variety

Elisa Gorla and Maike Massierer

Abstract

We discuss how to apply Gaudry’s index calculus algorithm for abelian varieties to solve the discrete logarithm problem in the trace zero variety of an elliptic curve. We treat in particular the practically relevant cases of field extensions of degree 3 or 5. Our theoretical analysis is compared to other algorithms present in the literature, and is complemented by results from a prototype implementation.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: elliptic curve cryptography discrete logarithm problem index calculus trace zero variety
Contact author(s): maike massierer @ inria fr
History: 2015-02-23: revised; 2014-05-06: received; See all versions
Short URL: https://ia.cr/2014/318
License: CC BY

BibTeX

@misc{cryptoeprint:2014/318,
      author = {Elisa Gorla and Maike Massierer},
      title = {Index calculus in the trace zero variety},
      howpublished = {Cryptology {ePrint} Archive, Paper 2014/318},
      year = {2014},
      url = {https://eprint.iacr.org/2014/318}
}