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 cryptographydiscrete logarithm problemindex calculustrace 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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2014/318}},
      url = {https://eprint.iacr.org/2014/318}
}
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