Paper 2009/236

Elliptic curves with weak coverings over cubic extensions of finite fields with odd characteristics

Fumiyuki Momose and Jinhui Chao

Abstract

In this paper, we present a classification of classes of elliptic curves defined over cubic extension of finite fields with odd characteristics, which have coverings over the finite fields therefore can be attacked by the GHS attack. We then show the density of these weak curves with hyperelliptic and non-hyperelliptic coverings respectively. In particular, we shown for elliptic curves defined in Legendre forms, about half of them are weak.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Published elsewhere. Journal of the Ramanujan Mathematical Society (JRMS)
Keywords
Elliptic curve cryptosystemhyperelliptic curve cryptosystemGHS attack
Contact author(s)
jchao @ ise chuo-ac jp
History
2013-09-03: last of 2 revisions
2009-05-30: received
See all versions
Short URL
https://ia.cr/2009/236
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2009/236,
      author = {Fumiyuki Momose and Jinhui Chao},
      title = {Elliptic curves with weak coverings over cubic extensions of finite fields with odd characteristics},
      howpublished = {Cryptology ePrint Archive, Paper 2009/236},
      year = {2009},
      note = {\url{https://eprint.iacr.org/2009/236}},
      url = {https://eprint.iacr.org/2009/236}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.