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
-
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},
url = {https://eprint.iacr.org/2009/236}
}
