Cryptology ePrint Archive: Report 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.

Category / Keywords: public-key cryptography / Elliptic curve cryptosystem, hyperelliptic curve cryptosystem, GHS attack

Original Publication (in the same form): Journal of the Ramanujan Mathematical Society (JRMS)

Date: received 25 May 2009, last revised 2 Sep 2013

Contact author: jchao at ise chuo-ac jp

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Version: 20130903:030039 (All versions of this report)

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