Cryptology ePrint Archive: Report 2006/347
Classification of Weil Restrictions Obtained by (2,...,2) Coverings of P^1
Fumiyuki Momose and Jinhui Chao
Abstract: In this paper, we show a general classification of
elliptic and hyperelliptic curves which can be attacked by
the Weil descent attack and index calculus algorithms.
In particular, we classfy all the Weil
restriction of these curves obtained by $(2,...,2)$ covering.
Density analysis of these curves are shown. Explicit
defintion equations of such weak curves are also provided.
Category / Keywords: public-key cryptography / elliptic curve cryptosystem
Date: received 15 Oct 2006, last revised 15 Oct 2006
Contact author: jchao at ise chuo-u ac jp
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Version: 20061020:100934 (All versions of this report)
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