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 cryptographically used 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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