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Classification of Weil Restrictions Obtained by (2,…,2) Coverings of P^1
Authors: Fumiyuki Momose, Jinhui ChaoAbstract:
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.
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