Welcome to the resource topic for 2005/277
Scholten Forms and Elliptic/Hyperelliptic Curves with Weak Weil Restrictions
Authors: Fumiyuki Momose, Jinhui ChaoAbstract:
In this paper, we show explicitly the classes of elliptic and hyperelliptic curves
of low genera defined over extension fields, which
have weak coverings,
i.e. their Weil restrictions can be attacked by either index calculus attacks to hyperelliptic curves or Diem’s recent attack to non-hyperelliptic curves.
In particular, we show how to construct such coverings from these curves and analyze density of the curves for them such construction is possible.
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