Scholten Forms and Elliptic/Hyperelliptic Curves with Weak Weil Restrictions

@article{Momose2005ScholtenFA,
  title={Scholten Forms and Elliptic/Hyperelliptic Curves with Weak Weil Restrictions},
  author={Fumiyuki Momose and Jinhui Chao},
  journal={IACR Cryptology ePrint Archive},
  year={2005},
  volume={2005},
  pages={277}
}
In this paper, we show explicitly the classes of elliptic and hyperelliptic curves of low genera dened over extension elds, 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 c o v erings from these curves and analyze density of the curves for them such construction is possible. 

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