Scholten Forms and Elliptic/Hyperelliptic Curves with Weak Weil Restrictions

Fumiyuki Momose; Jinhui Chao

Paper 2005/277 Original: eprint.iacr.org/2005/277 ↗

Scholten Forms and Elliptic/Hyperelliptic Curves with Weak Weil Restrictions

Fumiyuki Momose

Jinhui Chao

Abstract

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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2005-12-19: last updated; 2005-08-18: published
Short URL: https://ia.cr/2005/277
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2005/277,
      author = {Fumiyuki Momose and Jinhui Chao},
      title = {Scholten Forms and Elliptic/Hyperelliptic Curves with Weak Weil Restrictions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2005/277},
      year = {2005},
      url = {https://eprint.iacr.org/2005/277}
}