Cryptology ePrint Archive: Report 2005/277

Scholten Forms and Elliptic/Hyperelliptic Curves with Weak Weil Restrictions

Fumiyuki Momose and 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.

Category / Keywords: public-key cryptography / elliptic curve cryptosystem

Date: received 18 Aug 2005, last revised 19 Dec 2005

Contact author: jchao at ise chuo-u ac jp

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Version: 20051219:091532 (All versions of this report)

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