Classification of Weil Restrictions Obtained by (2,...,2) Coverings of P^1

Fumiyuki Momose; Jinhui Chao

Paper 2006/347

Classification of Weil Restrictions Obtained by (2,...,2) Coverings of P^1

Fumiyuki Momose and Jinhui Chao

Abstract

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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: elliptic curve cryptosystem
Contact author(s): jchao @ ise chuo-u ac jp
History: 2006-10-20: received
Short URL: https://ia.cr/2006/347
License: CC BY

BibTeX

@misc{cryptoeprint:2006/347,
      author = {Fumiyuki Momose and Jinhui Chao},
      title = {Classification of Weil Restrictions Obtained by (2,...,2) Coverings of P^1},
      howpublished = {Cryptology {ePrint} Archive, Paper 2006/347},
      year = {2006},
      url = {https://eprint.iacr.org/2006/347}
}