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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2006/347}},
      url = {https://eprint.iacr.org/2006/347}
}
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