Paper 2004/240

A Weil Descent Attack against Elliptic Curve Cryptosystems over Quartic Extension Fields

Seigo Arita, Kazuto Matsuo, Koh-ichi Nagao, and Mahoro Shimura

Abstract

This paper shows that many of elliptic curve cryptosystems over quartic extension fields of odd characteristics are reduced to genus two hyperelliptic curve cryptosystems over quadratic extension fields. Moreover, it shows that almost all of the genus two hyperelliptic curve cryptosystems over quadratic extension fields of odd characteristics come under Weil descent attack. This means that many of elliptic curve cryptosystems over quartic extension fields of odd characteristics can be attacked by Weil descent uniformly.

Metadata
Available format(s)
PDF PS
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
discrete logarithm problemelliptic curve cryptosystemnumber theoryWeil descent attack
Contact author(s)
nagao @ kanto-gakuin ac jp
History
2004-09-16: received
Short URL
https://ia.cr/2004/240
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2004/240,
      author = {Seigo Arita and Kazuto Matsuo and Koh-ichi Nagao and Mahoro Shimura},
      title = {A Weil Descent Attack against Elliptic Curve Cryptosystems over Quartic Extension Fields},
      howpublished = {Cryptology ePrint Archive, Paper 2004/240},
      year = {2004},
      note = {\url{https://eprint.iacr.org/2004/240}},
      url = {https://eprint.iacr.org/2004/240}
}
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