A Weil Descent Attack against Elliptic Curve Cryptosystems over Quartic Extension Fields(<Special Section>Discrete Mathematics and Its Applications)

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概要

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• This paper proposes a Weil descent attack against elliptic curve cryptosystems over quartic extension fields. The scenario of the attack is as follows: First, one reduces a DLP on a Weierstrass form over the quartic extention of a finite field k to a DLP on a special form, called Scholten form, over the same field. Second, one reduces the DLP on the Scholten form to a DLP on a genus two hyperelliptic curve over the quadratic extension of k. Then, one reduces the DLP on the hyperelliptic curve to one on a C_<ab> model over k. Finally, one obtains the discrete-log of original DLP by applying the Gaudry method to the DLP on the C_<ab> model. In order to carry out the scenario, this paper shows that many of elliptic curve discrete-log problems over quartic extension fields of odd characteristics are reduced to genus two hyperelliptic curve discrete-log problems over quadratic extension fields, and that almost all of the genus two hyperelliptic curve discrete-log problems 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 uniformly.

• 社団法人電子情報通信学会の論文
• 2006-05-01

著者

• MATSUO Kazuto

  Institute of Information Security

• Matsuo Kazuto

  Institute Of Information Security:rdi Of Chuo Univ.

• Nagao Koh-ichi

  Dept. Of Engineering Kanto-gakuin Univ.

• ARITA Seigo

  Institute of Information Security

• SHIMURA Mahoro

  Chuo Univ. 21st Century Center of Excellence Program

関連論文

• Skew-Frobenius Maps on Hyperelliptic Curves
• A Weil Descent Attack against Elliptic Curve Cryptosystems over Quartic Extension Fields(Discrete Mathematics and Its Applications)
• Index Calculus Attack for Jacobian of Hyperelliptic Curves of Small Genus Using Two Large Primes
• An Extension of GHS Weil Descent Attack(Public Key Cryptography)(Cryptography and Information Security)
• An Addition Algorithm in Jacobian of C_ Curve(Information Security)

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