Cryptology ePrint Archive: Report 2004/240
A Weil Descent Attack against Elliptic Curve Cryptosystems over Quartic Extension Fields
Seigo Arita and Kazuto Matsuo and 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.
Category / Keywords: public-key cryptography / discrete logarithm problem, elliptic curve cryptosystem, number theory, Weil descent attack
Date: received 15 Sep 2004
Contact author: nagao at kanto-gakuin ac jp
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Version: 20040916:184351 (All versions of this report)
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