## 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