The GHS Attack Revisited

Abstract. We generalize the Weil descent construction of the GHS attack to arbitrary Artin-Schreier extensions. We give a formula for the characteristic polynomial of Frobenius of the obtained curves and prove that the large cyclic factor of the input elliptic curve is not contained in the kernel of the composition of the conorm and norm maps. As an application we almost square the number of elliptic curves which succumb to the basic GHS attack, thereby weakening curves over F2155 further. We also discuss other possible extensions or variations of the GHS attack and conclude that they are not likely to yield further improvements.

• Type: Conference
• Year: 2003
• Where: EUROCRYPT
• Authors: Florian Hess
• Keywords: Cryptography, Elliptic Curves, EUROCRYPT 2003, GHS Attack, Weil Descent Construction