Weil descent of elliptic curves over finite fields of characteristic three

Abstract

The paper shows that some of elliptic curves over finite fields of characteristic three of composite degree are attacked by a more effective algorithm than Pollard’s ρ method. For such an elliptic curve E, we construct a Cab curve D on its Weil restriction in order to reduce the discrete logarithm problem on E to that on D. And we show that the genus of D is small enough so that D is attacked by a modified form of Gaudry’s variant for a suitable E. We also see such a weak elliptic curve is easily constructed.