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 p method. For such an elliptic curve, we construct a C{sub}ab curve D on its Weil restriction in order to reduce the discrete logarithm problem on D 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.
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