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Mathematics of Computation
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Computational methods in commutative algebra and algebraic geometry
Mathematics of Computation
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Mathematics of Computation
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Finite Fields and Their Applications
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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.