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 C ab 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.
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Arita, S. (2000). Weil Descent of Elliptic Curves over Finite Fields of Characteristic Three. In: Okamoto, T. (eds) Advances in Cryptology — ASIACRYPT 2000. ASIACRYPT 2000. Lecture Notes in Computer Science, vol 1976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44448-3_19
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DOI: https://doi.org/10.1007/3-540-44448-3_19
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