A WEIL PAIRING ON THE p-TORSION OF ORDINARY ELLIPTIC CURVES OVER K[ǫ]
نویسنده
چکیده
For an elliptic curve E over any field K, the Weil pairing en is a bilinear map on n-torsion. For K of characteristic p > 0, the map en is degenerate if and only if n is divisible by p. In this paper, we consider E over the dual numbers K[ǫ] and define a non-degenerate “Weil pairing on ptorsion” which shares many of the same properties of the Weil pairing. We also show that the discrete logarithm attacks on p-torsion subgroups of Semaev and Rück may be viewed as Weil-pairing-based attacks, just like the MOV attack. Finally, we describe an attack on the discrete logarithm problem on anomalous curves, analogous to that of Smart, using a lift of E over Fp[ǫ].
منابع مشابه
A Weil pairing on the p-torsion of ordinary elliptic curves over K[ ]
For an elliptic curve E over any field K, the Weil pairing en is a bilinear map on n-torsion. For K of characteristic p > 0, the map en is degenerate if and only if n is divisible by p. In this paper, we consider E over the dual numbers K[ ] and define a non-degenerate “Weil pairing on p-torsion” which shares many of the same properties of the Weil pairing. We also show that the discrete logari...
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