Elliptic curves in Huff’s model |
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基金项目: | Supported by the National Natural Science Foundation of China (11101002,10990011) |
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摘 要: | In this paper,we present the generalized Huff curves that contain Huff’s model as a special case.First,it is proved that every elliptic curve with three points of order 2 is isomorphic to a generalized Huff curve.Then,the fast and explicit formulae are derived for generalized Huff curves in projective coordinates.This paper also enumerates the number of isomorphism classes of generalized Huff curves over finite fields.Finally,the explicit formulae are presented for the doubling step and addition step in Miller’s algorithm to compute the Tate pairing on generalized Huff elliptic curves.
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关 键 词: | elliptic curve Huff curve cryptography scalar multiplication isomorphism classes |
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