Elliptic curves in Huff’s model

Abstract

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.