## Cryptology ePrint Archive: Report 2009/597

Twisted Jacobi Intersections Curves

Rongquan Feng, Menglong Nie, Hongfeng Wu

Abstract: In this paper, the twisted Jacobi intersections which contains Jacobi intersections as a special case is introduced. We show that every elliptic curve over the prime field with three points of order $2$ is isomorphic to a twisted Jacobi intersections curve. Some fast explicit formulae for twisted Jacobi intersections curves in projective coordinates are presented. These explicit formulae for addition and doubling are almost as fast as the Jacobi intersections. In addition, the scalar multiplication can be more effective in twisted Jacobi intersections than in Jacobi intersections. Moreover, we propose new addition formulae which are independent of parameters of curves and more effective in reality than the previous formulae in the literature.

Category / Keywords: foundations / elliptic curves, Jacobi intersections, twisted Jacobi intersections, scalar multiplication, isomorphic