Co-Z Addition Operation of Hessian Curve

This paper presents a co-Z addition operation of Hessian curve, which costs 8M to add two different points with the same z coordinate. By using of this operation, we propose a new method of precomputation for windows-based scalar multiplication, which needs only one field inversion to compute all precomputation points in afflne coordinate. Compared with the known fastest method based on extended projective coordinate, when less than 45 registers are available in the scalar multiplication, the proposed method can save up to 2.6% by using the fractional wNAF.