Speeding up Huff form of elliptic curves

This paper presents faster inversion-free point addition formulas for the curve y (1+ax^2) = cx (1+dy^2) . The proposed formulas improve the point doubling operation count record ( I , M , S , D , a are arithmetic operations over a field. I : inversion, M : multiplication, S : squaring, D : multiplication by a curve constant, a : addition/subtraction) from 6𝐌+ 5𝐒 to 8𝐌 and mixed addition operation count record from 10𝐌 to 8𝐌 . Both sets of formulas are shown to be 4-way parallel, leading to an effective cost of 2𝐌 per either of the group operations.