Note on scalar multiplication using division polynomials

Scalar multiplication is the most important and expensive operation in elliptic curve cryptosystems. In this study, the authors improve the efficiency of the elliptic net algorithm to compute scalar multiplication by using the equivalence of elliptic nets. The proposed method saves four multiplications by a constant in each iteration loop. Experimental results also indicate that the proposed algorithm will be more efficient than the previously known results on this line while it is still slower than the state-of-the-art algorithm to compute scalar multiplication.