A new addition formula for elliptic curves over GF(2n)

Abstract

In this paper, we propose a new addition formula in projective coordinates for elliptic curves over GF(2n). The new formula speeds up the elliptic curve scalar multiplication by reducing the number of field multiplications. This was achieved by rewriting the elliptic curve addition formula. The complexity analysis shows that the new addition formula speeds up the addition in projective coordinates by about 10-2 percent, which leads to enhanced scalar multiplication methods for random and Koblitz curves.