The multiplication of points on elliptic curves is the most important opera
tion in the implementation of elliptic curve cryptosystems. Based on Froben
ius map, a fast multiplication on the curves defined by y(2) + xy = x(3) x(2) + 1 over finite fields of characteristic 2 is given, and its optimalit
y in thr sense of using minimal numbers of additions of points is proved.