Elliptic curve cryptosystem is the focus of public cryptology nowadays

for it has many advantages which the RSA lacks.In this paper

a new elliptic curve scalar multiplication algorithm is proposed.The algorithm uses the Frobenius map on optimal extension field (OEF) and the logic operations of binary strings.Based on this algorithm

a new method of computing scalar multiplication of elliptic curve over an OEF is presented.The accurate analysis about it is given.The comparisons of traditional method and the new method are presented.The running time of new method is about 60%~80% of that of the traditional

φ

-adic scalar multiplication algorithms of elliptic curve over OEF.