Elliptic curves (EC) scalar multiplication over some finite fields, is an attractive research area, and it has been paid much attention by re- searchers in the recent years. Researchs still in progress to improve the imple- mentation of elliptic curves cryptography (ECC) and reducing its complexity. Elliptic curve point-halving algorithm proposed in [10], later double-base (DB) chain [3], and step multi-base representation (SMBR) [17] are among the ef- ficient techniques used in this field. The presented paper proposes a new algorithm combining SMBR and point halving. We extend the work done by [13], which combined DB chain with point halving technique. The experiment results show that our contribution can enhance EC scalar multiplication
