A new elliptic curve scalar multiplication algorithm is proposed. The algorithm uses the Frobenius map on optimal extension field (OEF) and addition sequence. We introduce a new algorithm on generating addition sequence efficiently and also give some analysis about it. Based on this algorithm, a new method of computing scalar multiplication of elliptic curve over an OEF is presented. The new method is more efficient than the traditional scalar multiplication algorithms of elliptic curve over OEF. The comparisons of traditional method and the new method are also given.
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