Elliptic curve cryptosystem is the focus of public key cryptology nowadays, for it has many advantages RSA lacks. This paper introduced a new heuristic algorithm on computing multiple scalar multiplications of a given point. Based on this algorithm, a new method of computing scalar multiplication of elliptic curve over optimal extension field (OEF) using Frobenius map was presented. The new method is more efficient than the traditional ones. In the last part of this paper, the comparison was given in the end.
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