This paper presents a new sliding window algorithm that is well-suited to an elliptic curve defined over an extension field for which the Frobenius map can be computed quickly, e.g., optimal extension field. The algorithm reduces elliptic curve group operations by approximately 15% for scalar multiplications for a practically used curve in compared to Lim-Hwang's results presented at PKC2000, which was the fastest previously reported. The algorithm was implemented on computers. Scalar multiplication can be accomplished in 573μs. 595μs, and 254μs on Pentium II (450MHz), 21164A (500MHz), and 21264 (500MHz) computers, respectively.
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