Cyclic window method applied to elliptic curve cryptosystems

摘要

This paper presents a new sliding window algorithm that is well-suited for an elliptic Curve defined over an extension field for which the Frobenius map can be computed quickly, for example, OEF. The algorithm reduces elliptic curve group operations by approximately 15 for scalar multiplication calculations for a practically used curve in comparison with Lim-Hwang's results presented at PKC2OOO that is the best previously known. We implemented the algorithm on computers. As a result, scalar multiplication can be accomplished in 571μs, 595μs, or 254μs on a Pentium II (450MHx), 21164A (500MHz), or 21264 (500MHz) computer, respectively.