A Cyclic Window Algorithm for Elliptic Curves over OEF

Tetsutaro KOBAYASHI  Fumitaka HOSHINO  Kazumaro AOKI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A   No.1   pp.121-128
Publication Date: 2003/01/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Asymmetric Ciphers
cyclic window algorithm,  optimal extension field,  base-φ expansion,  elliptic curve cryptosystem,  

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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 573 µs, 595 µs, and 254 µs on Pentium II (450 MHz), 21164A (500 MHz), and 21264 (500 MHz) computers, respectively.