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Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing (SNPD 2007)
Wide-w-NAF Method for Scalar Multiplication on Koblitz Curves
Haier International Training Center, Qingdao, China
July 30-August 01
ISBN: 0-7695-2909-7
Ming Li, Shandong University, China
Baodong Qin, Shandong University, China
Fanyu Kong, Shandong University, China
Daxing Li, Shandong University, China
At CRYPTO 1991, Koblitz proposed the anomalous binary curves for speeding up scalar multiplication in elliptic curve cryptosystem. At CRYPTO 1997, Solinas proposed the \tau-NAF method on Koblitz curves and reduced the Hamming weight of the scalar to n/3 over the field F_2n. AtPKC 2004, Avanzi et al combined the \tau-NAF with one point halving and reduced the Hamming weight of the scalar to 2n/7. Recently, Avanzi et al improved this method by introducing the wide-double-NAF whose Hamming weight is n/4. In this paper, we propose the wide-w-NAF, which is an extension of Avanzi?s wide-double-NAF, and reduce the Hamming weight to n/(w+1). When n \ge 144, our method is at least 43% -- 56% faster than Solinas?s \tau-NAF method and 21% -- 39% faster than Avanzi?s wide-double-NAF method without additional memory requirements.
Citation:
Ming Li, Baodong Qin, Fanyu Kong, Daxing Li, "Wide-w-NAF Method for Scalar Multiplication on Koblitz Curves," snpd, vol. 2, pp.143-148, Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing (SNPD 2007), 2007
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