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
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