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Title:
On the Optimal Pre-Computation of Window $\tau$NAF for Koblitz Curves
Authors: William R. Trost, Guangwu Xu
Abstract:Koblitz curves have been a nice subject of consideration for both theoretical and practical interests. The window \tau-adic algorithm of Solinas (window $\tau$NAF) is the most powerful method for computing point multiplication for Koblitz curves. Pre-computation plays an important role in improving the performance of point multiplication. In this paper, the concept of optimal pre-computation for window $\tau$NAF is formulated. In this setting, an optimal pre-computation has some mathematically natural and clean forms, and requires 2^{w-2}-1 point additions and two evaluations of the Frobenius map \tau, where w is the window width. One of the main results of this paper is to construct an optimal pre-computation scheme for each window width w from 4 to 15 (more than practical needs). These pre-computations can be easily incorporated into implementations of window $\tau$NAF. The ideas in the paper can also be used to construct other suitable pre-computations. This paper also includes a discussion of coefficient sets for window $\tau$NAF and the divisibility by powers of \tau through different approaches.
ePrint: https://eprint.iacr.org/2014/664
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