Abstract
Scalar multiplication nP is the core operation of elliptic curve public-key cryptosystems. Double bases representation of n is proposed to speed up scalar multiplication. Avanzi et al. presented a recoding algorithm for Koblitz curves which works in all cases with optimal constants [1]. However, their algorithm may be expensive to implement because it requires many divisions in ℤ[τ]. In this paper, we show that divisions in ℤ[τ] can be replaced by divisions in ℤ. Our improved version of the algorithm runs in about 33% of the time of the Avanzi et al. algorithm on the Koblitz curve K-163, with larger improvements as the size of the curve increases.
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