[Resource Topic] 2011/318: Scalar Multiplication on Koblitz Curves using $\tau^2-$NAF

Welcome to the resource topic for 2011/318

Title:
Scalar Multiplication on Koblitz Curves using $\tau^2-$NAF

Authors: Sujoy Sinha Roy, Chester Rebeiro, Debdeep Mukhopadhyay, Junko Takahashi, Toshinori Fukunaga

Abstract:

The paper proposes a $\tau^2-$NAF method for scalar multiplication on Koblitz curves, which requires asymptotically 0.215m point additions in GF(2^m). For $\tau^2-NAF method, point quading operation (a\rightarrow a^4) is performed instead of point squarings. The proposed method is faster than normal \tau-NAF method, which requires around \frac{m}{3}$ point additions. However, like width w based $\tau-NAF methods, there is an overhead of pre-computations in the \tau^2-NAF method. For extended binary fields of small size, the \tau^2-$NAF based scalar multiplication requires almost same number of point additions as in width 4 $\tau-NAF method. Though, complexity wise, \tau^2-$NAF based scalar multiplication and width $4-\tau-$NAF based scalar multiplication are similar, but the techniques are different.

ePrint: https://eprint.iacr.org/2011/318

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