Scalar Multiplication on Koblitz Curves using tau2-NAF

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