Efficient Scalar Multiplication on Koblitz Curves with Pre-computation

Scalar multiplication is the basic operation in elliptic curve cryptography. The double-base number system (DBNS) is an effective tool for speeding up scalar multiplication on elliptic curves. This paper proposes a novel decomposition algorithm for scalar n based on the specific double bases $$(\overline{\tau },\tau )$$ instead of the ordinary window $$\tau $$ -NAF. On $$\mu _{4}$$ -Koblitz curves, we evaluate the cost of our scalar multiplication method and compare it to related work. We also consider scalar multiplication using LD coordinates. Experiment results show that $$\mu _{4}$$ -Koblitz curves perform well.