Elliptic curve cryptography (ECC) is an efficient and widely used public-key cryptosystem. It uses relatively shorter keys compared to conventional cryptosystems hence offering faster computation. The efficiency of ECC relies heavily on the efficiency of scalar multiplication which internally depends on the representation of the scalar value. Based on the representation, the number of point additions and point doublings varies. Koblitz curves are binary elliptic curves defined over F_(2)and also known as anomalous binary curves. Scalar multiplication algorithms on these curves can be designed without any point doublings. In τ-NAF representation, we need 0.333 m point additions whereas in τ~(2)-NAF it is 0.215 m. This paper proposes a method to improve the efficiency of scalar multiplication on Koblitz curves using τ~(3)-NAF representation that further reduces the point additions to 0.143 m.
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