An efficient scalar multiplication algorithm on Koblitz curves using τ³-NAF
by Ponnuru Surya Ganesh; R. Padmavathy; Anil Pinapati
International Journal of Security and Networks (IJSN), Vol. 17, No. 4, 2022

Abstract: 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 F₂ 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 τ²-NAF it is 0.215 m. This paper proposes a method to improve the efficiency of scalar multiplication on Koblitz curves using τ³-NAF representation that further reduces the point additions to 0.143 m.

Online publication date: Wed, 23-Nov-2022

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