Title: An efficient scalar multiplication algorithm on Koblitz curves using τ³-NAF

Authors: Ponnuru Surya Ganesh; R. Padmavathy; Anil Pinapati

Addresses: Computer Science and Information Security, NIT, Warangal, India ' Department of Computer Science and Engineering, NIT, Warangal, India ' Department of Computer Science and Engineering, NIT, Calicut, India

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.

Keywords: Koblitz curves; scalar multiplication; Frobenius endomorphism; τ-NAF; τ²-NAF representation.

DOI: 10.1504/IJSN.2022.127152

International Journal of Security and Networks, 2022 Vol.17 No.4, pp.240 - 246

Received: 23 Nov 2021
Accepted: 10 Jan 2022
Published online: 23 Nov 2022 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article