A New Algorithm for Double Scalar Multiplication over Koblitz Curves

TL;DR

This paper introduces a new algorithm for double scalar multiplication on Koblitz curves that leverages a double-base number system to improve computational efficiency in elliptic curve cryptography.

Contribution

The paper presents a novel algorithm for generating sparse joint τ-adic representations, enhancing double scalar multiplication performance on Koblitz curves.

Findings

Achieved 12% speed improvement over existing methods

Developed a sparse joint τ-adic representation algorithm

Enhanced efficiency in elliptic curve cryptography computations

Abstract

Koblitz curves are a special set of elliptic curves and have improved performance in computing scalar multiplication in elliptic curve cryptography due to the Frobenius endomorphism. Double-base number system approach for Frobenius expansion has improved the performance in single scalar multiplication. In this paper, we present a new algorithm to generate a sparse and joint $\tau$-adic representation for a pair of scalars and its application in double scalar multiplication. The new algorithm is inspired from double-base number system. We achieve 12% improvement in speed against state-of-the-art $\tau$-adic joint sparse form.