Improved Arithmetic on Koblitz Curves over Binary Field

Abstract

The longest process in ECC is the elliptic curve scalar multiplication. The structure of this operation involves three mathematical levels; this work aims to study issues that arise in the efficient implementation of this operation, specifically targeting the point arithmetic level for the Koblitz curve over a binary field. Theorems have been made for a speedy point doubling and point addition operation, in these theorems Jacobian coordinate modification has been considered, where these coordinates represent each point:  refers to a point on a curve  over . This occurs when a coordinate system represents any point on a Koblitz curve over a binary field. By choosing the right coordinate system, it is possible to speed up the elliptic curve scalar multiplication using this method.