A variant of the Schnorr signature using an elliptic curve over a field of characteristic two

Abstract

Digital signature over elliptic curve is one of the most important applications of security because it is effective. Recently, it has been developed and defined in the various standard of security. The application of the digital signature are signer authentication, data integrity, and non-repudiation. Currently, the requirements to implement authentication process on a computer hardware with limited resource such as energy, memory and computing power are increasing. The developer should consider these factors along with security factor for the effective implement on the computer hardware with limited resource. In this paper, we propose the Schnorr signature scheme using Koblitz curve over a field of characteristic two. The advantage of Schnorr signature scheme is a good combination with Koblitz curve over a field of characteristic two, therefore its arithmetic can be performed in any computer. Moreover, we use Double-and-Add scalar multiplication to reduce time in the process of systems. In addition, this paper shows a result of time in the process of the system to compare the performance of the Schnorr signature scheme on Koblitz curve using Double-andAdd scalar multiplication with the Schnorr signature scheme on Koblitz curve using typical scalar multiplication. The result of this study is that both systems working correctly. However, the Schnorr signature scheme on Koblitz curve using Double-andAdd performs better in time efficiency than of Schnorr signature scheme on Koblitz curve using typical scalar multiplication.