Improved Software Implementation for Montgomery Elliptic Curve Cryptosystem

Abstract

The last decade witnessed rapid increase in multimedia and other applications that require transmitting and protecting huge amount of data streams simultaneously. For such applications, a high-performance cryptosystem is compulsory to provide necessary security services. Elliptic curve cryptosystem (ECC) has been introduced as a considerable option. However, the usual sequential implementation of ECC and the standard elliptic curve (EC) form cannot achieve required performance level. Moreover, the widely used Hardware implementation of ECC is costly option and may be not affordable. This research aims to develop a high-performance parallel software implementation for ECC. To achieve this, many experiments were performed to examine several factors affecting ECC performance including the projective coordinates, the scalar multiplication algorithm, the elliptic curve (EC) form, and the parallel implementation. The ECC performance was analyzed using the different factors to tune-up them and select the best choices to increase the speed of the cryptosystem. Experimental results illustrated that parallel Montgomery ECC implementation using homogenous projection achieves the highest performance level, since it scored the shortest time delay for ECC computations. In addition, results showed that NAF algorithm consumes less time to perform encryption and scalar multiplication operations in comparison with Montgomery ladder and binary methods. Java multi-threading technique was adopted to implement ECC computations in parallel. The proposed multithreaded Montgomery ECC implementation significantly improves the performance level compared to previously presented parallel and sequential implementations.