Review of Elliptic Curve Processor architectures

Abstract

Several Elliptic Curve Processors (ECP) have been proposed in the literature associated with various architectures using different and sometimes confusing terminologies. This paper is a short review study of ECP architectures, considering the hardware platforms used for their implementations. The main design parameters of the ECP architectures, including the field choice and scalar multiplication algorithms were identified. Based on these parameters, a statistical study is conducted on a large collection of the published work. From the analysis of the collected data, several conclusions were deduced, such as the notion that binary field is easier to be implemented in hardware than prime field as well as the polynomial basis is dominant over other bases representation. Another significant conclusion is that Montgomery scalar multiplier has been used more than Lopez-Dahab, Binary, and NAF methods, particularly with the dominance of Lopez-dahab Projective coordinate.