Review of Elliptic Curve Cryptography processor designs

Abstract

Elliptic Curve Cryptography (ECC) is a multilayer system with increased hardware implementation complexity. A wide range of parameters and design choices affect the overall implementation of ECC systems. A variety of hardware implementations of ECC system that vary in parameters are proposed in the literature. Implementation target, underlying finite fields, coordinate system and modular arithmetic algorithms are key design elements that impact the overall implementation outcome. In this paper, we survey the various implementation approaches with the aim of providing a useful reference for hardware designers for building efficient ECC processors. Our literature review consists of four components. First, we list the design options and discuss their impact on ECC implementation. Second, we summarize different approaches and algorithms used in the literature for implementing modular arithmetic operations. Third, we review best practices in the literature for data paths and overall architectures. Fourth, we review the existing parallelism and performance enhancement techniques. In addition, this paper provides comparison of the different binary extension, prime and dual 8 hardware implementations of ECC.