Computational cost analysis of elliptic curve arithmetic

Abstract

Elliptic curves are proposed for the asymmetrical cryptography by Neal Koblitz and Victor Miller in 1986 separately. Elliptic curve cryptography (ECC) is utilized by hardware embedded solutions on mobile equipments and smart cards after 2000. Currently, software implementation of ECC faces the computational speed problem. One of the proposed solutions is to do the arithmetic operations on different Euclidean coordinate systems. This paper concentrates on the research of this technique and delineates the performance results of the implementation of the aforementioned technique on the different cryptographic libraries such as CRYMPIX, GMP and MIRACL.