Performance Analysis and Comparison of Different Elliptic Curves on Smart Cards

Abstract

Elliptic curves are very often used in the cryptographic protocol design due to their memory efficiency and useful features, such as the bilinear pairing support. However, in many cryptographic papers, elliptic curves are used as a black box, without deeper consideration of their mathematical properties and, even more importantly, without considering implementation implications. As a consequence, novel cryptographic schemes are being published without any real chance of implementation on constrained devices due to their lack of support of basic EC operations like point addition or scalar point multiplication. This paper provides the necessary theoretical overview of main forms of elliptic curves, in particular considering their computational and memory complexity. Next, all major platforms of programmable smart cards are evaluated with respect to EC support and the performance of basic arithmetic operations is assessed using benchmarks. Finally, the evaluation of the implementations of ECC schemes, such as ECDH and ECDSA, is presented.