Analysis of Standard Elliptic Curves for the Implementation of Elliptic Curve Cryptography in Resource-Constrained E-commerce Applications

In the public key cryptography infrastructure of electronic commerce (E-commerce), use of the Rivest, Shamir, and Adleman (RSA) algorithm is very common. Due to the security requirements, the necessary key size of RSA is increasing exponentially. Because of this large key size, it is not convenient to use RSA in resource-constrained applications where computational speed, storage and bandwidth are limited. Elliptic Curve Cryptography (ECC) is the best alternative to the traditional RSA. ECC provides the same level of security as RSA but with reduced key size. The most important factor in the use of ECC is the selection of the correct elliptic curve. There are different types of elliptic curves suggested by various standards. The selection of the curve is dependent on various parameters, such as prime field size, the shape of the curve, etc. In this paper, sets of elliptic curves recommended by different standards for cryptography are selected, and the selected curves are analysed, focusing on the performance and security features. The performance of each curve is measured in terms of computation time. The analysis is performed by considering each curve for the implementation of the Elliptic Curve Diffie-Hellman (ECDH) algorithm and the Elliptic Curve Digital Signature Algorithm (ECDSA). The comparative table of selected curves is arranged according to the computation time taken by each curve to perform various operations when used for the ECC algorithms