Software Application to Evaluate the Complexity Theory of the RSA and Elliptic Curves Asymmetric Algorithms

In the current study, we performed a quantitative evaluation of digital signature algorithms between the asymmetric cryptographic scheme RSA (Rivest, Shamir, and Adleman) and ECDSA (Elliptic Curve Digital Signature Algorithm) with the purpose to limit or block illegal digital interferences. Mathematical foundations of asymmetric digital signature algorithms have been analyzed, giving a special focus to the mentioned algorithms. RSA and ECDSA have been coded in Java Development Environment, with their respective libraries. In addition, a Java software application has been designed and implemented with the respective algorithms of key generation and verification. We have used Scrum by articulating each of its phases with the architecture and extensible security elements of the Java platform. Thus, all of these processes have been applied, in order to establish the RSA or ECDSA with the most suitable characteristics for the performance and confidentiality of transmitted information. The own standards of asymmetric digital signature algorithms and elliptic curves have been taken into account, so that the comparison appears adequate and produces data that, besides of being measurable, are also sustainable. The results obtained have been visualized through a statistical process as products of the determination of the response times obtained during this process. To verify these results, we have used a mathematical validation, based on the Least Squares method.