Evaluation of Computational Approaches of Short Weierstrass Elliptic Curves for Cryptography

Abstract

The survey presents the evolution of Short Weierstrass elliptic curves after their introduction in cryptography. Subsequently, this evolution resulted in the establishment of present elliptic curve computational standards. We discuss the chronology of attacks on Elliptic Curve Discrete Logarithm Problem (ECDLP) and investigate their countermeasures to highlight the evolved selection criteria of cryptographically safe elliptic curves. Further, two popular deterministic and random approaches for selection of Short Weierstrass elliptic curve for cryptography are evaluated from computational, security and trust perspectives and a trend in existent computational standards is demonstrated. Finally, standard and non-standard elliptic curves are analysed to add a new insight into their usability. There is no such survey conducted in past to the best of our knowledge.

RSA and Elliptic Curve Encryption System

“…A survey of the development of Short Weierstrass elliptic curves since their emergence in cryptography was undertaken by Abhishek et al (2021). The authors highlighted the evolutionary selection criteria of cryptographically secure elliptic curves by examining numerous attacks on elliptic curve encryption and their defenses.…”