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<p>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.</p>
</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.

Evaluation of Computational Approaches of Short Weierstrass Elliptic Curves for Cryptography

Cybernetics and Information Technologies

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The survey presents the evolution of Short Weierstrass elliptic curves after their introduction in cryptography. Subsequently, this evolution resulted in the...

Evaluation of Computational Approaches of Short Weierstrass Elliptic Curves for Cryptography

Published Online: Dec 09, 2021

Page range: 105 - 118

Received: Jul 06, 2021

Accepted: Nov 08, 2021

DOI: https://doi.org/10.2478/cait-2021-0045

Keywords
Computational approaches, evaluation, cryptography, elliptic curve, ECDLP, security

© 2021 Kunal Abhishek et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Evaluation of Computational Approaches of Short Weierstrass Elliptic Curves for Cryptography

Published Online: Dec 09, 2021

Page range: 105 - 118

Received: Jul 06, 2021

Accepted: Nov 08, 2021

DOI: https://doi.org/10.2478/cait-2021-0045

KeywordsComputational approaches, evaluation, cryptography, elliptic curve, ECDLP, security

© 2021 Kunal Abhishek et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Computational approaches, evaluation, cryptography, elliptic curve, ECDLP, security