Evaluation of Computational Approaches of Short Weierstrass Elliptic Curves for Cryptography
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 Pro...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2021-12-01
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| Series: | Cybernetics and Information Technologies |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/cait-2021-0045 |
| _version_ | 1811272293369774080 |
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| author | Abhishek Kunal Raj E. George Dharma Prakash |
| author_facet | Abhishek Kunal Raj E. George Dharma Prakash |
| author_sort | Abhishek Kunal |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T22:37:44Z |
| format | Article |
| id | doaj.art-d6d32d7f5606450db7c92c680c406cc6 |
| institution | Directory Open Access Journal |
| issn | 1314-4081 |
| language | English |
| last_indexed | 2024-04-12T22:37:44Z |
| publishDate | 2021-12-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Cybernetics and Information Technologies |
| spelling | doaj.art-d6d32d7f5606450db7c92c680c406cc62022-12-22T03:13:49ZengSciendoCybernetics and Information Technologies1314-40812021-12-0121410511810.2478/cait-2021-0045Evaluation of Computational Approaches of Short Weierstrass Elliptic Curves for CryptographyAbhishek Kunal0Raj E. George Dharma Prakash1Society for Electronic Transactions and Security, Chennai, IndiaBharathidasan University, Tiruchirappalli, IndiaThe 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.https://doi.org/10.2478/cait-2021-0045computational approachesevaluationcryptographyelliptic curveecdlpsecurity |
| spellingShingle | Abhishek Kunal Raj E. George Dharma Prakash Evaluation of Computational Approaches of Short Weierstrass Elliptic Curves for Cryptography Cybernetics and Information Technologies computational approaches evaluation cryptography elliptic curve ecdlp security |
| title | Evaluation of Computational Approaches of Short Weierstrass Elliptic Curves for Cryptography |
| title_full | Evaluation of Computational Approaches of Short Weierstrass Elliptic Curves for Cryptography |
| title_fullStr | Evaluation of Computational Approaches of Short Weierstrass Elliptic Curves for Cryptography |
| title_full_unstemmed | Evaluation of Computational Approaches of Short Weierstrass Elliptic Curves for Cryptography |
| title_short | Evaluation of Computational Approaches of Short Weierstrass Elliptic Curves for Cryptography |
| title_sort | evaluation of computational approaches of short weierstrass elliptic curves for cryptography |
| topic | computational approaches evaluation cryptography elliptic curve ecdlp security |
| url | https://doi.org/10.2478/cait-2021-0045 |
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