Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography
Short Weierstrass elliptic curves with underlying hard Elliptic Curve Discrete Logarithm Problem (ECDLP) are widely used in cryptographic applications. A notion of security called Elliptic Curve Cryptography (ECC) security is also suggested in literature to safeguard the elliptic curve cryptosystems...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2021-06-01
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| Series: | Cybernetics and Information Technologies |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/cait-2021-0020 |
| _version_ | 1818745148503228416 |
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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 | Short Weierstrass elliptic curves with underlying hard Elliptic Curve Discrete Logarithm Problem (ECDLP) are widely used in cryptographic applications. A notion of security called Elliptic Curve Cryptography (ECC) security is also suggested in literature to safeguard the elliptic curve cryptosystems from their implementation flaws. In this paper, a new security notion called the “trusted security” is introduced for computational method of elliptic curves for cryptography. We propose three additional “trusted security acceptance criteria” which need to be met by the elliptic curves aimed for cryptography. Further, two cryptographically secure elliptic curves over 256 bit and 384 bit prime fields are demonstrated which are secure from ECDLP, ECC as well as trust perspectives. The proposed elliptic curves are successfully subjected to thorough security analysis and performance evaluation with respect to key generation and signing/verification and hence, proven for their cryptographic suitability and great feasibility for acceptance by the community. |
| first_indexed | 2024-12-18T02:55:36Z |
| format | Article |
| id | doaj.art-936f87d5253942129cd84e549e91d974 |
| institution | Directory Open Access Journal |
| issn | 1314-4081 |
| language | English |
| last_indexed | 2024-12-18T02:55:36Z |
| publishDate | 2021-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Cybernetics and Information Technologies |
| spelling | doaj.art-936f87d5253942129cd84e549e91d9742022-12-21T21:23:22ZengSciendoCybernetics and Information Technologies1314-40812021-06-01212708810.2478/cait-2021-0020Computation of Trusted Short Weierstrass Elliptic Curves for CryptographyAbhishek Kunal0Raj E. George Dharma Prakash1Society for Electronic Transactions and Security, Chennai, IndiaBharathidasan University, Tiruchirappalli, IndiaShort Weierstrass elliptic curves with underlying hard Elliptic Curve Discrete Logarithm Problem (ECDLP) are widely used in cryptographic applications. A notion of security called Elliptic Curve Cryptography (ECC) security is also suggested in literature to safeguard the elliptic curve cryptosystems from their implementation flaws. In this paper, a new security notion called the “trusted security” is introduced for computational method of elliptic curves for cryptography. We propose three additional “trusted security acceptance criteria” which need to be met by the elliptic curves aimed for cryptography. Further, two cryptographically secure elliptic curves over 256 bit and 384 bit prime fields are demonstrated which are secure from ECDLP, ECC as well as trust perspectives. The proposed elliptic curves are successfully subjected to thorough security analysis and performance evaluation with respect to key generation and signing/verification and hence, proven for their cryptographic suitability and great feasibility for acceptance by the community.https://doi.org/10.2478/cait-2021-0020short weierstrass elliptic curvesprime fieldcryptographyecdlp securityecc securitytrusted security |
| spellingShingle | Abhishek Kunal Raj E. George Dharma Prakash Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography Cybernetics and Information Technologies short weierstrass elliptic curves prime field cryptography ecdlp security ecc security trusted security |
| title | Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography |
| title_full | Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography |
| title_fullStr | Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography |
| title_full_unstemmed | Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography |
| title_short | Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography |
| title_sort | computation of trusted short weierstrass elliptic curves for cryptography |
| topic | short weierstrass elliptic curves prime field cryptography ecdlp security ecc security trusted security |
| url | https://doi.org/10.2478/cait-2021-0020 |
| work_keys_str_mv | AT abhishekkunal computationoftrustedshortweierstrassellipticcurvesforcryptography AT rajegeorgedharmaprakash computationoftrustedshortweierstrassellipticcurvesforcryptography |