<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

Computation of Trusted 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.

{"article-title":"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...

Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography

Publié en ligne: 01 juil. 2021

Pages: 70 - 88

Reçu: 02 févr. 2021

Accepté: 05 mars 2021

DOI: https://doi.org/10.2478/cait-2021-0020

Mots clés
Short Weierstrass elliptic curves, prime field, cryptography, ECDLP Security, ECC Security, Trusted Security

© 2021 Kunal Abhishek et al., published by Sciendo

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

Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography

Publié en ligne: 01 juil. 2021

Pages: 70 - 88

Reçu: 02 févr. 2021

Accepté: 05 mars 2021

DOI: https://doi.org/10.2478/cait-2021-0020

Mots clésShort Weierstrass elliptic curves, prime field, cryptography, ECDLP Security, ECC Security, Trusted Security

© 2021 Kunal Abhishek et al., published by Sciendo

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

Mots clés
Short Weierstrass elliptic curves, prime field, cryptography, ECDLP Security, ECC Security, Trusted Security