Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography

TL;DR

This paper proposes a new 'trusted security' framework for elliptic curve cryptography, introduces acceptance criteria, and demonstrates two secure elliptic curves over 256 and 384-bit fields with thorough security and performance evaluations.

Contribution

It introduces a novel 'trusted security' notion and acceptance criteria, and presents two cryptographically secure elliptic curves meeting these standards.

Findings

Two secure elliptic curves over 256 and 384-bit fields are demonstrated.

The proposed curves meet new 'trusted security' acceptance criteria.

Thorough security and performance analyses confirm their cryptographic suitability.

Abstract

Short Weierstrass's elliptic curves with underlying hard Elliptic Curve Discrete Logarithm Problems was widely used in Cryptographic applications. This paper introduces a new security notation 'trusted security' for computation methods of elliptic curves for cryptography. Three additional "trusted security acceptance criteria" is proposed 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.