  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.
