NIST elliptic-curve keys are stored using one of the following algorithm-name values, each corresponding to a different elliptic curve and key size:
ecdsa-sha2-nistp256’
ecdsa-sha2-nistp384’
ecdsa-sha2-nistp521’
The public key data has already provided the public elliptic curve point. The private key stores:
mpint: the private exponent, which is the discrete log of the public point.