An ECC private key is described by this S-expression:

(private-key (ecc (pp-mpi) (aa-mpi) (bb-mpi) (gg-point) (nn-mpi) (qq-point) (dd-mpi)))

`p-mpi`- Prime specifying the field GF(p).
`a-mpi``b-mpi`- The two coefficients of the Weierstrass equation y^2 = x^3 + ax + b
`g-point`- Base point g.
`n-mpi`- Order of g
`q-point`- The point representing the public key Q = dP.
`d-mpi`- The private key d

All point values are encoded in standard format; Libgcrypt does
currently only support uncompressed points, thus the first byte needs to
be `0x04`

.

The public key is similar with "private-key" replaced by "public-key"
and no `d-mpi`.

If the domain parameters are well-known, the name of this curve may be used. For example

(private-key (ecc (curve "NIST P-192") (qq-point) (dd-mpi)))

The `curve`

parameter may be given in any case and is used to replace
missing parameters.

Currently implemented curves are:

`NIST P-192`

`1.2.840.10045.3.1.1`

`prime192v1`

`secp192r1`

- The NIST 192 bit curve, its OID, X9.62 and SECP aliases.
`NIST P-224`

`secp224r1`

- The NIST 224 bit curve and its SECP alias.
`NIST P-256`

`1.2.840.10045.3.1.7`

`prime256v1`

`secp256r1`

- The NIST 256 bit curve, its OID, X9.62 and SECP aliases.
`NIST P-384`

`secp384r1`

- The NIST 384 bit curve and its SECP alias.
`NIST P-521`

`secp521r1`

- The NIST 521 bit curve and its SECP alias.

`OID.`

or `oid.`

.