ECC key parameters (The Libgcrypt Reference Manual)

6.2.3 ECC key parameters

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

(private-key
  (ecc
    (p p-mpi)
    (a a-mpi)
    (b b-mpi)
    (g g-point)
    (n n-mpi)
    (q q-point)
    (d d-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 = dG.
d-mpi: The private key d

All point values are encoded in standard format; Libgcrypt does in general only support uncompressed points, thus the first byte needs to be 0x04. However “EdDSA” describes its own compression scheme which is used by default; the non-standard first byte 0x40 may optionally be used to explicit flag the use of the algorithm’s native compression method.

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")
    (q q-point)
    (d d-mpi)))

Note that q-point is optional for a private key. The curve parameter may be given in any case and is used to replace missing parameters.

Currently implemented curves are:

Curve25519
X25519
1.3.6.1.4.1.3029.1.5.1
1.3.101.110: The RFC-8410 255 bit curve, its RFC name, OpenPGP and RFC OIDs.
X448
1.3.101.111: The RFC-8410 448 bit curve and its RFC OID.
Ed25519
1.3.6.1.4.1.11591.15.1
1.3.101.112: The signing variant of the RFC-8410 255 bit curve, its OpenPGP and RFC OIDs.
Ed448
1.3.101.113: The signing variant of the RFC-8410 448 bit curve and its RFC OID.
NIST P-192
1.2.840.10045.3.1.1
nistp192
prime192v1
secp192r1: The NIST 192 bit curve, its OID and aliases.
NIST P-224
1.3.132.0.33
nistp224
secp224r1: The NIST 224 bit curve, its OID and aliases.
NIST P-256
1.2.840.10045.3.1.7
nistp256
prime256v1
secp256r1: The NIST 256 bit curve, its OID and aliases.
NIST P-384
1.3.132.0.34
nistp384
secp384r1: The NIST 384 bit curve, its OID and aliases.
NIST P-521
1.3.132.0.35
nistp521
secp521r1: The NIST 521 bit curve, its OID and aliases.
brainpoolP160r1
1.3.36.3.3.2.8.1.1.1: The Brainpool 160 bit curve and its OID.
brainpoolP192r1
1.3.36.3.3.2.8.1.1.3: The Brainpool 192 bit curve and its OID.
brainpoolP224r1
1.3.36.3.3.2.8.1.1.5: The Brainpool 224 bit curve and its OID.
brainpoolP256r1
1.3.36.3.3.2.8.1.1.7: The Brainpool 256 bit curve and its OID.
brainpoolP320r1
1.3.36.3.3.2.8.1.1.9: The Brainpool 320 bit curve and its OID.
brainpoolP384r1
1.3.36.3.3.2.8.1.1.11: The Brainpool 384 bit curve and its OID.
brainpoolP512r1
1.3.36.3.3.2.8.1.1.13: The Brainpool 512 bit curve and its OID.
GOST2001-test
1.2.643.2.2.35.0
GOST2001-CryptoPro-A
1.2.643.2.2.35.1
GOST2001-CryptoPro-B
1.2.643.2.2.35.2
GOST2001-CryptoPro-C
1.2.643.2.2.35.3
GOST2001-CryptoPro-A
GOST2001-CryptoPro-XchA
GOST2001-CryptoPro-C
GOST2001-CryptoPro-XchB
GOST2001-CryptoPro-A
1.2.643.2.2.36.0
GOST2001-CryptoPro-C
1.2.643.2.2.36.1
GOST2012-256-tc26-A
1.2.643.7.1.2.1.1.1
GOST2001-CryptoPro-A
1.2.643.7.1.2.1.1.2
GOST2001-CryptoPro-A
GOST2012-256-tc26-B
GOST2001-CryptoPro-B
1.2.643.7.1.2.1.1.3
GOST2001-CryptoPro-B
GOST2012-256-tc26-C
GOST2001-CryptoPro-C
1.2.643.7.1.2.1.1.4
GOST2001-CryptoPro-C
GOST2012-256-tc26-D
GOST2012-512-test
GOST2012-test
GOST2012-512-test
1.2.643.7.1.2.1.2.0
GOST2012-512-tc26-A
GOST2012-tc26-A
GOST2012-512-tc26-B
GOST2012-tc26-B
GOST2012-512-tc26-A
1.2.643.7.1.2.1.2.1
GOST2012-512-tc26-B
1.2.643.7.1.2.1.2.2
GOST2012-512-tc26-C
1.2.643.7.1.2.1.2.3
secp256k1
1.3.132.0.10
sm2p256v1
1.2.156.10197.1.301

As usual the OIDs may optionally be prefixed with the string OID. or oid..