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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 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:

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.

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


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