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<a name="ECC-key-parameters"></a>
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<p>
Previous: <a href="DSA-key-parameters.html#DSA-key-parameters" accesskey="p" rel="prev">DSA key parameters</a>, Up: <a href="Used-S_002dexpressions.html#Used-S_002dexpressions" accesskey="u" rel="up">Used S-expressions</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="ECC-key-parameters-1"></a>
<h4 class="subsection">6.2.3 ECC key parameters</h4>

<a name="ecc_005fkeyparam"></a><p>An ECC private key is described by this S-expression:
</p>
<div class="example">
<pre class="example">(private-key
  (ecc
    (p <var>p-mpi</var>)
    (a <var>a-mpi</var>)
    (b <var>b-mpi</var>)
    (g <var>g-point</var>)
    (n <var>n-mpi</var>)
    (q <var>q-point</var>)
    (d <var>d-mpi</var>)))
</pre></div>

<dl compact="compact">
<dt><var>p-mpi</var></dt>
<dd><p>Prime specifying the field <em>GF(p)</em>.
</p></dd>
<dt><var>a-mpi</var></dt>
<dt><var>b-mpi</var></dt>
<dd><p>The two coefficients of the Weierstrass equation <em>y^2 = x^3 + ax + b</em>
</p></dd>
<dt><var>g-point</var></dt>
<dd><p>Base point <em>g</em>.
</p></dd>
<dt><var>n-mpi</var></dt>
<dd><p>Order of <em>g</em>
</p></dd>
<dt><var>q-point</var></dt>
<dd><p>The point representing the public key <em>Q = dG</em>.
</p></dd>
<dt><var>d-mpi</var></dt>
<dd><p>The private key <em>d</em>
</p></dd>
</dl>

<p>All point values are encoded in standard format; Libgcrypt does in
general only support uncompressed points, thus the first byte needs to
be <code>0x04</code>.  However &ldquo;EdDSA&rdquo; describes its own compression
scheme which is used by default; the non-standard first byte
<code>0x40</code> may optionally be used to explicit flag the use of the
algorithmâs native compression method.
</p>
<p>The public key is similar with &quot;private-key&quot; replaced by &quot;public-key&quot;
and no <var>d-mpi</var>.
</p>
<p>If the domain parameters are well-known, the name of this curve may be
used.  For example
</p>
<div class="example">
<pre class="example">(private-key
  (ecc
    (curve &quot;NIST P-192&quot;)
    (q <var>q-point</var>)
    (d <var>d-mpi</var>)))
</pre></div>

<p>Note that <var>q-point</var> is optional for a private key.  The
<code>curve</code> parameter may be given in any case and is used to replace
missing parameters.
</p>
<p>Currently implemented curves are:
</p><dl compact="compact">
<dt><code>NIST P-192</code></dt>
<dt><code>1.2.840.10045.3.1.1</code></dt>
<dt><code>prime192v1</code></dt>
<dt><code>secp192r1</code></dt>
<dd><p>The NIST 192 bit curve, its OID, X9.62 and SECP aliases.
</p>
</dd>
<dt><code>NIST P-224</code></dt>
<dt><code>secp224r1</code></dt>
<dd><p>The NIST 224 bit curve and its SECP alias.
</p>
</dd>
<dt><code>NIST P-256</code></dt>
<dt><code>1.2.840.10045.3.1.7</code></dt>
<dt><code>prime256v1</code></dt>
<dt><code>secp256r1</code></dt>
<dd><p>The NIST 256 bit curve, its OID, X9.62 and SECP aliases.
</p>
</dd>
<dt><code>NIST P-384</code></dt>
<dt><code>secp384r1</code></dt>
<dd><p>The NIST 384 bit curve and its SECP alias.
</p>
</dd>
<dt><code>NIST P-521</code></dt>
<dt><code>secp521r1</code></dt>
<dd><p>The NIST 521 bit curve and its SECP alias.
</p>
</dd>
</dl>
<p>As usual the OIDs may optionally be prefixed with the string <code>OID.</code>
or <code>oid.</code>.
</p>

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