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<li class="toctree-l2 current"><a class="current reference internal" href="#">ECDH: X25519</a><ul>
<li class="toctree-l3"><a class="reference internal" href="#key-generation">Key Generation</a></li>
<li class="toctree-l3"><a class="reference internal" href="#ecdh-shared-secret">ECDH Shared Secret</a></li>
<li class="toctree-l3"><a class="reference internal" href="#other-curves-p-256">Other Curves: P-256</a></li>
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<div class="section" id="ecdh-x25519">
<span id="hacl-curve25519"></span><h1>ECDH: X25519<a class="headerlink" href="#ecdh-x25519" title="Permalink to this headline">¶</a></h1>
<p>HACL* implements the X25519 Elliptic Curve Diffie Hellman (ECDH)
construction <a class="reference external" href="https://tools.ietf.org/html/rfc7748">IETF RFC 7748</a>.
The library includes two implementations of this construction,
both with the same API, but meant for use on different platforms:</p>
<ul class="simple">
<li><code class="docutils literal notranslate"><span class="pre">Hacl_Curve25519_51.h</span></code> contains a portable C implementation that
is optimized for use on 64-bit platforms that support 128-bit arithmetic,
but it will still compile and execute on 32-bit platforms (using an emulated
128-bit arithmetic library provided by KreMLin).</li>
<li><code class="docutils literal notranslate"><span class="pre">Hacl_Curve25519_64.h</span></code> contains a hybrid C/assembly implementation:
the field arithmetic functions are in Intel assembly (generated by Vale)
and rely on the Intel ADX and BMI2 instruction sets; the elliptic curve
functions and the main API are in portable C.</li>
</ul>
<p>Both versions provide functions that can be used to generate Curve25519 keypairs
and use them to compute ECDH shared secrets.</p>
<div class="section" id="key-generation">
<h2>Key Generation<a class="headerlink" href="#key-generation" title="Permalink to this headline">¶</a></h2>
<p>Any 32 byte array can be used as a Curve25519 private key. In
practice, private keys should be generated using a cryptographically
strong pseudo-random number generator (CSPRNG). In some cases, the
private key may be derived as the result of a key derivation function
such as HKDF.</p>
<p>Given a private key, the corresponding public key can be computed
using the <code class="docutils literal notranslate"><span class="pre">secret_to_public</span></code> function:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span>
<span class="kt">void</span><span class="w"> </span><span class="nf">Hacl_Curve25519_51_secret_to_public</span><span class="p">(</span><span class="kt">uint8_t</span><span class="w"> </span><span class="o">*</span><span class="n">pub</span><span class="p">,</span><span class="w"> </span><span class="kt">uint8_t</span><span class="w"> </span><span class="o">*</span><span class="n">priv</span><span class="p">);</span><span class="w"></span>
</pre></div>
</div>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span>
<span class="kt">void</span><span class="w"> </span><span class="nf">Hacl_Curve25519_64_secret_to_public</span><span class="p">(</span><span class="kt">uint8_t</span><span class="w"> </span><span class="o">*</span><span class="n">pub</span><span class="p">,</span><span class="w"> </span><span class="kt">uint8_t</span><span class="w"> </span><span class="o">*</span><span class="n">priv</span><span class="p">);</span><span class="w"></span>
</pre></div>
</div>
<p>The first argument is a pointer to the output public key <code class="docutils literal notranslate"><span class="pre">pub</span></code>;
the second argument is a pointer to the input private key <code class="docutils literal notranslate"><span class="pre">priv</span></code>.</p>
</div>
<div class="section" id="ecdh-shared-secret">
<h2>ECDH Shared Secret<a class="headerlink" href="#ecdh-shared-secret" title="Permalink to this headline">¶</a></h2>
<p>The ECDH operation is implemented by the following function:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span>
<span class="kt">bool</span><span class="w"> </span><span class="nf">Hacl_Curve25519_51_ecdh</span><span class="p">(</span><span class="kt">uint8_t</span><span class="w"> </span><span class="o">*</span><span class="n">out</span><span class="p">,</span><span class="w"> </span><span class="kt">uint8_t</span><span class="w"> </span><span class="o">*</span><span class="n">priv</span><span class="p">,</span><span class="w"> </span><span class="kt">uint8_t</span><span class="w"> </span><span class="o">*</span><span class="n">pub</span><span class="p">);</span><span class="w"></span>
</pre></div>
</div>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span>
<span class="kt">bool</span><span class="w"> </span><span class="nf">Hacl_Curve25519_64_ecdh</span><span class="p">(</span><span class="kt">uint8_t</span><span class="w"> </span><span class="o">*</span><span class="n">out</span><span class="p">,</span><span class="w"> </span><span class="kt">uint8_t</span><span class="w"> </span><span class="o">*</span><span class="n">priv</span><span class="p">,</span><span class="w"> </span><span class="kt">uint8_t</span><span class="w"> </span><span class="o">*</span><span class="n">pub</span><span class="p">);</span><span class="w"></span>
</pre></div>
</div>
<p>The first argument is a pointer to the output shared secret <code class="docutils literal notranslate"><span class="pre">out</span></code>;
the second argument is the private key of the caller <code class="docutils literal notranslate"><span class="pre">priv</span></code>;
the last argument is the public key of the peer <code class="docutils literal notranslate"><span class="pre">pub</span></code>.
The size of all three arrays must be (at least) 32 bytes.</p>
<p>The function returns a boolean since it may fail.
If the computed shared secret is an array of all zeroes,
then the function <code class="docutils literal notranslate"><span class="pre">ecdh</span></code> returns false to indicate that the operation failed.
Otherwise, it returns true.</p>
</div>
<div class="section" id="other-curves-p-256">
<h2>Other Curves: P-256<a class="headerlink" href="#other-curves-p-256" title="Permalink to this headline">¶</a></h2>
<p>A development branch includes a verified implementation of P-256,
which has not yet been merged to master. Contact the HACL* maintainers
if you wish to use this code.</p>
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