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<h1 id="public-keys-in-monero">Public Keys in Monero<a class="headerlink" href="#public-keys-in-monero" title="Permanent link">&para;</a></h1>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Author is nowhere close to being a cryptographer. Be sceptical on accuracy.</p>
</div>
<p>Public key is deterministically derived from private key based on <a href="/cryptography/asymmetric/edwards25519">edwards25519 curve</a> with a little Monero-specific twist.</p>
<p>Public key is meant to be shared. Assuming correct implementation, it is not practically possible to recover private key from public key. </p>
<p>Public key is a <strong>point (x,y)</strong> on the elliptic curve.</p>
<p>In equations points are represented by <strong>uppercase letters</strong>.</p>
<p>In user-facing contexts, public key is encoded in a <a href="https://en.wikipedia.org/wiki/Endianness#Little">little-endian</a> hexadecimal form, like:
<code>016a941812293cf9a86071060fb090ab38d67945e659968cb8cf30e1bc725683</code> </p>
<h2 id="deriving-public-key">Deriving public key<a class="headerlink" href="#deriving-public-key" title="Permanent link">&para;</a></h2>
<p>Say:</p>
<ul>
<li>P is a public key</li>
<li>x is a private key</li>
<li>G is a "base point"; this is simply a constant specific to <a href="/cryptography/asymmetric/edwards25519">edwards25519</a>; this point lies on the elliptic curve</li>
</ul>
<p>Then:</p>
<div class="highlight"><pre><span></span><code>P = xG
</code></pre></div>
<p>The public key is simply the base point (G) multiplied by the private key (x).
Multiplying the point is adding the point to itself a number of times.</p>
<p>However, the addition is <strong>not</strong> a simple vector addition. It has a very specific
definition nicely described in <a href="https://blog.cloudflare.com/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/">this article</a>.
What is important is that result of addition is always a point on the curve.
For example, G + G is another point on the curve.</p>
<h2 id="use-cases">Use cases<a class="headerlink" href="#use-cases" title="Permanent link">&para;</a></h2>
<p><a href="/public-address/standard-address">Monero address</a> is composed of public spend key and public view key.
These keys are used to build stealth addresses to receive payments. </p>
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