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<h1 id="private-keys-in-monero">Private Keys in Monero<a class="headerlink" href="#private-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>In Monero, the root private key is generated <a href="/cryptography/prng">randomly</a>. Other private keys are derived deterministically from the root private key.</p>
<p>Private key must be kept secret.</p>
<p>Private key is a <strong>large integer</strong> impossible to guess, like:
<code>108555083659983933209597798445644913612440610624038028786991485007418559037440</code></p>
<p>Private key is 256 bits long. </p>
<p>Private key is a <strong>scalar</strong>, meaning it is a single value.</p>
<p>In equations scalars are represented by <strong>lowercase letters</strong>. </p>
<h2 id="relation-to-ed25519">Relation to Ed25519<a class="headerlink" href="#relation-to-ed25519" title="Permanent link">&para;</a></h2>
<p>Being simply a random integer, private key is not specific to any particular asymmetric cryptography scheme.</p>
<p>In context of Monero EC cryptography the private key is a number the base point <code>G</code> is multiplied by.
The result of the multiplication is the public key <code>P</code> (another point on the curve).
Multiplication of a point by a number has a very special definition in EC cryptography.
See this <a href="https://blog.cloudflare.com/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/">this guide</a> for details.</p>
<h3 id="key-strength">Key strength<a class="headerlink" href="#key-strength" title="Permanent link">&para;</a></h3>
<p>Before deriving the public key, private key is subject to modulo <code>l</code>,
where <code>l</code> is the maximum scalar allowed by the <a href="/cryptography/asymmetric/edwards25519">edwards25519 curve</a>.</p>
<p>The <code>l</code> is on the order of 2^252, so the effective key strength is technically 252 bits, not 256 bits.
This is standard for EC cryptography and is more of a cosmetic nuance than any concern.</p>
<h2 id="encoding">Encoding<a class="headerlink" href="#encoding" title="Permanent link">&para;</a></h2>
<p>In user-facing contexts, the private key integer is:</p>
<ol>
<li>Taken modulo <code>l</code> to avoid malleability</li>
<li>Put as array of 32 bytes in a <a href="https://en.wikipedia.org/wiki/Endianness#Little">little-endian</a> direction (the first byte is the least significant)</li>
<li>Converted to hexadecimal form, like: <code>b3588a87056fb21dc4d052d59e83b54293882e646b543c29478e4cf45c28a402</code></li>
</ol>
<h2 id="private-spend-key">Private spend key<a class="headerlink" href="#private-spend-key" title="Permanent link">&para;</a></h2>
<p>Private spend key is used to spend moneros.</p>
<p>More specifically, it is used to build one-time private keys which allow to spend related outputs.</p>
<h2 id="private-view-key">Private view key<a class="headerlink" href="#private-view-key" title="Permanent link">&para;</a></h2>
<p>Private view key is used to recognize your incoming transactions on the otherwise opaque blockchain.</p>
<h2 id="one-time-private-keys">One-time private keys<a class="headerlink" href="#one-time-private-keys" title="Permanent link">&para;</a></h2>
<p>One-time private key like construct is used in <a href="https://monero.stackexchange.com/questions/1409/constructing-a-stealth-monero-address">stealth addresses</a>.</p>
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