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monero-wallet-gui </a> </li> <li class=md-nav__item> <a href=../../../interacting/monero-wallet-rpc-reference/ class=md-nav__link> monero-wallet-rpc </a> </li> <li class=md-nav__item> <a href=../../../interacting/monero-blockchain-export-reference/ class=md-nav__link> monero-blockchain-export </a> </li> <li class=md-nav__item> <a href=../../../interacting/monero-blockchain-import-reference/ class=md-nav__link> monero-blockchain-import </a> </li> </ul> </nav> </li> <li class=md-nav__item> <a href=../../../technical-specs/ class=md-nav__link> Technical specs </a> </li> <li class="md-nav__item md-nav__item--active md-nav__item--nested"> <input class="md-nav__toggle md-toggle" data-md-toggle=nav-4 type=checkbox id=nav-4 checked> <label class=md-nav__link for=nav-4> Cryptography <span class="md-nav__icon md-icon"></span> </label> <nav class=md-nav aria-label=Cryptography data-md-level=1> <label class=md-nav__title for=nav-4> <span class="md-nav__icon md-icon"></span> Cryptography </label> <ul class=md-nav__list data-md-scrollfix> <li class=md-nav__item> <a href=../../introduction/ class=md-nav__link> Introduction </a> </li> <li class="md-nav__item md-nav__item--active md-nav__item--nested"> <input class="md-nav__toggle md-toggle" data-md-toggle=nav-4-2 type=checkbox id=nav-4-2 checked> <label class=md-nav__link for=nav-4-2> Asymmetric <span class="md-nav__icon md-icon"></span> </label> <nav class=md-nav aria-label=Asymmetric data-md-level=2> <label class=md-nav__title for=nav-4-2> <span class="md-nav__icon md-icon"></span> Asymmetric </label> <ul class=md-nav__list data-md-scrollfix> <li class=md-nav__item> <a href=../introduction/ class=md-nav__link> Introduction </a> </li> <li class="md-nav__item md-nav__item--active"> <input class="md-nav__toggle md-toggle" data-md-toggle=toc type=checkbox id=__toc> <label class="md-nav__link md-nav__link--active" for=__toc> Private keys <span class="md-nav__icon md-icon"></span> </label> <a href=./ class="md-nav__link md-nav__link--active"> Private keys </a> <nav class="md-nav md-nav--secondary" aria-label="Table of contents"> <label class=md-nav__title for=__toc> <span class="md-nav__icon md-icon"></span> Table of contents </label> <ul class=md-nav__list data-md-scrollfix> <li class=md-nav__item> <a href=#relation-to-ed25519 class=md-nav__link> Relation to Ed25519 </a> <nav class=md-nav aria-label="Relation to Ed25519"> <ul class=md-nav__list> <li class=md-nav__item> <a href=#key-strength class=md-nav__link> Key strength </a> </li> </ul> </nav> </li> <li class=md-nav__item> <a href=#encoding class=md-nav__link> Encoding </a> </li> <li class=md-nav__item> <a href=#private-spend-key class=md-nav__link> Private spend key </a> </li> <li class=md-nav__item> <a href=#private-view-key class=md-nav__link> Private view key </a> </li> <li class=md-nav__item> <a href=#one-time-private-keys class=md-nav__link> One-time private keys </a> </li> </ul> </nav> </li> <li class=md-nav__item> <a href=../public-key/ class=md-nav__link> Public keys </a> </li> <li class=md-nav__item> <a href=../edwards25519/ class=md-nav__link> Edwards25519 curve </a> </li> <li class=md-nav__item> <a href=../key-image/ class=md-nav__link> Key image </a> </li> </ul> </nav> </li> <li class=md-nav__item> <a href=../../base58/ class=md-nav__link> Base58 </a> </li> <li class=md-nav__item> <a href=../../prng/ class=md-nav__link> PRNG </a> </li> <li class=md-nav__item> <a href=../../keccak-256/ class=md-nav__link> Keccak-256 </a> </li> </ul> </nav> </li> <li class="md-nav__item md-nav__item--nested"> <input class="md-nav__toggle md-toggle" data-md-toggle=nav-5 type=checkbox id=nav-5> <label class=md-nav__link for=nav-5> Address <span class="md-nav__icon md-icon"></span> </label> <nav class=md-nav aria-label=Address data-md-level=1> <label class=md-nav__title for=nav-5> <span class="md-nav__icon md-icon"></span> Address </label> <ul class=md-nav__list data-md-scrollfix> <li class=md-nav__item> <a 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Cryptocurrencies </a> </li> <li class=md-nav__item> <a href=../../../proof-of-work/cryptonight/ class=md-nav__link> CryptoNight </a> </li> <li class=md-nav__item> <a href=../../../proof-of-work/random-x/ class=md-nav__link> RandomX </a> </li> </ul> </nav> </li> <li class=md-nav__item> <a href=../../../multisignature/ class=md-nav__link> Multisignature </a> </li> <li class="md-nav__item md-nav__item--nested"> <input class="md-nav__toggle md-toggle" data-md-toggle=nav-8 type=checkbox id=nav-8> <label class=md-nav__link for=nav-8> Infrastructure <span class="md-nav__icon md-icon"></span> </label> <nav class=md-nav aria-label=Infrastructure data-md-level=1> <label class=md-nav__title for=nav-8> <span class="md-nav__icon md-icon"></span> Infrastructure </label> <ul class=md-nav__list data-md-scrollfix> <li class=md-nav__item> <a href=../../../infrastructure/networks/ class=md-nav__link> Mainnet, stagenet, testnet </a> </li> <li class=md-nav__item> <a 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for=nav-10> Accepting Monero <span class="md-nav__icon md-icon"></span> </label> <nav class=md-nav aria-label="Accepting Monero" data-md-level=1> <label class=md-nav__title for=nav-10> <span class="md-nav__icon md-icon"></span> Accepting Monero </label> <ul class=md-nav__list data-md-scrollfix> <li class=md-nav__item> <a href=../../../accepting-monero/overview/ class=md-nav__link> Overview </a> </li> </ul> </nav> </li> </ul> </nav> </div> </div> </div> <div class="md-sidebar md-sidebar--secondary" data-md-component=toc> <div class=md-sidebar__scrollwrap> <div class=md-sidebar__inner> <nav class="md-nav md-nav--secondary" aria-label="Table of contents"> <label class=md-nav__title for=__toc> <span class="md-nav__icon md-icon"></span> Table of contents </label> <ul class=md-nav__list data-md-scrollfix> <li class=md-nav__item> <a href=#relation-to-ed25519 class=md-nav__link> Relation to Ed25519 </a> <nav class=md-nav aria-label="Relation to Ed25519"> <ul class=md-nav__list> <li class=md-nav__item> <a href=#key-strength class=md-nav__link> Key strength </a> </li> </ul> </nav> </li> <li class=md-nav__item> <a href=#encoding class=md-nav__link> Encoding </a> </li> <li class=md-nav__item> <a href=#private-spend-key class=md-nav__link> Private spend key </a> </li> <li class=md-nav__item> <a href=#private-view-key class=md-nav__link> Private view key </a> </li> <li class=md-nav__item> <a href=#one-time-private-keys class=md-nav__link> One-time private keys </a> </li> </ul> </nav> </div> </div> </div> <div class=md-content> <article class="md-content__inner md-typeset"> <a href=https://github.com/monerodocs/md/edit/master/docs/cryptography/asymmetric/private-key.md title="Edit this page" class="md-content__button md-icon"> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M20.71 7.04c.39-.39.39-1.04 0-1.41l-2.34-2.34c-.37-.39-1.02-.39-1.41 0l-1.84 1.83 3.75 3.75M3 17.25V21h3.75L17.81 9.93l-3.75-3.75L3 17.25z"/></svg> </a> <h1 id=private-keys-in-monero>Private Keys in Monero<a class=headerlink href=#private-keys-in-monero title="Permanent link">¶</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">¶</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">¶</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">¶</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">¶</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">¶</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">¶</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> </article> </div> </div> </main> <footer class=md-footer> <div class=md-footer-nav> <nav class="md-footer-nav__inner md-grid" aria-label=Footer> <a href=../introduction/ class="md-footer-nav__link md-footer-nav__link--prev" rel=prev> <div class="md-footer-nav__button md-icon"> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12z"/></svg> </div> <div class=md-footer-nav__title> <div class=md-ellipsis> <span class=md-footer-nav__direction> Previous </span> Introduction </div> </div> </a> <a href=../public-key/ class="md-footer-nav__link md-footer-nav__link--next" rel=next> <div class=md-footer-nav__title> <div class=md-ellipsis> <span class=md-footer-nav__direction> Next </span> Public keys </div> </div> <div class="md-footer-nav__button md-icon"> <svg xmlns=http://www.w3.org/2000/svg viewbox="0 0 24 24"><path d="M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11H4z"/></svg> </div> </a> </nav> </div> <div class="md-footer-meta md-typeset"> <div class="md-footer-meta__inner md-grid"> <div class=md-footer-copyright style="margin: auto;"> <a href=http://bumz4sduzxzlobbgzy5fiufdflg3mo2jyecdwdx5rphrqldms7wlmiid.onion/ >Tor onion version</a> | <a href=https://qertoip.com/ >contact</a> | © 2021 MoneroDocs under <a href=https://opensource.org/licenses/MIT>MIT</a> | built w/ <a href=https://www.mkdocs.org/ >mkdocs</a> and <a href=https://squidfunk.github.io/mkdocs-material/ >squidfunk/material</a> </div> </div> </div> </footer> </div> <script src=../../../assets/javascripts/vendor.93c04032.min.js></script> <script src=../../../assets/javascripts/bundle.83e5331e.min.js></script><script id=__lang type=application/json>{"clipboard.copy": "Copy to clipboard", "clipboard.copied": "Copied to clipboard", "search.config.lang": "en", "search.config.pipeline": "trimmer, stopWordFilter", "search.config.separator": "[\\s\\-]+", "search.placeholder": "Search", "search.result.placeholder": "Type to start searching", "search.result.none": "No matching documents", "search.result.one": "1 matching document", "search.result.other": "# matching documents", "search.result.more.one": "1 more on this page", "search.result.more.other": "# more on this page", "search.result.term.missing": "Missing"}</script> <script>
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