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<ol class="chapter"><li class="chapter-item expanded "><a href="rln.html"><strong aria-hidden="true">1.</strong> RLN</a></li><li class="chapter-item expanded "><a href="overview.html"><strong aria-hidden="true">2.</strong> Overview</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.2.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.2.1.</strong> Circom circuit</a></li></ol></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.3.</strong> Uses</a></li></ol></li><li class="chapter-item expanded "><a href="how_to_use.html"><strong aria-hidden="true">3.</strong> How to use</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> JavaScript RLN</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> Rust RLN</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li><li class="chapter-item expanded "><a href="appendix.html"><strong aria-hidden="true">5.</strong> Appendix</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">5.1.</strong> A - Terminology</a></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">5.2.</strong> B - References</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded "><a href="about.html"><strong aria-hidden="true">1.</strong> About</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">2.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.2.</strong> Uses</a></li><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">2.3.</strong> Terminology</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.4.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.4.1.</strong> Circom Circuit</a></li></ol></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">2.5.</strong> References</a></li></ol></li><li class="chapter-item expanded "><a href="code.html" class="active"><strong aria-hidden="true">3.</strong> Usage</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> RLN in JavaScript</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> RLN in Rust</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li></ol>
<ol class="chapter"><li class="chapter-item expanded "><a href="rln.html"><strong aria-hidden="true">1.</strong> RLN</a></li><li class="chapter-item expanded "><a href="overview.html"><strong aria-hidden="true">2.</strong> Overview</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.2.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.2.1.</strong> Circom circuit</a></li></ol></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.3.</strong> Uses</a></li></ol></li><li class="chapter-item expanded "><a href="how_to_use.html" class="active"><strong aria-hidden="true">3.</strong> How to use</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> JavaScript RLN</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> Rust RLN</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li><li class="chapter-item expanded "><a href="appendix.html"><strong aria-hidden="true">5.</strong> Appendix</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">5.1.</strong> A - Terminology</a></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">5.2.</strong> B - References</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded "><a href="rln.html" class="active"><strong aria-hidden="true">1.</strong> RLN</a></li><li class="chapter-item expanded "><a href="overview.html"><strong aria-hidden="true">2.</strong> Overview</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.2.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.2.1.</strong> Circom circuit</a></li></ol></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.3.</strong> Uses</a></li></ol></li><li class="chapter-item expanded "><a href="how_to_use.html"><strong aria-hidden="true">3.</strong> How to use</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> JavaScript RLN</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> Rust RLN</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li><li class="chapter-item expanded "><a href="appendix.html"><strong aria-hidden="true">5.</strong> Appendix</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">5.1.</strong> A - Terminology</a></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">5.2.</strong> B - References</a></li></ol></li></ol>
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<p><strong>RLN</strong> (Rate-Limiting Nullifier) is part of (<strong>PSE</strong>) <a href="https://appliedzkp.org">Privacy &amp; Scaling Explorations</a>, a multidisciplinary team supported by the Ethereum Foundation. PSE explores new use cases for zero knowledge proofs and other cryptographic primitives.</p>
<h1 id="rln"><a class="header" href="#rln">RLN</a></h1>
<p><strong>RLN</strong> (Rate-Limiting Nullifier) is part of (<strong>PSE</strong>) <a href="https://appliedzkp.org">Privacy &amp; Scaling Explorations</a>, a multidisciplinary team supported by the Ethereum Foundation. PSE explores new use cases for zero-knowledge proofs and other cryptographic primitives.</p>
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<ol class="chapter"><li class="chapter-item expanded "><a href="about.html"><strong aria-hidden="true">1.</strong> About</a></li><li class="chapter-item expanded "><a href="concepts.html" class="active"><strong aria-hidden="true">2.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.2.</strong> Uses</a></li><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">2.3.</strong> Terminology</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.4.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.4.1.</strong> Circom Circuit</a></li></ol></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">2.5.</strong> References</a></li></ol></li><li class="chapter-item expanded "><a href="code.html"><strong aria-hidden="true">3.</strong> Usage</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> RLN in JavaScript</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> RLN in Rust</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li></ol>
<ol class="chapter"><li class="chapter-item expanded "><a href="rln.html"><strong aria-hidden="true">1.</strong> RLN</a></li><li class="chapter-item expanded "><a href="overview.html" class="active"><strong aria-hidden="true">2.</strong> Overview</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.2.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.2.1.</strong> Circom circuit</a></li></ol></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.3.</strong> Uses</a></li></ol></li><li class="chapter-item expanded "><a href="how_to_use.html"><strong aria-hidden="true">3.</strong> How to use</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> JavaScript RLN</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> Rust RLN</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li><li class="chapter-item expanded "><a href="appendix.html"><strong aria-hidden="true">5.</strong> Appendix</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">5.1.</strong> A - Terminology</a></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">5.2.</strong> B - References</a></li></ol></li></ol>
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<h1 id="concepts"><a class="header" href="#concepts">Concepts</a></h1>
<p>This section is a starting point for understanding the concepts of RLN.</p>
<h1 id="overview"><a class="header" href="#overview">Overview</a></h1>
<p>This section is a starting point for understanding the concepts of <strong>RLN</strong>.</p>
<p>Here we'll discuss:</p>
<ul>
<li>Basic explanation of the <strong>RLN</strong> protocol</li>
<li><strong>RLN</strong> protocol under the hood</li>
<li><strong>RLN</strong> uses</li>
</ul>
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<ol class="chapter"><li class="chapter-item expanded "><a href="about.html"><strong aria-hidden="true">1.</strong> About</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">2.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.2.</strong> Uses</a></li><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">2.3.</strong> Terminology</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.4.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.4.1.</strong> Circom Circuit</a></li></ol></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">2.5.</strong> References</a></li></ol></li><li class="chapter-item expanded "><a href="code.html"><strong aria-hidden="true">3.</strong> Usage</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> RLN in JavaScript</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> RLN in Rust</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li></ol>
<ol class="chapter"><li class="chapter-item expanded "><a href="rln.html"><strong aria-hidden="true">1.</strong> RLN</a></li><li class="chapter-item expanded "><a href="overview.html"><strong aria-hidden="true">2.</strong> Overview</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.2.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.2.1.</strong> Circom circuit</a></li></ol></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.3.</strong> Uses</a></li></ol></li><li class="chapter-item expanded "><a href="how_to_use.html"><strong aria-hidden="true">3.</strong> How to use</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> JavaScript RLN</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> Rust RLN</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li><li class="chapter-item expanded "><a href="appendix.html"><strong aria-hidden="true">5.</strong> Appendix</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">5.1.</strong> A - Terminology</a></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">5.2.</strong> B - References</a></li></ol></li></ol>
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@@ -135,34 +135,24 @@
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<h1 id="about"><a class="header" href="#about">About</a></h1>
<p><strong>RLN</strong> (Rate-Limiting Nullifier) is part of (<strong>PSE</strong>) <a href="https://appliedzkp.org">Privacy &amp; Scaling Explorations</a>, a multidisciplinary team supported by the Ethereum Foundation. PSE explores new use cases for zero knowledge proofs and other cryptographic primitives.</p>
<h1 id="rln"><a class="header" href="#rln">RLN</a></h1>
<p><strong>RLN</strong> (Rate-Limiting Nullifier) is part of (<strong>PSE</strong>) <a href="https://appliedzkp.org">Privacy &amp; Scaling Explorations</a>, a multidisciplinary team supported by the Ethereum Foundation. PSE explores new use cases for zero-knowledge proofs and other cryptographic primitives.</p>
<p><img src="./images/logo.svg" alt="alt text" /></p>
<p><strong>RLN</strong> team is working on the protocol (having the same name), implementations and different applications of it.</p>
<div style="break-before: page; page-break-before: always;"></div><h1 id="concepts"><a class="header" href="#concepts">Concepts</a></h1>
<p>This section is a starting point for understanding the concepts of RLN.</p>
<div style="break-before: page; page-break-before: always;"></div><h1 id="overview"><a class="header" href="#overview">Overview</a></h1>
<p>This section is a starting point for understanding the concepts of <strong>RLN</strong>.</p>
<p>Here we'll discuss:</p>
<ul>
<li>Basic explanation of the <strong>RLN</strong> protocol</li>
<li><strong>RLN</strong> protocol under the hood</li>
<li><strong>RLN</strong> uses</li>
</ul>
<div style="break-before: page; page-break-before: always;"></div><h1 id="what-is-rate-limiting-nullifier"><a class="header" href="#what-is-rate-limiting-nullifier">What is Rate-Limiting Nullifier?</a></h1>
<p><a href="https://ethresear.ch/t/semaphore-rln-rate-limiting-nullifier-for-spam-prevention-in-anonymous-p2p-setting/5009">Idea was proposed by Barry WhiteHat</a></p>
<p><a href="https://medium.com/privacy-scaling-explorations/rate-limiting-nullifier-a-spam-protection-mechanism-for-anonymous-environments-bbe4006a57d">RLN Overview</a></p>
<p><a href="https://hackmd.io/@aeAuSD7mSCKofwwx445eAQ/BJcfDByNF">RLN Spec</a></p>
<p><a href="https://rfc.vac.dev/spec/32/">VAC RLN Spec</a></p>
<div style="break-before: page; page-break-before: always;"></div><h1 id="uses"><a class="header" href="#uses">Uses</a></h1>
<div style="break-before: page; page-break-before: always;"></div><h1 id="terminology"><a class="header" href="#terminology">Terminology</a></h1>
<div class="table-wrapper"><table><thead><tr><th>Term</th><th>Description</th></tr></thead><tbody>
<tr><td>ZK-SNARK</td><td><a href="https://z.cash/technology/zksnarks/">z.cash/technology/zksnarks/</a></td></tr>
<tr><td>Stake</td><td>Financial or social stake required for registering in the RLN applications. Common stake examples are: locking cryptocurrency (financial), linking reputable social identity.</td></tr>
<tr><td>Identity secret</td><td>An array of two unique random components (identity nullifier and identity trapdoor), which must be kept private by the user. Secret hash and identity commitment are derived from this array.</td></tr>
<tr><td>Identity nullifier</td><td>Random 32 byte value used as component for identity secret generation.</td></tr>
<tr><td>Identity trapdoor</td><td>Random 32 byte value used as component for identity secret generation.</td></tr>
<tr><td>Identity secret hash</td><td>The hash of the identity secret, obtained using the Poseidon hash function. It is used for deriving the identity commitment of the user, and as a private input for zk proof generation. The secret hash should be kept private by the user.</td></tr>
<tr><td>Identity commitment</td><td>Hash obtained from the Identity secret hash by using the poseidon hash function. It is used by the users for registering in the protocol.</td></tr>
<tr><td>Signal</td><td>The message generated by a user. It is an arbitrary bit string that may represent a chat message, a URL request, protobuf message, etc.</td></tr>
<tr><td>Signal hash</td><td>Keccak hash of the signal, used as an input in the RLN circuit.</td></tr>
<tr><td>RLN Identifier</td><td>Random finite field value unique per RLN app. It is used for additional cross-application security. The role of the RLN identifier is protection of the user secrets being compromised if signals are being generated with the same credentials at different apps.</td></tr>
<tr><td>RLN membership tree</td><td>Merkle tree data structure, filled with identity commitments of the users. Serves as a data structure that ensures user registrations.</td></tr>
<tr><td>Merkle proof</td><td>Proof that a user is member of the RLN membership tree.</td></tr>
</tbody></table>
</div><div style="break-before: page; page-break-before: always;"></div><h1 id="under-the-hood"><a class="header" href="#under-the-hood">Under the hood</a></h1>
<div style="break-before: page; page-break-before: always;"></div><h1 id="under-the-hood"><a class="header" href="#under-the-hood">Under the hood</a></h1>
<div style="break-before: page; page-break-before: always;"></div><h1 id="circom-circuit-for-rln"><a class="header" href="#circom-circuit-for-rln">Circom Circuit for RLN</a></h1>
<pre class="mermaid">flowchart TB
@@ -206,12 +196,8 @@
end
</pre>
<div style="break-before: page; page-break-before: always;"></div><h1 id="references"><a class="header" href="#references">References</a></h1>
<p><a href="https://ethresear.ch/t/semaphore-rln-rate-limiting-nullifier-for-spam-prevention-in-anonymous-p2p-setting/5009">Idea was proposed by Barry WhiteHat</a></p>
<p><a href="https://medium.com/privacy-scaling-explorations/rate-limiting-nullifier-a-spam-protection-mechanism-for-anonymous-environments-bbe4006a57d">RLN Overview</a></p>
<p><a href="https://hackmd.io/@aeAuSD7mSCKofwwx445eAQ/BJcfDByNF">RLN Spec</a></p>
<p><a href="https://rfc.vac.dev/spec/32/">VAC RLN Spec</a></p>
<div style="break-before: page; page-break-before: always;"></div><h1 id="usage"><a class="header" href="#usage">Usage</a></h1>
<div style="break-before: page; page-break-before: always;"></div><h1 id="uses"><a class="header" href="#uses">Uses</a></h1>
<div style="break-before: page; page-break-before: always;"></div><h1 id="how-to-use"><a class="header" href="#how-to-use">How to use</a></h1>
<div style="break-before: page; page-break-before: always;"></div><h1 id="theory"><a class="header" href="#theory">Theory</a></h1>
<div style="break-before: page; page-break-before: always;"></div><h1 id="shamirs-secret-sharing-scheme"><a class="header" href="#shamirs-secret-sharing-scheme">Shamirs Secret Sharing Scheme</a></h1>
<p><em>Shamirs Secret Sharing</em> allows to split the secret to <code>n</code> parts and restore it upon presentation any <code>m</code> parts (<code>m &lt;= n</code>)</p>
@@ -299,6 +285,28 @@
// TODO: Add removal from tree example
}
</code></pre>
<div style="break-before: page; page-break-before: always;"></div><h1 id="appendix"><a class="header" href="#appendix">Appendix</a></h1>
<p>The following sections contain reference material you may find useful.</p>
<div style="break-before: page; page-break-before: always;"></div><h1 id="terminology"><a class="header" href="#terminology">Terminology</a></h1>
<div class="table-wrapper"><table><thead><tr><th>Term</th><th>Description</th></tr></thead><tbody>
<tr><td>ZK-SNARK</td><td><a href="https://z.cash/technology/zksnarks/">z.cash/technology/zksnarks/</a></td></tr>
<tr><td>Stake</td><td>Financial or social stake required for registering in the RLN applications. Common stake examples are: locking cryptocurrency (financial), linking reputable social identity.</td></tr>
<tr><td>Identity secret</td><td>An array of two unique random components (identity nullifier and identity trapdoor), which must be kept private by the user. Secret hash and identity commitment are derived from this array.</td></tr>
<tr><td>Identity nullifier</td><td>Random 32 byte value used as component for identity secret generation.</td></tr>
<tr><td>Identity trapdoor</td><td>Random 32 byte value used as component for identity secret generation.</td></tr>
<tr><td>Identity secret hash</td><td>The hash of the identity secret, obtained using the Poseidon hash function. It is used for deriving the identity commitment of the user, and as a private input for zk proof generation. The secret hash should be kept private by the user.</td></tr>
<tr><td>Identity commitment</td><td>Hash obtained from the Identity secret hash by using the poseidon hash function. It is used by the users for registering in the protocol.</td></tr>
<tr><td>Signal</td><td>The message generated by a user. It is an arbitrary bit string that may represent a chat message, a URL request, protobuf message, etc.</td></tr>
<tr><td>Signal hash</td><td>Keccak hash of the signal, used as an input in the RLN circuit.</td></tr>
<tr><td>RLN Identifier</td><td>Random finite field value unique per RLN app. It is used for additional cross-application security. The role of the RLN identifier is protection of the user secrets being compromised if signals are being generated with the same credentials at different apps.</td></tr>
<tr><td>RLN membership tree</td><td>Merkle tree data structure, filled with identity commitments of the users. Serves as a data structure that ensures user registrations.</td></tr>
<tr><td>Merkle proof</td><td>Proof that a user is member of the RLN membership tree.</td></tr>
</tbody></table>
</div><div style="break-before: page; page-break-before: always;"></div><h1 id="references"><a class="header" href="#references">References</a></h1>
<p><a href="https://ethresear.ch/t/semaphore-rln-rate-limiting-nullifier-for-spam-prevention-in-anonymous-p2p-setting/5009">Idea was proposed by Barry WhiteHat</a></p>
<p><a href="https://medium.com/privacy-scaling-explorations/rate-limiting-nullifier-a-spam-protection-mechanism-for-anonymous-environments-bbe4006a57d">RLN Overview</a></p>
<p><a href="https://hackmd.io/@aeAuSD7mSCKofwwx445eAQ/BJcfDByNF">RLN Spec</a></p>
<p><a href="https://rfc.vac.dev/spec/32/">VAC RLN Spec</a></p>
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<ol class="chapter"><li class="chapter-item expanded "><a href="about.html"><strong aria-hidden="true">1.</strong> About</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">2.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.2.</strong> Uses</a></li><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">2.3.</strong> Terminology</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.4.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.4.1.</strong> Circom Circuit</a></li></ol></li><li class="chapter-item expanded "><a href="references.html" class="active"><strong aria-hidden="true">2.5.</strong> References</a></li></ol></li><li class="chapter-item expanded "><a href="code.html"><strong aria-hidden="true">3.</strong> Usage</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> RLN in JavaScript</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> RLN in Rust</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li></ol>
<ol class="chapter"><li class="chapter-item expanded "><a href="rln.html"><strong aria-hidden="true">1.</strong> RLN</a></li><li class="chapter-item expanded "><a href="overview.html"><strong aria-hidden="true">2.</strong> Overview</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.2.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.2.1.</strong> Circom circuit</a></li></ol></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.3.</strong> Uses</a></li></ol></li><li class="chapter-item expanded "><a href="how_to_use.html"><strong aria-hidden="true">3.</strong> How to use</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> JavaScript RLN</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> Rust RLN</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li><li class="chapter-item expanded "><a href="appendix.html"><strong aria-hidden="true">5.</strong> Appendix</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">5.1.</strong> A - Terminology</a></li><li class="chapter-item expanded "><a href="references.html" class="active"><strong aria-hidden="true">5.2.</strong> B - References</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded "><a href="about.html" class="active"><strong aria-hidden="true">1.</strong> About</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">2.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.2.</strong> Uses</a></li><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">2.3.</strong> Terminology</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.4.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.4.1.</strong> Circom Circuit</a></li></ol></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">2.5.</strong> References</a></li></ol></li><li class="chapter-item expanded "><a href="code.html"><strong aria-hidden="true">3.</strong> Usage</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> RLN in JavaScript</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> RLN in Rust</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li></ol>
<ol class="chapter"><li class="chapter-item expanded "><a href="rln.html" class="active"><strong aria-hidden="true">1.</strong> RLN</a></li><li class="chapter-item expanded "><a href="overview.html"><strong aria-hidden="true">2.</strong> Overview</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.2.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.2.1.</strong> Circom circuit</a></li></ol></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.3.</strong> Uses</a></li></ol></li><li class="chapter-item expanded "><a href="how_to_use.html"><strong aria-hidden="true">3.</strong> How to use</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> JavaScript RLN</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> Rust RLN</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li><li class="chapter-item expanded "><a href="appendix.html"><strong aria-hidden="true">5.</strong> Appendix</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">5.1.</strong> A - Terminology</a></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">5.2.</strong> B - References</a></li></ol></li></ol>
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<h1 id="about"><a class="header" href="#about">About</a></h1>
<p><strong>RLN</strong> (Rate-Limiting Nullifier) is part of (<strong>PSE</strong>) <a href="https://appliedzkp.org">Privacy &amp; Scaling Explorations</a>, a multidisciplinary team supported by the Ethereum Foundation. PSE explores new use cases for zero knowledge proofs and other cryptographic primitives.</p>
<h1 id="rln"><a class="header" href="#rln">RLN</a></h1>
<p><strong>RLN</strong> (Rate-Limiting Nullifier) is part of (<strong>PSE</strong>) <a href="https://appliedzkp.org">Privacy &amp; Scaling Explorations</a>, a multidisciplinary team supported by the Ethereum Foundation. PSE explores new use cases for zero-knowledge proofs and other cryptographic primitives.</p>
<p><img src="./images/logo.svg" alt="alt text" /></p>
<p><strong>RLN</strong> team is working on the protocol (having the same name), implementations and different applications of it.</p>
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<ol class="chapter"><li class="chapter-item expanded "><a href="about.html"><strong aria-hidden="true">1.</strong> About</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">2.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.2.</strong> Uses</a></li><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">2.3.</strong> Terminology</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.4.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html" class="active"><strong aria-hidden="true">2.4.1.</strong> Circom Circuit</a></li></ol></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">2.5.</strong> References</a></li></ol></li><li class="chapter-item expanded "><a href="code.html"><strong aria-hidden="true">3.</strong> Usage</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> RLN in JavaScript</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> RLN in Rust</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li></ol>
<ol class="chapter"><li class="chapter-item expanded "><a href="rln.html"><strong aria-hidden="true">1.</strong> RLN</a></li><li class="chapter-item expanded "><a href="overview.html"><strong aria-hidden="true">2.</strong> Overview</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.2.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html" class="active"><strong aria-hidden="true">2.2.1.</strong> Circom circuit</a></li></ol></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.3.</strong> Uses</a></li></ol></li><li class="chapter-item expanded "><a href="how_to_use.html"><strong aria-hidden="true">3.</strong> How to use</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> JavaScript RLN</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> Rust RLN</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li><li class="chapter-item expanded "><a href="appendix.html"><strong aria-hidden="true">5.</strong> Appendix</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">5.1.</strong> A - Terminology</a></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">5.2.</strong> B - References</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded "><a href="about.html"><strong aria-hidden="true">1.</strong> About</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">2.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.2.</strong> Uses</a></li><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">2.3.</strong> Terminology</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.4.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.4.1.</strong> Circom Circuit</a></li></ol></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">2.5.</strong> References</a></li></ol></li><li class="chapter-item expanded "><a href="code.html"><strong aria-hidden="true">3.</strong> Usage</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> RLN in JavaScript</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> RLN in Rust</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html" class="active"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li></ol>
<ol class="chapter"><li class="chapter-item expanded "><a href="rln.html"><strong aria-hidden="true">1.</strong> RLN</a></li><li class="chapter-item expanded "><a href="overview.html"><strong aria-hidden="true">2.</strong> Overview</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.2.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.2.1.</strong> Circom circuit</a></li></ol></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.3.</strong> Uses</a></li></ol></li><li class="chapter-item expanded "><a href="how_to_use.html"><strong aria-hidden="true">3.</strong> How to use</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> JavaScript RLN</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> Rust RLN</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html" class="active"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li><li class="chapter-item expanded "><a href="appendix.html"><strong aria-hidden="true">5.</strong> Appendix</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">5.1.</strong> A - Terminology</a></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">5.2.</strong> B - References</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded "><a href="about.html"><strong aria-hidden="true">1.</strong> About</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">2.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.2.</strong> Uses</a></li><li class="chapter-item expanded "><a href="terminology.html" class="active"><strong aria-hidden="true">2.3.</strong> Terminology</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.4.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.4.1.</strong> Circom Circuit</a></li></ol></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">2.5.</strong> References</a></li></ol></li><li class="chapter-item expanded "><a href="code.html"><strong aria-hidden="true">3.</strong> Usage</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> RLN in JavaScript</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> RLN in Rust</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li></ol>
<ol class="chapter"><li class="chapter-item expanded "><a href="rln.html"><strong aria-hidden="true">1.</strong> RLN</a></li><li class="chapter-item expanded "><a href="overview.html"><strong aria-hidden="true">2.</strong> Overview</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.2.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.2.1.</strong> Circom circuit</a></li></ol></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.3.</strong> Uses</a></li></ol></li><li class="chapter-item expanded "><a href="how_to_use.html"><strong aria-hidden="true">3.</strong> How to use</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> JavaScript RLN</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> Rust RLN</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li><li class="chapter-item expanded "><a href="appendix.html"><strong aria-hidden="true">5.</strong> Appendix</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="terminology.html" class="active"><strong aria-hidden="true">5.1.</strong> A - Terminology</a></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">5.2.</strong> B - References</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded "><a href="about.html"><strong aria-hidden="true">1.</strong> About</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">2.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.2.</strong> Uses</a></li><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">2.3.</strong> Terminology</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.4.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.4.1.</strong> Circom Circuit</a></li></ol></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">2.5.</strong> References</a></li></ol></li><li class="chapter-item expanded "><a href="code.html"><strong aria-hidden="true">3.</strong> Usage</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> RLN in JavaScript</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> RLN in Rust</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html" class="active"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li></ol>
<ol class="chapter"><li class="chapter-item expanded "><a href="rln.html"><strong aria-hidden="true">1.</strong> RLN</a></li><li class="chapter-item expanded "><a href="overview.html"><strong aria-hidden="true">2.</strong> Overview</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.2.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.2.1.</strong> Circom circuit</a></li></ol></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.3.</strong> Uses</a></li></ol></li><li class="chapter-item expanded "><a href="how_to_use.html"><strong aria-hidden="true">3.</strong> How to use</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> JavaScript RLN</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> Rust RLN</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html" class="active"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li><li class="chapter-item expanded "><a href="appendix.html"><strong aria-hidden="true">5.</strong> Appendix</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">5.1.</strong> A - Terminology</a></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">5.2.</strong> B - References</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded "><a href="about.html"><strong aria-hidden="true">1.</strong> About</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">2.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.2.</strong> Uses</a></li><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">2.3.</strong> Terminology</a></li><li class="chapter-item expanded "><a href="under_the_hood.html" class="active"><strong aria-hidden="true">2.4.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.4.1.</strong> Circom Circuit</a></li></ol></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">2.5.</strong> References</a></li></ol></li><li class="chapter-item expanded "><a href="code.html"><strong aria-hidden="true">3.</strong> Usage</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> RLN in JavaScript</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> RLN in Rust</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li></ol>
<ol class="chapter"><li class="chapter-item expanded "><a href="rln.html"><strong aria-hidden="true">1.</strong> RLN</a></li><li class="chapter-item expanded "><a href="overview.html"><strong aria-hidden="true">2.</strong> Overview</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="under_the_hood.html" class="active"><strong aria-hidden="true">2.2.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.2.1.</strong> Circom circuit</a></li></ol></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.3.</strong> Uses</a></li></ol></li><li class="chapter-item expanded "><a href="how_to_use.html"><strong aria-hidden="true">3.</strong> How to use</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> JavaScript RLN</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> Rust RLN</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li><li class="chapter-item expanded "><a href="appendix.html"><strong aria-hidden="true">5.</strong> Appendix</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">5.1.</strong> A - Terminology</a></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">5.2.</strong> B - References</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded "><a href="about.html"><strong aria-hidden="true">1.</strong> About</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">2.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="uses.html" class="active"><strong aria-hidden="true">2.2.</strong> Uses</a></li><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">2.3.</strong> Terminology</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.4.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.4.1.</strong> Circom Circuit</a></li></ol></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">2.5.</strong> References</a></li></ol></li><li class="chapter-item expanded "><a href="code.html"><strong aria-hidden="true">3.</strong> Usage</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> RLN in JavaScript</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> RLN in Rust</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li></ol>
<ol class="chapter"><li class="chapter-item expanded "><a href="rln.html"><strong aria-hidden="true">1.</strong> RLN</a></li><li class="chapter-item expanded "><a href="overview.html"><strong aria-hidden="true">2.</strong> Overview</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.2.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.2.1.</strong> Circom circuit</a></li></ol></li><li class="chapter-item expanded "><a href="uses.html" class="active"><strong aria-hidden="true">2.3.</strong> Uses</a></li></ol></li><li class="chapter-item expanded "><a href="how_to_use.html"><strong aria-hidden="true">3.</strong> How to use</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> JavaScript RLN</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> Rust RLN</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li><li class="chapter-item expanded "><a href="appendix.html"><strong aria-hidden="true">5.</strong> Appendix</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">5.1.</strong> A - Terminology</a></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">5.2.</strong> B - References</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded "><a href="about.html"><strong aria-hidden="true">1.</strong> About</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">2.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html" class="active"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.2.</strong> Uses</a></li><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">2.3.</strong> Terminology</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.4.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.4.1.</strong> Circom Circuit</a></li></ol></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">2.5.</strong> References</a></li></ol></li><li class="chapter-item expanded "><a href="code.html"><strong aria-hidden="true">3.</strong> Usage</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> RLN in JavaScript</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> RLN in Rust</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li></ol>
<ol class="chapter"><li class="chapter-item expanded "><a href="rln.html"><strong aria-hidden="true">1.</strong> RLN</a></li><li class="chapter-item expanded "><a href="overview.html"><strong aria-hidden="true">2.</strong> Overview</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="what_is_rln.html" class="active"><strong aria-hidden="true">2.1.</strong> What is RLN</a></li><li class="chapter-item expanded "><a href="under_the_hood.html"><strong aria-hidden="true">2.2.</strong> Under the hood</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="rln_circuit.html"><strong aria-hidden="true">2.2.1.</strong> Circom circuit</a></li></ol></li><li class="chapter-item expanded "><a href="uses.html"><strong aria-hidden="true">2.3.</strong> Uses</a></li></ol></li><li class="chapter-item expanded "><a href="how_to_use.html"><strong aria-hidden="true">3.</strong> How to use</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">3.1.</strong> JavaScript RLN</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.2.</strong> Rust RLN</div></li></ol></li><li class="chapter-item expanded "><a href="theory.html"><strong aria-hidden="true">4.</strong> Theory</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="sss.html"><strong aria-hidden="true">4.1.</strong> Shamir's Secret Sharing</a></li></ol></li><li class="chapter-item expanded "><a href="appendix.html"><strong aria-hidden="true">5.</strong> Appendix</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="terminology.html"><strong aria-hidden="true">5.1.</strong> A - Terminology</a></li><li class="chapter-item expanded "><a href="references.html"><strong aria-hidden="true">5.2.</strong> B - References</a></li></ol></li></ol>
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