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<title data-rh="true">RLN-v3: Towards a Flexible and Cost-Efficient Implementation | Logos Research</title><meta data-rh="true" name="viewport" content="width=device-width,initial-scale=1"><meta data-rh="true" name="twitter:card" content="summary_large_image"><meta data-rh="true" property="og:url" content="https://research.logos.co/rlog/rln-v3"><meta data-rh="true" property="og:locale" content="en"><meta data-rh="true" name="docusaurus_locale" content="en"><meta data-rh="true" name="docusaurus_tag" content="default"><meta data-rh="true" name="docsearch:language" content="en"><meta data-rh="true" name="docsearch:docusaurus_tag" content="default"><meta data-rh="true" name="image" content="https://research.logos.co/_og/0a99af420bc509722f1437b39d9ccec1a33dd27c.png"><meta data-rh="true" property="og:title" content="RLN-v3: Towards a Flexible and Cost-Efficient Implementation | Logos Research"><meta data-rh="true" name="description" content="Improving on the previous version of RLN by allowing dynamic epoch sizes."><meta data-rh="true" property="og:description" content="Improving on the previous version of RLN by allowing dynamic epoch sizes."><meta data-rh="true" property="og:type" content="article"><meta data-rh="true" property="article:published_time" content="2024-05-13T12:00:00.000Z"><link data-rh="true" rel="icon" href="/theme/image/favicon.svg"><link data-rh="true" rel="canonical" href="https://research.logos.co/rlog/rln-v3"><link data-rh="true" rel="alternate" href="https://research.logos.co/rlog/rln-v3" hreflang="en"><link data-rh="true" rel="alternate" href="https://research.logos.co/rlog/rln-v3" hreflang="x-default"><script data-rh="true" type="application/ld+json">{"@context":"https://schema.org","@type":"BlogPosting","@id":"https://research.logos.co/rlog/rln-v3","mainEntityOfPage":"https://research.logos.co/rlog/rln-v3","url":"https://research.logos.co/rlog/rln-v3","headline":"RLN-v3: Towards a Flexible and Cost-Efficient Implementation","name":"RLN-v3: Towards a Flexible and Cost-Efficient Implementation","description":"Improving on the previous version of RLN by allowing dynamic epoch sizes.","datePublished":"2024-05-13T12:00:00.000Z","author":{"@type":"Person","name":"Aaryamann"},"keywords":[],"isPartOf":{"@type":"Blog","@id":"https://research.logos.co/rlog","name":"Research Blog"}}</script><link rel="alternate icon" type="image/png" href="/theme/image/favicon.png">
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id="__docusaurus_skipToContent_fallback" class="theme-layout-main main-wrapper mainWrapper_z2l0 blog-wrapper"><div class="container margin-vert--lg"><div class="row"><main class="col col--9 col--offset-1" itemscope="" itemtype="http://schema.org/Blog"><article class=""><header><nav class="theme-doc-breadcrumbs breadcrumbsContainer_RLvU" aria-label="Breadcrumbs"><ul class="breadcrumbs" itemscope="" itemtype="https://schema.org/BreadcrumbList"><a class="breadcrumbs__item" href="/blog"><span class="lsd-typography lsd-typography--body3">All posts</span></a><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="lsd-typography lsd-typography--body3 breadcrumbs__link" itemprop="name">RLN-v3: Towards a Flexible and Cost-Efficient Implementation</span><meta itemprop="position" content="1"></li></ul></nav><h1 class="title_f1Hy">RLN-v3: Towards a Flexible and Cost-Efficient Implementation</h1><div class="container_PkUo margin-vert--md"><time datetime="2024-05-13T12:00:00.000Z" itemprop="datePublished">May 13, 2024</time><div class="authors_dZ4g"><span class="lsd-typography lsd-typography--body2">by </span><div class="col col--6 authorCol_y4tx"><div class="avatar margin-bottom--sm"><div class="avatar__intro" itemprop="author" itemscope="" itemtype="https://schema.org/Person"><div class="avatar__name"><span class="lsd-typography lsd-typography--body2" itemprop="name">Aaryamann</span></div></div></div></div></div><div>7 min read</div></div><hr class="blog-divider"></header><div id="__blog-post-container" class="markdown"><p>Improving on the previous version of RLN by allowing dynamic epoch sizes.</p>
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<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="introduction">Introduction<a href="#introduction" class="hash-link" aria-label="Direct link to Introduction" title="Direct link to Introduction"></a></h2>
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<p>Recommended previous reading: <a href="https://research.logos.co/rlog/rln-anonymous-dos-prevention" target="_blank" rel="noopener noreferrer">Strengthening Anonymous DoS Prevention with Rate Limiting Nullifiers in Waku</a>.</p>
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<p>The premise of RLN-v3 is to have a variable message rate per variable epoch,
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which can be explained in the following way:</p>
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<ul>
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<li>
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<p><strong>RLN-v1:</strong> “Alice can send 1 message per global epoch”</p>
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<p>Practically, this is <code>1 msg/second</code></p>
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</li>
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<li>
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<p><strong>RLN-v2:</strong> “Alice can send <code>x</code> messages per global epoch”</p>
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<p>Practically, this is <code>x msg/second</code></p>
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</li>
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<li>
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<p><strong>RLN-v3:</strong> “Alice can send <code>x</code> messages within a time interval <code>y</code> chosen by herself.
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The funds she has to pay are affected by both the number of messages and the chosen time interval.
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Other participants can choose different time intervals fitting their specific needs.</p>
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<p>Practically, this is <code>x msg/y seconds</code></p>
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</li>
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</ul>
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<p>RLN-v3 allows higher flexibility and ease of payment/stake for users who have more predictable usage patterns and therefore,
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more predictable bandwidth usage on a p2p network (Waku, etc.).</p>
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<p>For example:</p>
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<ul>
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<li>An AMM that broadcasts bids, asks, and fills over Waku may require a lot of throughput in the smallest epoch possible and hence may register an RLN-v3 membership of <code>10000 msg/1 second</code>.
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They could do this with RLN-v2, too.</li>
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<li>Alice, a casual user of a messaging app built on Waku, who messages maybe 3-4 people infrequently during the day, may register an RLN-v3 membership of <code>100 msg/hour</code>,
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which would not be possible in RLN-v2 considering the <code>global epoch</code> was set to <code>1 second</code>.
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With RLN-v2, Alice would have to register with a membership of <code>1 msg/sec</code>,
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which would translate to <code>3600 msg/hour</code>. This is much higher than her usage and would
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result in her overpaying to stake into the membership set.</li>
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<li>A sync service built over Waku,
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whose spec defines that it MUST broadcast a set of public keys every hour,
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may register an RLN-v3 membership of <code>1 msg/hour</code>,
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cutting down the costs to enter the membership set earlier.</li>
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</ul>
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<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="theory">Theory<a href="#theory" class="hash-link" aria-label="Direct link to Theory" title="Direct link to Theory"></a></h2>
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<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="modification-to-leaves-set-in-the-membership-merkle-tree">Modification to leaves set in the membership Merkle tree<a href="#modification-to-leaves-set-in-the-membership-merkle-tree" class="hash-link" aria-label="Direct link to Modification to leaves set in the membership Merkle tree" title="Direct link to Modification to leaves set in the membership Merkle tree"></a></h3>
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<p>To ensure that a user’s epoch size (<code>user_epoch_limit</code>) is included within their membership we must modify the user’s commitment/leaf in the tree to contain it.
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A user’s commitment/leaf in the tree is referred to as a <code>rate_commitment</code>,
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which was previously derived from their public key (<code>identity_commitment</code>)
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and their variable message rate (<code>user_message_limit</code>).</p>
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<p>In <strong>RLN-v2:</strong></p>
|
||
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi mathvariant="normal">_</mi><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>i</mi><mi>t</mi><mi>m</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mi>p</mi><mi>o</mi><mi>s</mi><mi>e</mi><mi>i</mi><mi>d</mi><mi>o</mi><mi>n</mi><mo stretchy="false">(</mo><mo stretchy="false">[</mo><mi>i</mi><mi>d</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mi mathvariant="normal">_</mi><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>i</mi><mi>t</mi><mi>m</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo separator="true">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>r</mi><mi mathvariant="normal">_</mi><mi>m</mi><mi>e</mi><mi>s</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi mathvariant="normal">_</mi><mi>l</mi><mi>i</mi><mi>m</mi><mi>i</mi><mi>t</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">rate\_commitment = poseidon([identity\_commitment, user\_message\_limit])</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9695em;vertical-align:-0.31em"></span><span class="mord mathnormal" style="margin-right:0.02778em">r</span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mord mathnormal">e</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">co</span><span class="mord mathnormal">mmi</span><span class="mord mathnormal">t</span><span class="mord mathnormal">m</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.06em;vertical-align:-0.31em"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">ose</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mord mathnormal">o</span><span class="mord mathnormal">n</span><span class="mopen">([</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em">y</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">co</span><span class="mord mathnormal">mmi</span><span class="mord mathnormal">t</span><span class="mord mathnormal">m</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.02778em">ser</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">m</span><span class="mord mathnormal">ess</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.03588em">g</span><span class="mord mathnormal">e</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal" style="margin-right:0.01968em">l</span><span class="mord mathnormal">imi</span><span class="mord mathnormal">t</span><span class="mclose">])</span></span></span></span></span>
|
||
<p>In <strong>RLN-v3:</strong></p>
|
||
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi mathvariant="normal">_</mi><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>i</mi><mi>t</mi><mi>m</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mi>p</mi><mi>o</mi><mi>s</mi><mi>e</mi><mi>i</mi><mi>d</mi><mi>o</mi><mi>n</mi><mo stretchy="false">(</mo><mo stretchy="false">[</mo><mi>i</mi><mi>d</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mi mathvariant="normal">_</mi><mi>c</mi><mi>o</mi><mi>m</mi><mi>m</mi><mi>i</mi><mi>t</mi><mi>m</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo separator="true">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>r</mi><mi mathvariant="normal">_</mi><mi>m</mi><mi>e</mi><mi>s</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi mathvariant="normal">_</mi><mi>l</mi><mi>i</mi><mi>m</mi><mi>i</mi><mi>t</mi><mo separator="true">,</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>r</mi><mi mathvariant="normal">_</mi><mi>e</mi><mi>p</mi><mi>o</mi><mi>c</mi><mi>h</mi><mi mathvariant="normal">_</mi><mi>l</mi><mi>i</mi><mi>m</mi><mi>i</mi><mi>t</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">rate\_commitment = poseidon([identity\_commitment, user\_message\_limit, user\_epoch\_limit])</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9695em;vertical-align:-0.31em"></span><span class="mord mathnormal" style="margin-right:0.02778em">r</span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mord mathnormal">e</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">co</span><span class="mord mathnormal">mmi</span><span class="mord mathnormal">t</span><span class="mord mathnormal">m</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.06em;vertical-align:-0.31em"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">ose</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mord mathnormal">o</span><span class="mord mathnormal">n</span><span class="mopen">([</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em">y</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">co</span><span class="mord mathnormal">mmi</span><span class="mord mathnormal">t</span><span class="mord mathnormal">m</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.02778em">ser</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">m</span><span class="mord mathnormal">ess</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.03588em">g</span><span class="mord mathnormal">e</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal" style="margin-right:0.01968em">l</span><span class="mord mathnormal">imi</span><span class="mord mathnormal">t</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.02778em">ser</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">e</span><span class="mord mathnormal">p</span><span class="mord mathnormal">oc</span><span class="mord mathnormal">h</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal" style="margin-right:0.01968em">l</span><span class="mord mathnormal">imi</span><span class="mord mathnormal">t</span><span class="mclose">])</span></span></span></span></span>
|
||
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="modification-to-circuit-inputs">Modification to circuit inputs<a href="#modification-to-circuit-inputs" class="hash-link" aria-label="Direct link to Modification to circuit inputs" title="Direct link to Modification to circuit inputs"></a></h3>
|
||
<p>To detect double signaling,
|
||
we make use of a circuit output <code>nullifier</code>,
|
||
which remains the same if a user generates a proof with the same <code>message_id</code> and <code>external_nullifier</code>,
|
||
where the <code>external_nullifier</code> and <code>nullifier</code> are defined as:</p>
|
||
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>e</mi><mi>x</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">_</mi><mi>n</mi><mi>u</mi><mi>l</mi><mi>l</mi><mi>i</mi><mi>f</mi><mi>i</mi><mi>e</mi><mi>r</mi><mo>=</mo><mi>p</mi><mi>o</mi><mi>s</mi><mi>e</mi><mi>i</mi><mi>d</mi><mi>o</mi><mi>n</mi><mo stretchy="false">(</mo><mo stretchy="false">[</mo><mi>e</mi><mi>p</mi><mi>o</mi><mi>c</mi><mi>h</mi><mo separator="true">,</mo><mi>r</mi><mi>l</mi><mi>n</mi><mi mathvariant="normal">_</mi><mi>i</mi><mi>d</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>f</mi><mi>i</mi><mi>e</mi><mi>r</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mspace linebreak="newline"></mspace><mi>n</mi><mi>u</mi><mi>l</mi><mi>l</mi><mi>i</mi><mi>f</mi><mi>i</mi><mi>e</mi><mi>r</mi><mo>=</mo><mi>p</mi><mi>o</mi><mi>s</mi><mi>e</mi><mi>i</mi><mi>d</mi><mi>o</mi><mi>n</mi><mo stretchy="false">(</mo><mo stretchy="false">[</mo><mi>i</mi><mi>d</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>t</mi><mi>y</mi><mi mathvariant="normal">_</mi><mi>s</mi><mi>e</mi><mi>c</mi><mi>r</mi><mi>e</mi><mi>t</mi><mo separator="true">,</mo><mi>e</mi><mi>x</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>n</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">_</mi><mi>n</mi><mi>u</mi><mi>l</mi><mi>l</mi><mi>i</mi><mi>f</mi><mi>i</mi><mi>e</mi><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>e</mi><mi>s</mi><mi>s</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi mathvariant="normal">_</mi><mi>i</mi><mi>d</mi><mo stretchy="false">]</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">external\_nullifier = poseidon([epoch, rln\_identifier]) \\
|
||
nullifier = poseidon([identity\_secret, external\_nullifier, message\_id])</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0044em;vertical-align:-0.31em"></span><span class="mord mathnormal">e</span><span class="mord mathnormal">x</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.02778em">er</span><span class="mord mathnormal">na</span><span class="mord mathnormal" style="margin-right:0.01968em">l</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">n</span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.01968em">ll</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.02778em">er</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.06em;vertical-align:-0.31em"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">ose</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mord mathnormal">o</span><span class="mord mathnormal">n</span><span class="mopen">([</span><span class="mord mathnormal">e</span><span class="mord mathnormal">p</span><span class="mord mathnormal">oc</span><span class="mord mathnormal">h</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal" style="margin-right:0.02778em">r</span><span class="mord mathnormal" style="margin-right:0.01968em">l</span><span class="mord mathnormal">n</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.02778em">er</span><span class="mclose">])</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em"></span><span class="mord mathnormal">n</span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.01968em">ll</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.02778em">er</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.06em;vertical-align:-0.31em"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">ose</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mord mathnormal">o</span><span class="mord mathnormal">n</span><span class="mopen">([</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em">y</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">secre</span><span class="mord mathnormal">t</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">e</span><span class="mord mathnormal">x</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.02778em">er</span><span class="mord mathnormal">na</span><span class="mord mathnormal" style="margin-right:0.01968em">l</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">n</span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.01968em">ll</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.02778em">er</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">ess</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.03588em">g</span><span class="mord mathnormal">e</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">i</span><span class="mord mathnormal">d</span><span class="mclose">])</span></span></span></span></span>
|
||
<p>Where:</p>
|
||
<ul>
|
||
<li><code>epoch</code> is defined as the Unix epoch timestamp with seconds precision.</li>
|
||
<li><code>rln_identifier</code> uniquely identifies an application for which a user submits a proof.</li>
|
||
<li><code>identity_secret</code> is the private key of the user.</li>
|
||
<li><code>message_id</code> is the sequence number of the user’s message within <code>user_message_limit</code> in an epoch.</li>
|
||
</ul>
|
||
<p>In RLN-v2, the global epoch was 1 second,
|
||
hence we did not need to perform any assertions to the epoch’s value inside the circuit,
|
||
and the validation of the epoch was handled off-circuit (i.e., too old, too large, bad values, etc.).</p>
|
||
<p>In RLN-v3, we propose that the <code>epoch</code> that is passed into the circuit
|
||
must be a valid multiple of <code>user_epoch_limit</code>
|
||
since the user may pass in values of the <code>epoch</code> which do not directly correlate with the <code>user_epoch_limit</code>.</p>
|
||
<p>For example:</p>
|
||
<ul>
|
||
<li>A user with <code>user_epoch_limit</code> of 120
|
||
passes in an epoch of <code>237</code>
|
||
generates <code>user_message_limit</code> proofs with it,
|
||
can increment the epoch by <code>1</code>,
|
||
and generate <code>user_message_limit</code> proofs with it,
|
||
thereby allowing them to bypass the message per epoch restriction.</li>
|
||
</ul>
|
||
<p>One could say that we could perform this validation outside of the circuit,
|
||
but we maintain the <code>user_epoch_limit</code> as a private input to the circuit so that the user is not deanonymized by the anonymity set connected to that <code>user_epoch_limit</code>.
|
||
Since <code>user_epoch_limit</code> is kept private,
|
||
the verifier does not have access to that value and cannot perform validation on it.</p>
|
||
<p>If we ensure that the <code>epoch</code> is a multiple of <code>user_epoch_limit</code>,
|
||
we have the following scenarios:</p>
|
||
<ul>
|
||
<li>A user with <code>user_epoch_limit</code> of 120
|
||
passes in an epoch of <code>237</code>.
|
||
Proof generation fails since the epoch is not a multiple of <code>user_epoch_limit</code>.</li>
|
||
<li>A user with <code>user_epoch_limit</code> of 120
|
||
passes in an epoch of <code>240</code> and
|
||
can generate <code>user_message_limit</code> proofs without being slashed.</li>
|
||
</ul>
|
||
<p>Since we perform operations on the <code>epoch</code>, we must include it as a circuit input (previously, it was removed from the circuit inputs to RLN-v2).</p>
|
||
<p>Therefore, the new circuit inputs are as follows:</p>
|
||
<div class="language-c codeBlockContainer_EB2s codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#F8F8F2;--prism-background-color:rgba(var(--lsd-surface-secondary), 0.08)"><div class="codeBlockContent_QJqH"><pre tabindex="0" class="prism-code language-c codeBlock_bY9V thin-scrollbar" style="color:#F8F8F2;background-color:rgba(var(--lsd-surface-secondary), 0.08)"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#F8F8F2"><span class="token comment" style="color:rgb(98, 114, 164)">// unchanged</span><span class="token plain"></span><br></span><span class="token-line" style="color:#F8F8F2"><span class="token plain">private identity_secret</span><br></span><span class="token-line" style="color:#F8F8F2"><span class="token plain">private user_message_limit</span><br></span><span class="token-line" style="color:#F8F8F2"><span class="token plain">private message_id</span><br></span><span class="token-line" style="color:#F8F8F2"><span class="token plain">private pathElements</span><span class="token punctuation" style="color:rgb(248, 248, 242)">[</span><span class="token punctuation" style="color:rgb(248, 248, 242)">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#F8F8F2"><span class="token plain">private pathIndices</span><span class="token punctuation" style="color:rgb(248, 248, 242)">[</span><span class="token punctuation" style="color:rgb(248, 248, 242)">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#F8F8F2"><span class="token plain">public x </span><span class="token comment" style="color:rgb(98, 114, 164)">// messageHash</span><span class="token plain"></span><br></span><span class="token-line" style="color:#F8F8F2"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#F8F8F2"><span class="token plain"></span><span class="token comment" style="color:rgb(98, 114, 164)">// new/changed</span><span class="token plain"></span><br></span><span class="token-line" style="color:#F8F8F2"><span class="token plain">private user_epoch_limit</span><br></span><span class="token-line" style="color:#F8F8F2"><span class="token plain">private user_epoch_quotient </span><span class="token comment" style="color:rgb(98, 114, 164)">// epoch/user_epoch_limit to assert within circuit</span><span class="token plain"></span><br></span><span class="token-line" style="color:#F8F8F2"><span class="token plain">public epoch</span><br></span><span class="token-line" style="color:#F8F8F2"><span class="token plain">public rln_identifier</span><br></span></code></pre></div></div>
|
||
<p>The circuit outputs remain the same.</p>
|
||
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="additional-circuit-constraints">Additional circuit constraints<a href="#additional-circuit-constraints" class="hash-link" aria-label="Direct link to Additional circuit constraints" title="Direct link to Additional circuit constraints"></a></h3>
|
||
<ol>
|
||
<li>
|
||
<p>Since we accept the <code>epoch</code>, <code>user_epoch_quotient</code>, and <code>user_epoch_limit</code>,
|
||
we must ensure that the relation between these 3 values is preserved. I.e.:</p>
|
||
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>e</mi><mi>p</mi><mi>o</mi><mi>c</mi><mi>h</mi><mo>=</mo><mo>=</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>r</mi><mi mathvariant="normal">_</mi><mi>e</mi><mi>p</mi><mi>o</mi><mi>c</mi><mi>h</mi><mi mathvariant="normal">_</mi><mi>l</mi><mi>i</mi><mi>m</mi><mi>i</mi><mi>t</mi><mo>∗</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>r</mi><mi mathvariant="normal">_</mi><mi>e</mi><mi>p</mi><mi>o</mi><mi>c</mi><mi>h</mi><mi mathvariant="normal">_</mi><mi>q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>n</mi><mi>t</mi></mrow><annotation encoding="application/x-tex">epoch == user\_epoch\_limit * user\_epoch\_quotient</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em"></span><span class="mord mathnormal">e</span><span class="mord mathnormal">p</span><span class="mord mathnormal">oc</span><span class="mord mathnormal">h</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">==</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.0044em;vertical-align:-0.31em"></span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.02778em">ser</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">e</span><span class="mord mathnormal">p</span><span class="mord mathnormal">oc</span><span class="mord mathnormal">h</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal" style="margin-right:0.01968em">l</span><span class="mord mathnormal">imi</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:1.0044em;vertical-align:-0.31em"></span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.02778em">ser</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">e</span><span class="mord mathnormal">p</span><span class="mord mathnormal">oc</span><span class="mord mathnormal">h</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal" style="margin-right:0.03588em">q</span><span class="mord mathnormal">u</span><span class="mord mathnormal">o</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span></span></span></span></span>
|
||
</li>
|
||
<li>
|
||
<p>To ensure no overflows/underflows occur in the above multiplication,
|
||
we must constrain the inputs of <code>epoch</code>, <code>user_epoch_quotient</code>, and <code>user_epoch_limit</code>.
|
||
We have assumed <code>3600</code> to be the maximum valid size of the <code>user_epoch_quotient</code>.</p>
|
||
</li>
|
||
</ol>
|
||
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>s</mi><mi>i</mi><mi>z</mi><mi>e</mi><mo stretchy="false">(</mo><mi>e</mi><mi>p</mi><mi>o</mi><mi>c</mi><mi>h</mi><mo stretchy="false">)</mo><mo>≤</mo><mn>64</mn><mtext> </mtext><mi>b</mi><mi>i</mi><mi>t</mi><mi>s</mi><mspace linebreak="newline"></mspace><mi>s</mi><mi>i</mi><mi>z</mi><mi>e</mi><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>r</mi><mi mathvariant="normal">_</mi><mi>e</mi><mi>p</mi><mi>o</mi><mi>c</mi><mi>h</mi><mi mathvariant="normal">_</mi><mi>l</mi><mi>i</mi><mi>m</mi><mi>i</mi><mi>t</mi><mo stretchy="false">)</mo><mo>≤</mo><mn>12</mn><mtext> </mtext><mi>b</mi><mi>i</mi><mi>t</mi><mi>s</mi><mspace linebreak="newline"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>r</mi><mi mathvariant="normal">_</mi><mi>e</mi><mi>p</mi><mi>o</mi><mi>c</mi><mi>h</mi><mi mathvariant="normal">_</mi><mi>l</mi><mi>i</mi><mi>m</mi><mi>i</mi><mi>t</mi><mo>≤</mo><mn>3600</mn><mspace linebreak="newline"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>r</mi><mi mathvariant="normal">_</mi><mi>e</mi><mi>p</mi><mi>o</mi><mi>c</mi><mi>h</mi><mi mathvariant="normal">_</mi><mi>l</mi><mi>i</mi><mi>m</mi><mi>i</mi><mi>t</mi><mo>≤</mo><mi>e</mi><mi>p</mi><mi>o</mi><mi>c</mi><mi>h</mi><mspace linebreak="newline"></mspace><mi>u</mi><mi>s</mi><mi>e</mi><mi>r</mi><mi mathvariant="normal">_</mi><mi>e</mi><mi>p</mi><mi>o</mi><mi>c</mi><mi>h</mi><mi mathvariant="normal">_</mi><mi>q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi>i</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo><</mo><mi>u</mi><mi>s</mi><mi>e</mi><mi>r</mi><mi mathvariant="normal">_</mi><mi>e</mi><mi>p</mi><mi>o</mi><mi>c</mi><mi>h</mi><mi mathvariant="normal">_</mi><mi>l</mi><mi>i</mi><mi>m</mi><mi>i</mi><mi>t</mi></mrow><annotation encoding="application/x-tex">size(epoch) \leq 64\ bits \\
|
||
size(user\_epoch\_limit) \leq 12\ bits \\
|
||
user\_epoch\_limit \leq 3600 \\
|
||
user\_epoch\_limit \leq epoch \\
|
||
user\_epoch\_quotient < user\_epoch\_limit</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">i</span><span class="mord mathnormal">ze</span><span class="mopen">(</span><span class="mord mathnormal">e</span><span class="mord mathnormal">p</span><span class="mord mathnormal">oc</span><span class="mord mathnormal">h</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6944em"></span><span class="mord">64</span><span class="mspace"> </span><span class="mord mathnormal">bi</span><span class="mord mathnormal">t</span><span class="mord mathnormal">s</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.06em;vertical-align:-0.31em"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">i</span><span class="mord mathnormal">ze</span><span class="mopen">(</span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.02778em">ser</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">e</span><span class="mord mathnormal">p</span><span class="mord mathnormal">oc</span><span class="mord mathnormal">h</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal" style="margin-right:0.01968em">l</span><span class="mord mathnormal">imi</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6944em"></span><span class="mord">12</span><span class="mspace"> </span><span class="mord mathnormal">bi</span><span class="mord mathnormal">t</span><span class="mord mathnormal">s</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.0044em;vertical-align:-0.31em"></span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.02778em">ser</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">e</span><span class="mord mathnormal">p</span><span class="mord mathnormal">oc</span><span class="mord mathnormal">h</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal" style="margin-right:0.01968em">l</span><span class="mord mathnormal">imi</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">3600</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.0044em;vertical-align:-0.31em"></span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.02778em">ser</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">e</span><span class="mord mathnormal">p</span><span class="mord mathnormal">oc</span><span class="mord mathnormal">h</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal" style="margin-right:0.01968em">l</span><span class="mord mathnormal">imi</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em"></span><span class="mord mathnormal">e</span><span class="mord mathnormal">p</span><span class="mord mathnormal">oc</span><span class="mord mathnormal">h</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.0044em;vertical-align:-0.31em"></span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.02778em">ser</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">e</span><span class="mord mathnormal">p</span><span class="mord mathnormal">oc</span><span class="mord mathnormal">h</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal" style="margin-right:0.03588em">q</span><span class="mord mathnormal">u</span><span class="mord mathnormal">o</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel"><</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.0044em;vertical-align:-0.31em"></span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.02778em">ser</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal">e</span><span class="mord mathnormal">p</span><span class="mord mathnormal">oc</span><span class="mord mathnormal">h</span><span class="mord" style="margin-right:0.02778em">_</span><span class="mord mathnormal" style="margin-right:0.01968em">l</span><span class="mord mathnormal">imi</span><span class="mord mathnormal">t</span></span></span></span></span>
|
||
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="modifications-to-external-epoch-validation-waku-etc">Modifications to external epoch validation (Waku, etc.)<a href="#modifications-to-external-epoch-validation-waku-etc" class="hash-link" aria-label="Direct link to Modifications to external epoch validation (Waku, etc.)" title="Direct link to Modifications to external epoch validation (Waku, etc.)"></a></h3>
|
||
<p>For receivers of an RLN-v3 proof
|
||
to detect if a message is too old, we must use the higher bound of the <code>user_epoch_limit</code>, which has been set to <code>3600</code>.
|
||
The <strong>trade-off</strong> here is that we allow hour-old messages to propagate within the network.</p>
|
||
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="modifications-to-double-signaling-detection-scheme-waku-etc">Modifications to double signaling detection scheme (Waku, etc.)<a href="#modifications-to-double-signaling-detection-scheme-waku-etc" class="hash-link" aria-label="Direct link to Modifications to double signaling detection scheme (Waku, etc.)" title="Direct link to Modifications to double signaling detection scheme (Waku, etc.)"></a></h3>
|
||
<p>For verifiers of RLN-v1/v2 proofs,
|
||
a log of nullifiers seen in the last epoch is maintained,
|
||
and if there is a match with a pre-existing nullifier,
|
||
double signaling has been detected and the verifier MAY proceed to slash the spamming user.</p>
|
||
<p>With the RLN-v3 scheme,
|
||
we need to increase the size of the nullifier log used,
|
||
which previously cleared itself every second to the higher bound of the <code>user_epoch_limit</code>, which is <code>3600</code>.
|
||
Now, the RLN proof verifier must clear the nullifier log every <code>3600</code> seconds to satisfactorily detect double signaling.</p>
|
||
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="the-implementation">The implementation<a href="#the-implementation" class="hash-link" aria-label="Direct link to The implementation" title="Direct link to The implementation"></a></h2>
|
||
<p>An implementation of the RLN-v3 scheme in <a href="https://docs.gnark.consensys.io/" target="_blank" rel="noopener noreferrer">gnark</a> can be found <a href="https://github.com/vacp2p/gnark-rln/blob/9b05eddc89901a06d8f41b093ce8ce12fd0bb4e0/rln/rln.go" target="_blank" rel="noopener noreferrer">here</a>.</p>
|
||
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="comments-on-performance">Comments on performance<a href="#comments-on-performance" class="hash-link" aria-label="Direct link to Comments on performance" title="Direct link to Comments on performance"></a></h2>
|
||
<ul>
|
||
<li>Hardware: Macbook Air M2, 16GB RAM</li>
|
||
<li>Circuit: <a href="https://github.com/vacp2p/gnark-rln/blob/9b05eddc89901a06d8f41b093ce8ce12fd0bb4e0/rln/rln.go" target="_blank" rel="noopener noreferrer">RLN-v3</a></li>
|
||
<li>Proving system: <a href="https://eprint.iacr.org/2016/260.pdf" target="_blank" rel="noopener noreferrer"><code>Groth16</code></a></li>
|
||
<li>Framework: <a href="https://docs.gnark.consensys.io/" target="_blank" rel="noopener noreferrer"><code>gnark</code></a></li>
|
||
<li>Elliptic curve: <a href="https://eprint.iacr.org/2013/879.pdf" target="_blank" rel="noopener noreferrer"><code>bn254</code></a> (aka bn128) (not to be confused with the 254-bit Weierstrass curve)</li>
|
||
<li>Finite field: Prime-order subgroup of the group of points on the <code>bn254</code> curve</li>
|
||
<li>Default Merkle tree height: <code>20</code></li>
|
||
<li>Hashing algorithm: <a href="https://eprint.iacr.org/2019/458.pdf" target="_blank" rel="noopener noreferrer"><code>Poseidon</code></a></li>
|
||
<li>Merkle tree: <a href="https://github.com/rate-limiting-nullifier/pmtree" target="_blank" rel="noopener noreferrer"><code>Sparse Indexed Merkle Tree</code></a></li>
|
||
</ul>
|
||
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="proving">Proving<a href="#proving" class="hash-link" aria-label="Direct link to Proving" title="Direct link to Proving"></a></h3>
|
||
<p>The proving time for the RLN-v3 circuit is <code>90ms</code> for a single proof.</p>
|
||
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="verification">Verification<a href="#verification" class="hash-link" aria-label="Direct link to Verification" title="Direct link to Verification"></a></h3>
|
||
<p>The verification time for the RLN-v3 circuit is <code>1.7ms</code> for a single proof.</p>
|
||
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="conclusion">Conclusion<a href="#conclusion" class="hash-link" aria-label="Direct link to Conclusion" title="Direct link to Conclusion"></a></h2>
|
||
<p>The RLN-v3 scheme introduces a new epoch-based message rate-limiting scheme to the RLN protocol.
|
||
It enhances the user's flexibility in setting their message limits and cost-optimizes their stake.</p>
|
||
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="future-work">Future work<a href="#future-work" class="hash-link" aria-label="Direct link to Future work" title="Direct link to Future work"></a></h2>
|
||
<ul>
|
||
<li>Implementing the RLN-v3 scheme in <a href="https://github.com/vacp2p/zerokit" target="_blank" rel="noopener noreferrer">Zerokit</a></li>
|
||
<li>Implementing the RLN-v3 scheme in <a href="https://github.com/waku-org/nwaku" target="_blank" rel="noopener noreferrer">Waku</a></li>
|
||
<li>Formal security analysis of the RLN-v3 scheme</li>
|
||
</ul>
|
||
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="references">References<a href="#references" class="hash-link" aria-label="Direct link to References" title="Direct link to References"></a></h2>
|
||
<ul>
|
||
<li><a href="https://research.logos.co/rlog/rln-anonymous-dos-prevention" target="_blank" rel="noopener noreferrer">Strengthening Anonymous DoS Prevention with Rate Limiting Nullifiers in Waku</a></li>
|
||
<li><a href="https://github.com/rate-limiting-nullifier/circom-rln" target="_blank" rel="noopener noreferrer">RLN Circuits</a></li>
|
||
<li><a href="https://eprint.iacr.org/2016/260.pdf" target="_blank" rel="noopener noreferrer">Groth16</a></li>
|
||
<li><a href="https://docs.gnark.consensys.io/" target="_blank" rel="noopener noreferrer">Gnark</a></li>
|
||
<li><a href="https://eprint.iacr.org/2019/458.pdf" target="_blank" rel="noopener noreferrer">Poseidon Hash</a></li>
|
||
<li><a href="https://github.com/vacp2p/zerokit" target="_blank" rel="noopener noreferrer">Zerokit</a></li>
|
||
<li><a href="https://rfc.vac.dev/vac/32/rln-v1" target="_blank" rel="noopener noreferrer">RLN-v1 RFC</a></li>
|
||
<li><a href="https://rfc.vac.dev/vac/raw/rln-v2" target="_blank" rel="noopener noreferrer">RLN-v2 RFC</a></li>
|
||
<li><a href="https://waku.org" target="_blank" rel="noopener noreferrer">Waku</a></li>
|
||
</ul></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="Blog post page navigation"><a class="pagination-nav__link pagination-nav__link--prev" href="/rlog/vac101-membership-with-bloom-filters-and-cuckoo-filters"><div class="icon_S7Kx m_thRi"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="14" fill="none" viewBox="0 0 14 14"><path fill="#fff" d="M11.667 6.417h-7.1L7.83 3.156 7 2.333 2.334 7 7 11.667l.823-.823-3.255-3.26h7.099z"></path></svg></div><span class="lsd-typography lsd-typography--body2 pagination-nav__label">Logos Research 101: Membership with Bloom Filters and Cuckoo Filters</span></a><a class="pagination-nav__link pagination-nav__link--next" href="/rlog/rln-light-verifiers"><span class="lsd-typography lsd-typography--body2 pagination-nav__label">Verifying RLN Proofs in Light Clients with Subtrees</span><div class="icon_S7Kx m_thRi"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="14" fill="none" viewBox="0 0 14 14"><path fill="#fff" d="m7 2.334-.823.822 3.255 3.26H2.333v1.167h7.1l-3.256 3.261.823.823L11.667 7z"></path></svg></div></a></nav></main><div class="col col--2"><div class="tableOfContents_bqdL thin-scrollbar"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#introduction" class="table-of-contents__link toc-highlight">Introduction</a></li><li><a href="#theory" class="table-of-contents__link toc-highlight">Theory</a><ul><li><a href="#modification-to-leaves-set-in-the-membership-merkle-tree" class="table-of-contents__link toc-highlight">Modification to leaves set in the membership Merkle tree</a></li><li><a href="#modification-to-circuit-inputs" class="table-of-contents__link toc-highlight">Modification to circuit inputs</a></li><li><a href="#additional-circuit-constraints" class="table-of-contents__link toc-highlight">Additional circuit constraints</a></li><li><a href="#modifications-to-external-epoch-validation-waku-etc" class="table-of-contents__link toc-highlight">Modifications to external epoch validation (Waku, etc.)</a></li><li><a href="#modifications-to-double-signaling-detection-scheme-waku-etc" class="table-of-contents__link toc-highlight">Modifications to double signaling detection scheme (Waku, etc.)</a></li></ul></li><li><a href="#the-implementation" class="table-of-contents__link toc-highlight">The implementation</a></li><li><a href="#comments-on-performance" class="table-of-contents__link toc-highlight">Comments on performance</a><ul><li><a href="#proving" class="table-of-contents__link toc-highlight">Proving</a></li><li><a href="#verification" class="table-of-contents__link toc-highlight">Verification</a></li></ul></li><li><a href="#conclusion" class="table-of-contents__link toc-highlight">Conclusion</a></li><li><a href="#future-work" class="table-of-contents__link toc-highlight">Future work</a></li><li><a href="#references" class="table-of-contents__link toc-highlight">References</a></li></ul></div></div></div></div></div><footer 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