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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="circuits.html"><strong aria-hidden="true">2.2.1.</strong> Circuits</a></li><li class="chapter-item expanded "><a href="diagram.html"><strong aria-hidden="true">2.2.2.</strong> Diagram</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 class="menu-title">Rate-Limiting Nullifier</h1>
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<h1 id="rln"><a class="header" href="#rln">RLN</a></h1>
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<p><strong>RLN</strong> (Rate-Limiting Nullifier) is part of (<strong>PSE</strong>) <a href="https://appliedzkp.org">Privacy & 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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<p><img src="./images/logo.svg" alt="alt text" /></p>
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<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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<div style="break-before: page; page-break-before: always;"></div><h1 id="overview"><a class="header" href="#overview">Overview</a></h1>
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<p>This section is a starting point for understanding the concepts of <strong>RLN</strong>.</p>
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<p>Here we'll discuss:</p>
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<ul>
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<li>Basic explanation of the <strong>RLN</strong> protocol</li>
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<li><strong>RLN</strong> protocol under the hood</li>
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<li><strong>RLN</strong> uses</li>
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</ul>
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<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>
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<p><em>This topic is a part of <a href="https://medium.com/privacy-scaling-explorations/rate-limiting-nullifier-a-spam-protection-mechanism-for-anonymous-environments-bbe4006a57d">complete overview</a> by Blagoj</em>.</p>
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<hr />
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<p><strong>RLN</strong> is a construct based on zero-knowledge proofs that enables spam prevention mechanism for decentralized, anonymous environments. In anonymous environments, the identity of the entities is unknown.</p>
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<p>The anonymity property opens up the possibility for spam attack and sybil attack vectors for certain applications, which could seriously degrade the user experience and the overall functioning of the application. For example, imagine a chat application, where users are anonymous. Now, everyone can write unlimited number of spam messages, while we don't have ability to kick this member, because the spammer is anonymous. </p>
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<p><strong>RLN</strong> helps us identify and "kick" the spammer.</p>
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<p>Moreover RLN can be useful not only to prevent a spam attacks, but in general, to limit users (in anonymous environments) in the number of actions (f.e. to vote or to make a bid).</p>
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<h2 id="how-it-works"><a class="header" href="#how-it-works">How it works</a></h2>
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<p>The RLN construct’s functionality consists of three parts, which when integrated together provide spam and sybil attack protection. These parts should be integrated by the upstream applications which require anonymity and spam protection. The applications can be centralized or decentralized. For decentralized applications, each user maintains a separate storage and compute resources for the application. The three parts are:</p>
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<ul>
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<li>User registration</li>
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<li>User interaction</li>
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<li>User removal (slashing)</li>
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</ul>
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<h3 id="user-registration"><a class="header" href="#user-registration">User registration</a></h3>
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<p>Before registering to the application the user needs to generate a secret key and derive an identity commitment from the secret key using the <code>Poseidon</code> hash function <code>identityCommitment = posseidonHash(secretKey)</code>.</p>
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<p>The user registers to the application by providing a form of stake and their identity commitment, which is derived from the secret key. The application maintains a Merkle tree data structure (in the latest iteration of the RLN construct we use the Incremental Merkle Tree algorithm), which stores the identity commitments of the registered users. Upon successful registration the user’s identity commitment is stored in a leaf of the Merkle tree and an index is given to them, representing their position in the tree.</p>
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<h3 id="user-interaction"><a class="header" href="#user-interaction">User interaction</a></h3>
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<p>For each interaction that the user wants to make with the application, the user must generate a zero-knowledge proof which ensures the other participants (the verifiers) that they are a valid member of the application and their identity commitment is part of the membership Merkle tree.</p>
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<p>The interactions are app specific, such as voting for voting application and message sending for chat applications. The verifier is usually a server for centralized applications, or the other users for decentralized applications.</p>
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<p>So, as it's been said there is a problem with spam, therefore we introduced an "anti-spam rule". The rule is usually in the form of:
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<code>Users must not make more than X interactions per epoch</code>.</p>
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<p>The epoch can be translated as time interval of <code>Y</code> units of time unit <code>Z</code>. For simplicity sake, let’s transform the rule into: <code>Users must not send more than 1 message per second</code>.</p>
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<p>We can implement this using <code>Shamir's Secret Sharing</code> scheme (<a href="./sss.html"><em>read more</em></a>), which allows you to split a secret (f.e. to <code>n</code> parts) and recover it when any <code>m</code> of <code>n</code> parts (<code>m <= n</code>) are presented.</p>
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<p>Thus, users have to split their <code>secret_key</code> into <code>n</code> parts and for every interaction they have to reveal the new part of the <code>secret_key</code>. So, in addition to proving the membership in the <code>Merkle Tree</code>, users have to prove that the revealed part is truly the part of their <code>secret_key</code>.</p>
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<p>If they make more interactions than allowed per epoch their secret key can be fully reconstructed.</p>
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<h3 id="user-removal-slashing"><a class="header" href="#user-removal-slashing">User removal (slashing)</a></h3>
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<p>The final property of the RLN mechanism is that it allows for the users to be removed from the membership tree by anyone that knows their secret key. The membership tree contains the identity commitments of all registered users. User’s identity commitment is derived from their secret key, and the secret key of the user is only revealed in a spam event (except for the scenarios where the original users wants to remove themselves, which they can always do because they know their secret key). When an economic stake is present, the RLN mechanism can be implemented in a way that the spammer’s stake is sent to the first user that correctly reports the spammer by providing the reconstructed secret key of the spammer as a proof.</p>
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<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>
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<p>This section provides deep and technical <strong>RLN</strong> overview.</p>
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<p>We'll discuss:</p>
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<ul>
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<li>How circuits are implemented</li>
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<li><strong>RLN</strong> in general (diagram)</li>
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</ul>
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<div style="break-before: page; page-break-before: always;"></div><h1 id="circuits"><a class="header" href="#circuits">Circuits</a></h1>
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<p><em><a href="https://vitalik.ca/general/2022/06/15/using_snarks.html">zkSNARK</a> is used in the <strong>RLN</strong> core. Therefore, we need to represent the protocol in R1CS (as we use Groth16). Circom DSL was chosen for this. This section provides an explanation of RLN circuits.</em></p>
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<div style="break-before: page; page-break-before: always;"></div><h1 id="diagram"><a class="header" href="#diagram">Diagram</a></h1>
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<pre class="mermaid">flowchart TB
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subgraph Generate Secret Key
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random0(Random 32 bytes) --> a_0(Secret Key)
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random1(Random 32 bytes) --> a_0
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end
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subgraph RLN
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subgraph Identity Commitment
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a_0 --> h0(Poseidon Hash)
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h0 --> q(Identity Commitment)
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end
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subgraph Calculate Internal Nullifier
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a_0 --> h1(Poseidon Hash)
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epoch(Epoch) --> h1
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h1 --> a_1
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rln_identifier(RLN Identifier) --> h2(Poseidon Hash)
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a_1 --> h2
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h2 --> nullifier(RLN Internal Nullifier)
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end
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subgraph Merkle Tree
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q --> merkle_tree_inclusion_proof(Merkle Tree Inclusion Proof)
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merkle_tree_inclusion_proof --> root(ZKP of Merkle Tree Root)
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end
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subgraph Shamirs Secret Scheme
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a_0 --> plus(+)
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a_1 --> multiply(*)
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x(Hashed Messaage) --> multiply
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multiply --> plus
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plus --> share_y
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end
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nullifier --> proof(ZKP)
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root --> proof
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share_y --> proof
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end
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</pre>
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<div style="break-before: page; page-break-before: always;"></div><h1 id="uses"><a class="header" href="#uses">Uses</a></h1>
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<h2 id="zk-chat"><a class="header" href="#zk-chat">zk-chat</a></h2>
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<p>https://github.com/njofce/zk-chat</p>
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<h2 id=""><a class="header" href="#"></a></h2>
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<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>
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<p>This section provides information on how to use <strong>RLN</strong> in your project:</p>
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<ul>
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<li>JavaScript RLN (for <a href="https://github.com/Rate-Limiting-Nullifier/rlnjs">rln-js</a>)</li>
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<li>Rust RLN (for <a href="https://github.com/vacp2p/zerokit/tree/master/rln">zerokit-rln</a>)</li>
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</ul>
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<div style="break-before: page; page-break-before: always;"></div><h1 id="theory"><a class="header" href="#theory">Theory</a></h1>
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<p>This section provides theoretical information that underpins <strong>RLN</strong>.</p>
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<p>Here we'll discuss:</p>
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<ul>
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<li>Shamir's Secret Sharing</li>
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</ul>
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<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>
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<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 <= n</code>)</p>
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<p><a href="https://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing">Sharmir's Secret Sharing wikipedia</a> is a good reference to understand the concept.</p>
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<p>Reconstruction 1: https://github.com/akinovak/semaphore-lib/blob/5b9bb3210192c8e508eced7ef6579fd56e635ed0/src/rln.ts#L31</p>
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<pre><code class="language-js">retrievePrivateKey(x1: bigint, x2:bigint, y1:bigint, y2:bigint): Buffer | ArrayBuffer {
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const slope = Fq.div(Fq.sub(y2, y1), Fq.sub(x2, x1))
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const privateKey = Fq.sub(y1, Fq.mul(slope, x1));
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return bigintConversion.bigintToBuf(Fq.normalize(privateKey));
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}
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</code></pre>
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<p>Reconstruction 2: https://github.com/akinovak/semaphore-lib/blob/rln_signature_changes/test/index.ts#L250</p>
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<pre><code class="language-js">async function testRlnSlashingSimulation() {
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RLN.setHasher('poseidon');
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const identity = RLN.genIdentity();
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const privateKey = identity.keypair.privKey;
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const leafIndex = 3;
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const idCommitments: Array<any> = [];
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for (let i=0; i<leafIndex;i++) {
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const tmpIdentity = OrdinarySemaphore.genIdentity();
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const tmpCommitment: any = RLN.genIdentityCommitment(identity.keypair.privKey);
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idCommitments.push(tmpCommitment);
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}
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idCommitments.push(RLN.genIdentityCommitment(privateKey))
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const signal = 'hey hey';
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const x1: bigint = OrdinarySemaphore.genSignalHash(signal);
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const epoch: string = OrdinarySemaphore.genExternalNullifier('test-epoch');
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const vkeyPath: string = path.join('./rln-zkeyFiles', 'verification_key.json');
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const vKey = JSON.parse(fs.readFileSync(vkeyPath, 'utf-8'));
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const wasmFilePath: string = path.join('./rln-zkeyFiles', 'rln.wasm');
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const finalZkeyPath: string = path.join('./rln-zkeyFiles', 'rln_final.zkey');
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const witnessData: IWitnessData = await RLN.genProofFromIdentityCommitments(privateKey, epoch, signal, wasmFilePath, finalZkeyPath, idCommitments, 15, BigInt(0), 2);
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const a1 = RLN.calculateA1(privateKey, epoch);
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const y1 = RLN.calculateY(a1, privateKey, x1);
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const nullifier = RLN.genNullifier(a1);
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const pubSignals = [y1, witnessData.root, nullifier, x1, epoch];
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let res = await RLN.verifyProof(vKey, { proof: witnessData.fullProof.proof, publicSignals: pubSignals })
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if (res === true) {
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console.log("Verification OK");
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} else {
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console.log("Invalid proof");
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return;
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}
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const signalSpam = "let's try spamming";
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const x2: bigint = OrdinarySemaphore.genSignalHash(signalSpam);
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const witnessDataSpam: IWitnessData = await RLN.genProofFromIdentityCommitments(privateKey, epoch, signalSpam, wasmFilePath, finalZkeyPath, idCommitments, 15, BigInt(0), 2);
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const a1Spam = RLN.calculateA1(privateKey, epoch);
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const y2 = RLN.calculateY(a1Spam, privateKey, x2);
|
||
const nullifierSpam = RLN.genNullifier(a1Spam);
|
||
|
||
const pubSignalsSpam = [y2, witnessDataSpam.root, nullifierSpam, x2, epoch];
|
||
|
||
res = await RLN.verifyProof(vKey, { proof: witnessDataSpam.fullProof.proof, publicSignals: pubSignalsSpam })
|
||
if (res === true) {
|
||
console.log("Spam proof Verification OK");
|
||
} else {
|
||
console.log("Invalid proof");
|
||
return;
|
||
}
|
||
|
||
const identitySecret = RLN.calculateIdentitySecret(privateKey);
|
||
|
||
const retreivedPkey = bigintConversion.bufToBigint(RLN.retrievePrivateKey(x1, x2, y1, y2));
|
||
|
||
|
||
if(Fq.eq(identitySecret, retreivedPkey)) {
|
||
console.log("PK successfully reconstructed");
|
||
} else {
|
||
console.log("Error while reconstructing private key")
|
||
}
|
||
|
||
// 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>
|
||
<ul>
|
||
<li>Terminology</li>
|
||
<li>References</li>
|
||
</ul>
|
||
<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>zkSNARK</td><td>Proof construction where one can prove possession of certain information, e.g. a secret key, without revealing that information, and without any interaction between the prover and verifier.</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>
|
||
<ul>
|
||
<li>
|
||
<p><a href="https://ethresear.ch/t/semaphore-rln-rate-limiting-nullifier-for-spam-prevention-in-anonymous-p2p-setting/5009">First proposal of RLN by Barry WhiteHat</a></p>
|
||
</li>
|
||
<li>
|
||
<p><a href="https://medium.com/privacy-scaling-explorations/rate-limiting-nullifier-a-spam-protection-mechanism-for-anonymous-environments-bbe4006a57d">RLN Overview by Blagoj</a></p>
|
||
</li>
|
||
<li>
|
||
<p><a href="https://hackmd.io/@aeAuSD7mSCKofwwx445eAQ/BJcfDByNF">Demo RLN Spec</a></p>
|
||
</li>
|
||
<li>
|
||
<p><a href="https://rfc.vac.dev/spec/32/">VAC RLN Spec</a></p>
|
||
</li>
|
||
<li>
|
||
<p><a href="https://vitalik.ca/general/2016/12/10/qap.html">Understand zkSNARK</a></p>
|
||
</li>
|
||
<li>
|
||
<p><a href="https://docs.circom.io/">Circom docs</a></p>
|
||
</li>
|
||
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|
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