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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> Code</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="how_to_use.html"><strong aria-hidden="true">3.1.</strong> Usage</a></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>
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<h1 class="menu-title">Rate-Limiting Nullifier</h1>
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<h1 id="about"><a class="header" href="#about">About</a></h1>
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<p>RLN (Rate-Limiting Nullifier) is part of Privacy & Scaling Explorations (PSE), 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><a href="https://appliedzkp.org">appliedzkp.org</a></p>
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<div style="break-before: page; page-break-before: always;"></div><h1 id="concepts"><a class="header" href="#concepts">Concepts</a></h1>
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<p>This section is a starting point for understanding the concepts of RLN.</p>
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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><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>
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<p><a href="https://medium.com/privacy-scaling-explorations/rate-limiting-nullifier-a-spam-protection-mechanism-for-anonymous-environments-bbe4006a57d">RLN Overview</a></p>
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<p><a href="https://hackmd.io/@aeAuSD7mSCKofwwx445eAQ/BJcfDByNF">RLN Spec</a></p>
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<p><a href="https://rfc.vac.dev/spec/32/">VAC RLN Spec</a></p>
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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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<div style="break-before: page; page-break-before: always;"></div><h1 id="terminology"><a class="header" href="#terminology">Terminology</a></h1>
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<div class="table-wrapper"><table><thead><tr><th>Term</th><th>Description</th></tr></thead><tbody>
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<tr><td>ZK-SNARK</td><td><a href="https://z.cash/technology/zksnarks/">z.cash/technology/zksnarks/</a></td></tr>
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<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>
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<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>
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<tr><td>Identity nullifier</td><td>Random 32 byte value used as component for identity secret generation.</td></tr>
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<tr><td>Identity trapdoor</td><td>Random 32 byte value used as component for identity secret generation.</td></tr>
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<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>
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<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>
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<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>
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<tr><td>Signal hash</td><td>Keccak hash of the signal, used as an input in the RLN circuit.</td></tr>
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<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>
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<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>
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<tr><td>Merkle proof</td><td>Proof that a user is member of the RLN membership tree.</td></tr>
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</tbody></table>
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</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>
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<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>
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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="references"><a class="header" href="#references">References</a></h1>
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<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>
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<p><a href="https://medium.com/privacy-scaling-explorations/rate-limiting-nullifier-a-spam-protection-mechanism-for-anonymous-environments-bbe4006a57d">RLN Overview</a></p>
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<p><a href="https://hackmd.io/@aeAuSD7mSCKofwwx445eAQ/BJcfDByNF">RLN Spec</a></p>
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<p><a href="https://rfc.vac.dev/spec/32/">VAC RLN Spec</a></p>
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<div style="break-before: page; page-break-before: always;"></div><h1 id="code"><a class="header" href="#code">Code</a></h1>
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<div style="break-before: page; page-break-before: always;"></div><h1 id="usage"><a class="header" href="#usage">Usage</a></h1>
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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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<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><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-rs">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-rs">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);
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const nullifierSpam = RLN.genNullifier(a1Spam);
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const pubSignalsSpam = [y2, witnessDataSpam.root, nullifierSpam, x2, epoch];
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res = await RLN.verifyProof(vKey, { proof: witnessDataSpam.fullProof.proof, publicSignals: pubSignalsSpam })
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if (res === true) {
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console.log("Spam proof 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 identitySecret = RLN.calculateIdentitySecret(privateKey);
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const retreivedPkey = bigintConversion.bufToBigint(RLN.retrievePrivateKey(x1, x2, y1, y2));
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if(Fq.eq(identitySecret, retreivedPkey)) {
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console.log("PK successfully reconstructed");
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} else {
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console.log("Error while reconstructing private key")
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}
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// TODO: Add removal from tree example
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}
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</code></pre>
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