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331 lines
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<div id="content" class="content">
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<main>
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<h1><a class="header" href="#how-it-works" id="how-it-works">How it works</a></h1>
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<h2><a class="header" href="#inserting-identities" id="inserting-identities">Inserting identities</a></h2>
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<p>An identity is comprised of the following information:</p>
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<ol>
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<li>An <a href="https://en.wikipedia.org/wiki/EdDSA">EdDSA</a> private key. Note that it is
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<em>not</em> an Ethereum private key.</li>
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<li>An identity nullifier, whih is a random 32-byte value.</li>
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<li>An identity trapdoor, whih is a random 32-byte value.</li>
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</ol>
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<p>An identity commitment is the Pedersen hash of:</p>
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<ol>
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<li>The public key associated with the identity's private key.</li>
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<li>The identity nullifier.</li>
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<li>The identity trapdoor.</li>
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</ol>
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<p>To register an identity, the user must insert their identity commitment into
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Semaphore's identity tree. They can do this by calling the Semaphore contract's
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<code>insertIdentity(uint256 _identityCommitment)</code> function. See the <a href="./api.html">API
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reference</a> for more information.</p>
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<h2><a class="header" href="#broadcasting-signals" id="broadcasting-signals">Broadcasting signals</a></h2>
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<p>To broadcast a signal, the user must invoke this Semaphore contract function:</p>
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<pre><code>broadcastSignal(
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bytes memory _signal,
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uint256[8] memory _proof,
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uint256 _root,
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uint256 _nullifiersHash,
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uint232 _externalNullifier
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)
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</code></pre>
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<ul>
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<li><code>_signal</code>: the signal to broadcast.</li>
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<li><code>_proof</code>: a zk-SNARK proof (see below).</li>
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<li><code>_root</code>: The root of the identity tree, where the user's identity commitment
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is the last-inserted leaf.</li>
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<li><code>_nullifiersHash</code>: A uniquely derived hash of the external nullifier, user's
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identity nullifier, and the Merkle path index to their identity commitment.
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It ensures that a user cannot broadcast a signal with the same external
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nullifier more than once.</li>
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<li><code>_externalNullifier</code>: The external nullifier at which the signal is
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broadcast.</li>
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</ul>
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<p>To zk-SNARK proof must satisfy the constraints created by Semaphore's zk-SNARK
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circuit as described below:</p>
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<h3><a class="header" href="#the-zk-snark-circuit" id="the-zk-snark-circuit">The zk-SNARK circuit</a></h3>
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<p>The <a href="./circuits/circom/semaphore-base.circom">semaphore-base.circom</a> circuit
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helps to prove the following:</p>
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<h3><a class="header" href="#that-the-identity-commitment-exists-in-the-merkle-tree" id="that-the-identity-commitment-exists-in-the-merkle-tree">That the identity commitment exists in the Merkle tree</a></h3>
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<p><strong>Private inputs:</strong></p>
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<ul>
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<li><code>identity_pk</code>: the user's EdDSA public key</li>
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<li><code>identity_nullifier</code>: a random 32-byte value which the user should save</li>
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<li><code>identity_trapdoor</code>: a random 32-byte value which the user should save</li>
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<li><code>identity_path_elements</code>: the values along the Merkle path to the
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user's identity commitment</li>
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<li><code>identity_path_index[n_levels]</code>: the direction (left/right) per tree level
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corresponding to the Merkle path to the user's identity commitment</li>
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</ul>
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<p><strong>Public inputs:</strong></p>
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<ul>
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<li><code>root</code>: The Merkle root of the identity tree</li>
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</ul>
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<p><strong>Procedure:</strong></p>
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<p>The circuit hashes the public key, identity nullifier, and identity trapdoor to
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generate an <strong>identity commitment</strong>. It then verifies the Merkle proof against
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the Merkle root and the identity commitment.</p>
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<h3><a class="header" href="#that-the-signal-was-only-broadcasted-once" id="that-the-signal-was-only-broadcasted-once">That the signal was only broadcasted once</a></h3>
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<p><strong>Private inputs:</strong></p>
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<ul>
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<li><code>identity_nullifier</code>: as above</li>
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<li><code>identity_path_index</code>: as above</li>
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</ul>
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<p><strong>Public inputs:</strong></p>
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<ul>
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<li><code>external_nullifier</code>: the 29-byte external nullifier - see above</li>
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<li><code>nullifiers_hash</code>: the hash of the identity nullifier, external nullifier,
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and Merkle path index (<code>identity_path_index</code>)</li>
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</ul>
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<p><strong>Procedure:</strong></p>
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<p>The circuit hashes the given identity nullifier, external nullifier, and Merkle
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path index, and checks that it matches the given nullifiers hash. Additionally,
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the smart contract ensures that it has not previously seen this nullifiers
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hash. This way, double-signalling is impossible.</p>
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<h3><a class="header" href="#that-the-signal-was-truly-broadcasted-by-the-user-who-generated-the-proof" id="that-the-signal-was-truly-broadcasted-by-the-user-who-generated-the-proof">That the signal was truly broadcasted by the user who generated the proof</a></h3>
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<p><strong>Private inputs:</strong></p>
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<ul>
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<li><code>identity_pk</code>: as above</li>
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<li><code>auth_sig_r</code>: the <code>r</code> value of the signature of the signal</li>
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<li><code>auth_sig_s</code>: the <code>s</code> value of the signature of the signal</li>
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</ul>
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<p><strong>Public inputs:</strong></p>
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<ul>
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<li><code>signal_hash</code>: the hash of the signal</li>
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<li><code>external_nullifier</code>: the 29-byte external nullifier - see above</li>
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</ul>
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<p><strong>Procedure:</strong></p>
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<p>The circuit hashes the signal hash and the external nullifier, and verifies
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this output against the given public key and signature. This ensures the
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authenticity of the signal and prevents front-running attacks.</p>
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<h2><a class="header" href="#cryptographic-primitives" id="cryptographic-primitives">Cryptographic primitives</a></h2>
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<p>Semaphore uses MiMC for the Merkle tree, Pedersen commmitments for the identity
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commitments, Blake2 for the nullifiers hash, and EdDSA for the signature.</p>
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<p>MiMC is a relatively new hash function. We use the recommended MiMC
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construction from <a href="https://eprint.iacr.org/2016/492.pdf">Albrecht et al</a>, and
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there is a prize to break MiMC at <a href="http://mimchash.org">http://mimchash.org</a>
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which has not been claimed yet.</p>
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<p>We have also implemented a version of Semaphore which uses the Poseidon hash
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function for the Merkle tree and EdDSA signature verification. This may have
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better security than MiMC, allows identity insertions to save about 20% gas,
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and roughly halves the proving time. Note, however, that the Poseidon-related
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circuits and EVM bytecode generator have not been audited, so use it with
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caution. To use it, checkout the <code>feat/poseidon</code> branch of this repository.</p>
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