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238 lines
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238 lines
14 KiB
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<ol class="chapter"><li class="chapter-item expanded "><a href="overview.html" class="active"><strong aria-hidden="true">1.</strong> Overview</a></li><li class="chapter-item expanded "><a href="quick_start.html"><strong aria-hidden="true">2.</strong> Quick start</a></li><li class="chapter-item expanded "><a href="trusted_setup.html"><strong aria-hidden="true">3.</strong> Trusted Setup</a></li><li class="chapter-item expanded "><a href="cryptographic_specification.html"><strong aria-hidden="true">4.</strong> Cryptographic Specification</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="system_invariants.html"><strong aria-hidden="true">4.1.</strong> System invariants</a></li><li class="chapter-item expanded "><a href="insertion.html"><strong aria-hidden="true">4.2.</strong> Insertion</a></li><li class="chapter-item expanded "><a href="circuit_and_gates.html"><strong aria-hidden="true">4.3.</strong> The Circuit and Gates</a></li><li class="chapter-item expanded "><a href="precomputation_and_updates.html"><strong aria-hidden="true">4.4.</strong> Precomputation and updates</a></li><li class="chapter-item expanded "><a href="fiat_shamir_transcript.html"><strong aria-hidden="true">4.5.</strong> The Fiat-Shamir Transcript</a></li><li class="chapter-item expanded "><a href="proof_generation.html"><strong aria-hidden="true">4.6.</strong> Proof generation</a></li><li class="chapter-item expanded "><a href="verification.html"><strong aria-hidden="true">4.7.</strong> Proof verification</a></li></ol></li><li class="chapter-item expanded "><a href="lagrange_basis_polynomial_commitment_tree.html"><strong aria-hidden="true">5.</strong> The Lagrange Basis Polynomial Commitment Tree</a></li><li class="chapter-item expanded "><a href="mechanism_of_operation.html"><strong aria-hidden="true">6.</strong> Mechanism of Operation</a></li><li class="chapter-item expanded "><a href="ethereum_contracts.html"><strong aria-hidden="true">7.</strong> Ethereum contracts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="gas_costs.html"><strong aria-hidden="true">7.1.</strong> Gas costs</a></li></ol></li><li class="chapter-item expanded "><a href="performance_benchmarks.html"><strong aria-hidden="true">8.</strong> Performance and Benchmarks</a></li><li class="chapter-item expanded "><a href="credits.html"><strong aria-hidden="true">9.</strong> Credits</a></li></ol>
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<h1 class="menu-title">Semacaulk</h1>
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<h1 id="overview"><a class="header" href="#overview">Overview</a></h1>
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<p>Semacaulk is a zero-knowledge set membership protocol that works on Ethereum.</p>
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<p>Semacaulk allows a user to <em>commit</em> to an identity, represented by two secret
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values: an identity nullifier and an identity trapdoor. Next, any user who
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knows their secret values can generate a proof that they had previously
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committed to said identity, without revealing which member of the set they
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were. Moreover, when they submit such a proof, they can broadcast an arbitrary
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<em>signal</em> against an <em>external nullifier</em>, but only do so once per external
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nullifier. This enables applications like mixers, whistleblowing, and simple
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private voting systems. This is the same basic functionality as the <a href="https://github.com/semaphore-protocol/semaphore">Semaphore
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Protocol</a>.</p>
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<p>The source code for Semacaulk can be found
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<a href="https://github.com/geometryresearch/semacaulk">here</a>.</p>
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<h2 id="differences-from-semaphore"><a class="header" href="#differences-from-semaphore">Differences from Semaphore</a></h2>
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<p>Semacaulk differs from Semaphore in two key ways. First, instead of
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accumulating identity commitments in a Merkle tree, it updates a KZG
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commitment. This operations involves BN254 point multiplication and addition,
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rather than expensive zk-friendly hash operations. Secondly, the underlying
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proof system is a polynomial interactive oracle proof that combines <a href="https://eprint.iacr.org/2022/957">Caulk+
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lookups</a> and a <a href="https://zcash.github.io/halo2/design/proving-system/multipoint-opening.html">multipoint opening
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argument</a>.</p>
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<p>Thanks to these techniques, on-chain insertions are far cheaper in Semacaulk
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(around 68k gas) while the gas cost of verification (356k gas) is comparable to
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that of Semaphore. Moreover, proof generation comes in two phases - a
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<a href="precomputation_and_updates.html">precomputation stage</a> and a proof generation
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stage. The total time taken is comparable to Groth16 proof generation for a
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Semaphore circuit that supports the same number of insertions, but more
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imporantly, precomputation can be performed long in advance and efficiently
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updated, which imparts more flexibility which may lead to higher
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user-friendliness.</p>
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<h2 id="motivation"><a class="header" href="#motivation">Motivation</a></h2>
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<p>We intend Semacaulk to demonstrate the use of Caulk+ techniques for membership
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proofs in a gas-efficient manner to enable privacy-related applications. We
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believe these techniques, as are other new proving systems and lookup
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arguments, can be highly useful, and we hope that Semacaulk shows how to
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practically use them.</p>
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<p>We highly welcome and strongly encourage collaboration with projects who wish
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to build upon Semacaulk.</p>
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<p>Note that the techniques used in Semacaulk do not have to involve an end-to-end
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custom prover such as used here. We have done this only because we wanted to
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experiment with improving prover efficiency further. With only small changes,
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the same gas-efficient membership proof construction can be used with more
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generic and expressive SNARK-based programs.</p>
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<h2 id="security"><a class="header" href="#security">Security</a></h2>
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<p>The code base has not been audited. We do not recommend its use in production
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until a thorough audit has been performed.</p>
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