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<ol class="chapter"><li class="chapter-item expanded "><a href="0_0_zero_network.html"><strong aria-hidden="true">1.</strong> Zero Network</a></li><li class="chapter-item expanded "><a href="1_0_overview.html"><strong aria-hidden="true">2.</strong> Overview</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="1_1_what_is_privacy.html"><strong aria-hidden="true">2.1.</strong> What is Privacy</a></li><li class="chapter-item expanded "><a href="1_2_hide_transfer_amount.html"><strong aria-hidden="true">2.2.</strong> Hide Transfer Amount</a></li><li class="chapter-item expanded "><a href="1_3_gas_limit.html"><strong aria-hidden="true">2.3.</strong> Gas Limit</a></li><li class="chapter-item expanded "><a href="1_4_zero_knowledge_scheme.html" class="active"><strong aria-hidden="true">2.4.</strong> Zero Knowledge Scheme</a></li><li class="chapter-item expanded "><a href="1_5_transaction_constraints.html"><strong aria-hidden="true">2.5.</strong> Transaction Constraints</a></li></ol></li><li class="chapter-item expanded "><a href="2_0_transaction_constraints.html"><strong aria-hidden="true">3.</strong> Transaction Constraints</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="2_1_confidential_transfer.html"><strong aria-hidden="true">3.1.</strong> Confidential Transfer</a></li><li class="chapter-item expanded "><a href="2_2_confidential_smart_contract.html"><strong aria-hidden="true">3.2.</strong> Confidential Smart Contract</a></li></ol></li><li class="chapter-item expanded "><a href="3_0_primitive.html"><strong aria-hidden="true">4.</strong> Primitive</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="3_1_crypto.html"><strong aria-hidden="true">4.1.</strong> Crypto</a></li><li class="chapter-item expanded "><a href="3_2_jubjub.html"><strong aria-hidden="true">4.2.</strong> Jubjub</a></li><li class="chapter-item expanded "><a href="3_3_bls12_381.html"><strong aria-hidden="true">4.3.</strong> Bls12 381</a></li><li class="chapter-item expanded "><a href="3_4_elgamal.html"><strong aria-hidden="true">4.4.</strong> ElGamal</a></li><li class="chapter-item expanded "><a href="3_5_pairing.html"><strong aria-hidden="true">4.5.</strong> Pairing</a></li></ol></li><li class="chapter-item expanded "><a href="4_0_pallet.html"><strong aria-hidden="true">5.</strong> Pallet</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="4_1_plonk.html"><strong aria-hidden="true">5.1.</strong> Plonk</a></li><li class="chapter-item expanded "><a href="4_2_encrypted_balance.html"><strong aria-hidden="true">5.2.</strong> Encrypted Balance</a></li><li class="chapter-item expanded "><a href="4_3_confidential_transfer.html"><strong aria-hidden="true">5.3.</strong> Confidential Transfer</a></li></ol></li><li class="chapter-item expanded "><a href="5_0_related_tools.html"><strong aria-hidden="true">6.</strong> Related Tools</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="5_1_stealth_address.html"><strong aria-hidden="true">6.1.</strong> Stealth Address</a></li><li class="chapter-item expanded "><a href="5_2_pedersen_commitment.html"><strong aria-hidden="true">6.2.</strong> Pedersen Commitment</a></li><li class="chapter-item expanded "><a href="5_3_non_interactive_zero_knowlege_proof.html"><strong aria-hidden="true">6.3.</strong> Non Interactive Zero Knowledge Proof</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="5_3_1_qap.html"><strong aria-hidden="true">6.3.1.</strong> QAP</a></li><li class="chapter-item expanded "><a href="5_3_2_polynomial_commitment.html"><strong aria-hidden="true">6.3.2.</strong> Polynomial Commitment</a></li><li class="chapter-item expanded "><a href="5_3_3_homomorphic_encryption.html"><strong aria-hidden="true">6.3.3.</strong> Homomorphic Encryption</a></li></ol></li></ol></li><li class="chapter-item expanded "><a href="6_0_tutorial.html"><strong aria-hidden="true">7.</strong> Tutorial</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="6_1_plonk_pallet.html"><strong aria-hidden="true">7.1.</strong> pallet-plonk</a></li><li class="chapter-item expanded "><a href="6_2_confidential_transfer.html"><strong aria-hidden="true">7.2.</strong> confidential_transfer</a></li></ol></li><li class="chapter-item expanded "><a href="7_0_frequent_errors.html"><strong aria-hidden="true">8.</strong> Frequent Errors</a></li></ol>
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<h1 class="menu-title">Zero Network Documentation</h1>
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<h1 id="zero-knowledge-scheme"><a class="header" href="#zero-knowledge-scheme">Zero Knowledge Scheme</a></h1>
<p>In this section, we describe the zero knowledge scheme features.</p>
<h2 id="snarks-vs-starks-vs-bulletproofs"><a class="header" href="#snarks-vs-starks-vs-bulletproofs"><code>SNARKs</code> vs <code>STARKs</code> vs <code>Bulletproofs</code></a></h2>
<p>We compare the three types of zero knowledge scheme <code>zk-SNARKs</code>, <code>zk-STARKs</code> and <code>Bulletproofs</code>. The <code>zk-SNARKs</code> is the most efficient. We can verify the proof with const or almost const time and generate proof process is also efficient. The proof size is also small. However, it's necessary to setup the parameters. We can save a lot of workload because of this but it would be the critical security issue. The <code>zk-STARKs</code> doesn't need to setup parameters and it has quantum tolerance. However, its proof size is far bigger than <code>zk-SNARKs</code> and the workload of verification process also far bigger than <code>zk-SNARKs</code>. The <code>Bulletproofs</code> doesn't need to setup parameters and its feature is in the middle between <code>zk-SNARKs</code> and <code>zk-STARKs</code> but it doesn't have quantum tolerance.</p>
<h2 id="summerize"><a class="header" href="#summerize">Summerize</a></h2>
<p>To summerize the above comparison, it would be as following table.</p>
<div class="table-wrapper"><table><thead><tr><th>Scheme</th><th>Trusted Setup</th><th>Prover Cost</th><th>Verifier Cost</th><th>Proof Size</th><th>Quantum Tolerance</th></tr></thead><tbody>
<tr><td>zk-SNARKs</td><td>Necessary</td><td>Low</td><td>Low</td><td>Small</td><td>No</td></tr>
<tr><td>zk-STARKs</td><td>Unnecessary</td><td>Moderate</td><td>High</td><td>Large</td><td>Yes</td></tr>
<tr><td>Bulletproofs</td><td>Unnecessary</td><td>Low</td><td>Moderate</td><td>Moderate</td><td>No</td></tr>
</tbody></table>
</div>
<h2 id="privacy-preserving-transactions-friendly"><a class="header" href="#privacy-preserving-transactions-friendly">Privacy Preserving Transactions Friendly</a></h2>
<p>The <code>Bulletproofs</code> is mainly used for other privacy preserving transactions project for example <a href="https://aztec.network/"><code>Aztec</code></a>, <a href="https://crypto.stanford.edu/~buenz/papers/zether.pdf"><code>Zether</code></a> and so on. That's because these projects are Ethereum smart contract base projects so if they use the <code>zk-SNARKs</code>, it's necessary to setup the parameters for each deploy smart contracts. It's really hard to collect enough parties to setup the parameters for each deploy. We use the <code>zk-SNARKs</code> because of its efficiency and the <code>plonk</code> allows us to setup parameters without depending on circuit. In other words, once we setup the parameters, we can reuse them when we prove the transactions. </p>
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