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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"><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" class="active"><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="non-interactive-zero-knowledge-proof"><a class="header" href="#non-interactive-zero-knowledge-proof">Non Interactive Zero Knowledge Proof</a></h1>
<p>The <code>Non Interactive Zero Knowledge Proof</code> referred as to <code>NIZK</code> prove the statement without revealing any information about the statement. There are some types of <code>NIZK</code> for example <code>SNORKs</code>, <code>STARKs</code> and so on. In this section, we describe the <code>SNARKs</code> and especially <a href="https://eprint.iacr.org/2013/279.pdf"><code>Pinocchio Protocol</code></a>. It's a little bit complicated technology so I divide into three parts.</p>
<h2 id="abstract"><a class="header" href="#abstract">Abstract</a></h2>
<p>The <code>SNARKs</code> converts the computation problems into the polynomial equations. We can not only hide the computation itself but also verify the computation faster than compute it again. That's why the <code>SNARKs</code> is also used for scaling solution for example <code>zk rollup</code>.</p>
<h2 id="detail"><a class="header" href="#detail">Detail</a></h2>
<p>The <code>SNARKs</code> has three steps.</p>
<ol>
<li><a href="4_3_1_qap.html">QAP</a></li>
</ol>
<p>Converting computation which we want to prove without revealing additional information into polynomial equations. In <a href="https://eprint.iacr.org/2013/279.pdf"><code>Pinocchio Protocol</code></a>, we need to generate polynonial equations for each computation. The polynomial equations are decided for corresponding computation.</p>
<ol start="2">
<li><a href="4_3_2_polynomial_commitment.html">Polynomail Commitment</a></li>
</ol>
<p>Hiding the secret as polynomial coefficients, opening with evaluating that polynomials at point, and we can prove the computation was done correctly.</p>
<ol start="3">
<li><a href="4_3_3_homomorphic_encryption.html">Homomorphic Encryption</a></li>
</ol>
<p>The polynomial coefficients are encrypted to keep the secret so we need perform evaluation with remaining encrypted. The <code>Homomorphic Encryption</code> can perform the multiple time addition and one time multiplication for encrypted number using elliptic curve and pairing.</p>
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