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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" class="active"><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="stealth-address"><a class="header" href="#stealth-address">Stealth Address</a></h1>
<h2 id="abstract"><a class="header" href="#abstract">Abstract</a></h2>
<p>The <code>Stealth Address</code> is the technology which allows us to hide the <strong>recipient</strong> address.</p>
<h2 id="details"><a class="header" href="#details">Details</a></h2>
<p>The blockchain for example <code>Ethereum</code>, we generate the private key and the public key based on private key. The hash of the public key is going to be a address which specifies the <strong>recipient</strong>. This address corresponds one private key and public key pair so we can easily identify who is the <strong>recipient</strong> of the transaction. In our blockchain, we generate <strong>recipient</strong> address for each transactions and make it hard to identify the <strong>recipient</strong>.</p>
<ol>
<li>Generates recipient public key pairs</li>
<li>Generates recipient <code>Stealth Address</code></li>
<li>Prove the ownership of <code>Stealth Address</code></li>
</ol>
<p>Above sequence used for confidential transfer to keep the <strong>recipient</strong> address anonymous.</p>
<h2 id="generates-recipient-public-key-pairs"><a class="header" href="#generates-recipient-public-key-pairs">Generates Recipient Public Key Pairs</a></h2>
<p>Every transaction has <strong>recipient</strong> and we hide the <strong>recipient</strong> with stealth address. We assume Alice send transaction to Bod.</p>
<p>First of all, Bod generates the two key pairs (a, A) and (b, B) such that <code>aG = A</code> and <code>bG = B</code>. <code>a</code> and <code>b</code> are the private keys and, <code>A</code> and <code>B</code> are the public keys.</p>
<div class="table-wrapper"><table><thead><tr><th style="text-align: left">Variable</th><th style="text-align: left">Explanation</th><th style="text-align: left">Derivation</th></tr></thead><tbody>
<tr><td style="text-align: left">a</td><td style="text-align: left">Bob private key</td><td style="text-align: left">a ∈ Fp</td></tr>
<tr><td style="text-align: left">b</td><td style="text-align: left">Bob private key</td><td style="text-align: left">b ∈ Fp</td></tr>
<tr><td style="text-align: left">A</td><td style="text-align: left">Bob public key for <code>a</code></td><td style="text-align: left">a * G</td></tr>
<tr><td style="text-align: left">B</td><td style="text-align: left">Bob public key for <code>b</code></td><td style="text-align: left">b * G</td></tr>
</tbody></table>
</div>
<h2 id="generates-recipient-stealth-address"><a class="header" href="#generates-recipient-stealth-address">Generates Recipient <code>Stealth Address</code></a></h2>
<p>Secondly, Alice generates the Bob <strong>recipient</strong> address as referred to the <code>Stealth Address</code>. Alice selects the random number <code>r</code> and calculate the <code>Stealth Address</code> with Bob public keys such that following.</p>
<p>$$ P = H(r*A) * G + B $$</p>
<p>No one can link P address with <code>A</code> and <code>B</code> because it's concealed by elliptic curve arithmetic. Alice publish the <code>P</code> and <code>R</code> calculated as <code>R = rG</code>.</p>
<div class="table-wrapper"><table><thead><tr><th style="text-align: left">Variable</th><th style="text-align: left">Explanation</th><th style="text-align: left">Derivation</th></tr></thead><tbody>
<tr><td style="text-align: left">r</td><td style="text-align: left">randomness generated by Alice</td><td style="text-align: left">r ∈ Fp</td></tr>
<tr><td style="text-align: left">H</td><td style="text-align: left">one-way hash function which takes curve point and maps field element</td><td style="text-align: left">e: xG -> Fp</td></tr>
<tr><td style="text-align: left">R</td><td style="text-align: left">public value generated by Alice</td><td style="text-align: left">r * G</td></tr>
<tr><td style="text-align: left">P</td><td style="text-align: left">stealth address of Bob</td><td style="text-align: left">H(r*A) * G + B</td></tr>
</tbody></table>
</div>
<h2 id="prove-the-ownership-of-stealth-address"><a class="header" href="#prove-the-ownership-of-stealth-address">Prove the ownership of <code>Stealth Address</code></a></h2>
<p>Lastly, Bob needs to prove the ownership of <code>Stealth Address</code> to use assets associated with it. Bob knows his private keys <code>a</code> and <code>b</code>. He can calculate the private key of <code>P</code> with <code>x = H(a * R) + b</code>. This is the <a href="https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange#:~:text=Diffie%E2%80%93Hellman%20key%20exchange%20is,Whitfield%20Diffie%20and%20Martin%20Hellman.&text=Diffie%E2%80%93Hellman%20is%20used%20to%20secure%20a%20variety%20of%20Internet%20services."><code>Diffie–Hellman key exchange</code></a> algorithm. Only Bob can know the <code>x</code>. This is how concealing the <strong>recipient</strong> address. Next section, we explain how we conceal the <strong>amount</strong> of transactions.</p>
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