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@@ -215,48 +215,7 @@ We denote: <code>x = Poseidon(message), and y = A(x)</code>. </p>
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<p>Also, in our example (and <a href="https://github.com/njofce/zk-chat">zk-chat</a> implementation), we use linear polynomial, but <a href="sss.html">SSS</a> allows us to use various degree polynomials; therefore we can implement a protocol, where more than one signal (message) can be sent in per epoch. </p>
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<p>To learn more, check out the <a href="https://hackmd.io/7GR5Vi28Rz2EpEmLK0E0Aw?view">specification</a>; there are also <a href="https://github.com/privacy-scaling-explorations/rln/tree/master/circuits">circuits</a> implemented for various degree polynomials too.</p>
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<h1 id="diagram"><a class="header" href="#diagram">Diagram</a></h1>
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<pre class="mermaid">flowchart TB
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subgraph Generate Secret Key
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random0(Random 32 bytes) --> a_0(Secret Key)
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random1(Random 32 bytes) --> a_0
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end
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subgraph RLN
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subgraph Identity Commitment
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a_0 --> h0(Poseidon Hash)
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h0 --> q(Identity Commitment)
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end
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subgraph Calculate Internal Nullifier
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a_0 --> h1(Poseidon Hash)
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epoch(Epoch) --> h1
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h1 --> a_1
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rln_identifier(RLN Identifier) --> h2(Poseidon Hash)
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a_1 --> h2
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h2 --> nullifier(RLN Internal Nullifier)
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end
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subgraph Merkle Tree
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q --> merkle_tree_inclusion_proof(Merkle Tree Inclusion Proof)
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merkle_tree_inclusion_proof --> root(ZKP of Merkle Tree Root)
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end
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subgraph Shamirs Secret Scheme
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a_0 --> plus(+)
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a_1 --> multiply(*)
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x(Hashed Messaage) --> multiply
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multiply --> plus
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plus --> share_y
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end
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nullifier --> proof(ZKP)
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root --> proof
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share_y --> proof
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end
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</pre>
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<p><img src="./images/rln-circuit.png" alt="alt text" /></p>
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<div style="break-before: page; page-break-before: always;"></div><h1 id="circuits"><a class="header" href="#circuits">Circuits</a></h1>
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<p><em><a href="https://vitalik.ca/general/2022/06/15/using_snarks.html">zkSNARK</a> is used in the <strong>RLN</strong> core. Therefore, we must represent the protocol in <a href="https://www.zeroknowledgeblog.com/index.php/the-pinocchio-protocol/r1cs">R1CS</a> (as we use <a href="https://www.zeroknowledgeblog.com/index.php/groth16">Groth16</a>). <a href="https://docs.circom.io/">Circom</a> was chosen for this. This section explains <strong>RLN</strong> circuits for the linear polynomial case (one message per epoch). You can find implementation for the general case <a href="https://github.com/privacy-scaling-explorations/rln/blob/master/circuits/nrln-base.circom">here</a></em></p>
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<hr />
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@@ -167,48 +167,7 @@ We denote: <code>x = Poseidon(message), and y = A(x)</code>. </p>
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<p>Also, in our example (and <a href="https://github.com/njofce/zk-chat">zk-chat</a> implementation), we use linear polynomial, but <a href="sss.html">SSS</a> allows us to use various degree polynomials; therefore we can implement a protocol, where more than one signal (message) can be sent in per epoch. </p>
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<p>To learn more, check out the <a href="https://hackmd.io/7GR5Vi28Rz2EpEmLK0E0Aw?view">specification</a>; there are also <a href="https://github.com/privacy-scaling-explorations/rln/tree/master/circuits">circuits</a> implemented for various degree polynomials too.</p>
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<h1 id="diagram"><a class="header" href="#diagram">Diagram</a></h1>
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<pre class="mermaid">flowchart TB
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subgraph Generate Secret Key
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random0(Random 32 bytes) --> a_0(Secret Key)
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random1(Random 32 bytes) --> a_0
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end
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subgraph RLN
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subgraph Identity Commitment
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a_0 --> h0(Poseidon Hash)
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h0 --> q(Identity Commitment)
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end
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subgraph Calculate Internal Nullifier
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a_0 --> h1(Poseidon Hash)
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epoch(Epoch) --> h1
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h1 --> a_1
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rln_identifier(RLN Identifier) --> h2(Poseidon Hash)
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a_1 --> h2
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h2 --> nullifier(RLN Internal Nullifier)
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end
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subgraph Merkle Tree
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q --> merkle_tree_inclusion_proof(Merkle Tree Inclusion Proof)
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merkle_tree_inclusion_proof --> root(ZKP of Merkle Tree Root)
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end
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subgraph Shamirs Secret Scheme
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a_0 --> plus(+)
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a_1 --> multiply(*)
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x(Hashed Messaage) --> multiply
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multiply --> plus
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plus --> share_y
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end
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nullifier --> proof(ZKP)
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root --> proof
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share_y --> proof
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end
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</pre>
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<p><img src="./images/rln-circuit.png" alt="alt text" /></p>
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</main>
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