Zk Proofs Fundamentals

ZK Proofs Fundamentals

What is a Zero-Knowledge Proof

Prove statement is true WITHOUT revealing the secret/data used in the proof.

Example: "I know the solution to this sudoku" without showing the solution. On-chain: "I know a valid trade at this price" without revealing the actual price or identity.

SNARKs vs STARKs

SNARK: Groth16, Plonk (requires trusted setup ceremony — risky if not done correctly). STARK: DEEP-FRI (no trusted setup).

Circom (Circuit Language)

Describe computation in a circuit. Compiler generates constraints.

pragma circom 2.0.0;

// Sudoku solution verification circuit
template SudokuVerifier() {
    signal input solution[81];     // Sudoku solution (9x9)
    signal input puzzle[81];       // Puzzle clues
    signal output valid;            // 1 if valid, 0 otherwise

    // Check rows
    for (var i = 0; i < 9; i++) {
        var seen[10] = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
        for (var j = 0; j < 9; j++) {
            var idx = i * 9 + j;
            var val = solution[idx];
            // Check 1-9
            (val - 1) * (val - 9) === 0;
            // Check no duplicates (simplified)
            seen[val]++;
        }
    }
    // ... similar for columns and 3x3 boxes

    // Check puzzle constraints (where puzzle has clues)
    for (var i = 0; i < 81; i++) {
        if (puzzle[i] != 0) {
            solution[i] === puzzle[i];
        }
    }

    valid <== 1;  // All constraints satisfied
}

component main = SudokuVerifier();

Proving & Verification

Using snarkjs (JavaScript)

// 1. Compile circuit
const snarkjs = require("snarkjs");
const fs = require("fs");

const circuitCode = `pragma circom 2.0.0;
template Multiplier() { ... }`;

// Compile to R1CS
await snarkjs.wasm.wtnsCalculate(inputData, wasmFile, wtnsFile);

// 2. Perform trusted setup (generates proving/verification keys)
const zkey = await snarkjs.zkey.newZKey(r1cs, ptau, zkey_final);

// 3. Generate proof
const { proof, publicSignals } = await snarkjs.groth16.fullProve(
    { solution: solutionArray, puzzle: puzzleArray },
    wasmFile,
    zkeyFile
);

// 4. Verify proof (off-chain or on-chain)
const isValid = await snarkjs.groth16.verify(vkey, publicSignals, proof);

// Export for on-chain verification
const solidityProof = snarkjs.groth16.exportSolidityCallData(proof, publicSignals);
// solidityProof = ["0xa...", ["0xb...", "0xc..."], "0xd..."]

On-Chain Verification (Solidity)

contract SudokuVerifier {
    // Generated by snarkjs
    Pairing.VerifyingKey verifyingKey = ... ;

    function verifyProof(
        uint[2] memory a,
        uint[2][2] memory b,
        uint[2] memory c,
        uint[1] memory input
    ) public view returns (bool) {
        return verify(input, Proof(a, b, c));
    }
}

// In your market contract
function submitProof(uint[2] memory a, uint[2][2] memory b, uint[2] memory c) external {
    require(sudokuVerifier.verifyProof(a, b, c, [uint(1)]), "Invalid proof");
    // Proof verified — process trade or claim prize
}

Use Cases for ZK in Prediction Markets

1. Private Order Submission

Problem: CLOB order book reveals all pending orders (MEV risk). Solution: Submit ZK proof that you know a valid limit order at price X, without revealing X or your identity until trade matches.

2. Privacy-Preserving Resolution

Problem: Oracle reveals outcome before users claim. Solution: Oracle signs commitment hash, reveals actual outcome later. Users prove their position with ZK.

3. Proof of Reserves

Problem: Did the prize pool operator actually lock all prize money? Solution: ZK proof that vault contains >= claimed funds without revealing exact amount.

4. Scalability

Generate ZK proof that 1000 transactions are all valid, submit one proof on-chain instead of 1000 txs.

Risks & Limitations

• Circuits are hard: Small bugs → invalid proofs accepted or valid ones rejected
• Trusted setup: If ceremony is compromised, fake proofs can be generated
• Proof generation is slow: Creating a proof can take seconds-to-minutes (on-chain may not work)
• Circuit audits are expensive: ZK adds another layer to audit

For Agent Sparta: ZK is cool but not necessary yet. Focus on simple, auditable contracts first. Consider ZK for next phase if privacy/MEV is a problem.