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Zero-Knowledge Proofs

Overview

Zero-Knowledge (ZK) proofs allow one party (the prover) to prove to another party (the verifier) that a statement is true without revealing any information beyond the validity of the statement. In AIDDDMAP, ZK proofs are used to verify data properties, ownership, and access rights while maintaining privacy.

Implementation Details

Basic ZK Configuration

interface ZKConfig {
  proofSystem: "Groth16" | "PLONK" | "Bulletproofs";
  curve: "BN254" | "BLS12-381";
  securityLevel: number;
  constraintSystem: "R1CS" | "PLONKConstraints";
}

// Default configuration
const defaultZKConfig: ZKConfig = {
  proofSystem: "Groth16",
  curve: "BN254",
  securityLevel: 128,
  constraintSystem: "R1CS",
};

Core Proof Types

1. Basic Validity Proof

// Prove a value is within a range without revealing it
const rangeProof = await zkHandler.generateProof({
  type: "range",
  value: secretValue,
  range: { min: 0, max: 100 },
  publicInputs: { rangeMax: 100 },
});

// Verify the proof
const isValid = await zkHandler.verifyProof(rangeProof);

2. Advanced Range Proofs

// Complex range proof with multiple conditions
const advancedRangeProof = await zkHandler.generateProof({
  type: "multiRange",
  values: [value1, value2, value3],
  conditions: [
    { min: 0, max: 1000 },
    { min: 50, max: 150 },
    { min: -10, max: 10 },
  ],
  aggregation: "AND",
});

3. Merkle Proofs

// Prove membership in a Merkle tree
const merkleProof = await zkHandler.generateMerkleProof({
  leaf: dataPoint,
  tree: merkleTree,
  index: leafIndex,
});

// Advanced Merkle proof with multiple paths
const multiPathProof = await zkHandler.generateMultiMerkleProof({
  leaves: [data1, data2],
  tree: merkleTree,
  indices: [index1, index2],
});

4. Set Membership Proofs

// Single set membership
const setProof = await zkHandler.generateSetProof({
  element: secretElement,
  set: publicSet,
  hashFunction: "Poseidon",
});

// Multi-set membership
const multiSetProof = await zkHandler.generateMultiSetProof({
  elements: [elem1, elem2],
  sets: [set1, set2],
  relationship: "INTERSECTION",
});

5. Polynomial Evaluation Proofs

// Prove polynomial evaluation without revealing coefficients
const polyProof = await zkHandler.generatePolyProof({
  polynomial: coefficients,
  point: x,
  result: y,
  degree: 3,
});

6. Custom Circuit Proofs

// Define and prove custom circuit constraints
const customProof = await zkHandler.generateCircuitProof({
  circuit: customCircuit,
  privateInputs: {
    secret1: value1,
    secret2: value2,
  },
  publicInputs: {
    commitment: commitment,
    threshold: threshold,
  },
});

Security Considerations

Circuit Security

  1. Constraint Generation

  2. Validate all inputs

  3. Check for circuit soundness

  4. Ensure no information leakage

  5. Proof Generation

  6. Use secure randomness
  7. Implement timeouts
  8. Handle errors gracefully

Integration with Role-Based Access

// Role-based proof generation
const canGenerateProof = await roleManager.checkPermission(
  userId,
  "GENERATE_ZK_PROOFS",
);

if (canGenerateProof) {
  const proof = await zkHandler.generateProof(params);
}

Best Practices

1. Circuit Design

  • Keep circuits simple and modular
  • Minimize constraint complexity
  • Use standard components when possible

2. Performance Optimization

  • Cache frequently used circuits
  • Implement batch proof verification
  • Use efficient hash functions

3. Security Measures

  • Regular security audits
  • Secure parameter generation
  • Proper entropy sources

Error Handling

try {
  const proof = await zkHandler.generateProof(params);
} catch (error) {
  if (error instanceof ZKError) {
    switch (error.code) {
      case "INVALID_CIRCUIT":
        // Handle invalid circuit
        break;
      case "CONSTRAINT_VIOLATION":
        // Handle constraint violation
        break;
      case "PROOF_GENERATION_TIMEOUT":
        // Handle timeout
        break;
    }
  }
}

Audit Logging

interface ZKAuditLog {
  timestamp: number;
  proofType: string;
  userId: string;
  success: boolean;
  verificationResult?: boolean;
  metadata: {
    circuitHash: string;
    proofSystem: string;
    constraintCount: number;
  };
}

Performance Metrics

Proof Type Generation Time Verification Time Proof Size
Range 100ms 10ms 200 bytes
Merkle 150ms 20ms 500 bytes
Custom 200-500ms 50ms 1KB

Future Enhancements

  1. Planned Features

  2. Recursive SNARK support

  3. Zero-knowledge virtual machines

  4. Post-quantum secure schemes

  5. Research Areas

  6. Circuit optimization
  7. Novel proof systems
  8. Hardware acceleration

Integration Examples

1. Data Marketplace Integration

// Prove data ownership for marketplace listing
const ownershipProof = await zkHandler.generateOwnershipProof({
  data: dataset,
  owner: userId,
  timestamp: Date.now(),
});

// List dataset with proof
await marketplace.listDataset({
  dataset,
  ownershipProof,
  price,
});

2. Access Control Integration

// Prove access rights without revealing identity
const accessProof = await zkHandler.generateAccessProof({
  credentials: userCredentials,
  resource: resourceId,
  timestamp: Date.now(),
});

// Grant access based on proof
const accessGranted = await accessController.verifyAndGrant(accessProof);