Zero-Knowledge Proofs and Privacy
Implementing zero-knowledge proofs for privacy-preserving blockchain applications.
Advanced⏱️ 60 min📚 Prerequisites: 2
Zero-Knowledge Proofs and Privacy
Zero-knowledge proofs (ZKPs) allow proving knowledge of information without revealing the information itself.
What are Zero-Knowledge Proofs?
A zero-knowledge proof allows a prover to convince a verifier that they know a secret without revealing the secret.
Properties
- Completeness: If the statement is true, an honest prover can convince an honest verifier
- Soundness: If the statement is false, no prover can convince an honest verifier
- Zero-Knowledge: The verifier learns nothing about the secret
Types of ZKPs
zk-SNARKs (Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge)
- Succinct: Proofs are small and fast to verify
- Non-Interactive: No back-and-forth communication needed
- Used in: Zcash, Tornado Cash, Layer 2 rollups
zk-STARKs (Zero-Knowledge Scalable Transparent Arguments of Knowledge)
- Scalable: Verification time grows slowly with computation
- Transparent: No trusted setup required
- Post-Quantum: Resistant to quantum computers
Blockchain Applications
Privacy Coins
- Hide transaction amounts and participants
- Prove transaction validity without revealing details
Layer 2 Scaling
- Rollups bundle transactions and prove correctness
- Reduce on-chain data while maintaining security
Identity Verification
- Prove age, citizenship, etc. without revealing personal data
- Selective disclosure of credentials
Rust Libraries
- arkworks: Advanced cryptographic library with ZKP support
- bellman: zk-SNARK implementation
- bulletproofs: Range proofs without trusted setup
Example: Simple Range Proof
RUST// Proving a value is in a range without revealing the value struct RangeProof { commitment: Vec<u8>, proof: Vec<u8>, } fn prove_range(value: u64, min: u64, max: u64) -> RangeProof { // Generate commitment to value // Create proof that value is in [min, max] // Return proof } fn verify_range(proof: &RangeProof, min: u64, max: u64) -> bool { // Verify proof without learning the value }
Privacy Considerations
- Transaction Graph Analysis: Even with ZKPs, patterns can leak information
- Timing Attacks: When transactions occur can reveal relationships
- Amount Correlation: Similar amounts might link transactions
Real-World Examples
- Zcash: Uses zk-SNARKs for shielded transactions
- Tornado Cash: Privacy mixer using ZKPs
- zkSync: Layer 2 using zk-SNARKs for scaling
- StarkNet: Layer 2 using zk-STARKs
Code Examples
ZK Proof Concept
Conceptual implementation of zero-knowledge proof
RUST
// Simplified ZKP concept demonstration
struct SecretProof {
commitment: String,
proof_data: Vec<u8>,
}
struct Prover {
secret: u64,
}
struct Verifier;
impl Prover {
fn new(secret: u64) -> Self {
Prover { secret }
}
fn create_proof(&self, public_value: u64) -> SecretProof {
// In real ZKP: create cryptographic proof that secret satisfies condition
// Here simplified: commitment = hash(secret)
let commitment = format!("commit_{}", self.secret);
// Proof that secret * 2 == public_value (without revealing secret)
let proof_data = if self.secret * 2 == public_value {
vec![1, 2, 3] // Simplified proof
} else {
vec![0]
};
SecretProof {
commitment,
proof_data,
}
}
}
impl Verifier {
fn verify(&self, proof: &SecretProof, public_value: u64) -> bool {
// Verify proof without learning the secret
// In real ZKP: verify cryptographic proof
!proof.proof_data.is_empty() && proof.proof_data[0] != 0
}
}
fn main() {
let prover = Prover::new(42);
let verifier = Verifier;
let public_value = 84; // public_value = secret * 2
let proof = prover.create_proof(public_value);
println!("Proof created with commitment: {}", proof.commitment);
println!("Verification: {}", verifier.verify(&proof, public_value));
println!("Note: Verifier never learned the secret (42)");
}Explanation:
This demonstrates the concept: the prover knows a secret (42), creates a proof that it satisfies a condition (secret * 2 = 84), and the verifier can verify this without learning the secret. Real ZKPs use advanced cryptography.
Privacy-Preserving Transaction
Conceptual privacy transaction using ZKP
RUST
// Simplified privacy transaction concept
struct PrivacyTx {
// Public: proof that transaction is valid
validity_proof: Vec<u8>,
// Hidden: actual amounts and addresses
encrypted_data: Vec<u8>,
}
struct Account {
balance: u64,
address: String,
}
impl Account {
fn create_private_transfer(
&self,
recipient: &str,
amount: u64,
) -> Result<PrivacyTx, String> {
if self.balance < amount {
return Err(String::from("Insufficient balance"));
}
// In real implementation: create ZK proof that:
// 1. Sender has sufficient balance
// 2. Amounts balance (input = output + fee)
// 3. Transaction is properly signed
// Without revealing: sender address, recipient, amount
let validity_proof = vec![1, 2, 3, 4, 5]; // Simplified
let encrypted_data = vec![0; 32]; // Encrypted transaction data
Ok(PrivacyTx {
validity_proof,
encrypted_data,
})
}
}
fn verify_privacy_tx(tx: &PrivacyTx) -> bool {
// Verify ZK proof without decrypting transaction details
!tx.validity_proof.is_empty()
}
fn main() {
let account = Account {
balance: 1000,
address: String::from("0xAlice"),
};
match account.create_private_transfer("0xBob", 100) {
Ok(tx) => {
println!("Private transaction created");
println!("Verification: {}", verify_privacy_tx(&tx));
println!("Transaction details are hidden but verified!");
}
Err(e) => println!("Error: {}", e),
}
}Explanation:
Privacy transactions use ZKPs to prove validity without revealing transaction details. The blockchain can verify the transaction is valid (balances check out, properly signed) without knowing who sent to whom or how much.
Exercises
Simple Proof System
Create a simple proof system that proves knowledge without revealing!
Starter Code:
RUST
struct Proof {
commitment: String,
}
fn main() {
// Create a proof for a secret number
// Verify the proof
}