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零知识证明与 ZK Rollups 详解 🔐

1. 零知识证明基础

1.1 什么是零知识证明？

零知识证明（ZKP）允许证明者向验证者证明一个陈述的真实性，而无需透露除了该陈述是真实的这一事实之外的任何信息。

1.2 核心特性

1. 完整性：真实陈述总能被证明
2. 可靠性：虚假陈述无法被证明
3. 零知识：除了陈述的真实性外不泄露其他信息

2. ZK-SNARK 实现

2.1 电路构建

pragma circom 2.0.0;template Multiplier() {// 声明信号signal input a;signal input b;signal output c;// 约束c <== a * b;
}component main = Multiplier();

2.2 证明生成

const snarkjs = require("snarkjs");async function generateProof(input, circuitPath, provingKeyPath) {// 生成证明const { proof, publicSignals } = await snarkjs.groth16.fullProve(input,circuitPath,provingKeyPath);// 转换为可验证格式const calldata = await snarkjs.groth16.exportSolidityCallData(proof,publicSignals);return {proof,publicSignals,calldata};
}

3. ZK Rollup 实现

3.1 智能合约

contract ZKRollup {struct Transaction {address from;address to;uint256 amount;uint256 nonce;}struct Batch {bytes32 oldStateRoot;bytes32 newStateRoot;Transaction[] transactions;bytes32 withdrawalRoot;}mapping(bytes32 => bool) public processedBatches;bytes32 public currentStateRoot;function verifyAndApplyBatch(Batch calldata batch,bytes calldata proof) external {require(batch.oldStateRoot == currentStateRoot,"Invalid old state root");// 验证零知识证明require(verifyProof(proof,batch.oldStateRoot,batch.newStateRoot,batch.withdrawalRoot),"Invalid proof");// 更新状态currentStateRoot = batch.newStateRoot;emit BatchProcessed(batch.newStateRoot);}
}

3.2 状态管理

contract StateManager {struct Account {uint256 balance;uint256 nonce;mapping(bytes32 => bool) withdrawals;}mapping(address => Account) public accounts;function updateState(address[] calldata addresses,uint256[] calldata balances,uint256[] calldata nonces) internal {require(addresses.length == balances.length &&balances.length == nonces.length,"Length mismatch");for (uint i = 0; i < addresses.length; i++) {accounts[addresses[i]].balance = balances[i];accounts[addresses[i]].nonce = nonces[i];}}
}

4. 电路设计

4.1 基础电路组件

pragma circom 2.0.0;template MerkleTreeVerifier(levels) {signal input leaf;signal input path_elements[levels];signal input path_indices[levels];signal output root;component hashers[levels];signal intermediate[levels + 1];intermediate[0] <== leaf;for (var i = 0; i < levels; i++) {hashers[i] = HashLeft();hashers[i].left <== intermediate[i];hashers[i].right <== path_elements[i];intermediate[i + 1] <== hashers[i].hash;}root <== intermediate[levels];
}

4.2 交易验证电路

template TransactionVerifier() {// 公开输入signal input oldStateRoot;signal input newStateRoot;// 私有输入signal input sender;signal input recipient;signal input amount;signal input nonce;signal input signature;// 验证签名component sigVerifier = SignatureVerifier();sigVerifier.message <== hash(sender, recipient, amount, nonce);sigVerifier.signature <== signature;sigVerifier.pubkey <== sender;// 验证状态转换component stateUpdater = StateUpdater();stateUpdater.oldRoot <== oldStateRoot;stateUpdater.sender <== sender;stateUpdater.amount <== amount;stateUpdater.newRoot === newStateRoot;
}

5. 优化技术

5.1 批量处理优化

contract BatchOptimizer {struct ProofBatch {bytes32[] oldStateRoots;bytes32[] newStateRoots;bytes[] proofs;}function processBatchProofs(ProofBatch calldata batch) external {uint256 batchSize = batch.proofs.length;require(batchSize == batch.oldStateRoots.length &&batchSize == batch.newStateRoots.length,"Batch size mismatch");for (uint i = 0; i < batchSize; i++) {require(verifyProof(batch.proofs[i],batch.oldStateRoots[i],batch.newStateRoots[i]),"Invalid proof in batch");}// 批量更新状态updateStateBatch(batch.newStateRoots);}
}

5.2 电路优化

template OptimizedHasher() {signal input left;signal input right;signal output hash;// 使用预编译的哈希函数hash <== PoseidonHash(left, right);
}template OptimizedVerifier() {// 减少约束数量signal input data;signal output valid;component hasher = OptimizedHasher();hasher.left <== data;hasher.right <== 0;valid <== hasher.hash;
}

6. 安全考虑

6.1 可信设置

async function performTrustedSetup(circuit) {// 生成证明密钥和验证密钥const { provingKey, verifyingKey } = await snarkjs.zKey.newZKey(circuit,"pot12_final.ptau","circuit_final.zkey");// 验证设置const verified = await snarkjs.zKey.verifyFromInit("circuit_final.zkey","pot12_final.ptau","verification_key.json");if (!verified) {throw new Error("Trusted setup verification failed");}return { provingKey, verifyingKey };
}

6.2 电路验证

async function verifyCircuit(circuit) {// 检查电路完整性const constraints = await snarkjs.r1cs.info(circuit);// 验证约束系统const verification = await snarkjs.r1cs.verify(circuit,"verification_key.json");return {constraintCount: constraints.nConstraints,isValid: verification};
}

7. 性能监控

7.1 证明生成性能

class ProofPerformanceMonitor {constructor() {this.metrics = new Map();}async measureProofGeneration(input, circuit) {const startTime = process.hrtime();try {const proof = await generateProof(input, circuit);const [seconds, nanoseconds] = process.hrtime(startTime);this.metrics.set('proofTime', seconds + nanoseconds / 1e9);this.metrics.set('proofSize', JSON.stringify(proof).length);return proof;} catch (error) {this.metrics.set('error', error.message);throw error;}}getMetrics() {return Object.fromEntries(this.metrics);}
}

7.2 验证性能

async function benchmarkVerification(proof, verifyingKey) {const samples = 100;const times = [];for (let i = 0; i < samples; i++) {const start = performance.now();await snarkjs.groth16.verify(verifyingKey, proof);times.push(performance.now() - start);}return {averageTime: times.reduce((a, b) => a + b) / samples,minTime: Math.min(...times),maxTime: Math.max(...times)};
}

8. 相关资源

• ZK-SNARKs 教程
• Circom 文档
• zkSync 文档
• 零知识证明入门
• ZK Rollup 实现指南