零知识证明与 ZK Rollups 详解

零知识证明与 ZK Rollups 详解 🔐

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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

完整性：真实陈述总能被证明
可靠性：虚假陈述无法被证明
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)
    };
}