LP-9400: Automated Market Maker Protocol with Privacy

Abstract

This LP defines a privacy-preserving Automated Market Maker (AMM) protocol for Lux Network that combines traditional AMM mechanics with zero-knowledge proofs, enabling confidential swaps while maintaining MEV resistance. The protocol leverages zkSNARKs for transaction privacy, homomorphic encryption for private order books, and commit-reveal schemes for front-running protection.

Motivation

Traditional AMMs expose all transaction details on-chain, enabling:

Front-running and sandwich attacks
MEV extraction at users' expense
Privacy violations for traders
Information leakage about trading strategies

This standard addresses these issues through cryptographic privacy while maintaining:

Liquidity provider transparency
Verifiable fair pricing
Regulatory compliance options
Capital efficiency

Specification

Core Privacy AMM Interface

interface IPrivateAMM {
    // Commitment structure for private swaps
    struct SwapCommitment {
        bytes32 commitment;      // Hash of swap parameters
        uint256 timestamp;
        address committer;
        bool revealed;
    }

    // Zero-knowledge swap proof
    struct ZKSwapProof {
        bytes32 nullifier;       // Prevents double-spending
        bytes32 outputCommitment; // Commitment to output amounts
        bytes zkProof;           // zkSNARK proof
        bytes32 merkleRoot;      // State root for verification
    }

    // Events
    event PrivateSwapCommitted(
        bytes32 indexed commitment,
        address indexed committer,
        uint256 deadline
    );

    event PrivateSwapExecuted(
        bytes32 indexed nullifier,
        bytes32 outputCommitment
    );

    event ConfidentialLiquidityAdded(
        bytes32 indexed commitment,
        bytes32 poolId
    );

    // Commit-reveal swap mechanism
    function commitSwap(
        bytes32 commitment,
        uint256 deadline
    ) external payable returns (bytes32 swapId);

    function revealAndExecuteSwap(
        uint256 amountIn,
        uint256 amountOutMin,
        address[] calldata path,
        address to,
        uint256 deadline,
        uint256 nonce
    ) external returns (uint256[] memory amounts);

    // Zero-knowledge swap
    function privateSwap(
        ZKSwapProof calldata proof,
        bytes calldata encryptedData
    ) external returns (bool success);

    // Verify swap proof without execution
    function verifySwapProof(
        ZKSwapProof calldata proof
    ) external view returns (bool valid);
}

Homomorphic Order Book

interface IHomomorphicOrderBook {
    // Encrypted order structure
    struct EncryptedOrder {
        bytes encryptedAmount;    // Homomorphically encrypted amount
        bytes encryptedPrice;     // Homomorphically encrypted price
        bytes32 traderId;         // Anonymous trader identifier
        uint256 timestamp;
        bytes publicKey;          // For response encryption
    }

    // Private market making
    struct PrivateMarketMaker {
        bytes32 mmId;             // Anonymous MM identifier
        bytes encryptedLiquidity; // Total liquidity (encrypted)
        uint256 feeRate;          // Public fee rate
        bytes zkCredential;       // Proof of liquidity
    }

    event EncryptedOrderPlaced(
        bytes32 indexed orderId,
        bytes32 indexed traderId,
        bytes encryptedData
    );

    event PrivateMatchExecuted(
        bytes32 indexed orderId,
        bytes32 nullifier,
        bytes encryptedResult
    );

    function placeEncryptedOrder(
        EncryptedOrder calldata order
    ) external returns (bytes32 orderId);

    function matchOrders(
        bytes32 orderId1,
        bytes32 orderId2,
        bytes calldata matchProof
    ) external returns (bytes encryptedResult);

    function addPrivateLiquidity(
        bytes calldata encryptedAmount,
        bytes calldata liquidityProof
    ) external returns (bytes32 positionId);
}

MEV Protection Layer

interface IMEVProtection {
    // Time-locked transaction
    struct TimeLockTx {
        bytes32 txHash;
        uint256 unlockTime;
        uint256 priority;
        bytes encryptedContent;
    }

    // Batch auction for fair ordering
    struct BatchAuction {
        uint256 startBlock;
        uint256 endBlock;
        bytes32 merkleRoot;      // Root of all committed trades
        uint256 clearingPrice;
        bool settled;
    }

    event BatchAuctionCreated(
        uint256 indexed auctionId,
        uint256 startBlock,
        uint256 endBlock
    );

    event TradeCommittedToBatch(
        uint256 indexed auctionId,
        bytes32 commitment
    );

    event BatchSettled(
        uint256 indexed auctionId,
        uint256 clearingPrice,
        bytes32 merkleRoot
    );

    function submitToMempool(
        bytes calldata encryptedTx,
        uint256 maxDelay
    ) external payable returns (bytes32 txId);

    function commitToBatch(
        uint256 auctionId,
        bytes32 tradeCommitment
    ) external;

    function settleBatch(
        uint256 auctionId,
        uint256 clearingPrice,
        bytes32[] calldata merkleProof
    ) external;

    function executeTimeLocked(
        bytes32 txId,
        bytes calldata decryptionKey
    ) external;
}

zkSNARK Circuit Specifications

interface IZKSwapCircuit {
    // Public inputs for swap verification
    struct PublicInputs {
        bytes32 nullifierHash;
        bytes32 outputCommitmentHash;
        bytes32 poolStateRoot;
        uint256 timestamp;
    }

    // Private witness for swap proof
    struct PrivateWitness {
        uint256 inputAmount;
        uint256 outputAmount;
        address tokenIn;
        address tokenOut;
        uint256 nonce;
        bytes32 secret;
    }

    // Verify swap maintains constant product
    function verifyConstantProduct(
        uint256 reserveIn,
        uint256 reserveOut,
        uint256 amountIn,
        uint256 amountOut,
        bytes calldata proof
    ) external view returns (bool);

    // Verify slippage tolerance
    function verifySlippage(
        uint256 amountOut,
        uint256 amountOutMin,
        bytes calldata proof
    ) external view returns (bool);

    // Verify fee calculation
    function verifyFees(
        uint256 amountIn,
        uint256 fee,
        uint256 feeRate,
        bytes calldata proof
    ) external view returns (bool);
}

Confidential Liquidity Provision

interface IConfidentialLP {
    // Private liquidity position
    struct PrivatePosition {
        bytes32 positionId;
        bytes32 commitment;       // Commitment to amounts
        bytes encryptedData;      // Encrypted position details
        uint256 unlockTime;
        bytes32 nullifier;        // For withdrawal
    }

    // Shielded pool state
    struct ShieldedPool {
        bytes32 liquidityRoot;    // Merkle root of all positions
        bytes totalEncrypted;     // Homomorphic sum of liquidity
        uint256 publicReserve;    // Publicly visible reserve
        uint256 privateReserve;   // Approximate private reserve
    }

    event PrivateLiquidityAdded(
        bytes32 indexed positionId,
        bytes32 commitment
    );

    event PrivateLiquidityRemoved(
        bytes32 indexed nullifier,
        bytes32 newCommitment
    );

    function addPrivateLiquidity(
        bytes32 commitment,
        bytes calldata zkProof,
        bytes calldata encryptedAmounts
    ) external returns (bytes32 positionId);

    function removePrivateLiquidity(
        bytes32 positionId,
        bytes32 nullifier,
        bytes calldata zkProof
    ) external returns (bytes encryptedAmounts);

    function rebalancePrivatePool(
        bytes32 poolId,
        bytes calldata rebalanceProof
    ) external;
}

Regulatory Compliance Module

interface ICompliantPrivateAMM {
    // Viewing key for authorized parties
    struct ViewingKey {
        address authority;
        bytes publicKey;
        uint256 accessLevel;
        uint256 expiry;
    }

    // Selective disclosure
    struct DisclosureRequest {
        bytes32 transactionId;
        address requester;
        string reason;
        bytes signature;
    }

    event ViewingKeyGranted(
        address indexed authority,
        uint256 accessLevel
    );

    event SelectiveDisclosure(
        bytes32 indexed transactionId,
        address indexed authority
    );

    function grantViewingKey(
        address authority,
        bytes calldata publicKey,
        uint256 accessLevel
    ) external;

    function requestDisclosure(
        bytes32 transactionId,
        string calldata reason
    ) external returns (bytes encryptedData);

    function auditTransaction(
        bytes32 transactionId,
        bytes calldata viewingKey
    ) external view returns (
        uint256 amountIn,
        uint256 amountOut,
        address tokenIn,
        address tokenOut
    );
}

Rationale

zkSNARK-based Privacy

Zero-knowledge proofs provide:

Complete transaction privacy
Verifiable correctness without revealing details
Efficient on-chain verification
Composability with other protocols

Commit-Reveal for MEV Protection

The commit-reveal pattern ensures:

Transactions cannot be front-run
Order flow remains private until execution
Fair ordering through time-based priority
Protection against sandwich attacks

Homomorphic Encryption for Order Books

Enables:

Private order matching
Encrypted liquidity aggregation
Statistical arbitrage prevention
Market maker privacy

Hybrid Public-Private Pools

Maintaining both public and private liquidity:

Ensures price discovery
Provides fallback liquidity
Enables gradual privacy adoption
Supports regulatory requirements

Test Cases

Private Swap Test

function testPrivateSwap() public {
    IPrivateAMM privateAMM = IPrivateAMM(ammAddress);

    // Create swap commitment
    uint256 amountIn = 1000 * 10**18;
    uint256 nonce = 12345;
    bytes32 commitment = keccak256(abi.encode(
        amountIn,
        amountOutMin,
        path,
        msg.sender,
        nonce
    ));

    // Commit phase
    bytes32 swapId = privateAMM.commitSwap(
        commitment,
        block.timestamp + 100
    );

    // Wait for commitment period
    vm.warp(block.timestamp + 10);

    // Reveal and execute
    uint256[] memory amounts = privateAMM.revealAndExecuteSwap(
        amountIn,
        amountOutMin,
        path,
        msg.sender,
        deadline,
        nonce
    );

    assertTrue(amounts[amounts.length - 1] >= amountOutMin);
}

zkSNARK Swap Verification

function testZKSwapProof() public {
    IPrivateAMM privateAMM = IPrivateAMM(ammAddress);

    // Generate ZK proof (off-chain)
    ZKSwapProof memory proof = generateSwapProof(
        1000 * 10**18,  // input amount
        500 * 10**18,   // output amount
        address(tokenA),
        address(tokenB),
        nonce
    );

    // Verify proof on-chain
    assertTrue(privateAMM.verifySwapProof(proof));

    // Execute private swap
    bool success = privateAMM.privateSwap(
        proof,
        encryptedSwapData
    );

    assertTrue(success);
}

Backwards Compatibility

This LP introduces a new protocol that can coexist with existing AMM implementations:

Existing Pools: Standard Uniswap/SushiSwap-style pools continue to operate unchanged
Liquidity Migration: LPs can choose to migrate liquidity to privacy-enabled pools
Interface Compatibility: Core swap interface remains compatible with existing DEX aggregators
Token Standards: Compatible with existing LRC-20 and ERC-20 tokens
Router Integration: Private AMM exposes standard swap() interface with additional privacy parameters

Migration Path:

Deploy PrivateAMM contracts alongside existing pools
Create private pools for high-value pairs
Update DEX aggregators to route through private pools when privacy is requested
Existing integrations continue to work with public pools

Security Considerations

Cryptographic Assumptions

zkSNARK security relies on proper trusted setup
Use of Groth16 or PLONK proving systems
Regular security audits of circuits
Secure randomness for commitments

Privacy Guarantees

Nullifiers prevent double-spending
Commitments hide transaction details
Merkle trees provide membership proofs
Time delays prevent correlation attacks

MEV Resistance

Commit-reveal prevents front-running
Batch auctions ensure fair ordering
Encrypted mempool protects pending transactions
Time-locks prevent sandwich attacks

Emergency Procedures

function emergencyReveal(bytes32 txId) external onlyGovernance {
    // Force reveal for stuck transactions
}

function pausePrivateSwaps() external onlyGovernance {
    // Emergency pause for private operations
}

Implementation

Reference Implementation

Primary Locations:

Privacy protocols: standard/src/privacy/
AMM reference: standard/deploy/19_uniswapv2.ts (base AMM structure)
EVM precompiles: evm/precompile/contracts/pqcrypto/

Implementation Components:

Zero-Knowledge Circuits (standard/src/privacy/circuits/)
- Pederson commitment implementations
- Range proof circuits (bulletproofs)
- Balance validation circuits
- Swap correctness proofs
Homomorphic Encryption Module (standard/src/privacy/encryption/)
- Paillier homomorphic encryption (used in order books)
- Encrypted arithmetic for price aggregation
- Safe key generation and management
Privacy AMM Implementation (standard/src/privacy/amm/)
- IPrivateAMM.sol - Core interface and contract
- CommitReveal.sol - Commit-reveal swap mechanism
- OrderBook.sol - Encrypted order book with homomorphic matching
- MixingPool.sol - Privacy mixer for MEV prevention
zkSNARK Verifier Integration (evm/precompile/contracts/pqcrypto/)
- Groth16 proof verification via precompile address 0x0200000000000000000000000000000000000008
- PLONK proof support (extensible interface)
- Gas-efficient on-chain verification
Consensus Integration (node/vms/platformvm/)
- MEV protection via validator filtering
- Commit-reveal block production coordination
- Encrypted mempool implementation references

Related Specifications:

LP-402: Zero-Knowledge Swap Protocol (detailed privacy primitives)
LP-311: ML-DSA Post-Quantum Signatures (for validator proofs)
LP-700: Quasar Consensus (native privacy features)

Testing:

Unit tests: standard/src/privacy/test/*.spec.ts
Integration tests for AMM + privacy layer
Gas benchmarks for on-chain verification

GitHub Repository: https://github.com/luxfi/standard/tree/main/src/privacy

References

Buterin, V., et al. "Automated Market Makers with Concentrated Liquidity." 2021.
Ben-Sasson, E., et al. "Zerocash: Decentralized Anonymous Payments from Bitcoin." 2014.
Bünz, B., et al. "Zether: Towards Privacy in a Smart Contract World." 2020.
Aztec Protocol. "Privacy-Preserving DeFi on Ethereum." 2021.
Penumbra. "Private Decentralized Exchange." 2022.
Anoma. "Intent-Centric Privacy Architecture." 2023.

Automated Market Maker Protocol with Privacy