How to Implement ZK-Rollups for Scalable Private Markets

Prediction markets require high throughput for order matching and settlement, while user positions are sensitive financial data. ZK-Rollups address both needs by processing transactions off-chain and submitting validity proofs to a mainnet like Ethereum. This architecture can reduce transaction costs by 10-100x compared to operating entirely on a Layer 1. For a prediction market, a ZK-Rollup sequencer batches thousands of trades, resolves events, and generates a ZK-SNARK or ZK-STARK proof. This single proof, verified on-chain, confirms the integrity of all state transitions without revealing individual user trades, providing inherent privacy.

The core smart contract system consists of three main components. The Rollup Contract on Layer 1 stores the compressed state root and verifies ZK proofs. A Verifier Contract executes the proof verification logic, which is computationally intensive but gas-optimized for the EVM. An off-chain Sequencer/Prover node is responsible for ordering transactions, executing them against the rollup's state (e.g., an order book), and generating the cryptographic proof. Developers can use frameworks like StarkEx or zkSync's ZK Stack to bootstrap this infrastructure, which provide SDKs for custom logic and built-in proof systems.

Implementing market logic requires designing the off-chain state tree. A Merkle tree can represent user balances and open positions, with leaves hashing account data. The sequencer updates this tree for each batch. For example, settling a "Yes" share on an event outcome would credit the winner's account and debit the global liquidity pool within the proof's constraints. All conditional logic—checking market resolution, calculating payouts—is executed off-chain but is cryptographically enforced by the zero-knowledge circuit. This ensures the on-chain verifier only checks that the state transition was correct, not the details.

Privacy is achieved because the proof validates computations using hidden inputs. User trades and account balances are private inputs to the ZK circuit. The public output is the new, valid state root and potentially a list of public events (like final market resolution). Tools like Circom or Cairo are used to write the arithmetic circuits that define these rules. A circuit for a prediction market would include constraints to ensure: the sum of all payouts does not exceed the liquidity pool, users cannot spend more than their balance, and resolved markets pay out correctly based on the verified outcome.

To get started, a practical stack might use the StarkEx framework with its SHARP prover. Define your market settlement logic in a Cairo program. Deploy the StarkEx contracts to a testnet. Your off-chain service (the sequencer) would collect signed orders, run the Cairo program, and submit the proof for verification. Users interact with your frontend, which submits transactions to your sequencer API; their assets are custodied in the rollup contract. This setup allows for sub-cent trading fees and confirmation times under one second, while leveraging Ethereum's security for final settlement and censorship resistance.

Before writing any code, you need a solid foundation in core technologies. You should be proficient in a systems language like Rust or C++, as most zero-knowledge proof frameworks are built in these for performance. Familiarity with Ethereum and the EVM is mandatory, as ZK-Rollups settle finality on a Layer 1. You must also understand cryptographic primitives like hash functions, digital signatures, and the basic concept of a zero-knowledge proof (ZKP), which allows one party to prove a statement is true without revealing the underlying data.

The primary tool for development is a ZK-Rollup framework. For a private market, you will likely use a ZK-SNARK-based system like Aztec, which is designed for privacy, or a ZK-STARK-based system like StarkNet for its scalability. You will also need a proving system library. For SNARKs, this is often libsnark or bellman, while Winterfell or the StarkWare toolchain is used for STARKs. Finally, set up a local Ethereum development environment with Hardhat or Foundry to deploy and test your rollup's smart contracts.

Start by initializing your project and installing dependencies. For an Aztec-based private rollup, you would begin with their aztec CLI: npx @aztec/cli create my-private-market. This scaffolds a project with a contracts/ directory for your private market logic and a src/ directory for your circuit code. Your first critical step is to define the circuit—the program that generates proofs. This circuit encodes the rules of your market (e.g., a valid trade must have a signed order and sufficient balance) without exposing user balances or trade sizes.

A ZK-rollup for private markets is a Layer 2 scaling solution that executes transactions off-chain and submits validity proofs to a base layer (like Ethereum) to guarantee correctness. The system architecture comprises three main layers: the on-chain verifier contract, the off-chain sequencer/prover, and the user clients. The sequencer batches private transactions, updates a Merkle tree representing the system's state, and generates a zero-knowledge proof (e.g., a zk-SNARK) attesting that the new state root is valid. This proof, along with minimal data, is posted to the verifier contract, which allows anyone to trustlessly verify the integrity of the off-chain execution.

The state design is centered around a sparse Merkle tree (or a similar commitment scheme like a Verkle tree) where each leaf represents a user account. To preserve privacy, leaves store hashed commitments to account data (balance, position) rather than plaintext. A user's state is encrypted with their key, and only the hash of this ciphertext is stored on-chain. During a transaction, users provide ZK proofs of state transition directly to the sequencer, proving they own sufficient funds and are authorized to transact, without revealing their account details or the transaction amount to the network.

Implementing the core logic requires defining a circuit for your application. Using a framework like Circom or Halo2, you design constraints that represent valid state transitions. For a private market, this includes proving: - A valid cryptographic signature or nullifier for authorization. - That input note commitments exist in the state tree. - That output commitments are correctly formed. - That the transaction doesn't create or destroy value (conservation of assets). The circuit's public inputs are the old and new state roots, while private inputs are the user's secret keys and transaction details.

The sequencer's role is critical. It must: 1) Collect signed transactions from users. 2) Validate the attached ZK proofs locally. 3) Apply transactions to compute a new state root. 4) Generate a single rollup proof that validates the entire batch. For development, you can use a proving system like SnarkJS with Groth16. The sequencer code must manage the state tree (using libraries like circomlibjs's MerkleTree) and handle the proving workflow, which is computationally intensive and often delegated to specialized provers.

Finally, the on-chain verifier is a lightweight smart contract. Its sole function is to verify the ZK proof submitted by the sequencer against the public inputs (previous state root, new state root, and a list of nullifiers to prevent double-spends). Upon successful verification, it updates its stored state root. This design ensures the Layer 1 contract is a trustless anchor of security, while complexity and data remain off-chain. Developers must audit the circuit logic and the verifier contract, as bugs here compromise the entire system's safety.

The zero-knowledge circuit is the computational heart of a ZK-Rollup for private markets. It's a program, written in a domain-specific language like Circom or Noir, that defines the constraints for a valid state transition. For a private market, this circuit must prove that a batch of trades—such as swaps or limit orders—is valid without revealing sensitive details like individual trade sizes or wallet balances. The circuit takes private inputs (user secrets), public inputs (the new Merkle root), and outputs a zk-SNARK or zk-STARK proof. This proof is then verified on-chain by a smart contract, which updates the rollup's state if the proof is valid.

To implement the circuit, you first model the business logic. For a private order book, key constraints include: proving a user has sufficient balance (via a Merkle proof of inclusion in the state tree), verifying cryptographic signatures authorizing the trade, and ensuring the new state root is computed correctly after applying all trades. A common library for this is circomlib, which provides templates for cryptographic primitives like the Poseidon hash (gas-efficient for Merkle trees) and EdDSA signature verification. The circuit doesn't execute trades; it proves the correctness of their execution according to the predefined rules.

Here's a simplified Circom snippet outlining a constraint for a balance check in a private transfer:

circomCopy
template PrivateTransfer() {
    signal input privateBalance;
    signal input privateAmount;
    signal input senderLeafHash;
    signal input merklePath[levels];
    signal input merkleRoot;
    signal output newSenderLeafHash;

    // Constraint: Sufficient balance
    component gt = GreaterEqThan(252);
    gt.in[0] <== privateBalance;
    gt.in[1] <== privateAmount;
    gt.out === 1;

    // Constraint: Verify sender is in the current state tree
    component mt = MerkleTreeChecker(levels);
    mt.leaf <== senderLeafHash;
    for (var i = 0; i < levels; i++) {
        mt.path[i] <== merklePath[i];
    }
    mt.root <== merkleRoot;

    // Compute new leaf hash for sender
    newSenderLeafHash <== Poseidon([privateBalance - privateAmount]);
}

This template ensures the sender has enough funds and is part of the current state, all without revealing privateBalance or privateAmount.

After writing the circuit, you must compile it into an R1CS (Rank-1 Constraint System) and generate the proving and verification keys. This is typically done using the circuit compiler (e.g., circom command) and a trusted setup ceremony for zk-SNARKs, or a transparent setup for zk-STARKs. The proving key is used by the rollup's prover (often an off-chain server) to generate proofs for batches. The verification key is embedded in the on-chain verifier contract. For Ethereum, the snarkjs library is commonly used to integrate Circom circuits with Solidity verifiers. Performance optimization is critical; circuit size directly impacts proving time and cost.

Security auditing of the circuit is paramount. Bugs in constraint logic can lead to loss of funds or broken privacy. Audits should focus on: the correctness of arithmetic constraints (no overflows), the soundness of cryptographic primitives, and the accurate modeling of the state transition. Formal verification tools for Circom, like Picus, are emerging to help. Furthermore, the system's privacy guarantees depend on the zero-knowledge property—the prover must not leak information through the public inputs or the structure of the circuit itself. All user data must remain as private witness inputs.

Finally, the circuit is integrated into the broader rollup architecture. The sequencer collects off-chain transactions, executes them to compute a new state root, and uses the circuit to generate a validity proof. This proof and the new root are submitted to the L1 contract. The primary benefits for private markets are scale (thousands of trades per batch) and confidentiality (trade details hidden). However, developers must consider the trade-offs: proving time can be slow (seconds to minutes), and trusted setups require careful ceremony management for SNARKs. Projects like Aztec and zkSync provide frameworks that abstract some of this complexity.

A ZK-Rollup for private markets operates by executing transactions off-chain and posting compressed data with a cryptographic proof to a base layer like Ethereum. The system relies on two primary off-chain actors: the Sequencer and the Prover. The sequencer is responsible for ordering user transactions, executing them against the current state, and batching the resulting state transitions. The prover's job is to generate a Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARK) that cryptographically attests to the correctness of the sequencer's state transition, without revealing the private transaction details.

The sequencer implementation typically involves a state machine that manages user accounts, order books, and settlement logic. For a private market, this includes handling encrypted orders and executing matches while preserving confidentiality. After processing a batch of transactions, the sequencer produces a state diff—a minimal representation of what changed—and a Merkle root of the new state. This data, along with the transaction calldata, is submitted to an on-chain rollup contract. A critical design choice is the sequencer's decentralization strategy, which can range from a single permissioned entity to a decentralized network using consensus mechanisms like Tendermint.

The prover is the most computationally intensive component. It takes the sequencer's execution trace as input and runs a zk-SNARK circuit written in a domain-specific language like Circom or Halo2. This circuit encodes the business logic rules of the private market (e.g., "a trade only settles if signatures are valid and balances suffice"). The prover generates a proof that these rules were followed for every transaction in the batch. For production systems, this often requires specialized hardware or cloud-based proving services to achieve practical throughput. The final proof is submitted on-chain, where a verifier contract can validate it in milliseconds, ensuring the new state root is correct.

Integrating the sequencer and prover requires a robust data pipeline. The sequencer must output a structured witness—all the public and private inputs to the circuit—in the exact format the prover expects. A common practice is to use a commit-reveal scheme for privacy: orders are submitted as commitments on-chain, the sequencer processes the revealed orders off-chain, and the zk-proof verifies that the revealed orders match the earlier commitments. This ensures data availability and auditability while keeping details private until execution. The entire system's security hinges on the soundness of the zk-SNARK and the correct implementation of the circuit logic.

Developers can leverage existing frameworks to bootstrap development. StarkWare's Cairo and Polygon zkEVM provide toolchains for building app-specific rollups with built-in provers. For a custom implementation, using a library like arkworks (for Rust) or snarkjs (for JavaScript) is essential. The on-chain contracts need to manage state roots, store calldata, and verify proofs. A successful deployment for private markets must balance throughput (transactions per second), finality time (including proof generation), and cost (L1 data fees + proving costs) to be commercially viable.

A ZK-rollup's security and finality depend on its on-chain verifier. This is a smart contract, typically deployed on Ethereum L1, that validates zero-knowledge proofs (ZKPs) submitted by rollup operators. The verifier's sole function is to execute a computationally cheap verification algorithm, confirming that a batch of off-chain transactions was executed correctly according to the rollup's state transition rules. Popular proof systems like Groth16, PLONK, or STARKs each have specific verification circuits, and the corresponding verifier contract is often generated directly from these circuits using tools like snarkjs for Circom or the StarkWare Cairo toolchain.

The bridge contract acts as the secure gateway for assets moving between L1 and the rollup's L2. Users deposit assets by locking them in the bridge contract on L1, which triggers a corresponding minting event on L2. For withdrawals, users submit a withdrawal request on L2, which is included in a proven state batch. After the verifier confirms the proof, the bridge contract on L1 unlocks the assets. This design ensures that asset custody is always secured by the base layer's consensus. Key bridge functions include managing a merkle root of the L2 state and implementing challenge periods or instant withdrawals based on the rollup's security model.

Deploying this system involves a clear sequence. First, the verifier contract, with its hardcoded verification key, is deployed to L1. Next, the bridge contract is deployed, configured with the address of the verifier. The rollup's sequencer or prover node must be set up to submit periodic state updates—containing the new state root and a ZKP—to the verifier. A critical integration step is ensuring the off-chain prover generates proofs compatible with the on-chain verifier's expected format. For example, using the Circom circuit compiler and snarkjs, you would run snarkjs zkey export solidityverifier to generate the verifier Solidity code.

Security considerations are paramount. The verifier contract must be immutable after deployment; any bug requires a full system migration. Bridge contracts must guard against double-spend attacks by meticulously tracking deposit and withdrawal nonces. Use OpenZeppelin libraries for access control, pausability, and reentrancy guards. Thoroughly audit both contracts, focusing on the proof verification logic and the bridge's state synchronization. Testing should include edge cases like invalid proof submissions and malicious withdrawal attempts.

For developers, frameworks like StarkWare's StarkEx, zkSync's ZK Stack, or Polygon zkEVM provide production-ready, audited templates for verifiers and bridges, significantly reducing implementation risk. These frameworks abstract much of the cryptographic complexity, allowing teams to focus on application logic. However, a custom implementation offers maximum flexibility for novel state models or privacy features, such as those required for private markets where transaction details must be concealed within the validity proof.

To solidify your implementation, begin by selecting a ZK-Rollup framework like StarkEx or zkSync. These provide the essential proving and verification infrastructure, allowing you to focus on application logic. For private markets, you'll need to design your circuit logic to prove the validity of off-chain trades—such as order matching and balance updates—without revealing the underlying data. This involves writing your business rules in a domain-specific language like Cairo (for StarkNet) or Zinc (for zkSync).

Your next critical step is implementing a secure data availability solution. While some rollups post all data on-chain, for true privacy, you may opt for a validium model where data is held off-chain by a committee. You must design a robust Data Availability Committee (DAC) with cryptographic attestations or use a decentralized storage network like Celestia or EigenDA. This ensures users can always reconstruct the state, which is a non-negotiable requirement for trustlessness.

Finally, focus on the user and developer experience. Build a relayer service that batches user transactions, submits proofs to L1, and manages gas fees. Implement a standard front-end that interacts with your custom rollup contracts using SDKs like starknet.js. Thoroughly audit your circuits and smart contracts; firms like Trail of Bits and OpenZeppelin specialize in ZK systems. For further learning, explore the StarkNet documentation and the zkSync developer portal.