This bridge employs a sophisticated method for managing deposit and withdrawal requests by batching them into a single transaction, thus updating the bridge's state efficiently. The underlying structure of this system utilizes a secure and efficient Merkle tree to organize account data, ensuring the integrity and security of transactions.

The bridge operates through a recursive covenant Bitcoin script that enforces specific conditions on spending transactions, enabling persistent logic and state onchain, which is essential for any smart contract functionality within the Bitcoin network. This implementation showcases the use of advanced domain-specific language (DSL) by sCrypt for constructing the covenant scripts due to their inherent complexity.

Deposits and withdrawals are handled uniquely; users can independently submit deposit or withdrawal requests to their respective aggregation covenants. These requests are then batched into a Merkle tree, with the root of this tree being merged into the main bridge covenant for processing. In the case of deposits, the aggregation covenant ensures that the deposited satoshis are correctly accounted for up to the tree’s root, while withdrawal requests require authentication at the leaf level of their aggregation tree to ensure that only the rightful owner can withdraw funds.

The implementation details of this bridge are encapsulated in four smart contracts: DepositAggregator, WithdrawalAggregator, Bridge, and WithdrawalExpander. Each plays a crucial role in the bridge's overall functionality. The DepositAggregator and WithdrawalAggregator contracts handle the aggregation of deposit and withdrawal requests, respectively, performing necessary validations and preparing the data for integration with the main bridge covenant. The Bridge contract acts as the core component, maintaining the state of the bridge, including accounts and balances, and processes the aggregated transactions. Lastly, the WithdrawalExpander contract is responsible for distributing the aggregated withdrawal amounts back to individual users by reversing the aggregation process.

This proof-of-concept establishes a technical foundation for building bridges on Bitcoin, leveraging recursive covenants and Merkle trees to efficiently manage stateful interactions and facilitate interoperability with Layer 2 networks like Starknet. The entire codebase, including an end-to-end test, is made available on GitHub, offering a comprehensive resource for developers interested in exploring and contributing to the advancement of Bitcoin's ecosystem.