Circom is a popular programming language for writing arithmetic circuits that can be used to generate zero-knowledge proofs (ZKPs) like zk-SNARKS. ZKPs have received tremendous attention in protocols like zkRollups. The Circom circuits are compiled to Rank-1 Constraint Systems (R1CS) circuits, based on which zk-SNARK proofs are generated. However, one major challenge associated with R1CS circuits is the problem of under-constrained circuits, which are susceptible to allowing incorrect computations to pass verification due to insufficient constraints, potentially leading to security vulnerabilities. In this paper, we propose a novel framework CONSCS to automatically verify Circom circuits. Our contributions are threefold: 1) we propose novel circuit inference rules to help reduce the size of circuits and to extract more comprehensive information than existing works; 2) we introduce the novel Binary Property Graph (BPG) as a highly efficient reasoning engine, outperforming all existing tools in effectiveness and efficiency; 3) we leverage fine-grained domain-specific information to guide the SMT solving to address non-linear constraints, increasing the success rate of SMT queries of existing works from 2.68% to 48.84%. We conduct experiments to show that CONSCS enhances the solved rate of existing works from around 50-60% to above 80%.

Zero-knowledge layer 2 protocols emerge as a compelling approach to overcoming blockchain scalability issues by processing transactions through the transaction finalization process. During this process, transactions are efficiently processed off the main chain. Besides, both the transaction data and the zero-knowledge proofs of transaction executions are reserved on the main chain, ensuring the availability of transaction data as well as the correctness and verifiability of transaction executions. Hence, any bugs that cause the transaction finalization failure are crucial, as they impair the usability of these protocols and the scalability of blockchains.

Optimistic rollup protocols are widely adopted as the most popular blockchain scaling solutions. As a dominant implementation, Arbitrum has boasted a total locked value exceeding 18 billion USD, highlighting the significance of optimistic rollups in blockchain ecosystem. Despite their popularity, little research has been done on the security of optimistic rollup protocols, and potential vulnerabilities on them remain unknown.