Cryptographic certificates of validity for trustworthy AI

As AI agents increasingly perform autonomous actions—such as booking flights or deploying code—traditional methods like identity authentication and retrospective logging become insufficient for ensuring safety and compliance. This paper introduces a framework for cryptographic certificates of validity, which act as a bridge between formal verification and cryptographic authentication. By representing correctness conditions as logical predicates and compiling them into polynomial constraints, the system allows agents to attach a succinct cryptographic proof to their actions, demonstrating that they adhere to an agreed-upon policy.

The core of the proposal is an arithmetization of first-order logic. The author defines a syntax for terms and predicates that map to polynomial semantics. In this system, a predicate is considered 'valid' if its corresponding polynomial evaluates to zero. By composing these simple components, complex correctness conditions—including recursive computations—can be expressed as algebraic relations. This allows for the use of modern cryptographic proof systems (such as SNARKs or zkVMs) to verify that a witness exists for a given policy predicate.

In practice, this framework allows for a clear separation of concerns. A system operator defines a formal policy, which a compiler then translates into an algebraic relation. When an agent proposes an action, it generates a proof that its internal state (the witness) satisfies this relation. The verifier then checks this proof against the policy's verifier key. This process ensures that the verifier does not need to inspect the agent's internal implementation or re-run the agent's logic, providing a scalable and secure mechanism for accountability in heterogeneous, distributed AI systems.