🤖 AI Summary
This work addresses the absence of a machine-checked formal model for zk-STARK transparent proof protocols, which hinders rigorous assurance of their security and correctness. We present the first complete formalization of the zk-STARK protocol in Isabelle/HOL, constructing executable models of both prover and verifier, and carry out their specification and verification using a finite probabilistic state monad equipped with weakest preconditions calculus. Our main contributions include a phased soundness theorem with an explicit error probability bound, a rigorous proof of perfect completeness for honest executions, and the public release of all key definitions and theorems as Isabelle source code, thereby laying a foundation for high-assurance implementations of zero-knowledge proof protocols.
📝 Abstract
This report describes an Isabelle/HOL formalization of a STARK-style transparent proof protocol. The development contains an executable model of the prover and verifier, a finite probabilistic state monad with a weakest-precondition calculus, a zero-failure honestcompleteness theorem, and a staged soundness theorem with an explicit probability bound. The report is written for readers with a formal-methods background. It gives enough cryptographic context to explain the protocol, but its main emphasis is the formal model, the decomposition of the proofs, and the Isabelle source locations of the principal definitions and theorems.