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arXiv · 2311.08858

Formal Verification of Zero-Knowledge Circuits

Alessandro Coglio·Eric McCarthy·Eric W. Smith
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Abstract

Zero-knowledge circuits are sets of equality constraints over arithmetic expressions interpreted in a prime field; they are used to encode computations in cryptographic zero-knowledge proofs. We make the following contributions to the problem of ensuring that a circuit correctly encodes a computation: a formal framework for circuit correctness; an ACL2 library for prime fields; an ACL2 model of the existing R1CS (Rank-1 Constraint Systems) formalism to represent circuits, along with ACL2 and Axe tools to verify circuits of this form; a novel PFCS (Prime Field Constraint Systems) formalism to represent hierarchically structured circuits, along with an ACL2 model of it and ACL2 tools to verify circuits of this form in a compositional and scalable way; verification of circuits, ranging from simple to complex; and discovery of bugs and optimizations in existing zero-knowledge systems.

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Alessandro Coglio, Eric McCarthy, Eric W. Smith. 2023-11-15. Formal Verification of Zero-Knowledge Circuits. https://doi.org/10.4204/eptcs.393.9

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