# Formal Verification of Zero-Knowledge Circuits

arXiv: https://arxiv.org/abs/2311.08858 · HTML: https://mlsanity.com/paper/2311.08858/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2023.

## Built on by (most cited first, 1 of 1)

- [AC4: Algebraic Computation Checker for Circuit Constraints in ZKPs](https://mlsanity.com/paper/2403.15676/) (2024)

## Abstract (arXiv)

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.