vFHE: Verifiable Fully Homomorphic Encryption

Fully Homomorphic Encryption (FHE) is a powerful building block for secure and private applications. However, state-of-the-art FHE schemes do not offer any integrity guarantees, which can lead to devastating correctness and security issues when FHE is deployed in non-trivial settings. In this paper, we take a critical look at existing integrity solutions for FHE, and analyze their (often implicit) threat models, efficiency, and adequacy with real-world FHE deployments. We explore challenges of what we believe is the most flexible and promising integrity solution for FHE: namely, zero-knowledge Succinct Non-interactive ARguments of Knowledge (zkSNARKs); we showcase optimizations for both general-purpose zkSNARKs and zkSNARKs designed for FHE. We then present two software frameworks, circomlib-FHE and zkOpenFHE, which allow practitioners to automatically augment existing FHE pipelines with integrity guarantees. Finally, we leverage our tools to evaluate and compare different approaches to FHE integrity, and discuss open problems that stand in the way of a widespread deployment of FHE in real-world applications.