Systematic Review on Verifiable Fully Homomorphic Encryption: Integrity, Proofs and Open Problems

Fully Homomorphic Encryption (FHE) enables arbitrary computations on encrypted data but lacks mechanisms to ensure the integrity of those computations. In particular, verifying that algorithm inputs are correct or that the intended algorithm was indeed executed remains an open challenge. This article addresses the issue by making two key contributions. First, we perform a comprehensive analysis of integrity faults in FHE, culminating in the definition of verifiable FHE as a novel concept to tackle these concerns. Second, we present a systematic review of existing approaches aimed at providing verifiable FHE, assessing their strengths and weaknesses, as well as their applicability in practical settings. Our findings reveal that, despite promising advances, significant gaps persist in both the theoretical foundations and the practical deployment of verifiable FHE. We conclude by outlining future research directions necessary to achieve verifiable FHE computations.