Detecting and Understanding Vulnerabilities in Fully Homomorphic Encryption Frameworks

Fully Homomorphic Encryption (FHE) is a transformative technology that enables computation on encrypted data, protecting privacy in sensitive fields like healthcare and finance. To make this complex technology accessible, industry leaders have developed high-level frameworks (e.g., Zama's Concrete, Google's HEIR, IBM's HELayers) that translate user programs into cryptographic primitives. However, these frameworks are highly complex, involving multi-layered software stacks that handle noise management, parameter selection, and optimization. Because these frameworks are prone to logic bugs that can silently corrupt encrypted data, ensuring their correctness is critical to preventing severe security and financial consequences.

HERTA is an automated testing tool designed to uncover bugs across the entire FHE framework stack. It employs metamorphic testing (MT), a technique that verifies program correctness by checking output consistency under specific input transformations, bypassing the need for a manual ground truth (the oracle problem). HERTA implements three hierarchical metamorphic relations (MRs):

• Frontend Mutations: Transforms seed programs by modifying ciphertext types and dataflow structures.
• Intermediate Configurations: Uses priority-driven pairwise testing to explore the vast optimization space of FHE compilation.
• Backend Retargeting: Applies equivalent transformations across different FHE schemes and hardware backends to identify semantic inconsistencies.

By applying these hierarchical MRs, the researchers evaluated three leading industry frameworks and discovered 21 previously unknown bugs. These include 16 logic errors that lead to silent, incorrect calculations and 5 crashes during compilation. The authors performed a hazard analysis demonstrating that these bugs can compromise the integrity and availability of real-world privacy-preserving services. Several of these bugs have already been confirmed and fixed by the respective framework developers, highlighting the practical utility of HERTA in securing the FHE ecosystem.