Paper 2026/027

Practical SNARGs for Matrix Multiplications over Encrypted Data

Abstract

Fully Homomorphic Encryption (FHE) enables computations to be performed directly on encrypted data, without ever requiring decryption. This capability is particularly crucial for privacy-preserving outsourced computation in sensitive fields such as healthcare and finance. While FHE ensures data confidentiality under the honest-but-curious adversarial model, achieving full malicious security, encompassing both integrity and privacy, requires an additional layer of verifiability. To address this, a growing body of research has explored combining FHE with techniques from verifiable computation, leading to the notion of verifiable FHE (vFHE). However, the integration of these two paradigms often results in substantial computational overhead, making existing approaches largely impractical for real-world deployment. In this work, rather than targeting general-purpose verifiable FHE, we design a novel and practical verifiable homomorphic encryption scheme tailored for an important and widely used operation: matrix–vector multiplication. We provide an open-source implementation and our experimental results demonstrate that the proposed scheme achieves high efficiency, making it ready for practical adoption.

Note: Added acknowledgements.