Hades: Homomorphic Augmented Decryption for Efficient Symbol-comparison -- A Database's Perspective

Outsourced databases powered by fully homomorphic encryption (FHE) offer the promise of secure data processing on untrusted cloud servers. A crucial aspect of database functionality, and one that has remained challenging to integrate efficiently within FHE schemes, is the ability to perform comparisons on encrypted data. Such comparisons are fundamental for various database operations, including building indexes for efficient data retrieval and executing range queries to select data within specific intervals. While traditional approaches like Order-Preserving Encryption (OPE) could enable comparisons, they are fundamentally incompatible with FHE without significantly increasing ciphertext size, thereby exacerbating the inherent performance overhead of FHE and further hindering its practical deployment. This paper introduces HADES, a novel cryptographic framework that enables efficient and secure comparisons directly on FHE ciphertexts without any ciphertext expansion. Based on the Ring Learning with Errors (RLWE) problem, HADES provides CPA-security and incorporates perturbation-aware encryption to mitigate frequency-analysis attacks. Implemented using OpenFHE, HADES supports both integer and floating-point operations, demonstrating practical performance on real-world datasets and outperforming state-of-the-art baselines.