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

Dongfang Zhao

TL;DR

HADES tackles the challenge of performing secure symbol comparisons directly on ciphertexts in fully homomorphic encryption without increasing ciphertext size, a gap left by OPE/ORE approaches. It introduces the Compare-Eval Key (CEK) built on RLWE to achieve CPA-security, and an extended FA-Extension with perturbations to defend against frequency-analysis attacks while preserving correctness via a carefully chosen scaling factor. The framework is implemented in OpenFHE and demonstrated on real datasets with both BFV and CKKS, showing practical performance and competitive superiority over HOPE and POPE baselines. This work advances privacy-preserving outsourced databases by enabling efficient range queries, indexing, and sorting on encrypted data with strong security guarantees and scalability for real-world deployments.

Abstract

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.

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

TL;DR

HADES tackles the challenge of performing secure symbol comparisons directly on ciphertexts in fully homomorphic encryption without increasing ciphertext size, a gap left by OPE/ORE approaches. It introduces the Compare-Eval Key (CEK) built on RLWE to achieve CPA-security, and an extended FA-Extension with perturbations to defend against frequency-analysis attacks while preserving correctness via a carefully chosen scaling factor. The framework is implemented in OpenFHE and demonstrated on real datasets with both BFV and CKKS, showing practical performance and competitive superiority over HOPE and POPE baselines. This work advances privacy-preserving outsourced databases by enabling efficient range queries, indexing, and sorting on encrypted data with strong security guarantees and scalability for real-world deployments.

Abstract

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.
Paper Structure (72 sections, 3 theorems, 52 equations, 4 figures, 1 table, 4 algorithms)

This paper contains 72 sections, 3 theorems, 52 equations, 4 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Background and Motivation
  3. Proposed Work
  4. Experimental Validation
  5. Related Work
  6. Homomorphic Encryption
  7. Order-Preserving Encryption
  8. RLWE and Noise Augmentation
  9. Design Goals
  10. Feature Summary
  11. Correctness
  12. Security
  13. Efficiency
  14. Basic HADES
  15. Overview
  16. ...and 57 more sections

Key Result

theorem 1

Under the bounded noise assumption, the proposed scheme guarantees that the evaluation result reflects the relative comparison between plaintexts $m_0$ and $m_1$. Specifically: where $c_{\Delta,0}$ and $c_{\Delta,1}$ represent the components of the ciphertext difference $ct_{\Delta} = (c_{0,0} - c_{1,0}, c_{0,1} - c_{1,1})$. The sign of $\text{Eval}(cek, ct_0, ct_1)$ satisfies: ensuring correctn

Figures (4)

  • Figure 1: HADES Basic and FA-Extension (FAE) Performance for BFV bfv.
  • Figure 2: HADES Basic and FA-Extension (FAE) Performance for CKKS ckks.
  • Figure 3: HADES Performance Across Datasets for Key Operations.
  • Figure 4: Ciphertext Comparison Time of Different Protocols.

Theorems & Definitions (6)

  • theorem 1: Correctness of Evaluation
  • proof
  • theorem 2
  • proof
  • theorem 3
  • proof