[Paper Review] Homomorphic Encryption: An Analysis of its Applications in Searchable Encryption

Ivone Amorim, Ivan Costa|arXiv (Cornell University)|Jun 26, 2023

Cryptography and Data SecurityComputer Science77 references3 citations

TL;DR

This paper analyzes the integration of Homomorphic Encryption (HE) in Searchable Encryption (SE) schemes, identifying its role in enabling secure, efficient search over encrypted data. It reveals that Partially Homomorphic Encryption (PHE), especially Paillier’s cryptosystem, dominates HE usage in SE, with index-based structures and ranked search being most common, while functionalities like fuzzy keyword search, verifiability, and user revocation remain underdeveloped.

ABSTRACT

The widespread adoption of cloud infrastructures has revolutionised data storage and access. However, it has also raised concerns regarding the privacy of sensitive data stored in the cloud. To address these concerns, encryption techniques have been widely used. However, traditional encryption schemes limit the efficient search and retrieval of encrypted data. To tackle this challenge, innovative approaches have emerged, such as the utilisation of Homomorphic Encryption (HE) in Searchable Encryption (SE) schemes. This paper provides a comprehensive analysis of the advancements in HE-based privacy-preserving techniques, focusing on their application in SE. The main contributions of this work include the identification and classification of existing SE schemes that utilize HE, a comprehensive analysis of the types of HE used in SE, an examination of how HE shapes the search process structure and enables additional functionalities, and the identification of promising directions for future research in HE-based SE. The findings reveal the increasing usage of HE in SE schemes, particularly Partially Homomorphic Encryption. The analysis also highlights the prevalence of index-based SE schemes using HE, the support for ranked search and multi-keyword queries, and the need for further exploration in functionalities such as verifiability and the ability to authorise and revoke users. Future research directions include exploring the usage of other encryption schemes alongside HE, addressing omissions in functionalities like fuzzy keyword search, and leveraging recent advancements in Fully Homomorphic Encryption schemes.

Motivation & Objective

• To analyze the current state of Homomorphic Encryption (HE) in Searchable Encryption (SE) schemes.
• To classify and evaluate the types of HE used in SE, including PHE, FHE, and others.
• To examine how HE influences SE architecture, particularly in index construction and search functionality.
• To identify underexplored functionalities in HE-based SE, such as verifiability, user access control, and fuzzy keyword search.
• To propose future research directions, including hybrid schemes and leveraging recent FHE advancements.

Proposed method

• A systematic literature review was conducted on 23 recent SE schemes incorporating HE, selected using a defined methodology.
• The analysis categorized HE schemes by type (PHE, FHE, etc.), search structure (index-based vs. sequential), and supported functionalities.
• HE's role in enabling homomorphic computation of relevance scores (e.g., TF-IDF) was evaluated in ranked search schemes.
• The study examined the use of HE in access control mechanisms, including user authorization and revocation, and verifiability features.
• Cryptographic primitives like Homomorphic Message Authentication were analyzed for their role in enabling verifiability without direct HE use.
• The paper assessed the feasibility of integrating other encryption schemes (e.g., ABE, OPE) alongside HE to enhance functionality.

Figure 1: Conceptual overview of a cloud-based SE system.

Experimental results

Research questions

• RQ1 Which types of Homomorphic Encryption (HE) are most commonly used in Searchable Encryption (SE) schemes?
• RQ2 How does HE influence the design of SE systems, particularly in index construction and search functionality?
• RQ3 What are the most prevalent search functionalities supported by HE-based SE schemes, and which are missing?
• RQ4 To what extent are verifiability and user access control (authorization and revocation) supported in HE-based SE schemes?
• RQ5 What are the most promising future research directions for HE in SE, especially with recent advances in FHE?

Key findings

• Seventy-five percent of the analyzed HE-based SE schemes were published within the last three years, indicating a growing research trend.
• Partially Homomorphic Encryption (PHE), particularly Paillier’s cryptosystem, was the most widely used HE scheme due to its simplicity and proven security.
• Index-based SE schemes that use HE for constructing encrypted indexes were the most prevalent, as they avoid costly sequential scans in large databases.
• Ranked search using homomorphic computation of TF-IDF scores was the most common functionality, followed by support for multi-keyword queries (conjunctive/disjunctive).
• No HE-based SE scheme in the analysis supported fuzzy keyword search, despite its high practical value, indicating a significant research gap.
• Only one study (Wu et al., 2018) used HE for verifiability, and none addressed user authorization and revocation, highlighting underdeveloped access control features.

Figure 2: Key characteristics of a cloud-based SE scheme.