  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.
