A Survey of Oblivious Compression on Encrypted Data with Fully Homomorphic Encryption

Ensuring the security of private data during transmission and storage is increasingly crucial. Private information retrieval (PIR), which allows a client to retrieve specific data from a server's database without revealing any information to the server, offers a promising solution to this challenge. To design a PIR protocol, fully homomorphic encryption (FHE), which supports arbitrary computations on encrypted data, enables secure queries without exposing the queried data. However, PIR based on FHE often incurs high communication costs, leading to the development of oblivious ciphertext compression protocols that aim to reduce these costs while maintaining privacy. This paper reviews two recent techniques for oblivious ciphertext compression of encrypted data using FHE, which effectively reduce the data size transmitted between a server and a client. We examine these techniques along with their building blocks and related works in this field.