Fully Homomorphic Compression (FHC)

Abstract

Compression algorithms and functions have been extensively utilized in various applications, e.g., in digital storage and communication. In recent years and with the popularity of machine learning applications, researchers have utilized compression techniques for addressing key problems in machine learning, e.g., for compressing artificial neural networks or for optimizing KV-cache memory in LLMs. Due to extensive applications of compression algorithms in different domains, a whole new era of innovations and applications for data compression algorithms can be envisioned. In this article, we discuss that compression functions with interesting properties, e.g., fully homomorphic compression (FHC) algorithms, can have applications beyond compressing data. FHC algorithms can potentially enable performing computation on compressed (and encrypted) data. Thus, fully homomorphic compression techniques can be used for reducing the computational and communication costs of compute and communication-intensive workloads, such as fully homomorphic encryption (FHE) & zero-knowledge proof (ZKP) applications, (secure) vector databases (VDBs and SVDBs), blockchain-based technologies, image and video processing, privacy-preserving or private LLMs, and LLM & AI inference, etc.