A survey on fully homomorphic encryption compilers

Abstract Fully Homomorphic Encryption (FHE) enables computations on encrypted data without decryption, ensuring data privacy in cloud computing and preventing sensitive information leakage. In recent years, significant progress has been made in FHE research, resulting in the development of various FHE schemes and supporting libraries. However, FHE incurs substantial computational overhead, with execution times exceeding plaintext computation by 4-5 orders. As a result, optimized FHE programs can be several hundred times faster than their unoptimized counterparts, underscoring the critical importance of efficient FHE programming. However, the restricted set of primitive operations, numerous cryptographic parameters, and complexities in ciphertext management present significant challenges, rendering FHE programming prohibitively complex for users without cryptographic expertise. To address these challenges, numerous FHE programming tools, commonly referred to as FHE compilers, have been developed. These compilers aim to simplify FHE programming by allowing users to write standard plaintext programs, which are then automatically converted into ciphertext programs. They handle ciphertext management and parameter selection automatically, lowering the barrier for users. This paper systematically reviews existing FHE compilers, examining their techniques and effectiveness to explore the current state of the art and identify areas for future research. First, we analyze the challenges of FHE programming that compilers aim to address. We then outline a typical workflow of FHE compilers, classify compilers based on the problems they solve, and compare tools within each category. Finally, we provide a summary of the current state of research on FHE compilers and propose directions for future advancements in FHE programming tools.