BoostCom: Towards Efficient Universal Fully Homomorphic Encryption by Boosting the Word-wise Comparisons

Fully Homomorphic Encryption (FHE) allows for the execution of computations on encrypted data without the need to decrypt it first, offering significant potential for privacy-preserving computational operations. Emerging arithmetic-based FHE schemes (ar-FHE), like BGV, demonstrate even better performance in word-wise comparison operations over non-arithmetic FHE (na-FHE) schemes, such as TFHE, especially for basic tasks like comparing values, finding maximums, and minimums. This shows the universality of ar-FHE in effectively handling both arithmetic and non-arithmetic operations without the expensive conversion between arithmetic and non-arithmetic FHEs. We refer to universal arithmetic Fully Homomorphic Encryption as uFHE. The arithmetic operations in uFHE remain consistent with those in the original arithmetic FHE, which have seen significant acceleration. However, its non-arithmetic comparison operations differ, are slow, and have not been as thoroughly studied or accelerated. In this paper, we introduce BoostCom, a scheme designed to speed up word-wise comparison operations, enhancing the efficiency of uFHE systems. BoostCom involves a multi-prong optimizations including infrastructure acceleration (Multi-level heterogeneous parallelization and GPU-related improvements), and algorithm-aware optimizations (slot compaction, non-blocking comparison semantic). Together, BoostCom achieves an end-to-end performance improvement of more than an order of magnitude (11.1x faster) compared to the state-of-the-art CPU-based uFHE systems, across various FHE parameters and tasks.