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.

翻译：全同态加密（FHE）允许在无需先解密的情况下对加密数据执行计算，为隐私保护计算操作提供了重要潜力。新兴的基于算术的全同态加密方案（ar-FHE，如BGV）在字级比较操作上表现出优于非算术FHE方案（na-FHE，如TFHE）的性能，特别是在数值比较、求最大值和最小值等基础任务中。这表明ar-FHE能够有效处理算术与非算术操作，无需在算术与非算术FHE之间进行昂贵的转换，体现了其通用性。我们将这种通用算术全同态加密称为uFHE。uFHE中的算术操作与原始算术FHE保持一致，且已获得显著加速；然而其非算术比较操作则存在差异，速度较慢，且尚未得到充分研究或加速。本文提出BoostCom方案，旨在加速字级比较操作，从而提升uFHE系统的效率。BoostCom包含多维度优化：基础设施加速（多级异构并行化与GPU相关改进）和算法感知优化（槽位压缩、非阻塞比较语义）。综合这些优化，BoostCom在不同FHE参数和任务下，相比最先进的基于CPU的uFHE系统实现了超过一个数量级的端到端性能提升（加速比达11.1倍）。