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

TL;DR

This work tackles the bottleneck of non-arithmetic word-wise comparisons in universal FHE (uFHE) built on the BGV scheme. It introduces BoostCom, a multi-level heterogeneous CPU/GPU infrastructure that combines slot compaction and non-blocking comparison with GPU-accelerated primitives (BluesteinNTT, BluesteinFFT, and element-wise ops) via cuHElib on HELib. The approach yields an end-to-end average speedup of $11.1\times$ (up to $26.7\times$) over a 16-core CPU baseline and up to $553\%$ improvement over HE-Booster, across five applications, with notable memory savings and higher GPU utilization. These results demonstrate practical, scalable acceleration for uFHE comparisons, enabling faster privacy-preserving cloud computations at realistic scales.

Abstract

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.

Figures (13)

• Figure 1: Performing computations on encrypted data transferred to an untrusted server using FHE.
• Figure 2: Breakdown of BGV comparison time for Bivariate circuit with parameters $m=34511$, $p=3$, and $d=6$.
• Figure 3: Illustrating Boostcom's heterogeneous parallelism: digits are computed across multiple CPU threads, while primitive operations in each digit are offloaded to the GPU.
• Figure 4: Layout optimization for offloading the element-wise operation to the GPU, utilizing additional copying at the CPU side to maximize the CPU-GPU memcpy bandwidth and parallelization degree.
• Figure 5: Illustration of: (a) ResNet block containing convolution (Conv), batch normalization (BN), and ReLU; (b) Convolution filter; (c) Convolution steps on encrypted data resulting in unused slots; (d) Naive digit decomposition with many unused slots; and (e) Optimized digit decomposition with slot compaction.