HE-DAP: Homomorphic Encryption-based Dynamic Adaptive Parameter Optimization for Statistical Computation

초록

Homomorphic encryption (HE) enables privacy-preserving analytics but remains hindered by high computational overhead. We find that the inverse square root - a key primitive in many statistical and machine learning workloads - exhibits inconsistent and often sub-optimal performance across HE libraries and hardware. This stems from a core trade-off between two costly HE operations: evaluating high-degree Chebyshev polynomials to speed up Newton's method versus performing bootstrapping to manage ciphertext noise. Because their relative costs vary by up to 6× across environments, any fixed configuration proves inherently inefficient.To address this challenge, we present HE-DAP, a cross-platform optimization framework that automatically navigates this trade-off. By profiling an environment's unique performance characteristics, HE-DAP finds the optimal balance between polynomial degree and iteration count to accelerate the encrypted inverse square root computation for a given accuracy target. Our evaluation on Lattigo, HEaaN-CPU, and HEaaN-GPU shows that HE-DAP's adaptive approach yields significant performance gains. It accelerates the core inverse square root computation by up to 2.35× over the fixed configuration in PP-STAT while maintaining high numerical accuracy (MRE ≤ 3.1 × 10-8). We further demonstrate that optimizing this fundamental building block directly enhances the end-to-end performance of complex statistical analyses, confirming the practical benefits of our environment-aware approach. By automatically adapting to heterogeneous execution environments, HE-DAP demonstrates that principled parameter optimization can make privacy-preserving statistical analytics practical at scale. © 2026 Copyright held by the owner/author(s).

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