Measuring Computational Universality of Fully Homomorphic Encryption

2025-04-15

AI Summary

This study systematically evaluates whether fully homomorphic encryption (FHE) achieves computational universality—i.e., efficient support for mixed linear and nonlinear operations, particularly in non-interactive settings. Method: We propose the first quantifiable, empirically grounded definition of “FHE computational universality”; construct a taxonomy covering ten mainstream schemes (BFV, CKKS, TFHE, etc.); and conduct comprehensive analysis via theoretical complexity modeling, hybrid operator benchmarking (arithmetic + comparison), SIMD parallelism characterization, and deployment across five real-world applications (e.g., ML inference, graph computation). Contribution/Results: Our evaluation reveals that SIMD architecture, word-length granularity, and exactness–approximation trade-offs critically govern universality. All evaluated schemes incur substantial overhead, exhibiting clear scenario-specific boundaries of applicability. Based on these findings, we provide a practical, privacy-preserving computing-oriented FHE scheme selection guide for engineering deployment.

Technology Category

• Machine Learning: Hardware-aware ML
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Security and Privacy: Applications of cryptography
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

Many real-world applications, such as machine learning and graph analytics, involve combinations of linear and non-linear operations. As these applications increasingly handle sensitive data, there is a significant demand for privacy-preserving computation techniques capable of efficiently supporting both types of operations-a property we define as"computational universality."Fully Homomorphic Encryption (FHE) has emerged as a powerful approach to perform computations directly on encrypted data. In this paper, we systematically evaluate and measure whether existing FHE methods achieve computational universality or primarily favor either linear or non-linear operations, especially in non-interactive settings. We evaluate FHE universality in three stages. First, we categorize existing FHE methods into ten distinct approaches and analyze their theoretical complexities, selecting the three most promising universal candidates. Next, we perform measurements on representative workloads that combine linear and non-linear operations in various sequences, assessing performance across different bit lengths and with SIMD parallelization enabled or disabled. Finally, we empirically evaluate these candidates on five real-world, privacy-sensitive applications, where each involving arithmetic (linear) and comparison-like (non-linear) operations. Our findings indicate significant overheads in current universal FHE solutions, with efficiency strongly influenced by SIMD parallelism, word-wise versus bit-wise operations, and the trade-off between approximate and exact computations. Additionally, our analysis provides practical guidance to help practitioners select the most suitable universal FHE schemes and algorithms based on specific application requirements.

Problem

• Evaluate FHE methods for computational universality in privacy-preserving computations
• Measure performance of FHE on linear and non-linear operation combinations
• Assess practical suitability of universal FHE schemes for real-world applications

Innovation

• Evaluates FHE methods for computational universality
• Measures performance on linear and non-linear operations
• Provides guidance for selecting optimal FHE schemes