Measuring Computational Universality of Fully Homomorphic Encryption

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.

@article{xue2025_2504.11604,
  title={ Measuring Computational Universality of Fully Homomorphic Encryption },
  author={ Jiaqi Xue and Xin Xin and Wei Zhang and Mengxin Zheng and Qianqian Song and Minxuan Zhou and Yushun Dong and Dongjie Wang and Xun Chen and Jiafeng Xie and Liqiang Wang and David Mohaisen and Hongyi Wu and Qian Lou },
  journal={arXiv preprint arXiv:2504.11604},
  year={ 2025 }
}