Homomorphic Encryption for Confidential Statistical Computation: Feasibility and Challenges

Homomorphic encryption allows computations on encrypted data without revealing it to anyone other than an owner or an authorized collector. When combined with other tech-niques, homomorphic encryption offers an ideal solution for ensuring statistical confiden-tiality. TFHE (Fast Fully Homomorphic Encryption over the Torus) is a fully homomor-phic encryption scheme that supports efficient homomorphic operations on Booleans and integers. In this study, we use Zama’s Concrete compiler to explore the application of TFHE for performing statistical analysis on encrypted data, thereby demonstrating its vi-ability for ensuring statistical confidentiality. We provide implementations of traditional algorithms for basic statistical computations on encrypted datasets, including the five-number summary, mean, variance, and mode, and record the time required for each operation. The results show that basic tasks like mean and min/max work well for small datasets while keeping data encrypted. However, more complex tasks like median and variance slow down dramatically as datasets get larger. This work reinforces the theoretical promise of Fully Homomorphic Encryption (FHE) for statistical analysis and high-lights the need for substantial optimizations to make it viable for real-world applications