This study proposes a blockchain-based system that utilizes fully homomorphic encryption to provide data security and statistical privacy when data are shared with third parties for analysis or research purposes. The proposed system not only provides security of data in transit, at rest, and in use but also assures privacy and computational integrity for simple statistical computations. This is achieved by leveraging the attributes of the blockchain technology, which provides availability and data integrity, combined with homomorphic encryption, which provides confidentiality of data in use. The computations are performed on smart contracts residing on the blockchain, providing computational integrity. The proposed system is implemented on the Zama blockchain and performs statistical operations including mean, median, and variance on encrypted data. The results indicate that it is possible to perform fully homomorphic computations on the blockchain. Even though current computing limitations on the blockchain do not allow running the system for large data sets, the technology is available, and with advancements toward more efficient homomorphic operations on blockchains, the proposed system will provide an ultimate solution for providing the much-desired security properties in applications, including data and statistical privacy, confidentiality, and integrity at rest, in transit, and in use.

Statistical confidentiality focuses on protecting data to preserve its analytical value while preventing identity exposure, ensuring privacy and security in any system handling sensitive information. Homomorphic encryption allows computations on encrypted data without revealing it to anyone other than an owner or an authorized collector. When combined with other techniques, homomorphic encryption offers an ideal solution for ensuring statistical confidentiality. TFHE (Fast Fully Homomorphic Encryption over the Torus) is a fully homomorphic encryption scheme that supports efficient homomorphic operations on Booleans and integers. Building on TFHE, Zama’s Concrete project offers an open-source compiler that translates high-level Python code (version 3.9 or higher) into secure homomorphic computations. This study examines the feasibility of the Concrete compiler to perform core statistical analyses on encrypted data. We implement traditional algorithms for core statistical measures including the mean, variance, and five-point summary on encrypted datasets. Additionally, we develop a bitonic sort implementation to support the five-point summary. All implementations are executed within the Concrete framework, leveraging its built-in optimizations. Their performance is systematically evaluated by measuring circuit complexity, programmable bootstrapping count (PBS), compilation time, and execution time. We compare these results to findings from previous studies wherever possible. The results show that the complexity of sorting and statistical computations on encrypted data with the Concrete implementation of TFHE increases rapidly, and the size and range of data that can be accommodated is small for most applications. Nevertheless, this work reinforces the theoretical promise of Fully Homomorphic Encryption (FHE) for statistical analysis and highlights a clear path forward: the development of optimized, FHE-compatible algorithms.

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.