{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T03:49:07Z","timestamp":1766720947557,"version":"3.48.0"},"reference-count":31,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,12,25]],"date-time":"2025-12-25T00:00:00Z","timestamp":1766620800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JCP"],"abstract":"<jats:p>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\u2019s 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.<\/jats:p>","DOI":"10.3390\/jcp6010004","type":"journal-article","created":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T02:07:58Z","timestamp":1766714878000},"page":"4","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Homomorphic Encryption for Confidential Statistical Computation: Feasibility and Challenges"],"prefix":"10.3390","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2801-1962","authenticated-orcid":false,"given":"Yesem","family":"Kurt Peker","sequence":"first","affiliation":[{"name":"TSYS School of Computer Science, Columbus State University, Columbus, GA 31907, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rahul","family":"Raj","sequence":"additional","affiliation":[{"name":"TSYS School of Computer Science, Columbus State University, Columbus, GA 31907, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,25]]},"reference":[{"key":"ref_1","unstructured":"(2025, June 03). Statistical Confidentiality and Personal Data Protection\u2014Microdata\u2014Eurostat. Available online: https:\/\/ec.europa.eu\/eurostat\/web\/microdata\/statistical-confidentiality-and-personal-data-protection#."},{"key":"ref_2","unstructured":"(2025, June 03). 2.11 Confidential Information Protection and Statistical Efficiency Act (2002) | CIO.GOV, Available online: https:\/\/www.cio.gov\/handbook\/it-laws\/cipsea\/."},{"key":"ref_3","unstructured":"(2025, August 01). United States Census Bureau Statistical Safeguards, Available online: https:\/\/www.census.gov\/about\/policies\/privacy\/statistical_safeguards.html."},{"key":"ref_4","unstructured":"(2025, December 08). Innovations in Federal Statistics: Combining Data Sources While Protecting Privacy. Available online: https:\/\/mitsloan.mit.edu\/shared\/ods\/documents?DocumentID=4438."},{"key":"ref_5","unstructured":"(2025, June 03). Data Protection and Privacy Policy, Available online: https:\/\/www.census.gov\/about\/policies\/privacy.html."},{"key":"ref_6","unstructured":"(2025, June 03). Statistical Confidentiality | Insee. Available online: https:\/\/www.insee.fr\/en\/information\/2388575."},{"key":"ref_7","unstructured":"(2025, June 03). Statistical Standards Program\u2014Confidentiality Procedures, Available online: https:\/\/nces.ed.gov\/statprog\/confproc.asp."},{"key":"ref_8","unstructured":"(2025, June 03). Differential Privacy for Census Data Explained. Available online: https:\/\/www.ncsl.org\/technology-and-communication\/differential-privacy-for-census-data-explained."},{"key":"ref_9","unstructured":"(2025, June 03). Decennial Census Disclosure Avoidance, Available online: https:\/\/www.census.gov\/programs-surveys\/decennial-census\/disclosure-avoidance.html."},{"key":"ref_10","unstructured":"(2025, June 03). Welcome | Concrete. Available online: https:\/\/docs.zama.ai\/concrete."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1007\/s00145-019-09319-x","article-title":"TFHE: Fast Fully Homomorphic Encryption Over the Torus","volume":"33","author":"Chillotti","year":"2019","journal-title":"J. Cryptol."},{"key":"ref_12","unstructured":"Gentry, C. (June, January 31). Fully Homomorphic Encryption Using Ideal Lattices. Proceedings of the STOC \u201909: Symposium on Theory of Computing, Bethesda, MD, USA."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Cheon, J.H., Kim, A., Kim, M., and Song, Y. (2017, January 3\u20137). Homomorphic Encryption for Arithmetic of Approximate Numbers. Proceedings of the International Conference on the Theory and Application of Cryptology and Information Security, Hong Kong, China.","DOI":"10.1007\/978-3-319-70694-8_15"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Gentry, C., and Vaikuntanathan, V. (2012, January 8\u201310). (Leveled) Fully Homomorphic Encryption without Bootstrapping. Proceedings of the 3rd Innovations in Theoretical Computer Science Conference (ITCS 2012), Cambridge, MA, USA.","DOI":"10.1145\/2090236.2090262"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Chillotti, I., Gama, N., Georgieva, M., and Izabach\u00e8ne, M. (2016, January 4\u20138). Faster Fully Homomorphic Encryption: Bootstrapping in Less than 0.1 Seconds. Proceedings of the International Conference on the Theory and Application of Cryptology and Information Security, Hanoi, Vietnam.","DOI":"10.1007\/978-3-662-53887-6_1"},{"key":"ref_16","unstructured":"(2025, December 08). A Fully Homomorphic Encryption Application: SHA256 on Encrypted Input. Available online: https:\/\/webthesis.biblio.polito.it\/29342\/."},{"key":"ref_17","unstructured":"(2025, June 03). Zama\u2014Open Source Cryptography. Available online: https:\/\/www.zama.org\/."},{"key":"ref_18","unstructured":"(2025, June 03). MLIR. Available online: https:\/\/mlir.llvm.org\/."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1007\/s00145-023-09463-5","article-title":"Parameter Optimization and Larger Precision for (T)FHE","volume":"36","author":"Bergerat","year":"2023","journal-title":"J. Cryptol."},{"key":"ref_20","unstructured":"(2025, October 11). Implementation Strategies | Concrete. Available online: https:\/\/docs.zama.ai\/concrete\/guides\/self\/self-1\/strategies."},{"key":"ref_21","unstructured":"(2025, August 01). Microsoft SEAL: Fast and Easy-to-Use Homomorphic Encryption Library. Available online: https:\/\/www.microsoft.com\/en-us\/research\/project\/microsoft-seal\/."},{"key":"ref_22","unstructured":"(2025, August 01). IBM Z Content Solutions | Fully Homomorphic Encryption. Available online: https:\/\/www.ibm.com\/support\/z-content-solutions\/fully-homomorphic-encryption\/."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Feng, X.M., Li, X.D., Zhou, S.Y., and Jin, X. (2023, January 2\u20135). Homomorphic Comparison Method Based on Dynamically Polynomial Com-posite Approximating Sign Function. Proceedings of the 2023 IEEE Conference on Communications and Network Security (CNS), Orlando, FL, USA.","DOI":"10.1109\/CNS59707.2023.10288803"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4389","DOI":"10.1109\/TIFS.2021.3106167","article-title":"Efficient Sorting of Homomorphic Encrypted Data with K-Way Sort-ing Network","volume":"16","author":"Hong","year":"2021","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"59260","DOI":"10.1109\/ACCESS.2024.3390053","article-title":"Innovative Homomorphic Sorting of Environmental Data in Area Monitoring Wireless Sensor Networks","volume":"12","author":"Malvi","year":"2024","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Wang, C., Chen, J., Zhang, X., and Cheng, H. (2023, January 10\u201312). An Efficient Fully Homomorphic Encryption Sorting Algorithm Using Addition Over TFHE. Proceedings of the 2022 IEEE 28th International Conference on Parallel and Distributed Systems (ICPADS), Nanjing, China.","DOI":"10.1109\/ICPADS56603.2022.00037"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1186\/s42400-023-00187-4","article-title":"Practical Solutions in Fully Homomorphic Encryption: A Survey Analyzing Existing Acceleration Methods","volume":"7","author":"Gong","year":"2024","journal-title":"Cybersecurity"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Lu, W.J., Huang, Z., Hong, C., Ma, Y., and Qu, H. (2021, January 24\u201327). PEGASUS: Bridging Polynomial and Non-Polynomial Evaluations in Homomorphic Encryption. Proceedings of the 2021 IEEE Symposium on Security and Privacy (SP), San Francisco, CA, USA.","DOI":"10.1109\/SP40001.2021.00043"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1224","DOI":"10.1109\/TDSC.2023.3275649","article-title":"HEaaN-STAT: A Privacy-Preserving Statistical Analysis Toolkit for Large-Scale Numerical, Ordinal, and Categorical Data","volume":"21","author":"Lee","year":"2024","journal-title":"IEEE Trans. Dependable Secur. Comput."},{"key":"ref_30","unstructured":"Mazzone, F., Everts, M., Hahn, F., and Peter, A. (2025, January 13\u201315). Efficient Ranking, Order Statistics, and Sorting under CKKS. Proceedings of the 34th USENIX Conference on Security Symposium, Seattle, WA, USA."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Raj, R., Kurt Peker, Y., and Mutlu, Z.D. (2024). Blockchain and Homomorphic Encryption for Data Security and Statistical Privacy. Electronics, 13.","DOI":"10.3390\/electronics13153050"}],"container-title":["Journal of Cybersecurity and Privacy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2624-800X\/6\/1\/4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T02:45:33Z","timestamp":1766717133000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2624-800X\/6\/1\/4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,25]]},"references-count":31,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,2]]}},"alternative-id":["jcp6010004"],"URL":"https:\/\/doi.org\/10.3390\/jcp6010004","relation":{},"ISSN":["2624-800X"],"issn-type":[{"value":"2624-800X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,25]]}}}