Rounding-free differential privacy for discrete count data: A field-wrapped discrete-Laplace mechanism

Thanh-Phong Lam

doi:10.63065/ajafe.2026.2.006

Asian Journal of Applied Financial Econometrics (AJAFE)

Volume 1_Number 2 , Tháng 8/2026, Trang 80-90

Rounding-free differential privacy for discrete count data: A field-wrapped discrete-Laplace mechanism

Thanh-Phong Lam

DOI: 10.63065/ajafe.2026.2.006

Ngày nhận bài: 05/10/2026

Ngày nhận bài sửa: 12/08/2026

Ngày duyệt đăng: 18/08/2026

Email: limpaul.fin@gmail.com

Đơn vị công tác:

Lượt xem: 5

Downloads: 0

Các định dạng trích dẫn

Tóm tắt

Purpose – This paper develops a differentially private mechanism for releasing discrete banking aggregates that stays in the data’s native modular domain and avoids the rounding bias of continuous-noise mechanisms.

Design/methodology/approach – The mechanism adds two-sided geometric (discrete Laplace) integer noise to each cell count and reduces modulo the field order q. Pure ε-differential privacy follows from post-processing immunity of the modular map, and a closed-form per-cell error 1/sinh (ε) is derived. We evaluate it against uniform, continuous Laplace, and Gaussian baselines on synthetic State Bank of Vietnam frequency tables. The Python and R pipeline is reproducible.

Findings – The mechanism is provably pure ε-DP and unbiased, with per-cell error governed by ε alone, independent of the field order. It matches the utility-optimal discrete Laplace and stays below the rounded continuous Laplace at every budget. The uniform alternative is worse by up to two orders of magnitude and ignores ε.

Originality/value – The paper contributes a discrete, modular-closed differential privacy mechanism for banking disclosure. Releases reconcile exactly under modular addition, and the guarantee needs no computational-hardness assumption, giving regulators a provable, reproducible tool for confidential aggregate reporting.

Từ khóa

Bayesian budget allocation, Differential privacy, Discrete Laplace mechanism, Finite-field randomization, Vietnamese banking

Download

Tài liệu tham khảo

Abadi, M., Chu, A., Goodfellow, I., McMahan, H. B., Mironov, I., Talwar, K., & Zhang, L. (2016). Deep learning with differential privacy. In Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security (CCS) (pp. 308–318). ACM. https://doi.org/10.1145/2976749.2978318.

Abowd, J., Ashmead, R., Cumings-Menon, R., Garfinkel, S., Heineck, M., Heiss, C., Johns, R., Kifer, D., Leclerc, P., Machanavajjhala, A., Moran, B., Sexton, W., Spence, M., & Zhuravlev, P. (2022). The 2020 census disclosure avoidance system TopDown algorithm. Harvard Data Science Review, Special Issue 2. https://doi.org/10.1162/99608f92.529e3cb9.

Bun, M., & Steinke, T. (2016). Concentrated differential privacy: Simplifications, extensions, and lower bounds. In Theory of Cryptography Conference (TCC) (pp. 635-658). Springer. https://doi.org/10.1007/978-3-662-53641-4_24.

Canonne, C., Kamath, G., & Steinke, T. (2022). The discrete Gaussian for differential privacy. Journal of Privacy and Confidentiality, 12(1). https://doi.org/10.29012/jpc.784.

Canonne, C. L., Kamath, G., & Steinke, T. (2020). The discrete Gaussian for differential privacy. In Advances in Neural Information Processing Systems (NeurIPS) (Vol. 33, pp. 15676-15688). https://doi.org/10.48550/arXiv.2004.00010.

Cuff, P., & Yu, L. (2016). Differential privacy as a mutual information constraint. In Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security (CCS) (pp. 34-43). ACM. https://doi.org/10.1145/2976749.2978308.

Duchi, J. C., Jordan, M. I., & Wainwright, M. J. (2018). Minimax optimal procedures for locally private estimation. Journal of the American Statistical Association, 113(521), 182-201. https://doi.org/10.1080/01621459.2017.1389735.

Dwork, C., McSherry, F., Nissim, K., & Smith, A. (2006). Calibrating noise to sensitivity in private data analysis. In Theory of Cryptography Conference (TCC) (pp. 265-284). Springer. https://doi.org/10.1007/11681878_14.

Dwork, C., & Roth, A. (2014). The algorithmic foundations of differential privacy (Foundations and Trends in Theoretical Computer Science, Vol. 9). Now Publishers. https://doi.org/10.1561/0400000042.

Dwork, C., Rothblum, G. N., & Vadhan, S. (2010). Boosting and differential privacy. In Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS) (pp. 51-60). IEEE. https://doi.org/10.1109/FOCS.2010.12.

Erlingsson, U., Pihur, V., & Korolova, A. (2014). APPOR: Randomized aggregatable privacy-preserving ordinal response. In Proceedings of the 2014 ACM SIGSAC Conference on Computer and Communications Security (pp. 1054-1067). ACM. https://doi.org/10.1145/2660267.2660348.

European Commission and Government of Vietnam. (2020). EU-Vietnam free trade agreement, Annex 8B: Cross-border supply of services and data flows. https://trade.ec.europa.eu/access-to-markets/en/country/vietnam.

European Parliament and Council. (2016). Regulation (EU) 2016/679 (General Data Protection Regulation), Article 25: Data protection by design and by default. https://eur-lex.europa.eu/eli/reg/2016/679/oj.

Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis (3rd ed.). CRC Press. https://doi.org/10.1201/b16018.

Ghosh, A., Roughgarden, T., & Sundararajan, M. (2012). Universally utility-maximizing privacy mechanisms. SIAM Journal on Computing, 41(6), 1673-1693. https://doi.org/10.1137/09076828X.

IACR. (2025). Finite-field differential privacy for categorical data (Cryptology ePrint Archive Paper No. 2025/763). https://eprint.iacr.org/2025/763.

Ishai, Y., Kushilevitz, E., Ostrovsky, R., & Sahai, A. (2006). Cryptography from anonymity. In 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06) (pp. 239-248). IEEE. https://doi.org/10.1109/focs.2006.25.

Kairouz, P., Oh, S., & Viswanath, P. (2015). The composition theorem for differential privacy. In Proceedings of the 32nd International Conference on Machine Learning (ICML) (pp. 1376-1385). https://proceedings.mlr.press/v37/kairouz15.html.

Ninh, L. K. (2024). Self-selection out of formal credit markets: Evidence from rural Vietnam. Asian Journal of Economics and Banking, 9(1), 105-125. https://doi.org/10.1108/AJEB-02-2023-0011.

Liu, Y., Chen, Y.-M., Chen, L., & Wang, T.-Z. (2021). Fuzzy Bayesian knowledge tracing. IEEE Transactions on Fuzzy Systems, 29(10), 3131-3143. https://doi.org/10.1109/TFUZZ.2021.3083177.

Mironov, I. (2017). Rényi differential privacy. In IEEE 30th Computer Security Foundations Symposium (CSF) (pp. 263-275). IEEE. https://doi.org/10.1109/CSF.2017.11.

Murrar, A., Asfour, B., & Paz, V. (2024). Banking sector and economic growth in the digital transformation era: insights from maximum likelihood and Bayesian structural equation modeling. Asian Journal of Economics and Banking, 8(3), 335-353. https://doi.org/10.1108/AJEB-12-2023-0122.

National Institute of Standards and Technology. (2024a). FIPS 203: Module-lattice-based key-encapsulation mechanism standard (NIST Technical Report). https://doi.org/10.6028/NIST.FIPS.203.

National Institute of Standards and Technology. (2024b). FIPS 204: Module-lattice-based digital signature standard (NIST Technical Report). https://doi.org/10.6028/NIST.FIPS.204.

State Bank of Vietnam. (2020). Circular no. 09/2020/tt-nhnn on confidentiality of customer information at credit institutions. https://thuvienphapluat.vn/van-ban/Doanh-nghi/Thong-tu-09-2020-TT-NHNN-bao-mat-thong-tin-khach-hang-to-chuc-tin-dung-438939.aspx.

Sultana, R., Ghosh, R., & Sen, K. K. (2021). Impact of COVID-19 pandemic on financial reporting and disclosure practices: empirical evidence from Bangladesh. Asian Journal of Economics and Banking, 6(1), 122-139. https://doi.org/10.1108/AJEB-09-2021-0110.

Triastcyn, A., & Faltings, B. (2020). Bayesian differential privacy for machine learning (arXiv:2001.06244). arXiv. https://doi.org/10.48550/arXiv.2001.06244.

Warner, S. L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. Journal of the American Statistical Association, 60(309), 63-69. https://doi.org/10.1080/01621459.1965.10480775.

Zhu, T., Li, G., Zhou, W., & Yu, P. S. (2017). Differentially private data publishing and analysis: A survey. IEEE Transactions on Knowledge and Data Engineering, 29(8), 1619-1638. https://doi.org/10.1109/tkde.2017.2697856.