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

Thanh-Phong Lam

doi:10.63065/ajafe.2026.1.2.006

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.2026.1.2.006

Ngày nhận bài: 19/06/2026

Ngày nhận bài sửa: 12/08/2026

Ngày duyệt đăng: 18/08/2026

Email: limpaul.fin@gmail.com

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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

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Tài liệu tham khảo

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