# Exact zCDP Characterizations for Fundamental Differentially Private Mechanisms

arXiv: https://arxiv.org/abs/2510.25746 · HTML: https://mlsanity.com/paper/2510.25746/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2025.

## Built on by (most cited first, 2 of 2)

- [DPrivBench: Benchmarking LLMs' Reasoning for Differential Privacy](https://mlsanity.com/paper/2604.15851/) (2026)
- [Tight End-to-End Accounting for Differentially Private Synthetic Data](https://mlsanity.com/paper/2610.17249/) (2026)

## Abstract (arXiv)

Zero-concentrated differential privacy (zCDP) is a variant of differential privacy (DP) that is widely used partly thanks to its nice composition property. While a tight conversion from ε-DP to zCDP exists for the worst-case mechanism, many common algorithms satisfy stronger guarantees. In this work, we derive tight zCDP characterizations for several fundamental mechanisms. We prove that the tight zCDP bound for the ε-DP Laplace mechanism is exactly ε + e-ε - 1, confirming a recent conjecture by Wang (2022). We further provide tight bounds for the discrete Laplace mechanism, k-Randomized Response (for k ≤ 6), and RAPPOR. Lastly, we also provide a tight zCDP bound for the worst case bounded range mechanism.