Exact zCDP Characterizations for Fundamental Differentially Private Mechanisms

Fuente: arXiv
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Main Authors: Harrison, Charlie, Manurangsi, Pasin
Format: Preprint
Published: 2025
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author Harrison, Charlie
Manurangsi, Pasin
author_facet Harrison, Charlie
Manurangsi, Pasin
contents 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 $k \leq 6$), and RAPPOR. Lastly, we also provide a tight zCDP bound for the worst case bounded range mechanism.
format Preprint
id arxiv_https___arxiv_org_abs_2510_25746
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Exact zCDP Characterizations for Fundamental Differentially Private Mechanisms
Harrison, Charlie
Manurangsi, Pasin
Cryptography and Security
Data Structures and Algorithms
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 $k \leq 6$), and RAPPOR. Lastly, we also provide a tight zCDP bound for the worst case bounded range mechanism.
title Exact zCDP Characterizations for Fundamental Differentially Private Mechanisms
topic Cryptography and Security
Data Structures and Algorithms
url https://arxiv.org/abs/2510.25746