Exact zCDP Characterizations for Fundamental Differentially Private Mechanisms
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915585588199424 |
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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 |
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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 |