{"ID":2848705,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.25746","arxiv_id":"2510.25746","title":"Exact zCDP Characterizations for Fundamental Differentially Private Mechanisms","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2510.25746","url_pdf":"https://arxiv.org/pdf/2510.25746v1","authors":"[\"Charlie Harrison\",\"Pasin Manurangsi\"]","published":"2025-10-29T17:48:16Z","proceeding":"cs.CR","tasks":"[\"cs.CR\",\"cs.DS\"]","methods":"[]","has_code":false}