Approximate Differential Privacy of the ℓ₂ Mechanism

2025/02/21 by Matthew Joseph, Joseph, Matthew, Alex Kulesza +3
Computer Science · Social Sciences · #Cryptography and Data Security #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Privacy, Security, and Data Protection #Privacy-Preserving Technologies in Data

paper · pdf · doi:10.48550/arxiv.2502.15929

openalex publication_date 2025/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the ℓ₂ mechanism for computing a d-dimensional statistic with bounded ℓ₂ sensitivity under approximate differential privacy. Across a range of privacy parameters, we find that the ℓ₂ mechanism obtains lower error than the Laplace and Gaussian mechanisms, matching the former at d=1 and approaching the latter as d → ∞.

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