Differentially Private Sparse Vectors with Low Error, Optimal Space, and Fast Access
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- Differentially Private Sparse Vectors with Low Error, Optimal Space, and Fast Access
Submitted manuscript, 793 KB, PDF document
Representing a sparse histogram, or more generally a sparse vector, is a fundamental task in differential privacy. An ideal solution would use space close to information-theoretical lower bounds, have an error distribution that depends optimally on the desired privacy level, and allow fast random access to entries in the vector. However, existing approaches have only achieved two of these three goals. In this paper we introduce the Approximate Laplace Projection (ALP) mechanism for approximating k-sparse vectors. This mechanism is shown to simultaneously have information-theoretically optimal space (up to constant factors), fast access to vector entries, and error of the same magnitude as the Laplace-mechanism applied to dense vectors. A key new technique is a unary representation of small integers, which we show to be robust against "randomized response'' noise. This representation is combined with hashing, in the spirit of Bloom filters, to obtain a space-efficient, differentially private representation. Our theoretical performance bounds are complemented by simulations which show that the constant factors on the main performance parameters are quite small, suggesting practicality of the technique.
Original language | English |
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Title of host publication | CCS 2021 - Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security |
Publisher | Association for Computing Machinery |
Publication date | 2021 |
Pages | 1223-1236 |
ISBN (Electronic) | 9781450384544 |
DOIs | |
Publication status | Published - 2021 |
Event | 27th ACM Annual Conference on Computer and Communication Security, CCS 2021 - Virtual, Online, Korea, Republic of Duration: 15 Nov 2021 → 19 Nov 2021 |
Conference
Conference | 27th ACM Annual Conference on Computer and Communication Security, CCS 2021 |
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Land | Korea, Republic of |
By | Virtual, Online |
Periode | 15/11/2021 → 19/11/2021 |
Sponsor | ACM Special Interest Group on Security, Audit and Control (ACM SIGSAC), Korea Institute of Information Security and Cryptology (KIISC) |
Series | Proceedings of the ACM Conference on Computer and Communications Security |
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ISSN | 1543-7221 |
- algorithms, differential privacy, sparse vector
Research areas
ID: 301141144