TY - GEN

T1 - Differentially Private Sparse Vectors with Low Error, Optimal Space, and Fast Access

AU - Aumüller, Martin

AU - Lebeda, Christian Janos

AU - Pagh, Rasmus

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - algorithms

KW - differential privacy

KW - sparse vector

UR - http://www.scopus.com/inward/record.url?scp=85119327742&partnerID=8YFLogxK

U2 - 10.1145/3460120.3484735

DO - 10.1145/3460120.3484735

M3 - Article in proceedings

AN - SCOPUS:85119327742

T3 - Proceedings of the ACM Conference on Computer and Communications Security

SP - 1223

EP - 1236

BT - CCS 2021 - Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security

PB - Association for Computing Machinery

T2 - 27th ACM Annual Conference on Computer and Communication Security, CCS 2021

Y2 - 15 November 2021 through 19 November 2021

ER -