A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
Random walks and an O*(n5) volume algorithm for convex bodies
Random Structures & Algorithms
Revealing information while preserving privacy
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Practical privacy: the SuLQ framework
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Smooth sensitivity and sampling in private data analysis
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
The price of privacy and the limits of LP decoding
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Privacy, accuracy, and consistency too: a holistic solution to contingency table release
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The boundary between privacy and utility in data publishing
VLDB '07 Proceedings of the 33rd international conference on Very large data bases
Mechanism Design via Differential Privacy
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
A learning theory approach to non-interactive database privacy
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Universally utility-maximizing privacy mechanisms
Proceedings of the forty-first annual ACM symposium on Theory of computing
Proceedings of the forty-first annual ACM symposium on Theory of computing
Differentially private recommender systems: building privacy into the net
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Differential privacy: a survey of results
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Our data, ourselves: privacy via distributed noise generation
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Calibrating noise to sensitivity in private data analysis
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Interactive privacy via the median mechanism
Proceedings of the forty-second ACM symposium on Theory of computing
Optimizing linear counting queries under differential privacy
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
A firm foundation for private data analysis
Communications of the ACM
Differential privacy and the fat-shattering dimension of linear queries
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Differentially private data release through multidimensional partitioning
SDM'10 Proceedings of the 7th VLDB conference on Secure data management
Boosting the accuracy of differentially private histograms through consistency
Proceedings of the VLDB Endowment
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
iReduct: differential privacy with reduced relative errors
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
Privately releasing conjunctions and the statistical query barrier
Proceedings of the forty-third annual ACM symposium on Theory of computing
Differentially private data release for data mining
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Proceedings of the 4th ACM workshop on Security and artificial intelligence
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Protocol to compute polygon intersection in STC model
ICICA'11 Proceedings of the Second international conference on Information Computing and Applications
The power of the dinur-nissim algorithm: breaking privacy of statistical and graph databases
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Unconditional differentially private mechanisms for linear queries
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Optimal private halfspace counting via discrepancy
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Lower bounds in differential privacy
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Iterative constructions and private data release
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Integrating historical noisy answers for improving data utility under differential privacy
Proceedings of the 15th International Conference on Extending Database Technology
The application of differential privacy to health data
Proceedings of the 2012 Joint EDBT/ICDT Workshops
Low-rank mechanism: optimizing batch queries under differential privacy
Proceedings of the VLDB Endowment
Distributed private heavy hitters
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Differentially private iterative synchronous consensus
Proceedings of the 2012 ACM workshop on Privacy in the electronic society
Security of random output perturbation for statistical databases
PSD'12 Proceedings of the 2012 international conference on Privacy in Statistical Databases
Is privacy compatible with truthfulness?
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Non-interactive differential privacy: a survey
Proceedings of the First International Workshop on Open Data
On optimal differentially private mechanisms for count-range queries
Proceedings of the 16th International Conference on Database Theory
Optimal error of query sets under the differentially-private matrix mechanism
Proceedings of the 16th International Conference on Database Theory
A learning theory approach to noninteractive database privacy
Journal of the ACM (JACM)
Practical differential privacy via grouping and smoothing
Proceedings of the VLDB Endowment
The geometry of differential privacy: the sparse and approximate cases
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Differential privacy for functions and functional data
The Journal of Machine Learning Research
A general framework for privacy preserving data publishing
Knowledge-Based Systems
Redrawing the boundaries on purchasing data from privacy-sensitive individuals
Proceedings of the 5th conference on Innovations in theoretical computer science
Understanding hierarchical methods for differentially private histograms
Proceedings of the VLDB Endowment
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We consider the noise complexity of differentially private mechanisms in the setting where the user asks d linear queries f:Rn - R non-adaptively. Here, the database is represented by a vector in R and proximity between databases is measured in the l1-metric. We show that the noise complexity is determined by two geometric parameters associated with the set of queries. We use this connection to give tight upper and lower bounds on the noise complexity for any d ≤ n. We show that for d random linear queries of sensitivity 1, it is necessary and sufficient to add l2-error Θ(min d√d/ε,d√(log (n/d))/ε) to achieve ε-differential privacy. Assuming the truth of a deep conjecture from convex geometry, known as the Hyperplane conjecture, we can extend our results to arbitrary linear queries giving nearly matching upper and lower bounds. Our bound translates to error $O(min d/ε,√(d log(n/d)/ε)) per answer. The best previous upper bound (Laplacian mechanism) gives a bound of O(min (d/ε,√n/ε)) per answer, while the best known lower bound was Ω(√d/ε). In contrast, our lower bound is strong enough to separate the concept of differential privacy from the notion of approximate differential privacy where an upper bound of O(√{d}/ε) can be achieved.