2012/07/30 by Jonathan Ullman, Ullman, Jonathan · 1 citation
Computer Science · #Complexity and Algorithms in Graphs #Computational Complexity (cs.CC) #Cryptography and Data Security #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Privacy-Preserving Technologies in Data
paper · pdf · doi:10.48550/arxiv.1207.6945
openalex publication_date 2012/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A central problem in differentially private data analysis is how to design efficient algorithms capable of answering large numbers of counting queries on a sensitive database. Counting queries of the form "What fraction of individual records in the database satisfy the property q?" We prove that if one-way functions exist, then there is no algorithm that takes as input a database D in (0,1d)n, and k = n2+o(1) arbitrary efficiently computable counting queries, runs in time poly(d, n), and returns an approximate answer to each query, while satisfying differential privacy. We also consider the complexity of answering "simple" counting queries, and make some progress in this direction by showing that the above result holds even when we require that the queries are computable by constant depth (AC-0) circuits. Our result is almost tight in the sense that nearly n2 counting queries can be answered efficiently while satisfying differential privacy. Moreover, super-polynomially many queries can be answered in exponential time. We prove our results by extending the connection between differentially private counting query release and cryptographic traitor-tracing schemes to the setting where the queries are given to the sanitizer as input, and by constructing a traitor-tracing scheme that is secure in this setting.