Parity-based inference control for multi-dimensional range sum queries

Abstract

This paper studies the inference control of multi-dimensional range (MDR) sum queries. We show that existing inference control methods are usually inefficient for MDR queries. We then consider parity-based inference control that restricts users to queries involving an even number of sensitive values. Such a restriction renders inferences significantly more difficult, because an even number is closed under addition and subtraction, whereas inferences target at one value. However, more sophisticated inferences are still possible with only even MDR queries. We show that the collection of all even MDR queries causes inferences if and only if a special collection of sum-two queries (that is, the summation of exactly two values) does so. The result leads to an inference control method with an improved computational complexity $\mathit{O}\mathrm{(}\mathit{m}\mathit{n}\mathrm{)}$ (over the previous result of $\mathit{O}\mathrm{(}{\mathit{m}}^2\mathit{n}\mathrm{)}$ ) for m MDR queries over n values. We show that no odd MDR queries can be answered without causing inferences. We show how to check non-MDR queries for inferences in linear time. We also show how to find large inference-free subsets of even MDR queries when they do cause inferences.