On Sampling, Anonymization, and Differential Privacy: Or, k-Anonymization Meets Differential Privacy

TL;DR

This paper demonstrates that combining k-anonymization with random sampling can achieve differential privacy guarantees, offering a practical alternative to traditional output perturbation methods in privacy-preserving data analysis.

Contribution

It establishes that safe k-anonymization preceded by random sampling satisfies differential privacy and explores how sampling amplifies privacy protection and affects composition.

Findings

Sampling creates uncertainty aiding privacy guarantees.

Sampling can amplify privacy budgets in differentially-private algorithms.

Uncertainty-based privacy notions may not compose well.

Abstract

This paper aims at answering the following two questions in privacy-preserving data analysis and publishing: What formal privacy guarantee (if any) does $k$-anonymization provide? How to benefit from the adversary's uncertainty about the data? We have found that random sampling provides a connection that helps answer these two questions, as sampling can create uncertainty. The main result of the paper is that $k$-anonymization, when done "safely", and when preceded with a random sampling step, satisfies $(\epsilon,\delta)$-differential privacy with reasonable parameters. This result illustrates that "hiding in a crowd of $k$" indeed offers some privacy guarantees. This result also suggests an alternative approach to output perturbation for satisfying differential privacy: namely, adding a random sampling step in the beginning and pruning results that are too sensitive to change of a single tuple. Regarding the second question, we provide both positive and negative results. On the positive side, we show that adding a random-sampling pre-processing step to a differentially-private algorithm can greatly amplify the level of privacy protection. Hence, when given a dataset resulted from sampling, one can utilize a much large privacy budget. On the negative side, any privacy notion that takes advantage of the adversary's uncertainty likely does not compose. We discuss what these results imply in practice.