On the Privacy and Utility Properties of Triple Matrix-Masking

Privacy protection is an important requirement in many statistical studies. A recently proposed data collection method, triple matrix-masking, retains exact summary statistics without exposing the raw data at any point in the process. In this paper, we provide theoretical formulation and proofs showing that a modified version of the procedure is strong collection obfuscating: no party in the data collection process is able to gain knowledge of the individual level data, even with some partially masked data information in addition to the publicly published data. This provides a theoretical foundation for the usage of such a procedure to collect masked data that allows exact statistical inference for linear models, while preserving a well-defined notion of privacy protection for each individual participant in the study. This paper fits into a line of work tackling the problem of how to create useful synthetic data without having a trustworthy data aggregator. We achieve this by splitting the trust between two parties, the “masking service provider” and the “data collector.”