Optimal Disclosure Limitation Strategy in Statistical Databases: Deterring Tracker Attacks through Additive Noise

Abstract Disclosure limitation methods transform statistical databases to protect confidentiality, a practical concern of statistical agencies. A statistical database responds to queries with aggregate statistics. The database administrator should maximize legitimate data access while keeping the risk of disclosure below an acceptable level. Legitimate users seek statistical information, generally in aggregate form; malicious users—the data snoopers—attempt to infer confidential information about an individual data subject. Tracker attacks are of special concern for databases accessed online. This article derives optimal disclosure limitation strategies under tracker attacks for the important case of data masking through additive noise. Operational measures of the utility of data access and of disclosure risk are developed. The utility of data access is expressed so that trade-offs can be made between the quantity and the quality of data to be released. Application is made to Ohio data from the 1990 census. The article derives conditions under which an attack by a data snooper is better thwarted by a combination of query restriction and data masking than by either disclosure limitation method separately. Data masking by independent noise addition and data perturbation are considered as extreme cases in the continuum of data masking using positively correlated additive noise. Optimal strategies are established for the data snooper. Circumstances are determined under which adding autocorrelated noise is preferable to using existing methods of either independent noise addition or data perturbation. Both moving average and autoregressive noise addition are considered.