Seeded Database Matching under Noisy Column Repetitions

The re-identification or de-anonymization of users from anonymized data through matching with publicly-available correlated user data has raised privacy concerns, leading to the complementary measure of obfuscation in addition to anonymization. Recent research provides a fundamental understanding of the conditions under which privacy attacks are successful, either in the presence of obfuscation or synchronization errors stemming from the sampling of time-indexed databases. This paper presents a unified framework considering both obfuscation and synchronization errors and investigates the matching of databases under noisy column repetitions. By devising replica detection and seeded deletion detection algorithms, and using information-theoretic tools, sufficient conditions for successful matching are derived. It is shown that a seed size logarithmic in the row size is enough to guarantee the detection of all deleted columns. It is also proved that this sufficient condition is necessary, thus characterizing the database matching capacity of database matching under noisy column repetitions and providing insights on privacy-preserving publication of anonymized and obfuscated time-indexed data.