Database Matching Under Column Deletions

Abstract

Database de-anonymization typically involves matching an anonymized database with correlated publicly available data. Existing research focuses either on practical aspects without requiring knowledge of the data distribution yet provides limited guarantees, or on theoretical aspects assuming known distributions. This paper aims to bridge these two approaches, offering theoretical guarantees for database de-anonymization under synchronization errors and obfuscation without prior knowledge of data distribution. Using a modified replica detection algorithm and a new seeded deletion detection algorithm, we establish sufficient conditions on the database growth rate for successful matching, demonstrating a double-logarithmic seed size relative to row size is sufficient for detecting deletions in the database. Importantly, our findings indicate that these sufficient de-anonymization conditions are tight and are the same as in the distribution-aware setting, avoiding asymptotic performance loss due to unknown distributions. Finally, we evaluate the performance of our proposed algorithms through simulations, confirming their effectiveness in more practical, non-asymptotic, scenarios.

Seeded Database Matching Under Noisy Column Repetitions

“…We use the following definitions, some of which are adapted from [8], [10], [11] to formalize our problem. Definition 1.…”

“…Recently, matching correlated pairs of databases have been investigated from an information-theoretic point of view in [8]- [10]. In [9], Cullina et al proposed cycle mutual information as a metric of correlation and derived sufficient and necessary conditions for successful matching, with the performance criterion being the probability of error for all users.…”

“…In [10], motivated by the synchronization errors in the sampling of time-series datasets, we investigated the matching of two databases of the same number of users (rows), but of different number of attributes (columns), unlike [8] where the row and the column sizes of the databases are the same. In our model, one of the databases suffers from random column deletions, where the deletion indices are only partially and probabilistically available at the matching side.…”

“…In a companion paper [11], we investigate database matching under noiseless column repetition, a non-trivial extension of [10] to column repetitions. Under this generalized model, we devise a histogram-based repetition detection algorithm and derive an improved achievable rate.…”

“…of independent noise on the database entries. The presence of noise prevents us from using the histogram-based repetition detection algorithm of [11] and unlike [11] requires seed users whose identities are known in both databases [10], [12], [13]. Under these assumptions, we devise two algorithms: one for deletion detection and the other for replica detection.…”