Distribution-Agnostic Database De-Anonymization Under Synchronization Errors

Abstract

There has recently been an increased scientific interest in the de-anonymization of users in anonymized databases containing user-level microdata via multifarious matching strategies utilizing publicly available correlated data. Existing literature has either emphasized practical aspects where underlying data distribution is not required, with limited or no theoretical guarantees, or theoretical aspects with the assumption of complete availability of underlying distributions. In this work, we take a step towards reconciling these two lines of work by providing theoretical guarantees for the de-anonymization of random correlated databases without prior knowledge of data distribution. Motivated by time-indexed microdata, we consider database de-anonymization under both synchronization errors (column repetitions) and obfuscation (noise). By modifying the previously used replica detection algorithm to accommodate for the unknown underlying distribution, proposing a new seeded deletion detection algorithm, and employing statistical and information-theoretic tools, we derive sufficient conditions on the database growth rate for successful matching. Our findings demonstrate that a double-logarithmic seed size relative to row size ensures successful deletion detection. More importantly, we show that the derived sufficient conditions are the same as in the distribution-aware setting, negating any asymptotic loss of performance due to unknown underlying distributions.