Distribution-Agnostic Database De-Anonymization Under Synchronization Errors

There has recently been an increased scientific in-terest in the de-anonymization of users in anonymized databases containing user-level microdata via multifarious matching strate-gies utilizing publicly available correlated data. Existing literature has either emphasized practical aspects where underlying data distribution is not required, with limited or no theoret-ical 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.