Database Matching under Column Deletions

De-anonymizing user identities by matching various forms of user data available on the internet raises privacy concerns. A fundamental understanding of the privacy leakage in such scenarios requires a careful study of conditions under which correlated databases can be matched. Motivated by synchronization errors in time indexed databases, in this work, matching of random databases under random column deletion is investigated. Adapting tools from information theory, in particular ones developed for the deletion channel, conditions for database matching in the absence and presence of deletion location information are derived, showing that partial deletion information significantly increases the achievable database growth rate for successful matching. Furthermore, given a batch of correctly-matched rows, a deletion detection algorithm that provides partial deletion information is proposed and a lower bound on the algorithm's deletion detection probability in terms of the column size and the batch size is derived. The relationship between the database size and the batch size required to guarantee a given deletion detection probability using the proposed algorithm suggests that a batch size growing double-logarithmic with the row size is sufficient for a nonzero detection probability guarantee.