  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, in the form of database
matching, are successful in the presence of obfuscation. Motivated by
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
entry repetitions. By investigating different structures for the repetition
pattern, replica detection and seeded deletion detection algorithms are devised
and sufficient and necessary conditions for successful matching are derived.
Finally, the impacts of some variations of the underlying assumptions, such as
the adversarial deletion model, seedless database matching, and zero-rate
regime, on the results are discussed. Overall, our results provide insights
into the privacy-preserving publication of anonymized and obfuscated
time-indexed data as well as the closely related problem of the capacity of
synchronization channels.
