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Quasi-identifier-based deidentification techniques (QI-deidentification) are widely used in practice, including k-anonymity, ℓ-diversity, and t-closeness. We present three new attacks on QI-deidentification: two theoretical attacks and one practical attack on a real dataset. In contrast to prior work, our theoretical attacks work even if every attribute is a quasi-identifier. Hence, they apply to k-anonymity, ℓ-diversity, t-closeness, and most other QI-deidentification techniques. First, we introduce a new class of privacy attacks called downcoding attacks, and prove that every QI-deidentification scheme is vulnerable to downcoding attacks if it is minimal and hierarchical. Second, we convert the downcoding attacks into powerful predicate singling-out (PSO) attacks, which were recently proposed as a way to demonstrate that a privacy mechanism fails to legally anonymize under Europe's General Data Protection Regulation. Third, we use this http URL to reidentify 3 students in a k-anonymized dataset published by EdX (and show thousands are potentially vulnerable), undermining EdX's claimed compliance with the Family Educational Rights and Privacy Act. The significance of this work is both scientific and political. Our theoretical attacks demonstrate that QI-deidentification may offer no protection even if every attribute is treated as a quasi-identifier. Our practical attack demonstrates that even deidentification experts acting in accordance with strict privacy regulations fail to prevent real-world reidentification. Together, they rebut a foundational tenet of QI-deidentification and challenge the actual arguments made to justify the continued use of k-anonymity and other QI-deidentification techniques.