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The authors consider the power of "Linear reconstruction attacks" in statistical data privacy, showing that they can be applied to a much wider range of settings than previously understood. Linear attacks have been studied before [3, 6, 11, 1, 14] but have so far been applied only in settings with releases that are "Obviously" linear. Consider a database curator who manages a database of sensitive information but wants to release statistics about how a sensitive attribute (say, disease) in the database relates to some non-sensitive attributes (e.g., postal code, age, gender, etc). This setting is widely considered in the literature, partly since it arises with medical data.
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