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We show that the problem of reconstructing encrypted databases from access pattern leakage is closely related to statistical learning theory. This new viewpoint enables us to develop broader attacks that are supported by streamlined performance analyses. First, we address the problem of ε-approximate database reconstruction (ε-ADR) from range query leakage, giving attacks whose query cost scales only with the relative error ε, and is independent of the size of the database, or the number N of possible values of data items. This already goes significantly beyond the state-of-the-art for such attacks, as represented by Kellaris et al. (ACM CCS 2016) and Lacharité et al. (IEEE S&P 2018). We also study the new problem of ε-approximate order reconstruction (ε-AOR), where the adversary is tasked with reconstructing the order of records, except for records whose values are approximately equal. We show that as few …