Effective query recovery attacks against Searchable Symmetric Encryption (SSE) schemes typically rely on auxiliary ground-truth information about the queries or dataset. Query recovery is also possible under the weaker statistical auxiliary information assumption, although statistical-based attacks achieve lower accuracy and are not considered a serious threat. In this work we present IHOP, a statistical-based query recovery attack that formulates query recovery as a quadratic optimization problem and reaches a solution by iterating over linear assignment problems. We perform an extensive evaluation with five real datasets, and show that IHOP outperforms all other statistical-based query recovery attacks under different parameter and leakage configurations, including the case where the client uses some access-pattern obfuscation defenses. In some cases, our attack achieves almost perfect query recovery accuracy. Finally, we use IHOP in a frequency-only leakage setting where the client's queries are correlated, and show that our attack can exploit query dependencies even when PANCAKE, a recent frequency-hiding defense by Grubbs et al., is applied. Our findings indicate that statistical query recovery attacks pose a severe threat to privacy-preserving SSE schemes.
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