Leakage Perturbation is Not Enough: Breaking Structured Encryption Using Simulated Annealing

Structured encryption (STE) is a form of database encryption that enables searching directly over symmetrically encrypted “structured databases”. STE is known to be vulnerable to leakage-abuse attacks that allow data/query reconstruction given only some auxiliary information about the original database. Many existing countermeasures against leakage-abuse attacks perturb the leakage from STE schemes so as to render the attacks infeasible in practice. We present the first leakage-abuse attacks that achieve practically efficient and highly scalable query reconstruction against state-of-the-art STE schemes with perturbed leakage profiles while relying only no noisy co-occurrence pattern leakage and without making strong assumptions on the auxiliary information available to the adversary. Our attacks subvert the query privacy guarantees of STE schemes with differentially private access patterns (Chen et al., INFOCOM’18) and STE schemes built in a naturally efficient manner from volume-hiding encrypted multi-maps (Kamara and Moataz, Eurocrypt’19 and Patel et al., CCS’19). Many existing leakage-abuse attacks only work in a strong known-data model where the auxiliary information available to the adversary is either an exact replica of or a “noise-free” subset of the target database. Our attacks are the first to work in a weaker and more realistic inference model where the auxiliary information available to the adversary is sampled independently from but statistically close to the target database. Compared to (a handful of) existing inference attacks, our attacks make significantly relaxed assumptions about the nature of auxiliary information available to the adversary. Technically, our attacks exploit insufficiencies in existing leakage-perturbation techniques as well as novel observations surrounding inevitable system-wide leakage from efficient realizations of STE. We model the attacks as optimization problems with carefully designed objective functions that are maximized via simulated annealing. We demonstrate the practical effectiveness of our attacks via extensive experimentation over real-world databases. Our attacks achieve up to 90% query reconstruction against STE implementations using recommended security parameters, with 5x greater scalability than any existing attack exploiting access pattern leakage.