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In this work, we present the first database reconstruction attacks against response-hiding private range search schemes on encrypted databases of arbitrary dimensions. Falzon et al. (VLDB 2022) present a number of range-supporting schemes on arbitrary dimensions exhibiting different security and efficiency trade-offs. Additionally, they characterize a form of leakage, structure pattern leakage, also present in many one-dimensional schemes e.g., Demertzis et al. (SIGMOD 2016) and Faber et al. (ESORICS 2015). We present the first systematic study of this leakage and attack a broad collection of schemes, including schemes that allow the responses to contain false-positives (often considered the gold standard in security). We characterize the information theoretic limitations of a passive persistent adversary. Our work shows that for range queries, structure pattern leakage can be as vulnerable to attacks as access pattern leakage. We give a comprehensive evaluation of our attacks with a complexity analysis, a prototype implementation, and an experimental assessment on real-world datasets. 

We present ARQ, a systematic framework for creating cryptographic schemes that handle range aggregate queries (sum, minimum, median, and mode) over encrypted datasets. Our framework does not rely on trusted hardware or specialized cryptographic primitives such as property-preserving or homomorphic encryption. Instead, ARQ unifies structures from the plaintext data management community with existing structured encryption primitives. We prove how such combinations yield efficient (and secure) constructions in the encrypted setting. We also propose a series of domain reduction techniques that can improve the space efficiency of our schemes against sparse datasets at the cost of small leakage. As part of this work, we designed and implemented a new, open-source, encrypted search library called Arca and implemented the ARQ framework using this library in order to evaluate ARQ’s practicality. Our experiments on real-world datasets demonstrate the efficiency of the schemes derived from ARQ in comparison to prior work. 

In the past few years, we have seen multiple attacks on one-dimensional databases that support range queries. These attacks achieve full database reconstruction by exploiting access pattern leakage along with known query distribution or search pattern leakage. We are the first to go beyond one dimension, exploring this threat in two dimensions. We unveil an intrinsic limitation of reconstruction attacks by showing that there can be an exponential number of distinct databases that produce equivalent leakage. Next, we present a full database reconstruction attack. Our algorithm runs in polynomial time and returns a poly-size encoding of all databases consistent with the given leakage profile. We implement our algorithm and observe real-world databases that admit a large number of equivalent databases, which aligns with our theoretical results.