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Due to increasing concerns of data privacy, databases are being encryptedbefore they are stored on an untrusted server. To enable search operations onthe encrypted data, searchable encryption techniques have been proposed.Representative schemes use order-preserving encryption (OPE) for supportingefficient Boolean queries on encrypted databases. Yet, recent works showed thepossibility of inferring plaintext data from OPE-encrypted databases, merelyusing the order-preserving constraints, or combined with an auxiliary plaintextdataset with similar frequency distribution. So far, the effectiveness of suchattacks is limited to single-dimensional dense data (most values from thedomain are encrypted), but it remains challenging to achieve it onhigh-dimensional datasets (e.g., spatial data) which are often sparse innature. In this paper, for the first time, we study data inference attacks onmulti-dimensional encrypted databases (with 2-D as a special case). Weformulate it as a 2-D order-preserving matching problem and explore bothunweighted and weighted cases, where the former maximizes the number of pointsmatched using only order information and the latter further considers pointswith similar frequencies. We prove that the problem is NP-hard, and thenpropose a greedy algorithm, along with a polynomial-time algorithm withapproximation guarantees. Experimental results on synthetic and real-worlddatasets show that the data recovery rate is significantly enhanced comparedwith the previous 1-D matching algorithm.

Data Inference from Encrypted Databases: A Multi-dimensional Order-Preserving Matching Approach