Paper 2017/701

Improved Reconstruction Attacks on Encrypted Data Using Range Query Leakage

Marie-Sarah Lacharité, Brice Minaud, and Kenneth G. Paterson

Abstract

We analyse the security of database encryption schemes supporting range queries against persistent adversaries. The bulk of our work applies to a generic setting, where the adversary's view is limited to the set of records matched by each query (known as access pattern leakage). We also consider a more specific setting where certain rank information is also leaked. The latter is inherent to multiple recent encryption schemes supporting range queries, including Kerschbaum's FH-OPE scheme (CCS 2015), Lewi and Wu's order-revealing encryption scheme (CCS 2016), and the recently proposed Arx scheme of Poddar et al. (IACR eprint 2016/568, 2016/591). We provide three attacks. First, we consider full reconstruction, which aims to recover the value of every record, fully negating encryption. We show that for dense datasets, full reconstruction is possible within an expected number of queries $N \log N + O(N)$, where $N$ is the number of distinct plaintext values. This directly improves on a $O(N^2 \log N)$ bound in the same setting by Kellaris et al. (CCS 2016). We also provide very efficient, data-optimal algorithms that succeed with the minimum possible number of queries (in a strong, information theoretical sense), and prove a matching data lower bound for the number of queries required. Second, we present an approximate reconstruction attack recovering all plaintext values in a dense dataset within a constant ratio of error (such as a 5% error), requiring the access pattern leakage of only $O(N)$ queries. We also prove a matching lower bound. Third, we devise an attack in the common setting where the adversary has access to an auxiliary distribution for the target dataset. This third attack proves highly effective on age data from real-world medical data sets. In our experiments, observing only 25 queries was sufficient to reconstruct a majority of records to within 5 years. In combination, our attacks show that current approaches to enabling range queries offer little security when the threat model goes beyond snapshot attacks to include a persistent server-side adversary.