Paper 2020/1531 Original: eprint.iacr.org/2020/1531 ↗

Reconstructing with Less: Leakage Abuse Attacks in Two-Dimensions

Abstract

Access and search pattern leakage from range queries are detrimental to the security of encrypted databases, as evidenced by a large body of work on efficient attacks that reconstruct one-dimensional databases. Recently, the first attack from 2D range queries showed that higher-dimensional databases are also in danger. This attack requires complete information for reconstruction. In this paper, we develop reconstructions that require less information. We present an order reconstruction attack that only depends on access pattern leakage, and empirically show that the order allows the attacker to infer the geometry of the underlying data. Notably, this attack also achieves full database reconstruction when the 1D horizontal and vertical projections of the points are dense. We also give an approximate database reconstruction attack that is distribution-agnostic and works with any subset of the possible search pattern, given the order of the database. Finally, we show how knowledge of auxiliary information such as the centroid of a related dataset allows to improve the reconstruction. We support our results with formal analysis and experiments on real-world databases and queries drawn from various distributions.