Privacy-Preserving k-Nearest Neighbour Query on Outsourced Database

Abstract

Cloud computing brought a shift from the traditional client-server model to DataBase as a Service (DBaaS), where the data owner outsources her database as well as the data management function to the cloud service provider. Although cloud services relieve the clients from the data management burdens, a significant concern about the data privacy remains. In this work, we focus on privacy-preserving k-nearest neighbour (k-NN) query, and provide the first sublinear solution (with preprocessing) with computational complexity $\tilde{O}(k\text {log}^4n)$ in the honest-but-curious adversarial setting. Our constructions use the data structure called kd-tree to achieve sublinear query complexity. In order to protect data access patterns, garbled circuits are used to simulate Oblivious RAM (ORAM) for accessing data in the kd-tree. Compared to the existing solutions, our scheme imposes little overhead on both the data owner and the querying client.

This work was partially done during R.X.’s internship at I$^2$R.

This work was partially done when K.M. was with IMI, Kyushu University.

This work was partially done when Y.Y. was with I$^2$R.

This research was supported by JST CREST.

Appendices

Appendix

A Toy Example of kd-tree Construction and Iterative NN Query Algorithm

We provide a toy example for constructing a kd-tree and use it to iteratively query the nearest neighbour of a point.

We take 2D points as an example for illustrating how to construct a kd-tree from a static dataset. The dataset contains 10 2D points $(p_0,\ldots ,p_9)$. See Fig. 3a for the geometric display of the dataset. Refer to Fig. 3b for the illustration. Figure 3c shows the representation of the kd-tree as a binary tree.

Fig. 3.

Construction of kd-tree.

We use the toy example to explain how the iterative NN query algorithm works.

Fig. 4.

Iterative NN query algorithm using kd-tree.

Figure 4a illustrates the dataset and the query point Q. Let guess be the estimation for the nearest neighbour, S be the stack used in the algorithm, curr is the current point we are visiting. We also use p[r] to denote that the point p is a return point. See Fig. 4b for the change of the stack elements during the whole query processing.

B Oblivious Protocol for NN Query

Protocol 1 (see below) is our main protocol for the oblivious nearest neighbour query problem. This protocol is run between two non-colluding cloud servers. We defer its detailed explanation to the full version of this paper.

C Oblivious Bounded Priority Queue

The basic unit of storage on the ORAM is called node. Each node is constructed as $node := (id, label, key, lid, llabel, rid, rlabel,)$ where “id” and “label” are the identity of the node and the leaf label in the ORAM tree, “key” is the priority of the node, “lid”, “llabel” are the identity and the leaf label of its left child, and “rid” and “rlabel” for the right child respectively. From Protocol 2 (see below) we can observe that for each Con_Dequeue_And_Enqueue() operation we have $3\log k$ ORAM operation, and each ORAM operation can be simulated using garbled circuits with complexity $\tilde{O}(\log ^3 k)$. Therefore, one oblivious such operation has complexity $\tilde{O}(\log ^4 k)$.