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RISK: Efficiently processing rich spatial-keyword queries on encrypted geo-textual data

Zhen Lv, Cong Cao, Hongwei Huo, Jiangtao Cui, Yanguo Peng, Hui Li, Yingfan Liu

TL;DR

RISK is a model for rich spatial-keyword queries on encrypted geo-textual data that seamlessly supports both secure range and k-nearest neighbor queries, is provably secure under IND-CKA2 model, and extensible to multi-party scenarios and dynamic updates.

Abstract

Symmetric searchable encryption (SSE) for geo-textual data has attracted significant attention. However, existing schemes rely on task-specific, incompatible indices for isolated specific secure queries (e.g., range or k-nearest neighbor spatial-keyword queries), limiting practicality due to prohibitive multi-index overhead. To address this, we propose RISK, a model for rich spatial-keyword queries on encrypted geo-textual data. In a textual-first-then-spatial manner, RISK is built on a novel k-nearest neighbor quadtree (kQ-tree) that embeds representative and regional nearest neighbors, with the kQ-tree further encrypted using standard cryptographic tools (e.g., keyed hash functions and symmetric encryption). Overall, RISK seamlessly supports both secure range and k-nearest neighbor queries, is provably secure under IND-CKA2 model, and extensible to multi-party scenarios and dynamic updates. Experiments on three real-world and one synthetic datasets show that RISK outperforms state-of-the-art methods by at least 0.5 and 4 orders of magnitude in response time for 1% range queries and 10-nearest neighbor queries, respectively.

RISK: Efficiently processing rich spatial-keyword queries on encrypted geo-textual data

TL;DR

RISK is a model for rich spatial-keyword queries on encrypted geo-textual data that seamlessly supports both secure range and k-nearest neighbor queries, is provably secure under IND-CKA2 model, and extensible to multi-party scenarios and dynamic updates.

Abstract

Symmetric searchable encryption (SSE) for geo-textual data has attracted significant attention. However, existing schemes rely on task-specific, incompatible indices for isolated specific secure queries (e.g., range or k-nearest neighbor spatial-keyword queries), limiting practicality due to prohibitive multi-index overhead. To address this, we propose RISK, a model for rich spatial-keyword queries on encrypted geo-textual data. In a textual-first-then-spatial manner, RISK is built on a novel k-nearest neighbor quadtree (kQ-tree) that embeds representative and regional nearest neighbors, with the kQ-tree further encrypted using standard cryptographic tools (e.g., keyed hash functions and symmetric encryption). Overall, RISK seamlessly supports both secure range and k-nearest neighbor queries, is provably secure under IND-CKA2 model, and extensible to multi-party scenarios and dynamic updates. Experiments on three real-world and one synthetic datasets show that RISK outperforms state-of-the-art methods by at least 0.5 and 4 orders of magnitude in response time for 1% range queries and 10-nearest neighbor queries, respectively.
Paper Structure (30 sections, 1 theorem, 23 equations, 10 figures, 2 tables, 5 algorithms)

This paper contains 30 sections, 1 theorem, 23 equations, 10 figures, 2 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Progress in range spatial-keyword query
  4. Progress in k-nearest neighbor spatial-keyword query
  5. Summary of related works
  6. System model and preliminaries
  7. System model and problem formalization
  8. Threat and security models
  9. Preliminaries
  10. Secure hybrid index
  11. Construction of kNN quadtree
  12. Construction of secure kNN quadtree
  13. Construction of RISK
  14. Setup
  15. IndexGen
  16. ...and 15 more sections

Key Result

Theorem 1

RISK is IND-CKA2 $(\mathcal{L}_1,\mathcal{L}_2)$-secure in the random oracle model. For any probabilistic polynomial-time adversary $\mathcal{A}$ attempting to break RISK, its advantage is bounded by Herein, $\mathsf{Game}_{\mathcal{R}}$ and $\mathsf{Game}_{\mathcal{S}}$ denote the real and simulated games, respectively, and $\epsilon$ is an adjustable polynomial expansion factor for range querie

Figures (10)

  • Figure 1: Application scenarios for range and $2$NN spatial-keyword queries.
  • Figure 2: The architecture of RISK. Here, the dotted arrows indicate off-line processes, and the continuous arrows are on-line processes which directly affects query time and is therefore critical to user experience. Thus, RISK mainly aims at reducing on-line time.
  • Figure 3: Generic indexing concept ($k_{\max}=2$ and $d=3$). Virtual nodes (i.e., inner nodes), which only store structural semantics, are denoted by circles; real nodes (i.e., leaf nodes), which store objects, are represented by diamonds. All light blue numbers in the cells are unique identifiers, identical to the path of their corresponding nodes.
  • Figure 4: An example for generating trapdoors for RISK. Here, in the left region, the red circle denotes a RSK query $q_r$ and the object $q_k$ colored by red dot is the center for both NSK and kSK queries. Here, $k=2$ is for kSK query. For both regions, the patterned, light-colored, and dark-colored cells indicate touched cells and nodes for RSK, NSK, and kSK queries, respectively.
  • Figure 5: The parameter tuning results for RISK.
  • ...and 5 more figures

Theorems & Definitions (5)

  • Definition 1: Secure range spatial-keyword query problem
  • Definition 2: Secure k-nearest neighbor spatial-keyword query problem
  • Definition 3: IND-CKA2 security
  • Theorem 1: IND-CKA2 security for RISK
  • Proof 1