A Hybrid Technique for Private Location-Based Queries with

Database Protection

Gabriel Ghinita1 Panos Kalnis2

Murat Kantarcioglu3 Elisa Bertino1

1 Purdue University2 KAUST University

3 UT Dallas

3

Location-Based Services (LBS) LBS users

Mobile devices with GPS capabilities

Spatial Queries E.g., NN Queries Location server is NOT trusted

“Find closest hospital to my present location”

Problem Statement:

How to protect the

identity and location

of the query source?

4

Spatial Cloaking Privacy through Cloaking Regions (CRs)

Spatial Anonymity (e.g., CliqueCloak, Casper) Spatial Diversity (PROBE)

6

Private Information Retrieval (PIR)

Computationally hard to find i from q(i) Bob can easily find Xi from r (trap-door)

7

PIR Protocol for Binary Data

0 1 01

1 1 01

0 1 01

0 1 11

a

b

Get X10

a=2, b=3, N=35

QNR={3,12,13,17,27,33}

QR={1,4,9,11,16,29}

4 16 17 33

QNR

z 4

z 3

z 2

z 1

z2=QNR => X10=1

z2=QR => X10=0

4

1)1(4

jjiji yXz

[KO97 ]E. Kushilevitz and R. Ostrovsky. Replication is NOT needed: Single database, computationally-private

information retrieval. In IEEE Symposium on Foundations of Computer Science, pages 364–373, 1997.

X10

27

3

27

16

8

Approximate Nearest Neighbor

Data organized as a square matrix Each column corresponds to index leaf An entire leaf is retrieved – the closest to the user

p4 p6

p5 p8

p1

p2

p7 p9 p3u

9

Motivation Spatial Cloaking

Cheap, but vulnerable

PIR Secure, but expensive

Severe disclosure of POI information O(|D|), O(√|D|), respectively

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Hybrid Approach Overview

Apply PIR to a dynamic window Hide enclosure relationship Minimize leaf fragmentation

Dataspace

CR

POI Index

a b c d e f Leaf Nodes

CR

a b c

PIR Matrix

11

Homomorphic Encryption (Paillier) plaintext space E[m1] * E[m2] = E[m1+m2] (mod N2) E[m]r = E[r*m] (mod N2)

Protocol to determine privately sign(b-a) Paillier encryption + random blinding

Private Point-Rectangle Enclosure

NΖ

12

Private Evaluation of (b-a)

|a-b|<M, M << N

A: m1= N-a --- E[m1] -->

B: m2= b

<-- E[m1+m2] ---

A: res= D[E[m1+m2]]

0 N-1M N-M

a ≤ b a > b

res:

13

Private Evaluation of sign(b-a)

|a-b|<M, M << N, r < M/N

A: m1= N-a --- E[m1] -->

B: m2= b

<-- E[m1+m2]^r ---

A: res= D[E[m1+m2]]

0 N-1M N-M

a ≤ b a > b

res:

N/2

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Fragmentation-aware Indexing

Assume Disclosure Threshold is 3 Median SplitOur Approach

15

Experimental Settings Datasets

Sequoia dataset: 62K POI

Modulus up to 1280 bits

P4, 2.8GHz CPU

16

POI Disclosure

17

Execution Time

18

Communication Overhead

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Conclusions Hybrid LBS privacy

Limit the amount of POI disclosure Reduce processing overhead

Future work Support more complex types of queries

Apply fully homomorphic functions Investigate less costly PIR protocols

27

Spatial Cloaking Privacy through Cloaking Regions (CRs)

Spatial Anonymity (e.g., CliqueCloak, Casper) Spatial Diversity (PROBE)