Private Location-based Query Processing Using PIR Layla Pournajaf - - PowerPoint PPT Presentation

• Nov. 2016

Private Location-based Query Processing Using PIR

Guest Lecture

Data Privacy and Security

Emory University

Computer Science Department 1

Layla Pournajaf

Motivation

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I want the list of nearest restaurants

Motivation

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I want the list of nearest restaurants Give me your location first

Private Information Retrieval

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Suppose that a server maintains a database consisting of N sequential blocks. PIR protocols enable a client to retrieve the ith block from the server, without the server discovering which block was requested (i.e., index i).

PIR Implementations

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• Computational PIR methods [3] rely on the computational intractability
• f well-known problems. However, they entail expensive operations linear

in the database size, which lead to prohibitive processing costs (in the

• rder of thousands of seconds even for moderate database sizes).
• Secure hardware PIR [4] is currently the only practical PIR mechanism.

It relies on a tamper-resistant CPU that is positioned at the server and is trusted by the clients. This CPU receives a client block request, which is unreadable by the server. It obliviously extracts the requested block from the server’s disk, and returns it to the client in an encrypted form decipherable solely by the client. This paradigm leads to constant communication cost, and amortized polylogarithmic computational cost. The latter translates to processing times close to a second even for Gigabyte databases.

Private Information Retrieval

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SYSTEM MODEL SCOP: A trusted secure coprocessor implementation of PIR protocol

PIR- Aware Query Processing

Location-based Queries Using PIR

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• Server-side Indexing of Data
• Spatial Indexing
• Compact Storage
• Enable data retrieval in minimal number of PIR requests
• Client-side query processing
• Query processing with minimal information
• Retrieval of the same number of PIR requests for any query

Nearest Neighbor Query Using PIR [2]: Server-side Indexing of Data: Voronoi Tessellation

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Nearest Neighbor Query Using PIR [2]: Server-side Indexing of Data: Voronoi Tessellation

Nearest Neighbor Query Using PIR [2]

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Nearest Neighbor Queries Using PIR [2]

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• Server-side Indexing of Data
• Spatial Indexing (Voronoi Tessellation)
• Efficient Storage (Storage of max 3 points per cell)
• Data retrieval in minimal number of PIR requests (1 request per

query)

• Client-side query processing
• Query processing with minimal information (find the query cell index,

request the index)

• Retrieval of the same number of PIR requests for any query (1

request per query)

K-Nearest Neighbor Queries Using PIR [1]

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K-Nearest Neighbor Queries Using PIR [1]

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• Server-side Indexing of Data
• Spatial Indexing (Grid Structure)
• Efficient Storage (Not very efficient (Too many dummy points))
• Data retrieval in minimal number of PIR requests (Empty cells may

be requested with no use. Too many points in a cell may need several requests)

• Client-side query processing
• Query processing with minimal information
• Retrieval of the same number of PIR requests for any query

K-Nearest Neighbor Queries Using PIR [1]

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• Server-side Indexing of Data
• Spatial Indexing (Grid Structure)
• Efficient Storage (Not very efficient (Too many dummy points))
• Data retrieval in minimal number of PIR requests (Empty cells may

be requested with no use. Too many points in a cell may need several requests)

• Client-side query processing
• Query processing with minimal information
• Retrieval of the same number of PIR requests for any query

Query Plan

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• Goal:
• Ensuring the same number of PIR requests per query
• Approach:
• Finding the maximum number of PIR requests

considering any query point (QP)

• Regardless of the location of query, all users should

ask for QP blocks

kNN – Smarter Indexing [1]

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Query Plan

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[1] S. Papadopoulos, S. Bakiras, and D. Papadias, “Nearest neighbor search with strong location privacy,” Proceedings of the VLDB Endowment,

• vol. 3, no. 1-2, pp. 619–629, 2010.

[2] A. Khoshgozaran, C. Shahabi, and H. Shirani-Mehr, “Location privacy: going beyond k-anonymity, cloaking and anonymizers,” Knowledge and Information Systems, vol. 26, no. 3, pp. 435–465, 2011. [3] G. Ghinita, P. Kalnis, A. Khoshgozaran, C. Shahabi, and K.-L. Tan, “Private queries in location based services: anonymizers are not necessary,” in Proceedings of the 2008 ACM SIGMOD international conference on Management of data. ACM, 2008, pp. 121–132. [4] P. Williams and R. Sion, “Usable pir.” in NDSS, 2008.

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References

Thank You!

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 Finding RKNN query without LBS deducing the location

• f client.

p2 is the nearest neighbor of q p1 and p4 are the reverse nearest neighbors of q

My Research: Reverse k-Nearest Neighbor Queries Using PIR

 Pruning

 Shrink the search space by removing the points that can not be

the answer

 The remaining points are considered Candidates

 Verification

 Compute kNN for all candidates. For each candidate, if its

kNN includes the query point, it is an answer of RkNN query

Reverse k-Nearest Neighbor Queries

Pruning Strategies

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Pruning Strategies

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Reverse k-Nearest Neighbor Queries Using PIR: Server-Side Indexing Method 1

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 DB_cnt: < c:pre, c:count >  DB_loc: <p.id, p.x, p.y, p.ptr>  DB_dtl: <p:id, p:payload >

Server

Solution 1 Overview

Client

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 Aware of grid structure, query plan and DB_cnt  Pruning Phase

 Determine candidate and influenced cells

 Verification Phase

 Retrieve the location coordination and find the results

 Indexing Data

 Create Hilbert curve on fix grid  Create DB_cnt, DB_loc and DB_dtl

 Query Plan

 Uncertain half-plane pruning for uncertain queries  Modified Verification

Pruning method in Query Plan

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 Uncertain half-plane pruning for uncertain queries

R

M N O P

Q

D A B E

H’M:B H’P:A H’N:E

H’O:D

C

HM:B HP:A

Reverse k-Nearest Neighbor Queries Using PIR: Server-Side Indexing Method 2

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 Hilbert-Rtree: hybrid structure based on B+-tree and R-tree  Internal nodes : < MBR, HLV, Ptr >  leaf nodes : < mbr, Pid >  Nodes and points reside in HRT based on their Hilbert number.  nodes are separated based on the largest Hilbert value  In case of overflow in a node, it is handled by applying s, s+1 policy.

Server

Solution 2 Overview

Client

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 Aware of Hilbert-Rtree structure, query plan and

level_0 of HRT (< MBR, LHV, c >)

 Pruning Phase  Verification Phase  Indexing Data

 Create Hilbert-Rtree structure  Create DB_loc and DB_dtl

 Query Plan

 Uncertain half-plane pruning for uncertain queries  Modified Verification

Advantage: Instead of probing small cell

• f Grid, assess the MBR in

which might contain more cells

Thank You!

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