Overview Study an important privacy preserving method, namely k-anonymity

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Overview Study an important privacy preserving method, namely k-anonymity

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Overview Study an important privacy preserving method, namely k-anonymity

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2D representation of the original and generalized table.

Name

Age

Start-year

Salary

Alice

25

2001

7k

Bob

30

2004

1k

Christina

35

1990

2k

Complexity and Approximation Ratio

d: dimensionality n: the size of dataset

Daniel

40

1995

3k

Emily

45

2000

6k

William

55

1985

3k

Algorithm

Time Complexity

Approximation Ratio

The original payroll table

DAG

O(3ddnlog2n)

8d

MMG

O(dn2d+1)

2d+1

Age

Start-year

Salary

NNG

O(dn2)

6d

[25, 45]

[2000, 2004]

7k

[25, 45]

[2000, 2004]

1k

[35, 55]

[1985, 1995]

2k

[35, 55]

[1985, 1995]

3k

[25, 45]

[2000, 2004]

6k

[35, 55]

[1985, 1995]

3k

A 3-anonymous generalization

The Institute for Information AssuranceOn Multidimensional k-Anonymity with Local Recoding GeneralizationPresented by: Yang DuCollege of Computer and Information ScienceNortheastern University, Boston, MA 02115duy@ccs.neu.edu

- Overview
- Study an important privacy preserving method, namely k-anonymity
- Show it is provably hard, even to find a good enough approximate answer
- Develop three algorithms with different tradeoffs between the approximation ratio and complexity
- Introduction
- Motivation is privacy preserving
- Publish sensitive data to allow accurate analysis without revealing the privacy

- Simply removing the id column is not enough
- Attackers can use some other attributions, called quasi-identifiers, to restore the identities

- Generalization is necessarily
- The quasi-identifiers are replaced by values in more general forms

- K-anonymity is often a requirement
- Make the quasi-identifiers of each tuple undistinguishable with at least those of other (k-1) tuples

- Approximation Algorithms
- The Divide-and-Group (DAG) Algorithm
- Divide the space into square cells with proper size
- Find a set of non-overlapping tiles of 2 x 2 cells to cover the points, such that each tile covers at least k points
- Assign the rest of (uncovered) points to the nearest tile

- Problem Mapping
- Given a table R containing d quasi-identifier attributes
- Map each quasi-identifier attribute to one dimension
- Map each tuple in the table to a point in d-dimensional space
- Map the k-anonymous generalization problem to a partition problem
- Partition a set of d-dimensional points into some groups
- Each point belongs to one and only one group
- Each group contains at least k points
- Each point is generalized to the minimum bounding rectangle (MBR) of its group

- Quality Measuring
- The smaller the MBRs are, the more accurate the analysis results are.
- The size of each MBR is measured by its perimeter.
- Objective
- Find the optimal partition that minimizes the maximum size (perimeter) among all MBRs.

- The Min-MBR-Group (MMG) Algorithm
- For each point p, find the smallest MBR which covers at least k points including p
- Find a set of non-overlapping MBRs from the result of previous step
- Assign the points to the nearest MBR

- The Nearest-MBR-Group (NNG) Algorithm
- For each point p, find the MBR which covers p and its k-1 nearest neighbors
- Find a set of non-overlapping MBRs from the result of previous step
- Assign the points to the nearest MBR

- Hardness of the Problem
- Finding the optimal partition is NP-hard (cannot be done within polynomial time).
- Finding a partition with approximation ratio less than 5/4, i.e. the maximum perimeter is 5/4 of the maximum perimeter of the optimal partition, is also NP-hard.

- For more information:
- http://www.ccs.neu.edu/research/dblab
- Prof. Donghui Zhang – donghui@ccs.neu.edu
- Yang Du – duy@ccs.neu.edu