Preservation of Proximity Privacy in Publishing Numerical Sensitive Data

1. Preservation of Proximity Privacy in Publishing Numerical Sensitive Data J. Li, Y. Tao, and X. Xiao SIGMOD 08 Presented by Hongwei Tian

2. Outline • What is PPDP • Existing Privacy Principles • Proximity Attack • (ε, m)-anonymity • Determine εand m • Algorithm • Experiments and Conclusion

3. Privacy Preservation Data Publishing • A true story in Massachusetts, 1997 • GIC • 20 dollars • Governor Weld

4. PPDP • Privacy • Sensitive information of individuals should be protected in the published data • More anonymized data • Utility • The published data should be useful • More accurate data

5. PPDP • Anonymization Technique • Generalization • Specific value -> General value • Maintain the semantic meaning • 78256 -> 7825*, UTSA -> University, 28 -> [20, 30] • Perturbation • One value -> another random value • Huge information loss -> poor utility

6. PPDP • Example of Generalization

7. Some Existing Privacy Principles • Generalization • SA – Categorical • k-anonymity • l-diversity, (α, k)-anonymity, m-invariance, … • (c, k)-safety, Skyline-privacy • … • SA – Numerical • (k, e)-anonymity, Variance Control • t-closeness • δ-presence • …

8. Next… • What is PPDP • Existing Privacy Principles • Proximity Attack • (ε, m)-anonymity • Determine εand m • Algorithm • Experiments and Conclusion

9. Proximity Attack

10. (ε, m)-anonymity • I(t) • private neighborhood of tuple t • I(t) = [t.SA − ε, t.SA + ε] • I(t) = [t.SA·(1 − ε), t.SA·(1 + ε)] • P(t) • the risk of proximity breach of tuple t • P(t) = x / |G|

11. (ε, m)-anonymity • ε = 20 • I(t1) = [980, 1020] • x = 3, |G| = 4 • P(t1) = 3/4

12. (ε, m)-anonymity • Principle • Given a real value ε and an integer m ≥ 1, a generalized table T∗ fulfills absolute (relative) (ε,m)-anonymity, if P(t) ≤ 1/m for every tuple t ∈ T. • Larger ε and m mean stricter privacy requirement

13. (ε, m)-anonymity • What is the Meaning of m? • |G| ≥ m • The best situation is for any two tuples ti and tj in G, and • Similar to l-diversity when the equivalence class has l tuples with distinct SA values.

14. (ε, m)-anonymity • How to make tj.SA does not fall in I(ti)? • All tuples in G are sorted in ascending order of their SA values • | j – i | ≧ max{ |left(tj,G)|, |right(ti,G)| }

15. (ε, m)-anonymity • Let maxsize(G) = max∀t∈G { max{ |left(t,G)|, |right(t,G)| } } • | j – i | ≧ maxsize(G)

16. (ε, m)-anonymity • Partitioning • Ascending order of tuples in G according to SA values • Hash the ith tuple into the jth bucket using function j = (i mod maxsize(G))+1 • Thus, all tuples (SA values) in the same bucket do not fall into the neighborhood of each other.

17. (ε, m)-anonymity • (6, 2)-anonymity • Privacy is breached • P(t3)= ¾ >1/m =1/2 • Need partitioning • An ascending order is ready according to SA values • g = maxsize(G) = 2 • j = (i mod 2)+1 • New P(t3)= 1/2

18. Determine εand m • Given εand m • Check if an equivalence class G satisfies (ε, m)-anonymity • Theorem: G has at least one (ε, m)-anonymous generalization, iff • Scan the sorted tuples in G to find maxsize(G) • Predict whether G can be partitioned or not

19. Algorithm • Step 1: Splitting • Mondrain, ICDE 2006. • Splitting is only based on QI-attributes • Iteratively find median value of frequency sets on one selected QI-dimension to cut G into G1 and G2, and make sure G1 and G2 are legal to be partitioned.

20. Algorithm • Splitting ((6, 2)-anonymity) 10 40 20 25 50 30

21. Algorithm • Step 2: Partitioning • After step 1 stops • Check all G produced by splitting • Release directly if G satisfies (ε, m)-anonymity • Otherwise, Partitioning, and then release new buckets

22. Algorithm • Partitioning ((6, 2)-anonymity) 10 40 20 25 50 30

23. Next… • What is PPDP • Evolution of Privacy Preservation • Proximity Attack • (ε, m)-anonymity • determine εand m • algorithm • Experiments and Conclusion

24. Experiments • Real Database SAL http://ipums.org • Attributes are Age, Birthplace, Occupation and Income with domains [16,93], [1,710], [1,983], and [1k, 100k], respectively. • 500K tuples • Compare to a perturbation method (OLAP, SIGMOD 2005 )

25. Experiments - Utility • Use count query with workload = 1000

26. Experiments - Utility

27. Experiments - Efficiency

28. Conclusion • Discuss most of existing privacy principles in PPDP • Identify the proximity attack and propose (ε, m)-anonymity to prevent this attack • Verify that the method is effective and efficient experimentally

29. Any Question?