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 ε and 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 ε and 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 t i and t j 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 t j.SA does not fall in I(t i )?  All tuples in G are sorted in ascending order of their SA values  | j – i | ≧ max{ |left(t j,G)|, |right(t i,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(t 3 )= 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(t 3 )= 1/2 tupleNoQISA 1q10 2q20 3q25 4q30

18. Determine ε and m Given ε and 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) 20 30 25 1040 50

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) 20 30 25 1040 50

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

24. Experiments Real Database SAL http://ipums.orghttp://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?