Auburn University http://www.eng.auburn.edu/~xqin COMP 7370 Advanced Computer and Network Security The VectorCover Algorithm (2) Dr. Xiao Qin Auburn University http://www.eng.auburn.edu/~xqin xqin@auburn.edu Parking problem. Go to office at 6:30 or 8:30 to bypass traffic jam Spring, 2011

Minimal Distance Vectors Note: show Fig. 4 (a) in the k-anonymity paper on the white board. Explain distance vector Intuitively, the the minimal generalizations of table Ti are exactly those tables Tj satisfying k-anonymity with minimal distance vectors DVi;j . For instance, with reference to the generalized tables illustrated in Figure 3 we have already noticed how, for k = 3, GT[1;1] cannot be minimal because GT[0;1] and GT[1;0] also satisfy k-anonimity.

The Outlier Set and All Set Outliers: Tuples which have less than k occurrences All: a set of distinct tuples in a table

Pair – (strategy, tuples) New data structure Represents a transformation strategy Represents a set of tuples after applying such a transformation. Strategy = Distrance Vectors

Distance between Two Tuples

The VectorCover Algorithm Draw (1) Fig. 3 table PT and (2) Fig. 4(a) on the white board

COMP 7370 Advanced Computer and Network Security The MinGen Algorithm Dr. Xiao Qin Auburn University http://www.eng.auburn.edu/~xqin xqin@auburn.edu Parking problem. Go to office at 6:30 or 8:30 to bypass traffic jam Spring, 2011

Step 1: PT vs. PT[QI] vs.

Step 2: history <- [d_1, … d_n] Use subscripts to represent generalization strategies. n =2 E_0 -> d_1 = 0 Z_0 -> d_2 = 0 Use subscripts to represent generalization strategies. E_1 -> d_1 = ? Z_2 -> d_2 = ? E_1 -> d_1 = 1 Z_2 -> d_2 = 2

Step 2: history <- [d_1, … d_n] Note: E_i and Z_j must be specific when you implement the MinGen algorithm. You must specify your generalization strategies. For example: Use subscripts to represent generalization strategies.

Step 2: E_i, Z_j n =2 E_0 -> d_1 = 0 Z_0 -> d_2 = 0 Use subscripts to represent generalization strategies. E_1 -> d_1 = ? Z_2 -> d_2 = ? E_1 -> d_1 = 1 Z_2 -> d_2 = 2

Step 3: Check single attributes Each single attribute must satisfy k-anonymity E -> MGT[E] v = a -> freq(a, MGT[E]) = ? If 4 < k then what does this mean? What should we do? 4

Step 3.1: Check single attributes Each single attribute must satisfy k-anonymity 4 If 4 < k then we need data generalization! V_E = [d_E, d_Z] = [1, 0] not [0, 1] Note: move one step at a time.

Step 3.2: the generalize() function Each single attribute must satisfy k-anonymity E -> MGT[E] Value v = a -> freq(a, MGT[E]) = ? If 4 < k then what does this mean? V_E = [d_E, d_Z] = [1, 0] MGT <- generalize(MGT, V_E, [0,0]) 4

Step 3.2: the generalize() function Each single attribute must satisfy k-anonymity MGT <- generalize(MGT, v, h) Generalize() transform MGT based on a generalization strategy specified by v, h.

Step 3.3: update the history vector Each single attribute must satisfy k-anonymity Can you give me an example to illustrate how step 3.3 works? History [d_E, d_Z] = [0, 0] V_E = [1, 0] New History [0, 0] + [1, 0] = [1, 0]

Step 6.2

Step 6.3