COMP 7370 Advanced Computer and Network Security The VectorCover Algorithm (2)

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Dr. Xiao Qin

Auburn Universityhttp://www.eng.auburn.edu/~xqin

[email protected]

Spring, 2011

COMP 7370 Advanced Computer and Network Security

The VectorCover Algorithm (2)

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Minimal Distance Vectors

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The Outlier Set and All Set

• Outliers: Tuples which have less than k occurrences

• All: a set of distinct tuples in a table

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Pair – (strategy, tuples)

• New data structure

• Represents a transformation strategy

• Represents a set of tuples after applying such a transformation.

• Strategy = Distrance Vectors

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Distance between Two Tuples

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The VectorCover Algorithm

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Dr. Xiao Qin

Auburn Universityhttp://www.eng.auburn.edu/~xqin

[email protected]

Spring, 2011

COMP 7370 Advanced Computer and Network Security

The MinGen Algorithm

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Step 1: PT vs. PT[QI]

vs.

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Step 2: history <- [d_1, … d_n]

n =2

E_0 -> d_1 = 0

Z_0 -> d_2 = 0

E_1 -> d_1 = ?

Z_2 -> d_2 = ?

E_1 -> d_1 = 1

Z_2 -> d_2 = 2

Use subscripts to represent generalization strategies.

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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:

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Step 2: E_i, Z_j

n =2

E_0 -> d_1 = 0

Z_0 -> d_2 = 0

E_1 -> d_1 = ?

Z_2 -> d_2 = ?

E_1 -> d_1 = 1

Z_2 -> d_2 = 2

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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?

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Step 3.1: Check single attributes• Each single attribute must satisfy k-anonymity

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.

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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])

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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.

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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

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Step 6.3

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