Privacy Preserving Data Mining

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Privacy Preserving Data Mining

• Yehuda Lindell Benny Pinkas

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Summary

• Objective
• Various components / tools needed
• Algorithm

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Objective

• Perform Data-mining on union of two private
  databases
• Data stays private i.e. no party learns anything
  but output

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Assumptions

• Large Databases Generic Solutions not possible
• Semi-Honest Parties

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Classification by Decision Tree Learning

• ltattribute,valuegt

Attributes
Class Attribute
Want to Predict Class, using only non-class
attributes
Transaction
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Decision Tree

• Rooted tree with nodes/edges
• Internal Nodes gt Attributes
• Edges leaving nodes gt Possible values
• Leaves gt Expected Class for transaction
• Traverse tree using known attributes
• Predict class given leaf nodes value

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Constructing Tree

• Top-down
• At each level find attribute that best
  classifies transactions gt gives least overhead
• Best gt Attribute that minimizes entropy
  (maximizes information gain)
• Entropy -xlnx
• Entropy of class 0

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Entropy calcluations

• Entropy H(T) sum (-x ln x )
• Hc(T) gt Info needed to ID class of transaction T
• X set of transactions for each class
• Sum over all possible classes
• Hc(T A) gt Info needed to ID class of
  transaction T, Given value v of attribute A
• X transactions with value v for attribute A
• Gain Hc(T) Hc(T A)

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Private Computation

• Given only x1 and f1(x1,y), function S1 exists
  s.t.
• P2 provides input x1 to P1
• P2 can compute corresponding view of P1s DB
  (desired ltatt,valuegt pairs)

S1
View
Party 2
f1(x1,y)
x1
f1
Party 1
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Oblivious Evaluation

• What if in previous example Party 2 does not
  want Party 1 to know what input (x1) it is
  providing?
• Oblivious Evaluation Receiver obtains P(x)
  without learning anything else about polynomial
  P. Sender learns nothing about x.

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Oblivious Evaluation (2) Simplified Version

• ri receivers random number
• Ri senders random number
• X input from rcvr

• Sender Receiver
• s (secret key)
• (ari, asrj ax)

• (aRi, asR aP(x) asri)

Divide 2nd element by 1st element raised to power
s to get P(x)
a P(x) (aRi, asR aP(x) asri) /
(aRi ari)s
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Algorithm

• Step 1 - Each party computes ID3 decision tree
  learning (O( attributes))
• Step 2 - Combine results using cryptographic
  protocols like oblivious evaluation -
  (O(log(transactions)))
• Result - Each party gains results of data-mining
  without learning more than necessary

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Algorithm (2)Finding best attribute is hardest
part

• Each party computes their share of entropy
• For each attribute, combine values from each
  party
• Results in private computation of Entropy (-xlnx)
• Choose attribute that minimizes entropy
• Provides maximum information gain
• Ensures most efficient tree with least overhead
• Use oblivious Evaluation

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Discussion of Algorithm

• Efficient
• Large Databases accommodated Algorithm relies on
  number of possible values for attributes NOT
  number of transactions in database
• Private
• Each step depends on local computation and
  private protocol
• Uses techniques like oblivious transfer /
  evaluation to exchange information
• Paper proves individual steps are private, AND
  can predict control flow between steps ONLY based
  on input/output so also private

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Discussion of Algorithm (2)

• Approximate ID3 used instead of actual ID3
  shown to be as secure and provide same information