Privacy-preserving Data Mining: current research and trends

Stan MatwinSchool of Information Technology and Engineering

University of Ottawa, Canadastan@site.uottawa.ca

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Few words about our researchUniversit[é|y] [d’|of] Ottawa is thelargest bilingual university in Canada

• Applied research and tech transfer – Profiles of digital game players/ active learning, co-

training, instance selection– Classification of medical abstracts

• Privacy-aware Data Mining

• Text Analysis and Machine Learning group

• Learning with previous knowledge

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Plan • What is [data] privacy?• Privacy and Data Mining• Privacy-preserving Data mining: main

approaches– Anonymization– Obfuscation– Cryptographic hiding

• Challenges– Definition of privacy– Mining mobile data– Mining medical data

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Privacy

• Freedom to be left alone• …ability to control who knows what about

us [Westin; Moor] [=database views]• Jeopardized with the Internet – greased

data• Moral obligation for the community to find

solutions

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Privacy and data mining

• Individual Privacy– Nobody should know more about any entity after the

data mining than they did before– Approaches: Data Obfuscation, Value swapping

• Organization Privacy– Protect knowledge about a collection of entities– Individual entity values are not disclosed to all parties

• The results alone need not violate privacy

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Basic ideas

• Camouflage • Hiding

obfuscation k-anonymity

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Why naïve anonymization does not work

• The [Sweeney 01] experiment• purchased the voter registration list for Cambridge, MA

– 54,805 people

• 69% unique on postal code and birth date; 87% US-wide with all three

• Also, we do not know with what other data sources we may do joins in the future

• Solution: k-anonymization

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Randomization Approach Overview

50 | 40K | ...30 | 70K | ... ...

...

Randomizer Randomizer

ReconstructDistribution

of Age

ReconstructDistributionof Salary

ClassificationAlgorithm Model

65 | 20K | ... 25 | 60K | ... ...Age 30

becomes 65

(30+35)

Salary 70K

becomes 20K

Alice’s age

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Reconstruction Problem

• Original values x1, x2, ..., xn from probability distribution X (unknown)

• To hide these values, we use y1, y2, ..., ynfrom known distribution Y

• Given– x1+y1, x2+y2, ..., xn+yn

– the probability distribution of Y Estimate the probability distribution of X.

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Intuition (Reconstruct single point)

• Use Bayes' rule for density functions

10 90Age

V

Original distribution for AgeProbabilistic estimate of original value of V

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Works well

0

200

400

600

800

1000

1200

20 60

Age

Num

ber

of P

eopl

e

OriginalRandomizedReconstructed

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Recap: Why is privacy preserved?

• Cannot reconstruct individual values accurately.

• Can only reconstruct distributions.

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Classification

• Naïve Bayes– Assumes independence between attributes.

• Decision Tree– Correlations are weakened by randomization,

not destroyed.

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Decision Tree Example

Age Salary Repeat Visitor?

23 50K Repeat17 30K Repeat43 40K Repeat68 50K Single32 70K Single20 20K Repeat

Age < 25

Salary < 50K

Repeat

Repeat

Single

Yes

Yes

No

No

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Decision Tree Experiments

Fn 1 Fn 2 Fn 3 Fn 4 Fn 550

60

70

80

90

100

Acc

urac

y Original

Randomized

Reconstructed

100% Randomization Level

100% privacy: attribute cannot be estimated(with 95% confidence) any closer than the entire range for the attribute

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• For very high privacy, discretization will lead to a poor model

• Gaussian provides more privacy at higher confidence levels

• In fact, it can be de-randomized using advanced control theory approach [Kargupta 2003]

Issues

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Association Rule Mining Algorithm [Agrawal et al. 1993]

1. = large 1-itemsets2. for do begin3. 4. for all candidates do begin5. compute c.count 6. end7. 8. end9. Return

1L);;2( 1 ++≠= − kLk k φ)( 1−−= kk LgenaprioriC

kCc ∈

sup}min.|{ −≥∈= countcCcL kk

kk LL U=

c.count is the frequency count for a given itemset.

Key issue: to compute the frequency count, we needs to access attributes that belong to different parties.

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An Example

• c.count is the vector product.• Let’s use A to denote Alice’s

attribute vector and B to denote Bob’s attribute vector.

• AB is a candidate frequent itemset, then c.count = A • B = 3.

• How to conduct this computation across parties without compromising each party’s data privacy?

A B

Alice Bob

11101

01111

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Homomorphic Encryption [Paillier 1999]

• Privacy-preserving protocols are based on Homomorphic Encryption.

• Specifically, we use the following additive homomorphism property:

• Where e is an encryption function and is the data to be encrypted and .

)()()()( 2121 nn mmmemememe +++=××× LL

im0)( ≠ime

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Digital Envelope[Chaum85]

• A digital envelope is a random number (a set of random numbers) only known by the owner of private data.

V V + R VV

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The Objective

Solution

Homomorphic Encryption Digital Envelope

Correctness

Privacy

Efficiency

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Frequency Count Protocol• Assume Alice’s attribute vector is A and Bob’s

attribute vector is B.• Each vector contains N elements.• : the ith element of A.• : the ith element of B.• One of parties is randomly chosen as a key

generator, e.g, Alice, who generates (e, d) and an integer X > N. e and X will be shared with Bob.

• Let’s use e(.) to denote encryption and d(.) to denote decryption.

iA

iB

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……

Alice

XRA ×+ 11

Digital envelopes

XRA ×+ 22 XRA NN ×+

NRRR ,, 21 L A set of random integers generated by Alice

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XRA ×+ 22XRA NN ×+……

Alice

)( 11 XRAe ×+ )( 22 XRAe ×+ )( XRAe NN ×+……

XRA ×+ 11

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)( 22 XRAe ×+ )( XRAe NN ×+……)( 11 XRAe ×+

Alice

Bob

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1111 )( BXRAeW ××+= 2222 )( BXRAeW ××+=NNNN BXRAeW ××+= )(…

Bob

)()(100

XRAeBXRAeWBWB

iiiiiii

ii

×+=××+=⇒==⇒=

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• Bob multiplies all the for those that are not equal to 0. In other words, Bob computes the multiplication of all non-zero , e.g., where .

sWi sBi

sWi ∏= iWW

0≠iW

jWWWW ×××= L21

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jWWWW ×××= L21

])([])([])([ 222111 jjj BXRAeBXRAeBXRAe ××+××××+×××+= L||

1

||

1

||

1

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jWWWW ×××= L21

]1)([]1)([]1)([ 2211 ××+××××+×××+= XRAeXRAeXRAe jjL

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jWWWW ×××= L21

)()()( 2211 XRAeXRAeXRAe jj ×+×××+××+= L

))(( 2121 XRRRAAAe jj ×+++++++= LL

According to the property of homomorphic encryption

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• Bob generates an integer .

• Bob then computes

'R

)'(' XReWW ××=

Alice

))'(( 2121 XRRRRAAAe jj ×++++++++= LL

According to the property of homomorphic encryption

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The Final Step

• Alice decrypts and computes modulo X.

• She then obtains for those Aj for which corresponding Bj are 0, which is = c.count

'W

XXRRRRAAAedcountc

jj mod)))'(((.

2121 ×++++++++= LL

0mod))'((

)(

21

21

=×++++

<≤+++

XXRRRR

XNAAA

j

j

L

L

1 2 jA A A+ + +L

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Privacy Analysis

• All the information that Bob obtains from Alice is.

• Since Bob doesn’t know the decryption key d, he cannot get Alice’s original data values.

)(,),(),( 2211 XRAeXRAeXRAe NN ×+×+×+ L

Goal: Bob never sees Alice’s data values.

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Privacy Analysis

The information that Alice obtains from Bob is for those .

Alice computes . She only obtains the frequencycount and cannot know Bob’s original data values.

XWd mod)'(

))'((' 2121 XRRRRAAAeW jj ×++++++++= LL 1=iB

Goal: Alice never sees Bob’s data values.

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Complexity Analysis

)1( +Nα αwhere N is the total number transactions and is the number of bits for each encrypted element.

Linear in the number of transactions

The total number elements in each attribute vector

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Complexity Analysis

The computational cost is (10N + 20 + g) where N is the total numbertransactions and g is the computational cost for generating a key pair.

Linear in the number of transactions

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Other Privacy-Oriented Protocols

Multi-Party Frequency Count Protocol

Multi-Party Summation Protocol

Multi-Party Comparison Protocol

Multi-Party Sorting Protocol

[Zhan et al. 2005 (a)]

[Zhan et al. 2005 (f)]

[Zhan et al. 2006 (a)]

[Zhan et al. 2006 (a)]

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What about the results of DM?

• Can DM results reveal personal information?• In some cases, yes [Atzori et al. 05]:Suppose an association rule is found:

This meansthen therefore has support=1, and

identifies one person!!

1 2 3 4[sup 80, 98.7%]a a a a conf∧ ∧ ⇒ = =

1 2 3 4a a a a∧ ∧ ∧¬

1 2 3 4sup({ , , , }) 80a a a a =1 2 3 4

1 2 3sup({ , , , }) 0.8sup({ , , }) 81.05

0.987 .0987a a a aa a a = = =

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• They propose an approach called k-anonymous patterns and an algorithm (inference channels) which detects violations of k-anonymity

• The algorithm is expensive computationally• We have a new approach which embeds k-

anonimity into the concept lattice association rule algorithm [Zaki, Ogihara 98]

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Conclusion

• Important problem, challenge for the field• Lots of creative work, but lack of systematic

approach• Medical data particularly sensitive, but also

makes de-identification easier: genotype-phenotype inferences, location-visit patterns, family structures, etc. [Malin 2005]

• Lack of an operational, agreed upon definition of privacy: inspiration in economics?