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Privacy Preserving Data Mining –
Secure multiparty computation and
random response techniques
Li Xiong
CS573 Data Privacy and Security
Outline
• Privacy preserving two-party decision tree mining using SMC protocols (Lindell & Pinkas ’00)
• Primitive SMC protocols
– Secure sum
– Secure union (encryption based)– Secure union (encryption based)
– Secure max (probabilistic random response based)
– Secure union (probabilistic and randomization based)
• Secure data mining using sub protocols
• Random response for privacy preserving data mining or data sanitization
Random response protocols
• Multi-round probabilistic protocols
• Randomization probability associated with
each round
• Random response with randomization • Random response with randomization
probability
• Multiple rounds
• Randomization Probability at round r :
– Pr(r) =
• Local algorithm at round r and node i:
Max Protocol – multi-round random
response
1
0*−rdP
• Local algorithm at round r and node i:
4
gi-1(r)>=vi gi-1(r)<vi
gi(r) gi-1(r) w/ prob Pr:
rand [gi-1(r), vi)
w/ prob 1-Pr:
vi
igi-1(r) gi(r)
vi
Min/Max Protocol - Correctness
• Precision bound:
– Converges with r
– Smaller p0 and d provides faster convergence
2
)1(
01*1)Pr(1
−
=−≥−∏
rrrr
jdPj
6
Min/Max Protocol - Cost
• Communication cost
– single round: O(n)
– Minimum # of rounds given
precision guarantee (1-e):
7
Min/Max Protocol - Security
• Probability/confidence based metric: P(C|IR,R)
– Different types of exposures based on claim
• Data value: v =a
0.50 1
Absolute Privacy Provable Exposure
8
• Data value: vi=a
• Data ownership: Vi contains a
– Change of beliefs
• P(C|IR,R) – P(C|R)
• P(C|IR, R) / P(C|R)
• Relationship to privacy in anonymization
– Change of beliefs P(C|D*, BR) – P(C|BR)
Min/Max Protocol – Security (Analysis)
• Upper bound for average expected change of beliefs:
max r 1/2r-1 * (1-P0*dr-1)
• Larger p0 and d provides better privacy
9
Min/Max Protocol – Security (Experiments)
10
• Loss of privacy decreases with increasing number of nodes
• Probabilistic protocol achieves better privacy (close to 0)
• When n is large, anonymous protocol is actually okay!
Union
• Commutative encryption based approach
– Number of rounds: 2 rounds
– Each round: encryption and decryption
• Multi-round random-response approach?• Multi-round random-response approach?
Vector
1
0b1
b2
…p1
0
1
…
p2
1
0
…
pc
OR OR OR… =
1
1
VG
…
• Each database has a boolean vector of the data items
• Union vector is a logical OR of all vectors
0bL
…
0
…
0
…
0
…
Privacy Preserving Indexing of Documents on the Network, Bawa, 2003
Group Vector Protocol
…
Pex=1/2r, Pin=1-Pex
for(i=1; i<L; i++)
if (Vs[i]=1 and VG’[i]=0)
Processing of VG’ at ps of round r…
0
1
0
v1
0
0
1
…
v2
0
1
0
…
vc
0
0
0
…
vG’
0
0
1
…
vG’
r=1, Pex=1/2, Pin=1/2
if (Vs[i]=1 and VG’[i]=0)
Set VG’[i]=1 with prob. Pin
if (Vs[i]=0 and VG’[i]=1)
Set VG’[i]=0 with prob. Pex
v1v2
vc
r=2, Pex=1/4, Pin=3/40
0
1
…
vG’
0
1
1
…
vG’
0
1
1
…
vG’
0
0
1
…
vG’
0
1
1
…
vG’
p1p2 pc
Random Shares based Secure Union• Phase 1: random item addition
– Multiple rounds with permutated ring
– Each node sends a random share of its item set and a random share of a random
item set
• Phase 2: random item removal
– Each node subtracts its random items set
14
Random Shares based Secure Union -
Analysis
• Item exposure attack
– An adversary makes a claim C on a particular item a node i contributes to the final result (C: vi in xi)
• Set exposure attack
– An adversary makes a claim C on the whole set of – An adversary makes a claim C on the whole set of items a node i contributes to the final union result X (C: xi = ai).
• Change of beliefs (posterior probability and prior probability)
– P(C|IR,X) - P(C|X)
– P(C|IR,X)/P(C|X)
15
Exposure Risk – Set Exposure
• Disclosure decreases with increasing number of generated
random items and increasing number of participating nodes
• Set exposure risk is or close to 0 for probabilistic and crypto
approach
16
Exposure Risk – Risk Exposure
• Item exposure risk decreases with increasing number of
generated random items and participating nodes
• Item exposure risk for probabilistic approach is quite high
17
Cost Comparison
• Commutative protocol and anonymous communication protocol efficient but sensitive to union size
• Probabilistic protocol efficient but sensitive to domain size
• Estimated runtime for the general circuit-based protocol implemented by FairplayMP framework is 15 days, 127 days and 1.4 years for the domain sizes tested
18
Open issues
� Tradeoff between accuracy, efficiency, and security
� How to quantify security
� How to design adjustable protocols
� Can we generalize the random-response algorithms � Can we generalize the random-response algorithms
and randomization algorithms for operators based on
their properties
� Operators: sum, union, max, min …
� Properties: commutative, associative, invertible,
randomizable
•Secure Sum
•Secure Comparison
•Association Rule Mining
•Decision Trees
Data Mining on Horizontally
Partitioned DataSpecific Secure Tools
•Secure Union
•Secure Logarithm
•Secure Poly. Evaluation
•EM Clustering
•Naïve Bayes Classifier
•Secure Comparison
•Secure Set Intersection
•Association Rule Mining
•Decision Trees
Data Mining on Vertically
Partitioned DataSpecific Secure Tools
•Secure Dot Product
•Secure Logarithm
•Secure Poly. Evaluation
•K-means Clustering
•Naïve Bayes Classifier
•Outlier Detection
Summary of SMC Based PPDDM
• Mainly used for distributed data mining.
• Efficient/specific cryptographic solutions for many distributed data mining problems are developed.
• Random response or randomization based • Random response or randomization based protocols offer tradeoff between accuracy, efficiency, and security
• Mainly semi-honest assumption(i.e. parties follow the protocols)
Ongoing research
• New models that can trade-off better
between efficiency and security
• Game theoretic / incentive issues in PPDM
Outline
• Privacy preserving two-party decision tree mining using SMC protocols (Lindell & Pinkas ’00)
• Primitive SMC protocols
– Secure sum
– Secure union (encryption based)– Secure union (encryption based)
– Secure max (probabilistic random response based)
– Secure union (probabilistic and randomization based)
• Secure data mining using sub protocols
• Random response for privacy preserving data mining or data collection
Randomized Response
Do you smoke?
Head Yes
The true
answer is
“Yes”
)5.0(
)(
≠
=
θ
θYesP
P'(Yes) = P(Yes) ⋅ θ + P(No) ⋅ (1−θ)
P'(No) = P(Yes) ⋅ (1−θ) + P(No) ⋅ θ
Head
TailNo
YesBiased coin:
5.0
)(
≠
=
θ
θHeadP
Randomized Response
• Multiple attributes encoded in bits
)5.0(
)(
≠
=
θ
θYesPHead True answer E: 110
Biased coin:
)( = θHeadP )5.0( ≠θ
TailFalse answer !E: 0015.0
)(
≠
=
θ
θHeadP
Using Randomized Response Techniques for Privacy-Preserving Data Mining, Du, 2003
Generalization for Multi-Valued Categorical
Data
Si
Si+1
Si+2
q1
q2
q3
q4
True Value: Si Si+3
q4
P'(s1)
P'(s2)
P'(s3)
P'(s4)
=
q1 q4 q3 q2
q2 q1 q4 q3
q3 q2 q1 q4
q4 q3 q2 q1
P(s1)
P(s2)
P(s3)
P(s4)
M
A Generalization
• RR Matrices [Warner 65], [R.Agrawal 05], [S. Agrawal 05]
• RR Matrix can be arbitrary
• Can we find optimal RR matrices?
M =
a11 a12 a13 a14
a21 a22 a23 a24
a31 a32 a33 a34
a41 a42 a43 a44
OptRR:Optimizing Randomized Response Schemes for Privacy-Preserving Data Mining, Huang,
2008
What is an optimal matrix?
• Which of the following is better?
M1 =
1 0 0
0 1 0
M2 =
13
13
13
13
13
13
M1 = 0 1 0
0 0 1
2 3 3 3
13
13
13
What is an optimal matrix?
• Which of the following is better?
M1 =
1 0 0
0 1 0
M2 =
13
13
13
13
13
13
M1 = 0 1 0
0 0 1
2 3 3 3
13
13
13
Privacy: M2 is better
Utility: M1 is better
So, what is an optimal matrix?
Optimal RR Matrix
• An RR matrix M is optimal if no other RR
matrix’s privacy and utility are both better
than M (i, e, no other matrix dominates M).
– Privacy Quantification– Privacy Quantification
– Utility Quantification
• A number of privacy and utility metrics have
been proposed.
– Privacy: how accurately one can estimate individual info.
– Utility: how accurately we can estimate aggregate info.
Optimization Methods
• Approach 1: Weighted sum:
w1 Privacy + w2 Utility
• Approach 2
– Fix Privacy, find M with the optimal Utility.– Fix Privacy, find M with the optimal Utility.
– Fix Utility, find M with the optimal Privacy.
– Challenge: Difficult to generate M with a fixed privacy or utility.
• Proposed Approach: Multi-Objective Optimization
Optimization algorithm
• Evolutionary Multi-Objective Optimization (EMOO)
• The algorithm
– Start with a set of initial RR matrices
– Repeat the following steps in each iteration
• Mating: selecting two RR matrices in the pool• Mating: selecting two RR matrices in the pool
• Crossover: exchanging several columns between the two RR matrices
• Mutation: change some values in a RR matrix
• Meet the privacy bound: filtering the resultant matrices
• Evaluate the fitness value for the new RR matrices.
Note : the fitness values is defined in terms of privacy and utility metrics
Output of Optimization
Worse
M5M6
The optimal set is often plotted in the objective space as
Pareto front.
Privacy
Utility
Better
M1M2
M4
M3
M7M8