Privacy Preserving Serial Data Publishing By Role Composition

1
Privacy Preserving Serial Data Publishing By Role
Composition

• Yingyi Bu1, Ada Wai-Chee Fu1, Raymond Chi-Wing
  Wong2,
• Lei Chen2, Jiuyong Li3
• The Chinese University of Hong Kong1The Hong
  Kong University of Science and Technology2
• University of South Australia3

Prepared by Raymond Chi-Wing Wong Presented by
Raymond Chi-Wing Wong
2
Outline

• Sequential Releases
• Existing Privacy Models
• m-invariance
• Privacy breaches
• Our Proposed Privacy Model
• l-scarcity
• Experiments
• Conclusion

3
1. Sequential Releases
Time 1
Public
This table satisfies some privacy
requirements(e.g., m-invariance)
Published Data
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
Medical Data
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
4
1. Sequential Releases
This table satisfies some privacy
requirements(e.g., m-invariance)
Time 1
Time 2
Public
Public
Published Data
Published Data
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
Medical Data
Medical Data
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
Insertions, deletions and updates
5
1. Sequential Releases
This table satisfies some privacy
requirements(e.g., m-invariance)
Time 1
Time 2
Time 3
Public
Public
Public
Published Data
Published Data
Published Data
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
Medical Data
Medical Data
Medical Data
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
Insertions, deletions and updates
6
1. Sequential Releases
Problem At the current time t, we want to
generate a table which satisfies some privacy
requirements (e.g., m-invariance) with respect to
all published tables at any time lt t
Time 1
Time 2
Time 3
Public
Public
Public
Published Data
Published Data
Published Data
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
Medical Data
Medical Data
Medical Data
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
7
2. Existing Privacy Models
Problem At the current time t, we want to
generate a table which satisfies some privacy
requirements (e.g., m-invariance) with respect to
all published tables at any time lt t
Considers insertions only Does not consider
deletions and updates

1. Byun et al., Secure Anonymization for
   Incremental datasets, Secure Data Management,
   2006

Considers insertions only Does not consider
deletions and updates

1. Fung et al, Anonymity for Continuous Data
   Publishing, EDBT, 2008

Considers insertions and deletions only Does not
consider updates

1. Xiao et al, m-invariance Towards Privacy
   Preserving Re-publication of Dynamic Datasets,
   SIGMOD, 2007

Updates cannot simply be regarded as a deletion
and then an insertion when privacy is considered.
Our proposed privacy model (l-scarcity) -
Considers insertions, deletions and updates
together
8
2. Existing Privacy Models
Problem At the current time t, we want to
generate a table which satisfies some privacy
requirements (e.g., m-invariance) with respect to
all published tables at any time lt t

• Sensitive Diseases
• Transient diseases
• Permanent diseases

e.g., If an individual is linked to flu in a
published table, s/he can be linked to flu or
not in the later published table.

• curable
• E.g. flu, fever

• incurable
• E.g., HIV

e.g., If an individual is linked to HIV in a
published table, s/he MUST be linked to HIV in
the later published table (that they exist in).
We are the first to study these two kinds of
sensitive values.
9
2. Existing Privacy Models
Problem At the current time t, we want to
generate a table which satisfies some privacy
requirements (e.g., m-invariance) with respect to
all published tables at any time lt t
Does not consider transient/permanent values
Considers insertions only Does not consider
deletions and updates

1. Byun et al., Secure Anonymization for
   Incremental datasets, Secure Data Management,
   2006

• Contributions
• We consider a more realistic setting of
  sequential releases.
• Insertions, deletions and updates
• Transient/permanent values

Considers insertions only Does not consider
deletions and updates

1. Fung et al, Anonymity for Continuous Data
   Publishing, EDBT, 2008

We cannot simply adapt these existing privacy
models to this realistic setting.
Considers insertions and deletions only Does not
consider updates

1. Xiao et al, m-invariance Towards Privacy
   Preserving Re-publication of Dynamic Datasets,
   SIGMOD, 2007

Also considers transient/permanent values
Our proposed privacy model (l-scarcity) -
Considers insertions, deletions and updates
together
10
2. Existing Privacy Models
Problem At the current time t, we want to
generate a table which satisfies some privacy
requirements (e.g., m-invariance) with respect to
all published tables at any time lt t
Problem (m-invariance) At the current time t,
we want to generate a table which satisfies the
following. Probability that an individual is
linked to a sensitive value wrt all published
tables at any time lt t is at most 1/m.

1. Byun et al., Secure Anonymization for
   Incremental datasets, Secure Data Management,
   2006

Problem (l-scarcity) At the current time t, we
want to generate a table which satisfies the
following. Probability that an individual is
linked to a sensitive value wrt all published
tables at any time lt t is at most 1/l.

1. Fung et al, Anonymity for Continuous Data
   Publishing, EDBT, 2008

1. Xiao et al, m-invariance Towards Privacy
   Preserving Re-publication of Dynamic Datasets,
   SIGMOD, 2007

Our proposed privacy model (l-scarcity) -
Considers insertions, deletions and updates
together
11
Public
Voter Registration List
Medical Data Some Useful Attributes
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Fever
Alice p4 26 18310 HIV
Bob p5 25 25000 Flu
John p6 20 29000 Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Fever
Alice p4 26 18310 HIV
Bob p5 25 25000 Flu
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
12
Public
Voter Registration List
Medical Data Some Useful Attributes
Age Zip Code Disease
23 16355 Flu
22 15500 HIV
21 12900 Fever
26 18310 HIV
25 25000 Flu
20 29000 Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Fever
Alice p4 26 18310 HIV
Bob p5 25 25000 Flu
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
13
Public
Generalization
Voter Registration List
Medical Data Some Useful Attributes
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
3-diversity
Each individual is linked to HIV with
probability at most 1/3 in THIS PUBLISHED TABLE
3-diversity only focuses on ONE-TIME
publishing 3-invariance focuses on MULTIPLE-TIME
publishingIt also makes use of the idea of
3-diversity Idea Each individual is linked to
HIV with probability at most 1/3 with respect
to MULTIPLE PUBLISHED TABLES
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Fever
Alice p4 26 18310 HIV
Bob p5 25 25000 Flu
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
14
3-invariance
Time 1
Public
Voter Registration List
Medical Data Some Useful Attributes
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Fever
Alice p4 26 18310 HIV
Bob p5 25 25000 Flu
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
15
3-invariance
Time 1
Public
Time 1
Voter Registration List
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
PID Signature
p1
p2
p3
p4
p5
p6
Flu, HIV, Fever
p1
p2
p3
Flu, HIV, Fever
Flu, HIV, Fever
Flu, HIV, Fever
p4
p5
p6
Flu, HIV, Fever
Flu, HIV, Fever
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Fever
Alice p4 26 18310 HIV
Bob p5 25 25000 Flu
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
16
3-invariance
Time 1
Public
Time 1
Voter Registration List
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
PID Signature
p1
p2
p3
p4
p5
p6
Flu, HIV, Fever
Flu, HIV, Fever
Flu, HIV, Fever
Flu, HIV, Fever
Flu, HIV, Fever
Flu, HIV, Fever
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Fever
Alice p4 26 18310 HIV
Bob p5 25 25000 Flu
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
17
3-invariance
Time 1
Public
Time 1
Voter Registration List
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
PID Signature
p1
p2
p3
p4
p5
p6
Flu, HIV, Fever
Flu, HIV, Fever
Flu, HIV, Fever
Flu, HIV, Fever
Flu, HIV, Fever
Flu, HIV, Fever
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Fever
Alice p4 26 18310 HIV
Bob p5 25 25000 Flu
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
18
3-invariance
Time 1
Public
Voter Registration List
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
PID Signature
p1
p2
p3
p4
p5
p6
Flu, HIV, Fever
Time 1
Flu, HIV, Fever
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Flu, HIV, Fever
Flu, HIV, Fever
Flu, HIV, Fever
Flu, HIV, Fever
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Fever
Alice p4 26 18310 HIV
Bob p5 25 25000 Flu
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
19
3-invariance
Time 1
Time 1
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Voter Registration List
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
PID Signature
p1
p2
p3
p4
p5
p6
Flu, HIV, Fever
Flu, HIV, Fever
Flu, HIV, Fever
Flu, HIV, Fever
Flu, HIV, Fever
Flu, HIV, Fever
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Fever
Alice p4 26 18310 HIV
Bob p5 25 25000 Flu
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
20
3-invariance
Time 1
Time 1
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Voter Registration List
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Fever
Alice p4 26 18310 HIV
Bob p5 25 25000 Flu
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
21
3-invariance
Time 1
Time 1
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Voter Registration List
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Fever
Alice p4 26 18310 HIV
Bob p5 25 25000 Flu
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
22
3-invariance
Time 2
Time 1
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Voter Registration List
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Flu
Alice p4 26 18310 HIV
Bob p5 25 25000 Fever
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Flu
Alice p4 HIV
Bob p5 Fever
John p6 Fever
23
3-invariance
Time 2
Time 1
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Medical Data Some Useful Attributes
Voter Registration List
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
p2
p3
p6
p1
p4
p5
Hospital
This table satisfies 3-invariance. This is
because each individual is linked to the SAME
signature.
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Flu
Alice p4 26 18310 HIV
Bob p5 25 25000 Fever
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Flu
Alice p4 HIV
Bob p5 Fever
John p6 Fever
Idea of 3-invariance Each individual is linked
to the SAME signature in each published table.
24
3-invariance
Time 2
Time 1
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Time 2
Voter Registration List
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Flu
Alice p4 26 18310 HIV
Bob p5 25 25000 Fever
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Flu
Alice p4 HIV
Bob p5 Fever
John p6 Fever
25
3-invariance
Time 2
Time 1
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Voter Registration List
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Time 2
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Flu
Alice p4 26 18310 HIV
Bob p5 25 25000 Fever
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Flu
Alice p4 HIV
Bob p5 Fever
John p6 Fever
26
3-invariance
Time 2
Time 1
Time 2
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Voter Registration List
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Flu
Alice p4 26 18310 HIV
Bob p5 25 25000 Fever
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Flu
Alice p4 HIV
Bob p5 Fever
John p6 Fever
27
3-invariance
Time 2
Time 1
Time 2
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Voter Registration List
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Flu
Alice p4 26 18310 HIV
Bob p5 25 25000 Fever
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Flu
Alice p4 HIV
Bob p5 Fever
John p6 Fever
28
3-invariance
Time 2
Time 1
Time 2
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Voter Registration List
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Flu
Alice p4 26 18310 HIV
Bob p5 25 25000 Fever
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Flu
Alice p4 HIV
Bob p5 Fever
John p6 Fever
29
3-invariance
Time 3
Time 1
Time 2
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Voter Registration List
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 15000
John p6 20 29000

David pRL 31 31000
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Flu
Alice p4 26 18310 HIV
Bob p5 25 15000 Fever
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Flu
Alice p4 HIV
Bob p5 Fever
John p6 Fever
30
3-invariance
Time 3
Time 1
Time 2
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Voter Registration List
Medical Data Some Useful Attributes
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 15000
John p6 20 29000

David pRL 31 31000
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
p2
p3
p5
p1
p4
p6
Hospital
Medical Data Some Useful Attributes
Medical Data
This table satisfies 3-invariance. This is
because each individual is linked to the SAME
signature.
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Flu
Alice p4 26 18310 HIV
Bob p5 25 15000 Fever
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Flu
Alice p4 HIV
Bob p5 Fever
John p6 Fever
31
3-invariance
Time 3
Time 1
Time 2
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Time 3
Voter Registration List
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 15000
John p6 20 29000

David pRL 31 31000
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Flu
Alice p4 26 18310 HIV
Bob p5 25 15000 Fever
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Flu
Alice p4 HIV
Bob p5 Fever
John p6 Fever
32
3-invariance
Time 3
Time 1
Time 2
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Voter Registration List
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 15000
John p6 20 29000

David pRL 31 31000
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Time 3
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Flu
Alice p4 26 18310 HIV
Bob p5 25 15000 Fever
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Flu
Alice p4 HIV
Bob p5 Fever
John p6 Fever
33
3-invariance
Time 3
Time 1
Time 2
Time 3
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Voter Registration List
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 15000
John p6 20 29000

David pRL 31 31000
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Flu
Alice p4 26 18310 HIV
Bob p5 25 15000 Fever
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Flu
Alice p4 HIV
Bob p5 Fever
John p6 Fever
34
3-invariance
Time 3
Time 1
Time 2
Time 3
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Voter Registration List
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 15000
John p6 20 29000

David pRL 31 31000
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Flu
Alice p4 26 18310 HIV
Bob p5 25 15000 Fever
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Flu
Alice p4 HIV
Bob p5 Fever
John p6 Fever
35
3-invariance
Time 3
Time 1
Time 2
Time 3
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Public
Voter Registration List
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 15000
John p6 20 29000

David pRL 31 31000
Hospital
Medical Data Some Useful Attributes
Medical Data
Name PID Age Zip Code Disease
Raymond p1 23 16355 Flu
Peter p2 22 15500 HIV
Mary p3 21 12900 Flu
Alice p4 26 18310 HIV
Bob p5 25 15000 Fever
John p6 20 29000 Fever
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Flu
Alice p4 HIV
Bob p5 Fever
John p6 Fever
36
3-invariance
Time 1
Time 2
Time 3
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Time 3
Time 1
Time 2
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
37
3-invariance
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
Name PID Age Zip Code
Raymond p1 23 16355
Peter p2 22 15500
Mary p3 21 12900
Alice p4 26 18310
Bob p5 25 25000
John p6 20 29000

David pRL 31 31000
Knowledge 1
Time 3
Time 1
Time 2
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
38
3-invariance
PID Signature
p1 Flu, HIV, Fever
p2 Flu, HIV, Fever
p3 Flu, HIV, Fever
p4 Flu, HIV, Fever
p5 Flu, HIV, Fever
p6 Flu, HIV, Fever
I can deduce that p1 and p6 cannot be linked to
HIV.
Knowledge 1
Time 3
Time 1
Time 2
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
39
PID HIV?
p1
p2
p3
p4
p5
p6
Yes
No
No
I can deduce that p1 and p6 cannot be linked to
HIV.
Proof by contradiction.
Suppose p1 is linked to HIV.
Knowledge 1
Time 3
Time 1
Time 2
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
40
PID HIV?
p1
p2
p3
p4
p5
p6
Yes
No
No
I can deduce that p1 and p6 cannot be linked to
HIV.
No
No
Proof by contradiction.
Suppose p1 is linked to HIV.
Knowledge 1
Time 3
Time 1
Time 2
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
41
PID HIV?
p1
p2
p3
p4
p5
p6
Yes
No
No
I can deduce that p1 and p6 cannot be linked to
HIV.
No
No
Proof by contradiction.
No
Suppose p1 is linked to HIV.
Knowledge 1
Time 3
Time 1
Time 2
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
42
PID HIV?
p1
p2
p3
p4
p5
p6
Yes
No
No
I can deduce that p1 and p6 cannot be linked to
HIV.
No
No
p1 CANNOT be linked to HIV.
Proof by contradiction.
No
Suppose p1 is linked to HIV.
Contradiction!
Knowledge 1
Time 3
Time 1
Time 2
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
43
PID HIV?
p1
p2
p3
p4
p5
p6
No
I can deduce that p1 and p6 cannot be linked to
HIV.
No
Proof by contradiction.
Yes
Suppose p6 is linked to HIV.
Knowledge 1
Time 3
Time 1
Time 2
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
44
PID HIV?
p1
p2
p3
p4
p5
p6
No
No
No
I can deduce that p1 and p6 cannot be linked to
HIV.
No
Proof by contradiction.
Yes
Suppose p6 is linked to HIV.
Knowledge 1
Time 3
Time 1
Time 2
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
45
PID HIV?
p1
p2
p3
p4
p5
p6
No
No
No
No
I can deduce that p1 and p6 cannot be linked to
HIV.
No
Proof by contradiction.
Yes
Suppose p6 is linked to HIV.
Knowledge 1
Time 3
Time 1
Time 2
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
46
PID HIV?
p1
p2
p3
p4
p5
p6
No
No
No
No
I can deduce that p1 and p6 cannot be linked to
HIV.
No
p6 CANNOT be linked to HIV.
Proof by contradiction.
Yes
Suppose p6 is linked to HIV.
Contradiction!
Knowledge 1
Time 3
Time 1
Time 2
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
47
Problem (m-invariance) At the current time t,
we want to generate a table which satisfies the
following. Probability that an individual is
linked to a sensitive value wrt all published
tables at any time lt t is at most 1/m.
I can deduce that p1 and p6 cannot be linked to
HIV.
I can deduce that p4 MUST be linked to HIV.
Privacy breaches!
Knowledge 1
Time 3
Time 1
Time 2
Why?
3-invariance
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
48
Original Medical Data
Time 1
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
HIV-decoys (i.e., p1 and p3) are used to reduce
the strong linkage between p2 and HIV.
p2 is an HIV-holder.
p1 is an HIV-decoy.
I can deduce that p4 MUST be linked to HIV.
p3 is an HIV-decoy.
Privacy breaches!
Knowledge 1
Time 3
Time 1
Time 2
Why?
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
49
Original Medical Data
Time 1
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
p2
p1
p3
p2 is an HIV-holder.
HIV-decoy
p1 is an HIV-decoy.
HIV-holder
HIV-decoy
I can deduce that p4 MUST be linked to HIV.
p3 is an HIV-decoy.
Privacy breaches!
Knowledge 1
Time 3
Time 1
Time 2
Why?
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
50
Original Medical Data
p4
p6
p5
Time 1
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
p2
p1
p3
HIV-decoy
HIV-holder
HIV-decoy
p4 is an HIV-holder.
I can deduce that p4 MUST be linked to HIV.
Privacy breaches!
Knowledge 1
p5 is an HIV-decoy.
Time 3
Time 1
Time 2
Why?
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p6 is an HIV-decoy.
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
51
Original Medical Data
p4
p6
p5
Time 1
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
p2
p1
p3
HIV-decoy
HIV-holder
HIV-decoy
I can deduce that p4 MUST be linked to HIV.
Privacy breaches!
Knowledge 1
Time 3
Time 1
Time 2
Why?
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
52
Original Medical Data
p4
p6
p5
Time 1
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
p2
p1
p3
HIV-decoy
HIV-holder
HIV-decoy
I can deduce that p4 MUST be linked to HIV.
Privacy breaches!
Knowledge 1
Time 3
Time 1
Time 2
Why?
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
53
Original Medical Data
p4
p6
p5
Time 1
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
p2
p1
p3
HIV-decoy
HIV-holder
HIV-decoy
I can deduce that p4 MUST be linked to HIV.
Privacy breaches!
Knowledge 1
Time 3
Time 1
Time 2
Why?
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
54
Original Medical Data
p4
p6
p5
Time 1
Name PID Disease
Raymond p1 Flu
Peter p2 HIV
Mary p3 Fever
Alice p4 HIV
Bob p5 Flu
John p6 Fever
p2
p1
p3
p1 and p6 are in the same cohort.Besides, they
are in the same group of the published table at
time 3
HIV-decoy
Idea This kind of grouping can lead to privacy
breaches.
HIV-holder
HIV-decoy
I can deduce that p4 MUST be linked to HIV.
We can protect privacy by avoiding this kind of
grouping.
Privacy breaches!
Knowledge 1
Time 3
Time 1
Time 2
Why?
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
55
Time 3
3-scarcity
p4
p6
p5
Age Zip Code Disease
22,25 15k,17k HIV
22,25 15k,17k Flu
22,25 15k,17k Fever
20,26 12k,29k Flu
20,26 12k,29k HIV
20,26 12k,29k Fever
p2
p1
p3
p1
p2
p5
p3
p4
p6
HIV-decoy
HIV-holder
HIV-decoy
Knowledge 1
Time 3
Time 1
Time 2
3-invariance
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
Age Zip Code Disease
21,25 12k,16k HIV
21,25 12k,16k Flu
21,25 12k,16k Fever
20,26 16k,29k Flu
20,26 16k,29k HIV
20,26 16k,29k Fever
p1
p2
p3
p2
p3
p6
p2
p3
p5
p1
p4
p6
p4
p5
p6
p1
p4
p5
56
Time 3
3-scarcity
p4
p6
p5
Age Zip Code Disease
22,25 15k,17k HIV
22,25 15k,17k Flu
22,25 15k,17k Fever
20,26 12k,29k Flu
20,26 12k,29k HIV
20,26 12k,29k Fever
p2
p1
p3
p1
p2
p5
p3
p4
p6
HIV-decoy
HIV-holder
HIV-decoy
Knowledge 1
Time 1
Time 2
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
p1
p2
p3
p2
p3
p6
p4
p5
p6
p1
p4
p5
57
p4
p6
p5
p2
p1
p3
Probability that an individual is linked to a
sensitive value wrt these three tables is at most
1/3.
HIV-decoy
HIV-holder
HIV-decoy
Knowledge 1
3-scarcity
Time 3
Time 1
Time 2
Age Zip Code Disease
22,25 15k,17k HIV
22,25 15k,17k Flu
22,25 15k,17k Fever
20,26 12k,29k Flu
20,26 12k,29k HIV
20,26 12k,29k Fever
Age Zip Code Disease
21,23 12k,17k Flu
21,23 12k,17k HIV
21,23 12k,17k Fever
20,26 18k,29k HIV
20,26 18k,29k Flu
20,26 18k,29k Fever
Age Zip Code Disease
20,22 12k,29k HIV
20,22 12k,29k Flu
20,22 12k,29k Fever
23,26 16k,25k Flu
23,26 16k,25k HIV
23,26 16k,25k Fever
p1
p2
p3
p1
p2
p5
p2
p3
p6
p3
p4
p6
p4
p5
p6
p1
p4
p5
58
3. Algorithm

• Propose an algorithm which follows the principle
• Whenever we form one group,
• choose one member from each cohort

59
3. Guarantee

• Theorem Our proposed algorithm can generate a
  table which satisfies the following.Probability
  that an individual is linked to a sensitive value
  wrt all published tables at any time lt t is at
  most 1/l (i.e., l-scarcity)

60
4. Experiments

• Real Data Set (CADRMP)
• http//www.hc-sc.gc.ca/dhp-mps/medeff/databasdon/i
  ndex_e.html
• Real hospital database
• Patient Information (Voter Registration List)
• 40,478 tuples
• Medical Record
• 105,420 tuples
• Each patient can be linked to multiple diseases

61
4. Experiments

• Studies
• Privacy Breaches of an existing model
• m-invariance
• Performance of our proposed algorithm

62
4.1 Privacy Breaches of an existing model

• Breach Rate
• The proportion of tuples with privacy breaches
• m-invariance

63
4.2 Performance of our proposed algorithm

• Measurements
• Computation Cost
• Relative Average Error
• Variations
• Parameter l (used in l-scarcity)
• No. of publishe