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CS5322 - Groupe 6
1
Implementation (Group 6) Monika (A0066244H)Damien Forest (A0066246A)Rattanak Chhung (A0066240N)Yann-Loup Phan Van Song (A0066238B)
A Privacy-Preserving Index for Range Queries
CS5322 - Groupe 6
2
Introduction
•What we will present in this presentation▫Query-Optimal-Bucketization Algorithm▫Attack 2 x 1D (cutting partitions)▫Two attributes with Hilbert curve
•What we have also done:▫Controlled-Diffusion Algorithm▫Remake Experiments
CS5322 - Groupe 6
3
Query-Optimal-Bucketization1 attribute
CS5322 - Groupe 6
4
value freq
0 1
1 4
2 0
3 3
4 2
5 1
6 6
7 1
8 0
9 1
Dataset of plain values
Inputs
find the bucketization that reduces the number of total false positives
Our goal:
For all the sub-problems with max 2 buckets compute H[k][2] = (BC(1, i) + BC(i + 1,K))
Store optimal-partition-point ibest in OPP[k][2]Do the same for more than 2 buckets:
H[k][l] = (H[i][l - 1] + BC(i + 1, k))Store optimal-partition-point ibest in OPP[k][l]Reconstrcut the buckets by taking:btemp = new Bucket(V[OPP[j - 1][M - 1 - i]], V[j - 1])
Principle:
BC (i , j)=∑i=1
j
f t .(vj−vi+1)
CS5322 - Groupe 6
5
BC table
1 0 0 0 0 0 0 0
10 4 0 0 0 0 0 0
15 8 0 0 0 0 0 0
32 21 3 0 0 0 0 0
50 36 10 2 0 0 0 0
66 50 18 6 1 0 0 0
119 96 48 27 14 6 0 0
144 119 65 40 24 14 1 0
190 162 98 66 45 32 6 1
j
ittij fvvjiBC )1(),(
BC=
CS5322 - Groupe 6
6
value freq
0 1
1 4
2 0
3 3
4 2
5 1
6 6
7 1
8 0
9 1
Dataset of plain values
Inputs
Intermediary results
Bucket Bucketization cost
[0-4] (4+1).(10)
[5-9] (4+1).9
First Step: M=2MinCost = 95
CS5322 - Groupe 6
7
value freq
0 1
1 4
2 0
3 3
4 2
5 1
6 6
7 1
8 0
9 1
Dataset of plain values
Inputs
Outputs
[ 0 - 2] [ 3 - 5 ] [ 6 - 6 ] [ 7 - 9 ]
5
6 6
2
Buckets Bucketization cost
[ 0 - 2 ] 3.5
[ 3 - 5 ] 3.6
[ 6 - 6 ] 1.6
[ 7 - 9 ] 3.2
Last Step: M=4MinCost = 45
Note: Depending on what we want we can include or not the values that have 0 frequency
CS5322 - Groupe 6
8
0.15 0.20 0.25 0.30 0.35 0.400
10
20
30
40
50
60
70
MinCost on our DataSet
value freq
0 1
1 4
2 0
3 3
4 2
5 1
6 6
7 1
8 0
9 1
Dataset of plain values
Inputs
Link with privacy
MinCost strictly decreasing with M but might increase the likeliness of an attack (Cf.[1] Damiani et al.)-> Tradeoff Performance-Privacy
CS5322 - Groupe 6
9
Attacks
CS5322 - Groupe 6
10
value freq
(1 ; 4) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
Dataset of plain values
Partition attribute 1
Partition attribute 2
Encrypted table
Inputs
CS5322 - Groupe 6
11
value freq
(1 ; 4) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
Context
To match the indexes and the buckets
Our goal:
How ?
Working with cardinalities
CS5322 - Groupe 6
12
value freq
(1 ; 4) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
Algorithm
Based on propagation, this is the Sudoku algorithm:
- First, identify some indexes
- While some new indexes are identified
Do propagation
Trigger (first attack):Done by BAA and BAA2. Their goal is to identify one or several indexes to launch the propagation
Propagation (loop):The identification of an index decreases the cardinalities in couples and helps to identify new indexes…
CS5322 - Groupe 6
13
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
First attack - BAA
B11 = [
BAA :
CS5322 - Groupe 6
14
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
First attack - BAA
B11 = [
BAA :
CS5322 - Groupe 6
15
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
First attack - BAA
BAA :
B11 = [
73 ,
CS5322 - Groupe 6
16
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
First attack - BAA
BAA :
B11 = [
73 , 15 ]
CS5322 - Groupe 6
17
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
First attack - BAA
B11 = [
73 , 15 ]
B12 = [
73 , 15 ]
B13 = [
79 , 30 ]
B14 = [
79 , 30 ]
B21 = [
20 , 45 ]
B22 = [
9 , 74 ]
B23 = [B24 = [
9 , 74 ]
20 , 45 ]
BAA :
BAA2 :
No identified index …
CS5322 - Groupe 6
18
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
B11 = [
73 , 15 ]
B12 = [
73 , 15 ]
B13 = [
79 , 30 ]
B14 = [
79 , 30 ]
B21 = [
20 , 45 ]
B22 = [
9 , 74 ]
B23 = [B24 = [
9 , 74 ]
20 , 45 ]
BAA :
BAA2 :
No identified index …
First attack - BAA2
value freq
(73 ; 45)
1
(73 ; 20)
1
(15 ; 9) 2
(79 ; 45)
1
(79 ; 74)
1
(79 ; 20)
1
(30 ; 74)
2
(30 ; 9) 1
B11 = [B12 = [B13 = [B14 = [B21 = [B22 = [B23 = [B24 = [
CS5322 - Groupe 6
19
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
BAA2 :
B11 = [B12 = [B13 = [B14 = [B21 = [B22 = [B23 = [B24 = [
|B11;B21| =
value freq
(73 ; 45)
1
(73 ; 20)
1
(15 ; 9) 2
(79 ; 45)
1
(79 ; 74)
1
(79 ; 20)
1
(30 ; 74)
2
(30 ; 9) 1
First attack - BAA2
CS5322 - Groupe 6
20
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
BAA2 :
B11 = [B12 = [B13 = [B14 = [B21 = [B22 = [B23 = [B24 = [
|B11;B21| =
1
value freq
(73 ; 45)
1
(73 ; 20)
1
(15 ; 9) 2
(79 ; 45)
1
(79 ; 74)
1
(79 ; 20)
1
(30 ; 74)
2
(30 ; 9) 1
First attack - BAA2
CS5322 - Groupe 6
21
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
BAA2 :
B11 = [B12 = [B13 = [B14 = [B21 = [B22 = [B23 = [B24 = [
|B11;B21| =
1
73 , 79 , 30
45 , 20 , 74 , 9
value freq
(73 ; 45)
1
(73 ; 20)
1
(15 ; 9) 2
(79 ; 45)
1
(79 ; 74)
1
(79 ; 20)
1
(30 ; 74)
2
(30 ; 9) 1
First attack - BAA2
CS5322 - Groupe 6
22
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
BAA2 :
B11 = [B12 = [B13 = [B14 = [B21 = [B22 = [B23 = [B24 = [
|B11;B21| =
1
73 , 79 , 30
45 , 20 , 74 , 9
value freq
(73 ; 45)
1
(73 ; 20)
1
(15 ; 9) 2
(79 ; 45)
1
(79 ; 74)
1
(79 ; 20)
1
(30 ; 74)
2
(30 ; 9) 1
First attack - BAA2
CS5322 - Groupe 6
23
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
BAA2 :
B11 = [B12 = [B13 = [B14 = [B21 = [B22 = [B23 = [B24 = [
|B11;B21| =
1
73 , 79 , 30
45 , 20 , 74 , 9
|B11;B22| =
0
value freq
(73 ; 45)
1
(73 ; 20)
1
(15 ; 9) 2
(79 ; 45)
1
(79 ; 74)
1
(79 ; 20)
1
(30 ; 74)
2
(30 ; 9) 1
First attack - BAA2
CS5322 - Groupe 6
24
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
BAA2 :
B11 = [B12 = [B13 = [B14 = [B21 = [B22 = [B23 = [B24 = [
|B11;B21| =
1
73 , 79 , 30
45 , 20 , 74 , 9
|B11;B22| =
0
value freq
(73 ; 45)
1
(73 ; 20)
1
(15 ; 9) 2
(79 ; 45)
1
(79 ; 74)
1
(79 ; 20)
1
(30 ; 74)
2
(30 ; 9) 1
|B11;B23| =
0
First attack - BAA2
CS5322 - Groupe 6
25
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
BAA2 :
B11 = [B12 = [B13 = [B14 = [B21 = [B22 = [B23 = [B24 = [
|B11;B21| =
1
73 , 79 , 30
45 , 20 , 74 , 9
|B11;B22| =
0
value freq
(73 ; 45)
1
(73 ; 20)
1
(15 ; 9) 2
(79 ; 45)
1
(79 ; 74)
1
(79 ; 20)
1
(30 ; 74)
2
(30 ; 9) 1
|B11;B23| =
0|B11;B24| =
First attack - BAA2
CS5322 - Groupe 6
26
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
BAA2 :
B11 = [B12 = [B13 = [B14 = [B21 = [B22 = [B23 = [B24 = [
|B11;B21| =
1
73 , 79 , 30
45 , 20 , 74 , 9
|B11;B22| =
0
value freq
(73 ; 45)
1
(73 ; 20)
1
(15 ; 9) 2
(79 ; 45)
1
(79 ; 74)
1
(79 ; 20)
1
(30 ; 74)
2
(30 ; 9) 1
|B11;B23| =
0|B11;B24| =
1
First attack - BAA2
CS5322 - Groupe 6
27
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
BAA2 :
B11 = [B12 = [B13 = [B14 = [B21 = [B22 = [B23 = [B24 = [
|B11;B21| =
1
73 , 79 , 30
45 , 20 , 74 , 9
|B11;B22| =
0
value freq
(73 ; 45)
1
(73 ; 20)
1
(15 ; 9) 2
(79 ; 45)
1
(79 ; 74)
1
(79 ; 20)
1
(30 ; 74)
2
(30 ; 9) 1
|B11;B23| =
0|B11;B24| =
1
45 , 20 , 74 , 9
First attack - BAA2
CS5322 - Groupe 6
28
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
BAA2 :
B11 = [B12 = [B13 = [B14 = [B21 = [B22 = [B23 = [B24 = [
|B11;B21| =
1
73 , 79 , 30
45 , 20 , 74 , 9
|B11;B22| =
0
value freq
(73 ; 45)
1
(73 ; 20)
1
(15 ; 9) 2
(79 ; 45)
1
(79 ; 74)
1
(79 ; 20)
1
(30 ; 74)
2
(30 ; 9) 1
|B11;B23| =
0|B11;B24| =
1
45 , 20 , 74 , 9
First attack - BAA2
CS5322 - Groupe 6
29
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
BAA2 :
B11 = [B12 = [B13 = [B14 = [B21 = [B22 = [B23 = [B24 = [
|B11;B21| =
1
73 , 79 , 30 ]
45 , 20 , 74 , 9 ]
|B11;B22| =
0
value freq
(73 ; 45)
1
(73 ; 20)
1
(15 ; 9) 2
(79 ; 45)
1
(79 ; 74)
1
(79 ; 20)
1
(30 ; 74)
2
(30 ; 9) 1
|B11;B23| =
0|B11;B24| =
1
45 , 20 , 74 , 9 ]
|B12;B21| = |B12;B22| = |B12;B23| = |B12;B24| = |B13;B21| = |B13;B22| = |B13;B23| = |B13;B24| = |B14;B21| = |B14;B22| = |B14;B23| = |B14;B24| =
15 , 30 ]
73 , 79 , 30 ]73 , 15 , 79 , 30 ]
45 , 20 , 74 , 9 ]45 , 20 , 74 , 9 ]
No identified index …
0 0 2 0
1 0 1 1
0 2 1 0
First attack - BAA2
CS5322 - Groupe 6
30
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
First attack - intersection
BAA2 :
B11 = [B12 = [B13 = [B14 = [B21 = [B22 = [B23 = [B24 = [
73 , 79 , 30 ]
45 , 20 , 74 , 9 ]
45 , 20 , 74 , 9 ]
15 , 30 ]
73 , 79 , 30 ]73 , 15 , 79 , 30 ]
45 , 20 , 74 , 9 ]45 , 20 , 74 , 9 ]
No identified index …
B11 = [
73 , 15 ]
B12 = [
73 , 15 ]
B13 = [
79 , 30 ]
B14 = [
79 , 30 ]
B21 = [
20 , 45 ]
B22 = [
9 , 74 ]
B23 = [B24 = [
9 , 74 ]
20 , 45 ]
BAA :
No identified index …
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
CS5322 - Groupe 6
31
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
BAA2 :
B11 = [B12 = [B13 = [B14 = [B21 = [B22 = [B23 = [B24 = [
73 , 79 , 30 ]
45 , 20 , 74 , 9 ]
45 , 20 , 74 , 9 ]
15 , 30 ]
73 , 79 , 30 ]73 , 15 , 79 , 30 ]
45 , 20 , 74 , 9 ]45 , 20 , 74 , 9 ]
No identified index …
B11 = [
73 , 15 ]
B12 = [
73 , 15 ]
B13 = [
79 , 30 ]
B14 = [
79 , 30 ]
B21 = [
20 , 45 ]
B22 = [
9 , 74 ]
B23 = [B24 = [
9 , 74 ]
20 , 45 ]
BAA :
No identified index …
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
First attack - intersection
CS5322 - Groupe 6
32
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
BAA2 :
B11 = 73 B12 = 15B13 = [ 79,
30 ]B14 = [ 79, 30 ]B21 = [ 20, 45 ]B22 = [ 9, 74 ]B23 = [ 9, 74 ]B24 = [ 20, 45 ]
BAA &
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
First attack - intersection
CS5322 - Groupe 6
33
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
BAA2 :
B11 = 73 B12 = 15B13 = [ 79,
30 ]B14 = [ 79, 30 ]B21 = [ 20, 45 ]B22 = [ 9, 74 ]B23 = [ 9, 74 ]B24 = [ 20, 45 ]
BAA &
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
First attack - intersection
CS5322 - Groupe 6
34
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Creation of couples of indexes
B11 = 73 B12 = 15
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = [ 9, 74 ]B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [
CS5322 - Groupe 6
35
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = [ 9, 74 ]B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [(45;1),
B11 = 73 B12 = 15
Creation of couples of indexes
CS5322 - Groupe 6
36
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = [ 9, 74 ]B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [(45;1),
B11 = 73 B12 = 15
Creation of couples of indexes
(20;1)])
CS5322 - Groupe 6
37
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = [ 9, 74 ]B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [ (45;1), (20;1)])
(15 ; [
B11 = 73 B12 = 15
Creation of couples of indexes
CS5322 - Groupe 6
38
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = [ 9, 74 ]B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [ (45;1), (20;1)])
(15 ; [ (9;2)])
B11 = 73 B12 = 15
Creation of couples of indexes
CS5322 - Groupe 6
39
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = [ 9, 74 ]B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [(45;1),(20;1)])(15 ; [(9;2)])
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2),(9;1)])
(45 ; [(73;1),(79;1)])(9 ; [(15;2),(30;1)])(74 ; [(79;1),(30;2)])(20 ; [(79;1),(73;1)])
B11 = 73 B12 = 15
Creation of couples of indexes
CS5322 - Groupe 6
40
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Remove known indexes from sets
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = [ 9, 74 ]B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [(45;1),(20;1)])(15 ; [(9;2)])
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2),(9;1)])
(45 ; [(73;1),(79;1)])(9 ; [(15;2),(30;1)])(74 ; [(79;1),(30;2)])(20 ; [(79;1),(73;1)])
B11 = 73 B12 = 15
CS5322 - Groupe 6
41
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = [ 9, 74 ]B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [(45;1),(20;1)])(15 ; [(9;2)])
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2),(9;1)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])(20 ; [(79;1)])
B11 = 73 B12 = 15
Remove known indexes from sets
CS5322 - Groupe 6
42
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Propagation 1 - look for new indexes
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = [ 9, 74 ]B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [(45;1),(20;1)])(15 ; [(9;2)])
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2),(9;1)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
B11 = 73 B12 = 15
(20 ; [(79;1)])
CS5322 - Groupe 6
43
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Propagation 1 - look for new indexes
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = [ 9, 74 ]B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [(45;1),(20;1)])(15 ; [(9;2)])
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2),(9;1)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
B11 = 73 B12 = 15
(20 ; [(79;1)])
CS5322 - Groupe 6
44
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Propagation 1 - look for new indexes
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = [ 9, 74 ]B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [(45;1),(20;1)])(15 ; [(9;2)])
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2),(9;1)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
B11 = 73 B12 = 15
(20 ; [(79;1)])
CS5322 - Groupe 6
45
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = [ 9, 74 ]B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [(45;1),(20;1)])(15 ; [(9;2)])
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2),(9;1)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
B11 = 73 B12 = 15
(20 ; [(79;1)])
Propagation 1 - look for new indexes
Same cardinality: no way to distinguish them !
CS5322 - Groupe 6
46
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = [ 9, 74 ]B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [(45;1),(20;1)])(15 ; [(9;2)])
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2),(9;1)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
B11 = 73 B12 = 15
(20 ; [(79;1)])
Propagation 1 - look for new indexes
CS5322 - Groupe 6
47
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = [ 9, 74 ]B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [(45;1),(20;1)])(15 ; [(9;2)])
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2),(9;1)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
Propagation 1 - identify the new index
B11 = 73 B12 = 15
(20 ; [(79;1)])
CS5322 - Groupe 6
48
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = [ 9, 74 ]B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [(45;1),(20;1)])(15 ; [(9;2)])
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2),(9;1)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
B11 = 73 B12 = 15
(20 ; [(79;1)])
Propagation 1 - identify the new index
CS5322 - Groupe 6
49
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = 9B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [(45;1),(20;1)])(15 ; [(9;2)])
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2),(9;1)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
B11 = 73 B12 = 15
(20 ; [(79;1)])
Propagation 1 - identify the new index
CS5322 - Groupe 6
50
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Propagation 1 - add the new index to the list
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = 9B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : 73, 15
New identified indexes :
(73 ; [(45;1),(20;1)])(15 ; [(9;2)])
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2),(9;1)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
9
B11 = 73 B12 = 15
(20 ; [(79;1)])
51
CS5322 - Groupe 6
value freq
(1 ; 2) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Propagation 1 - remove deprecated data
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 9, 74 ]
B23 = 9B24 = [ 20, 45 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
New identified indexes : New identified indexes :
(73 ; [(45;1),(20;1)])(15 ; [(9;2)])
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2),(9;1)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
973, 15
B11 = 73 B12 = 15
(20 ; [(79;1)])
CS5322 - Groupe 6
52
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B13 B14
[ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 74 ]
B23 = 9B24 = [ 20, 45 ]
Ind1 Ind2
79 45
79 74
30 74
30 9
79 20
30 74
New identified indexes : New identified indexes :
(73 ; [(45;1),(20;1)])(15 ; [(9;2)])
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
973, 15
B11 = 73 B12 = 15
(20 ; [(79;1)])
Propagation 1 - remove deprecated data
CS5322 - Groupe 6
53
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B13 B14
[ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 74 ]
B23 = 9B24 = [ 20, 45 ]
Ind1 Ind2
79 45
79 74
30 74
30 9
79 20
30 74
New identified indexes : New identified indexes :
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
9
B11 = 73 B12 = 15
(20 ; [(79;1)])
Propagation 2 - look for new indexes
CS5322 - Groupe 6
54
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B13 B14
[ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 74 ]
B23 = 9B24 = [ 20, 45 ]
Ind1 Ind2
79 45
79 74
30 74
30 9
79 20
30 74
New identified indexes : New identified indexes :
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
9
B11 = 73 B12 = 15
(20 ; [(79;1)])
Propagation 2 - look for new indexes
CS5322 - Groupe 6
55
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B13 B14
[ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 74 ]
B23 = 9B24 = [ 20, 45 ]
New identified indexes : New identified indexes :
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
9
B11 = 73 B12 = 15
Ind1 Ind2
79 45
79 74
30 74
30 9
79 20
30 74(20 ; [(79;1)])
Propagation 2 - identify the new index
CS5322 - Groupe 6
56
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B13 B14
[ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B13 = [ 79, 30 ]B14 = [ 79, 30 ]
B21 = [ 20, 45 ]B22 = [ 74 ]
B23 = 9B24 = [ 20, 45 ]
New identified indexes : New identified indexes :
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
9
B11 = 73 B12 = 15
Ind1 Ind2
79 45
79 74
30 74
30 9
79 20
30 74(20 ; [(79;1)])
Propagation 2 - identify the new index
CS5322 - Groupe 6
57
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B13 B14
[ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = [ 79, 30 ]B14 = 30
B21 = [ 20, 45 ]B22 = [ 74 ]
B23 = 9B24 = [ 20, 45 ]
New identified indexes : New identified indexes :
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
9
Ind1 Ind2
79 45
79 74
30 74
30 9
79 20
30 74(20 ; [(79;1)])
Propagation 2 - identify the new index
CS5322 - Groupe 6
58
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B13 B14
[ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = [ 79, 30 ]B14 = 30
B21 = [ 20, 45 ]B22 = [ 74 ]
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
930
Ind1 Ind2
79 45
79 74
30 74
30 9
79 20
30 74(20 ; [(79;1)])
Propagation 2 - add the new index to the list
CS5322 - Groupe 6
59
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B13 B14
[ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = [ 79, 30 ]B14 = 30
B21 = [ 20, 45 ]B22 = [ 74 ]
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1),(30;2)])
930
Ind1 Ind2
79 45
79 74
30 74
30 9
79 20
30 74(20 ; [(79;1)])
Propagation 2 - remove deprecated data
CS5322 - Groupe 6
60
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(14 ; 5)
1
B13 B14
[ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = [ 79 ]B14 = 30
B21 = [ 20, 45 ]B22 = [ 74 ]
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(9 ; [(30;1)])
(74 ; [(79;1)])
930
Ind1 Ind2
79 45
79 74
30 74
79 20
30 74(20 ; [(79;1)])
Propagation 2 - remove deprecated data
CS5322 - Groupe 6
61
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(14 ; 5)
1
B13 B14
[ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = [ 79 ]B14 = 30
B21 = [ 20, 45 ]B22 = [ 74 ]
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(74 ; [(79;1)])
30
Ind1 Ind2
79 45
79 74
30 74
79 20
30 74(20 ; [(79;1)])
Propagation 3 - look for new indexes
CS5322 - Groupe 6
62
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(14 ; 5)
1
B13 B14
[ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = [ 79 ]B14 = 30
B21 = [ 20, 45 ]B22 = [ 74 ]
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(74 ; [(79;1)])
30
Ind1 Ind2
79 45
79 74
30 74
79 20
30 74(20 ; [(79;1)])
Propagation 3 - look for new indexes
CS5322 - Groupe 6
63
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(14 ; 5)
1
B13 B14
[ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = [ 79 ]B14 = 30
B21 = [ 20, 45 ]B22 = [ 74 ]
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(74 ; [(79;1)])
30
Ind1 Ind2
79 45
79 74
30 74
79 20
30 74(20 ; [(79;1)])
Propagation 3 - identify the new index
CS5322 - Groupe 6
64
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(14 ; 5)
1
B13 B14
[ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = [ 79 ]B14 = 30
B21 = [ 20, 45 ]B22 = [ 74 ]
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(74 ; [(79;1)])
30
Ind1 Ind2
79 45
79 74
30 74
79 20
30 74(20 ; [(79;1)])
Propagation 3 - identify the new index
CS5322 - Groupe 6
65
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(14 ; 5)
1
B13 B14
[ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = [ 79 ]B14 = 30
B21 = [ 20, 45 ]B22 = 74
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(74 ; [(79;1)])
30
Ind1 Ind2
79 45
79 74
30 74
79 20
30 74(20 ; [(79;1)])
Propagation 3 - identify the new index
CS5322 - Groupe 6
66
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(14 ; 5)
1
B13 B14
[ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = [ 79 ]B14 = 30
B21 = [ 20, 45 ]B22 = 74
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(74 ; [(79;1)])
30 74
Ind1 Ind2
79 45
79 74
30 74
79 20
30 74(20 ; [(79;1)])
Propagation 3 - add the new index to the list
CS5322 - Groupe 6
67
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(14 ; 5)
1
B13 B14
[ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = [ 79 ]B14 = 30
B21 = [ 20, 45 ]B22 = 74
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(74;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(74 ; [(79;1)])
30 74
Ind1 Ind2
79 45
79 74
30 74
79 20
30 74(20 ; [(79;1)])
Propagation 3 - remove deprecated data
CS5322 - Groupe 6
68
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
B13
[ 7 ; 11 ]
B21 B22 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = [ 79 ]B14 = 30
B21 = [ 20, 45 ]B22 = 74
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(20;1)])
(30 ; [(74;2)])
(45 ; [(79;1)])
(74 ; [(79;1)])
30 74
Ind1 Ind2
79 45
79 74
79 20(20 ; [(79;1)])
Propagation 3 - remove deprecated data
CS5322 - Groupe 6
69
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
B13
[ 7 ; 11 ]
B21 B22 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = [ 79 ]B14 = 30
B21 = [ 20, 45 ]B22 = 74
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(20;1)])
(45 ; [(79;1)])
(74 ; [(79;1)])
74
Ind1 Ind2
79 45
79 74
79 20(20 ; [(79;1)])
Propagation 4 - look for new indexes
CS5322 - Groupe 6
70
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
B13
[ 7 ; 11 ]
B21 B22 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = [ 79 ]B14 = 30
B21 = [ 20, 45 ]B22 = 74
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(20;1)])
(45 ; [(79;1)])
(74 ; [(79;1)])
74
Ind1 Ind2
79 45
79 74
79 20(20 ; [(79;1)])
Propagation 4 - look for new indexes
CS5322 - Groupe 6
71
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
B13
[ 7 ; 11 ]
B21 B22 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = [ 79 ]B14 = 30
B21 = [ 20, 45 ]B22 = 74
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(20;1)])
(45 ; [(79;1)])
(74 ; [(79;1)])
74
Ind1 Ind2
79 45
79 74
79 20(20 ; [(79;1)])
Propagation 4 - identify the new index
CS5322 - Groupe 6
72
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
B13
[ 7 ; 11 ]
B21 B22 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = [ 79 ]B14 = 30
B21 = [ 20, 45 ]B22 = 74
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(20;1)])
(45 ; [(79;1)])
(74 ; [(79;1)])
74
Ind1 Ind2
79 45
79 74
79 20(20 ; [(79;1)])
Propagation 4 - identify the new index
CS5322 - Groupe 6
73
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
B13
[ 7 ; 11 ]
B21 B22 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = 79B14 = 30
B21 = [ 20, 45 ]B22 = 74
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(20;1)])
(45 ; [(79;1)])
(74 ; [(79;1)])
74
Ind1 Ind2
79 45
79 74
79 20(20 ; [(79;1)])
Propagation 4 - identify the new index
CS5322 - Groupe 6
74
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
B13
[ 7 ; 11 ]
B21 B22 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = 79B14 = 30
B21 = [ 20, 45 ]B22 = 74
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(20;1)])
(45 ; [(79;1)])
(74 ; [(79;1)])
74 79
Ind1 Ind2
79 45
79 74
79 20(20 ; [(79;1)])
Propagation 4 - add the new index to the list
CS5322 - Groupe 6
75
value freq
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
B13
[ 7 ; 11 ]
B21 B22 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = 79B14 = 30
B21 = [ 20, 45 ]B22 = 74
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(20;1)])
(45 ; [(79;1)])
(74 ; [(79;1)])
(20 ; [(79;1)])
74 79
Ind1 Ind2
79 45
79 74
79 20
Propagation 4 - remove deprecated data
CS5322 - Groupe 6
76
value freq
(7 ; 2) 1
(7 ; 11)
1
B13
[ 7 ; 11 ]
B21 B24
[ 0 ; 3 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = 79B14 = 30
B21 = [ 20, 45 ]B22 = 74
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(20;1)])
(45 ; [ ])
(74 ; [(79;1)])
(20 ; [ ])
74 79
Ind1 Ind2
79 45
79 20
Propagation 4 - remove deprecated data
CS5322 - Groupe 6
77
value freq
(7 ; 2) 1
(7 ; 11)
1
B13
[ 7 ; 11 ]
B21 B24
[ 0 ; 3 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = 79B14 = 30
B21 = [ 20, 45 ]B22 = 74
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(20;1)])
(45 ; [ ])
(20 ; [ ])
79
Ind1 Ind2
79 45
79 20
Propagation 5 - look for new indexes
CS5322 - Groupe 6
78
value freq
(7 ; 2) 1
(7 ; 11)
1
B13
[ 7 ; 11 ]
B21 B24
[ 0 ; 3 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = 79B14 = 30
B21 = [ 20, 45 ]B22 = 74
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(20;1)])
(45 ; [ ])
(20 ; [ ])
79
Ind1 Ind2
79 45
79 20
Propagation 5 - look for new indexes
No way! Impossible to identify them
CS5322 - Groupe 6
79
value freq
(7 ; 2) 1
(7 ; 11)
1
B13
[ 7 ; 11 ]
B21 B24
[ 0 ; 3 ] [ 10 ; 15 ]
B11 = 73 B12 = 15
B13 = 79B14 = 30
B21 = [ 20, 45 ]B22 = 74
B23 = 9B24 = [ 20, 45 ]
New identified indexes :
New identified indexes :
(79 ; [(45;1),(20;1)])
(45 ; [ ])
(20 ; [ ])
Propagation 5 - STOP
79
Ind1 Ind2
79 45
79 20
No other index: we have to stop!
CS5322 - Groupe 6
80
value freq
(1 ; 4) 1
(1 ; 11)
1
(4 ; 8) 1
(5 ; 9) 1
(7 ; 2) 1
(7 ; 11)
1
(9 ; 4) 1
(12 ; 4)
1
(13 ; 7)
1
(14 ; 5)
1
B11 B12 B13 B14
[ 0 ; 2 ] [ 3 ; 6 ] [ 7 ; 11 ]
[ 12 ; 15 ]
B21 B22 B23 B24
[ 0 ; 3 ] [ 4 ; 5 ] [ 6 ; 9 ] [ 10 ; 15 ]
Ind1 Ind2
73 45
15 9
79 45
79 74
30 74
30 9
15 9
79 20
30 74
73 20
Results
B11 = 73
B12 = 15
B13 = 79
B14 = 30
B21 = [ 20, 45 ]B22 = 74
B23 = 9
B24 = [ 20, 45 ]
CS5322 - Groupe 6
81
Two attributes
CS5322 - Groupe 6
82
Hilbert curve
col1
col2
0 12 3
3
2
1
0
Hilbert value
Col1 value
Col2 value
0 0 0
1 1 0
2 1 1
3 0 1
4 0 2
5 0 3
6 1 3
7 1 2
8 2 2
9 2 3
10 3 3
11 3 2
12 3 1
13 2 1
14 2 0
15 3 0
NN ²
83
Hilbert curve
col1
col2
0 12 3
3
2
1
0
CS5322 - Groupe 6
Id Col1
Col2
HV
1 0 0 0
2 1 1 3
3 1 1 3
4 1 1 3
5 1 1 3
6 0 2 4
7 1 2 7
8 1 2 7
9 1 2 7
10 2 3 9
11 3 3 10
12 2 1 13
13 2 1 13
CS5322 - Groupe 6
84
Two dimensions -> One dimension
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1
0 0
4
1
0 0
3
0
1 1
0 0
2
0 0
Hibert value
Fre
quency
M = 5
B1 B3 B4 B5B2
85
Hilbert curve
col1
col2
0 12 3
3
2
1
0
CS5322 - Groupe 6
Id Col1
Col2
HV B
1 0 0 0 B1
2 1 1 3
3 1 1 3
4 1 1 3
5 1 1 3
6 0 2 4 B2
7 1 2 7 B3
8 1 2 7
9 1 2 7
10 2 3 9 B4
11 3 3 10
12 2 1 13 B5
13 2 1 13
B3
B2 B4
B1 B5
86
Hilbert curve
col1
col2
0 12 3
3
2
1
0
CS5322 - Groupe 6
Id Col1
Col2
HV B
1 0 0 0 B1
2 1 1 3
3 1 1 3
4 1 1 3
5 1 1 3
6 0 2 4 B2
7 1 2 7 B3
8 1 2 7
9 1 2 7
10 2 3 9 B4
11 3 3 10
12 2 1 13 B5
13 2 1 13
B2 B4
B1 B5
Range query on [1-1] for col1
… WHERE Col1 = 1
B3
87
Hilbert curve
col1
col2
0 12 3
3
2
1
0
CS5322 - Groupe 6
Id Col1
Col2
HV B
1 0 0 0 B1
2 1 1 3
3 1 1 3
4 1 1 3
5 1 1 3
6 0 2 4 B2
7 1 2 7 B3
8 1 2 7
9 1 2 7
10 2 3 9 B4
11 3 3 10
12 2 1 13 B5
13 2 1 13
B3
B2 B4
B1 B5
Range query on [1-2] for col2
… WHERE Col2 in [1-2]
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88
Hilbert curve
Range query?
col1
col2
CS5322 - Groupe 6
89
Conclusion
•What we did:▫(Model)▫Implementation QOB and CD▫Remake Experiment▫Attacks▫Two attributes for QOB
•What we could have done more:▫Comparison 2 x QOB-1D, 1 x QOB-2D and
another multi-attributes partition (e.g. Mondrian)
▫Analyze of attacks in function of privacy indicators
CS5322 - Groupe 6
90
Thank you. Any questions?
CS5322 - Groupe 6
91
[1] E. Damiani, S. D. C. Vimercati, S. Jajodia, S. Paraboschi, and P. Samarati. Balancing Condentiality and Eciency in Untrusted RelationalDBMSs. In CCS '03: Proceedings of the 10th ACM conference on Computer and communications security, pages 93-102, New York, NY, USA, 2003. ACM.
[3] H. Hacgıümüs, B. Iyer, C. Li, and S. Mehrotra. Executin SQL over Encrypted Date in the Database-Service-Provider Model. In IGMOD '02: Proceedings of the 2002 ACM SIGMOD international conference on Management of data, pages 216-227, New York, NY, USA, 2002. ACM.
[5] B. Hore, S. Mehrotra, and G. Tsudik. A Privacy Preserving Index for Range Queries. In VLDB '04: Proceedings of the Thirtieth International conference on Very large data bases, pages 720-731. VLDB Endowment, 2004.
[2] Eclipse. http://www.eclipse.org/.
[4] Hilbert curves in more (or fewer) than two dimensions. http://www.tiac.net/sw/2008/10/Hilbert/.
[6] Hilbert Space-Filling Curves. http://people.csail.mit.edu/jaer/Geometry/HSFC.
[7] JUnit. http://www.junit.org/ .
[8] Project Locker. https://www.projectlocker.com/.
[9] Subclise. http://subclipse.tigris.org/.
[10] Gaussian distribution. http://en.wikipedia.org/wiki/Gaussian_distribution.
[11] Sudoku.http://en.wikipedia.org/wiki/Sudoku.
[12] Variance - Discrete case. http://en.wikipedia.org/wiki/Variance#Discrete_case.
References
CS5322 - Groupe 6
92
CS5322 - Groupe 6
93
Annexes
CS5322 - Groupe 6
94
Controlled-Diffusion
CS5322 - Groupe 6
95
Controlled-DiffusionId Val. OB
1 0
2 0
3 1
4 1
5 2
6 2
7 4
8 4
9 4
10 5
11 6
12 6
13 6
14 7
15 9
16 9
CB1 CB2
CB3 CB4
CS5322 - Groupe 6
96
Controlled-DiffusionId Val. OB
1 0
2 0
3 1
4 1
5 2
6 2
7 4
8 4
9 4
10 5
11 6
12 6
13 6
14 7
15 9
16 9
CB1 CB2
1;
CB3 CB4
CS5322 - Groupe 6
97
Controlled-DiffusionId Val. OB
1 0
2 0
3 1
4 1
5 2
6 2
7 4
8 4
9 4
10 5
11 6
12 6
13 6
14 7
15 9
16 9
CB1
2;
CB2
1;
CB3 CB4
CS5322 - Groupe 6
98
Controlled-DiffusionId Val. OB
1 0
2 0
3 1
4 1
5 2
6 2
7 4
8 4
9 4
10 5
11 6
12 6
13 6
14 7
15 9
16 9
CB1
2; 3;
CB2
1;
CB3 CB4
CS5322 - Groupe 6
99
Controlled-DiffusionId Val. OB
1 0
2 0
3 1
4 1
5 2
6 2
7 4
8 4
9 4
10 5
11 6
12 6
13 6
14 7
15 9
16 9
CB1
2; 3;
CB2
1; 4;
CB3 CB4
CS5322 - Groupe 6
100
Controlled-DiffusionId Val. OB
1 0
2 0
3 1
4 1
5 2
6 2
7 4
8 4
9 4
10 5
11 6
12 6
13 6
14 7
15 9
16 9
CB1
2; 3;
CB2
1; 4;
CB3
5; 6; 8
CB4
7; 9;
CS5322 - Groupe 6
101
Controlled-DiffusionId Val. OB
1 0
2 0
3 1
4 1
5 2
6 2
7 4
8 4
9 4
10 5
11 6
12 6
13 6
14 7
15 9
16 9
CB1
2; 3;
10; 13;
CB2
1; 4;
CB3
5; 6; 811; 12;
CB4
7; 9;
CS5322 - Groupe 6
102
Controlled-DiffusionId Val. OB
1 0
2 0
3 1
4 1
5 2
6 2
7 4
8 4
9 4
10 5
11 6
12 6
13 6
14 7
15 9
16 9
CB1
2; 3;
10; 13.
CB2
1; 4;
14; 16.
CB3
5; 6; 811; 12.
CB4
7; 9;
15.
CS5322 - Groupe 6
103
Controlled-DiffusionId Val. OB
1 0
2 0
3 1
4 1
5 2
6 2
7 4
8 4
9 4
10 5
11 6
12 6
13 6
14 7
15 9
16 9
CB1
2; 3;
10; 13.
CB2
1; 4;
14; 16.
CB3
5; 6; 811; 12.
CB4
7; 9;
15.
Range query: [3,5]
CS5322 - Groupe 6
104
« Remake » experiments
105
CS5322 - Groupe 6
DataFigure 7: Uniform distrib. Figure 8: Normal distrib.
-756 -289 -124 40 204 368 532 696 860 1024118813670
20
40
60
80
100
120
140
160
0 66 1321982643303964625285946607267928589249900
20
40
60
80
100
120
140
160
]999,0[U
500μ 5.333,83² σ510# tuples
²,N
106
CS5322 - Groupe 6
Ratio of precisionFigure 9: Uniform distrib. Figure 10: Normal distrib.
KM
M
CP
OP
,AQP
AQP
100 150 200 250 300 350 4000
2
4
6
8
10
12
k=2 k=4 k=6 k=8 k=10
Number of Buckets
AQ
P(O
ptP
art
)/A
QP
(Com
pP
art
)
100 150 200 250 300 350 4000
2
4
6
8
10
12
k=2 k=4 k=6 k=8 k=10
Number of Buckets
AQ
P(O
ptP
art
)/A
QP
(Com
pP
art
)
107
CS5322 - Groupe 6
Ratio of average standard deviationFigure 11: Uniform distrib. Figure 12: Normal distrib.
M
KM
OPbuckets
CPbuckets
buckets
buckets
)σ(mean
)σ(mean,
100 150 200 250 300 350 4000
20
40
60
80
100
120
140
160
180
k=2 k=4 k=6 k=8 k=10
Number of Buckets
σ(C
om
pP
art
)/σ
(OptP
art
)
100 150 200 250 300 350 4000
50
100
150
200
250
300
350
400
450
k=2 k=4 k=6 k=8 k=10
Number of Buckets
σ(C
om
pP
art
)/σ
(OptP
art
)
108
CS5322 - Groupe 6
Ratio of average entropyFigure 13: Uniform distrib. Figure 14: Normal distrib.
100 150 200 250 300 350 4000
0.5
1
1.5
2
2.5
3
3.5
k=2 k=4 k=6 k=8 k=10
Number of Buckets
H(C
om
pP
art
)/H
(OptP
art
)
100 150 200 250 300 350 4000
0.5
1
1.5
2
2.5
k=2 k=4 k=6 k=8 k=10
Number of Buckets
H(C
om
pP
art
)/H
(OptP
art
)
M
KM
OPbuckets
CPbuckets
buckets
buckets
)H(mean
)H(mean,
109
CS5322 - Groupe 6
Trade-off (precision vs std. dev.)Figure 15: Uniform distrib. Figure 16: Normal distrib.
0 0.2 0.4 0.6 0.8 1 1.20
50
100
150
200
250
300
OPk=2k=4k=6k=8k=10
Precision
Sta
ndard
Devia
tion
0 0.2 0.4 0.6 0.8 1 1.20
50
100
150
200
250
300
OPk=2k=4k=6k=8k=10
Precision
Sta
ndard
Devia
tion
110
CS5322 - Groupe 6
Trade-off (precision vs entropy)Figure 17: Uniform distrib. Figure 18: Normal distrib.
0 0.2 0.4 0.6 0.8 1 1.20
1
2
3
4
5
6
7
OPk=2k=4k=6k=8k=10
Precision
Entr
opy
0 0.2 0.4 0.6 0.8 1 1.20
1
2
3
4
5
6
7
OPk=2k=4k=6k=8k=10
Precision
Entr
opy
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