1. Implementation (Group 6) Monika (A0066244H) Damien Forest (A0066246A) Rattanak Chhung (A0066240N) Yann-Loup Phan Van Song (A0066238B) 1 CS5322 - Groupe 6 A Privacy-Preserving Index for Range Queries

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 2

3. 1 attribute CS5322 - Groupe 6 3

4. 4 valuefreq 01 14 20 33 42 51 66 71 80 91 Dataset of plain values Inputs find the bucketization that reduces the number of total false positives Our goal: Principle:

5. BC table 10000000 104000000 158000000 3221300000 50361020000 66501861000 11996482714600 1441196540241410 1901629866453261 CS5322 - Groupe 6 5 BC=

6. CS5322 - Groupe 6 6 valuefreq 01 14 20 33 42 51 66 71 80 91 Dataset of plain values Inputs Intermediary results BucketBucketization cost [0-4](4+1).(10) [5-9](4+1).9 First Step: M=2 MinCost = 95

7. CS5322 - Groupe 6 7 valuefreq 01 14 20 33 42 51 66 71 80 91 Dataset of plain values Inputs Outputs BucketsBucketization cost [ 0 - 2 ] 3.5 [ 3 - 5 ] 3.6 [ 6 - 6 ] 1.6 [ 7 - 9 ] 3.2 Last Step: M=4 MinCost = 45 Note: Depending on what we want we can include or not the values that have 0 frequency

8. CS5322 - Groupe 6 8 valuefreq 01 14 20 33 42 51 66 71 80 91 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

9. CS5322 - Groupe 6 9

10. 10 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 Dataset of plain values Partition attribute 1 Partition attribute 2 Encrypted table Inputs

11. CS5322 - Groupe 6 11 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 Context To match the indexes and the buckets Our goal: How ? Working with cardinalities

12. CS5322 - Groupe 6 12 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 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…

13. CS5322 - Groupe 6 13 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 First attack - BAA B11 = [ BAA :

14. CS5322 - Groupe 6 14 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 First attack - BAA B11 = [ BAA :

15. CS5322 - Groupe 6 15 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 First attack - BAA BAA : B11 = [73,

16. CS5322 - Groupe 6 16 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 First attack - BAA BAA : B11 = [73,15 ]

17. CS5322 - Groupe 6 17 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 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 … 

18. CS5322 - Groupe 6 18 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 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 valuefreq (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 = [

19. CS5322 - Groupe 6 19 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] BAA2 : B11 = [ B12 = [ B13 = [ B14 = [ B21 = [ B22 = [ B23 = [ B24 = [ |B11;B21| = valuefreq (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

20. CS5322 - Groupe 6 20 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] BAA2 : B11 = [ B12 = [ B13 = [ B14 = [ B21 = [ B22 = [ B23 = [ B24 = [ |B11;B21| = 1 valuefreq (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

21. CS5322 - Groupe 6 21 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 valuefreq (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

22. CS5322 - Groupe 6 22 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 valuefreq (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

23. CS5322 - Groupe 6 23 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 valuefreq (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

24. CS5322 - Groupe 6 24 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 valuefreq (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

25. CS5322 - Groupe 6 25 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 valuefreq (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

26. CS5322 - Groupe 6 26 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 valuefreq (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

27. CS5322 - Groupe 6 27 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 valuefreq (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

28. CS5322 - Groupe 6 28 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 valuefreq (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

29. CS5322 - Groupe 6 29 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 valuefreq (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 ] No identified index …  0 0 2 0 1 0 1 1 0 2 1 0 First attack - BAA2

30. CS5322 - Groupe 6 30 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 ] 15, 30 ] 73, 79, 30 ] 73, 15, 79, 30 ] 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 …  Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320

31. CS5322 - Groupe 6 31 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] BAA2 : B11 = [ B12 = [ B13 = [ B14 = [ B21 = [ B22 = [ B23 = [ B24 = [ 73, 79, 30 ] 45, 20, 74, 9 ] 15, 30 ] 73, 79, 30 ] 73, 15, 79, 30 ] 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 …  Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 First attack - intersection

32. CS5322 - Groupe 6 32 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] BAA2 : B11 = 73 B12 = 15 B13 = [ 79, 30 ] B14 = [ 79, 30 ] B21 = [ 20, 45 ] B22 = [ 9, 74 ] B23 = [ 9, 74 ] B24 = [ 20, 45 ] BAA & Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 First attack - intersection

33. CS5322 - Groupe 6 33 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] BAA2 : B11 = 73 B12 = 15 B13 = [ 79, 30 ] B14 = [ 79, 30 ] B21 = [ 20, 45 ] B22 = [ 9, 74 ] B23 = [ 9, 74 ] B24 = [ 20, 45 ] BAA & Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New identified indexes : First attack - intersection

34. CS5322 - Groupe 6 34 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New identified indexes : (73 ; [

35. CS5322 - Groupe 6 35 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New identified indexes : (73 ; [(45;1), B11 = 73 B12 = 15 Creation of couples of indexes

36. CS5322 - Groupe 6 36 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New identified indexes : (73 ; [(45;1), B11 = 73 B12 = 15 Creation of couples of indexes (20;1)])

37. CS5322 - Groupe 6 37 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New identified indexes : (73 ; [ (45;1), (20;1)]) (15 ; [ B11 = 73 B12 = 15 Creation of couples of indexes

38. CS5322 - Groupe 6 38 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New identified indexes : (73 ; [ (45;1), (20;1)]) (15 ; [ (9;2)]) B11 = 73 B12 = 15 Creation of couples of indexes

39. CS5322 - Groupe 6 39 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New 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

40. CS5322 - Groupe 6 40 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New 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

41. CS5322 - Groupe 6 41 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New 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

42. CS5322 - Groupe 6 42 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New 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)])

43. CS5322 - Groupe 6 43 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New 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)])

44. CS5322 - Groupe 6 44 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New 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)])

45. CS5322 - Groupe 6 45 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New 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 !

46. CS5322 - Groupe 6 46 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New 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

47. CS5322 - Groupe 6 47 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New 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)])

48. CS5322 - Groupe 6 48 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New 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

49. CS5322 - Groupe 6 49 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] B13 = [ 79, 30 ] B14 = [ 79, 30 ] B21 = [ 20, 45 ] B22 = [ 9, 74 ] B23 = 9 B24 = [ 20, 45 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New 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

50. CS5322 - Groupe 6 50 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 = 9 B24 = [ 20, 45 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 New identified indexes : 73, 15New 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 51 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 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 = 9 B24 = [ 20, 45 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 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)])

52. CS5322 - Groupe 6 52 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 (12 ; 4)1 (13 ; 7)1 (14 ; 5)1 B13B14 [ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] B13 = [ 79, 30 ] B14 = [ 79, 30 ] B21 = [ 20, 45 ] B22 = [ 74 ] B23 = 9 B24 = [ 20, 45 ] Ind1Ind2 7945 7974 3074 309 7920 3074 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

53. CS5322 - Groupe 6 53 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 (12 ; 4)1 (13 ; 7)1 (14 ; 5)1 B13B14 [ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] B13 = [ 79, 30 ] B14 = [ 79, 30 ] B21 = [ 20, 45 ] B22 = [ 74 ] B23 = 9 B24 = [ 20, 45 ] Ind1Ind2 7945 7974 3074 309 7920 3074 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

54. CS5322 - Groupe 6 54 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 (12 ; 4)1 (13 ; 7)1 (14 ; 5)1 B13B14 [ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] B13 = [ 79, 30 ] B14 = [ 79, 30 ] B21 = [ 20, 45 ] B22 = [ 74 ] B23 = 9 B24 = [ 20, 45 ] Ind1Ind2 7945 7974 3074 309 7920 3074 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

55. CS5322 - Groupe 6 55 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 (12 ; 4)1 (13 ; 7)1 (14 ; 5)1 B13B14 [ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] B13 = [ 79, 30 ] B14 = [ 79, 30 ] B21 = [ 20, 45 ] B22 = [ 74 ] B23 = 9 B24 = [ 20, 45 ] 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 Ind1Ind2 7945 7974 3074 309 7920 3074 (20 ; [(79;1)]) Propagation 2 - identify the new index

56. CS5322 - Groupe 6 56 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 (12 ; 4)1 (13 ; 7)1 (14 ; 5)1 B13B14 [ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] B13 = [ 79, 30 ] B14 = [ 79, 30 ] B21 = [ 20, 45 ] B22 = [ 74 ] B23 = 9 B24 = [ 20, 45 ] 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 Ind1Ind2 7945 7974 3074 309 7920 3074 (20 ; [(79;1)]) Propagation 2 - identify the new index

57. CS5322 - Groupe 6 57 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 (12 ; 4)1 (13 ; 7)1 (14 ; 5)1 B13B14 [ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = [ 79, 30 ] B14 = 30 B21 = [ 20, 45 ] B22 = [ 74 ] B23 = 9 B24 = [ 20, 45 ] 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 Ind1Ind2 7945 7974 3074 309 7920 3074 (20 ; [(79;1)]) Propagation 2 - identify the new index

58. CS5322 - Groupe 6 58 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 (12 ; 4)1 (13 ; 7)1 (14 ; 5)1 B13B14 [ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = [ 79, 30 ] B14 = 30 B21 = [ 20, 45 ] B22 = [ 74 ] B23 = 9 B24 = [ 20, 45 ] 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 Ind1Ind2 7945 7974 3074 309 7920 3074 (20 ; [(79;1)]) Propagation 2 - add the new index to the list

59. CS5322 - Groupe 6 59 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 (12 ; 4)1 (13 ; 7)1 (14 ; 5)1 B13B14 [ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = [ 79, 30 ] B14 = 30 B21 = [ 20, 45 ] B22 = [ 74 ] B23 = 9 B24 = [ 20, 45 ] 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 Ind1Ind2 7945 7974 3074 309 7920 3074 (20 ; [(79;1)]) Propagation 2 - remove deprecated data

60. CS5322 - Groupe 6 60 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 (12 ; 4)1 (14 ; 5)1 B13B14 [ 7 ; 11 ][ 12 ; 15 ] B21B22B24 [ 0 ; 3 ][ 4 ; 5 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = [ 79 ] B14 = 30 B21 = [ 20, 45 ] B22 = [ 74 ] B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(74;1),(20;1)]) (30 ; [(74;2)]) (45 ; [(79;1)]) (9 ; [(30;1)]) (74 ; [(79;1)]) 930 Ind1Ind2 7945 7974 3074 7920 3074 (20 ; [(79;1)]) Propagation 2 - remove deprecated data

61. CS5322 - Groupe 6 61 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 (12 ; 4)1 (14 ; 5)1 B13B14 [ 7 ; 11 ][ 12 ; 15 ] B21B22B24 [ 0 ; 3 ][ 4 ; 5 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = [ 79 ] B14 = 30 B21 = [ 20, 45 ] B22 = [ 74 ] B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(74;1),(20;1)]) (30 ; [(74;2)]) (45 ; [(79;1)]) (74 ; [(79;1)]) 30 Ind1Ind2 7945 7974 3074 7920 3074 (20 ; [(79;1)]) Propagation 3 - look for new indexes

62. CS5322 - Groupe 6 62 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 (12 ; 4)1 (14 ; 5)1 B13B14 [ 7 ; 11 ][ 12 ; 15 ] B21B22B24 [ 0 ; 3 ][ 4 ; 5 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = [ 79 ] B14 = 30 B21 = [ 20, 45 ] B22 = [ 74 ] B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(74;1),(20;1)]) (30 ; [(74;2)]) (45 ; [(79;1)]) (74 ; [(79;1)]) 30 Ind1Ind2 7945 7974 3074 7920 3074 (20 ; [(79;1)]) Propagation 3 - look for new indexes

63. CS5322 - Groupe 6 63 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 (12 ; 4)1 (14 ; 5)1 B13B14 [ 7 ; 11 ][ 12 ; 15 ] B21B22B24 [ 0 ; 3 ][ 4 ; 5 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = [ 79 ] B14 = 30 B21 = [ 20, 45 ] B22 = [ 74 ] B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(74;1),(20;1)]) (30 ; [(74;2)]) (45 ; [(79;1)]) (74 ; [(79;1)]) 30 Ind1Ind2 7945 7974 3074 7920 3074 (20 ; [(79;1)]) Propagation 3 - identify the new index

64. CS5322 - Groupe 6 64 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 (12 ; 4)1 (14 ; 5)1 B13B14 [ 7 ; 11 ][ 12 ; 15 ] B21B22B24 [ 0 ; 3 ][ 4 ; 5 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = [ 79 ] B14 = 30 B21 = [ 20, 45 ] B22 = [ 74 ] B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(74;1),(20;1)]) (30 ; [(74;2)]) (45 ; [(79;1)]) (74 ; [(79;1)]) 30 Ind1Ind2 7945 7974 3074 7920 3074 (20 ; [(79;1)]) Propagation 3 - identify the new index

65. CS5322 - Groupe 6 65 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 (12 ; 4)1 (14 ; 5)1 B13B14 [ 7 ; 11 ][ 12 ; 15 ] B21B22B24 [ 0 ; 3 ][ 4 ; 5 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = [ 79 ] B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(74;1),(20;1)]) (30 ; [(74;2)]) (45 ; [(79;1)]) (74 ; [(79;1)]) 30 Ind1Ind2 7945 7974 3074 7920 3074 (20 ; [(79;1)]) Propagation 3 - identify the new index

66. CS5322 - Groupe 6 66 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 (12 ; 4)1 (14 ; 5)1 B13B14 [ 7 ; 11 ][ 12 ; 15 ] B21B22B24 [ 0 ; 3 ][ 4 ; 5 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = [ 79 ] B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(74;1),(20;1)]) (30 ; [(74;2)]) (45 ; [(79;1)]) (74 ; [(79;1)]) 30 74 Ind1Ind2 7945 7974 3074 7920 3074 (20 ; [(79;1)]) Propagation 3 - add the new index to the list

67. CS5322 - Groupe 6 67 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 (12 ; 4)1 (14 ; 5)1 B13B14 [ 7 ; 11 ][ 12 ; 15 ] B21B22B24 [ 0 ; 3 ][ 4 ; 5 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = [ 79 ] B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(74;1),(20;1)]) (30 ; [(74;2)]) (45 ; [(79;1)]) (74 ; [(79;1)]) 30 74 Ind1Ind2 7945 7974 3074 7920 3074 (20 ; [(79;1)]) Propagation 3 - remove deprecated data

68. CS5322 - Groupe 6 68 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 B13 [ 7 ; 11 ] B21B22B24 [ 0 ; 3 ][ 4 ; 5 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = [ 79 ] B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(20;1)]) (30 ; [(74;2)]) (45 ; [(79;1)]) (74 ; [(79;1)]) 30 74 Ind1Ind2 7945 7974 7920 (20 ; [(79;1)]) Propagation 3 - remove deprecated data

69. CS5322 - Groupe 6 69 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 B13 [ 7 ; 11 ] B21B22B24 [ 0 ; 3 ][ 4 ; 5 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = [ 79 ] B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(20;1)]) (45 ; [(79;1)]) (74 ; [(79;1)]) 74 Ind1Ind2 7945 7974 7920 (20 ; [(79;1)]) Propagation 4 - look for new indexes

70. CS5322 - Groupe 6 70 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 B13 [ 7 ; 11 ] B21B22B24 [ 0 ; 3 ][ 4 ; 5 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = [ 79 ] B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(20;1)]) (45 ; [(79;1)]) (74 ; [(79;1)]) 74 Ind1Ind2 7945 7974 7920 (20 ; [(79;1)]) Propagation 4 - look for new indexes

71. CS5322 - Groupe 6 71 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 B13 [ 7 ; 11 ] B21B22B24 [ 0 ; 3 ][ 4 ; 5 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = [ 79 ] B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(20;1)]) (45 ; [(79;1)]) (74 ; [(79;1)]) 74 Ind1Ind2 7945 7974 7920 (20 ; [(79;1)]) Propagation 4 - identify the new index

72. CS5322 - Groupe 6 72 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 B13 [ 7 ; 11 ] B21B22B24 [ 0 ; 3 ][ 4 ; 5 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = [ 79 ] B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(20;1)]) (45 ; [(79;1)]) (74 ; [(79;1)]) 74 Ind1Ind2 7945 7974 7920 (20 ; [(79;1)]) Propagation 4 - identify the new index

73. CS5322 - Groupe 6 73 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 B13 [ 7 ; 11 ] B21B22B24 [ 0 ; 3 ][ 4 ; 5 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = 79 B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(20;1)]) (45 ; [(79;1)]) (74 ; [(79;1)]) 74 Ind1Ind2 7945 7974 7920 (20 ; [(79;1)]) Propagation 4 - identify the new index

74. CS5322 - Groupe 6 74 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 B13 [ 7 ; 11 ] B21B22B24 [ 0 ; 3 ][ 4 ; 5 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = 79 B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(20;1)]) (45 ; [(79;1)]) (74 ; [(79;1)]) 74 79 Ind1Ind2 7945 7974 7920 (20 ; [(79;1)]) Propagation 4 - add the new index to the list

75. CS5322 - Groupe 6 75 valuefreq (7 ; 2)1 (7 ; 11)1 (9 ; 4)1 B13 [ 7 ; 11 ] B21B22B24 [ 0 ; 3 ][ 4 ; 5 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = 79 B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(20;1)]) (45 ; [(79;1)]) (74 ; [(79;1)]) (20 ; [(79;1)]) 74 79 Ind1Ind2 7945 7974 7920 Propagation 4 - remove deprecated data

76. CS5322 - Groupe 6 76 valuefreq (7 ; 2)1 (7 ; 11)1 B13 [ 7 ; 11 ] B21B24 [ 0 ; 3 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = 79 B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(20;1)]) (45 ; [ ]) (74 ; [(79;1)]) (20 ; [ ]) 74 79 Ind1Ind2 7945 7920 Propagation 4 - remove deprecated data

77. CS5322 - Groupe 6 77 valuefreq (7 ; 2)1 (7 ; 11)1 B13 [ 7 ; 11 ] B21B24 [ 0 ; 3 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = 79 B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(20;1)]) (45 ; [ ]) (20 ; [ ]) 79 Ind1Ind2 7945 7920 Propagation 5 - look for new indexes

78. CS5322 - Groupe 6 78 valuefreq (7 ; 2)1 (7 ; 11)1 B13 [ 7 ; 11 ] B21B24 [ 0 ; 3 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = 79 B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(20;1)]) (45 ; [ ]) (20 ; [ ]) 79 Ind1Ind2 7945 7920 Propagation 5 - look for new indexes No way! Impossible to identify them

79. CS5322 - Groupe 6 79 valuefreq (7 ; 2)1 (7 ; 11)1 B13 [ 7 ; 11 ] B21B24 [ 0 ; 3 ][ 10 ; 15 ] B11 = 73 B12 = 15 B13 = 79 B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ] New identified indexes : (79 ; [(45;1),(20;1)]) (45 ; [ ]) (20 ; [ ]) Propagation 5 - STOP 79 Ind1Ind2 7945 7920 No other index: we have to stop!

80. CS5322 - Groupe 6 80 valuefreq (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 B11B12B13B14 [ 0 ; 2 ][ 3 ; 6 ][ 7 ; 11 ][ 12 ; 15 ] B21B22B23B24 [ 0 ; 3 ][ 4 ; 5 ][ 6 ; 9 ][ 10 ; 15 ] Ind1Ind2 7345 159 7945 7974 3074 309 159 7920 3074 7320 Results B11 = 73 B12 = 15 B13 = 79 B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ]

81. CS5322 - Groupe 6 81

82. Hilbert curve col1 col2 01230123 32103210 82 CS5322 - Groupe 6 Hilbert value Col1 value Col2 value 000 110 211 301 402 503 613 712 822 923 1033 1132 1231 1321 1420 1530

83. Hilbert curve col1 col2 01230123 32103210 83 CS5322 - Groupe 6 IdCol1Col2HV 1000 2113 3113 4113 5113 6024 7127 8127 9127 10239 113310 122113 21

84. Two dimensions -> One dimension CS5322 - Groupe 6 84 M = 5 B1B3B4B5B2

85. Hilbert curve col1 col2 01230123 32103210 85 CS5322 - Groupe 6 IdCol1Col2HVB 1000B1 2113 3113 4113 5113 6024B2 7127B3 8127 9127 10239B4 113310 122113B5 1321 B3 B2B4 B1 B5

86. Hilbert curve col1 col2 01230123 32103210 86 CS5322 - Groupe 6 IdCol1Col2HVB 1000B1 2113 3113 4113 5113 6024B2 7127B3 8127 9127 10239B4 113310 122113B5 1321 B2B4 B1 B5 Range query on [1-1] for col1 … WHERE Col1 = 1 B3

87. Hilbert curve col1 col2 01230123 32103210 87 CS5322 - Groupe 6 IdCol1Col2HVB 1000B1 2113 3113 4113 5113 6024B2 7127B3 8127 9127 10239B4 113310 122113B5 1321 B3 B2B4 B1 B5 Range query on [1-2] for col2 … WHERE Col2 in [1-2]

88. Hilbert curve CS5322 - Groupe 6 88 Range query? col1 col2

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 89

90. CS5322 - Groupe 6 90

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/. http://www.eclipse.org/ [4] Hilbert curves in more (or fewer) than two dimensions. http://www.tiac.net/sw/2008/10/Hilbert/. http://www.tiac.net/sw/2008/10/Hilbert/ [6] Hilbert Space-Filling Curves. http://people.csail.mit.edu/jaer/Geometry/HSFC. http://people.csail.mit.edu/jaer/Geometry/HSFC [7] JUnit. http://www.junit.org/. http://www.junit.org/ [8] Project Locker. https://www.projectlocker.com/. https://www.projectlocker.com/ [9] Subclise. http://subclipse.tigris.org/. http://subclipse.tigris.org/ [10] Gaussian distribution. http://en.wikipedia.org/wiki/Gaussian_distribution. http://en.wikipedia.org/wiki/Gaussian_distribution [11] Sudoku. http://en.wikipedia.org/wiki/Sudoku. http://en.wikipedia.org/wiki/Sudoku [12] Variance - Discrete case. http://en.wikipedia.org/wiki/Variance#Discrete_case. http://en.wikipedia.org/wiki/Variance#Discrete_case 91 CS5322 - Groupe 6 References

92. CS5322 - Groupe 6 92

93. Annexes CS5322 - Groupe 6 93

94. CS5322 - Groupe 6 94

95. Controlled-Diffusion IdVal.OB 10 20 31 41 52 62 74 84 94 105 116 126 136 147 159 169 CB1CB2 CB3CB4 95 CS5322 - Groupe 6

96. Controlled-Diffusion IdVal.OB 10 20 31 41 52 62 74 84 94 105 116 126 136 147 159 169 CB1CB2 1; CB3CB4 96 CS5322 - Groupe 6

97. Controlled-Diffusion IdVal.OB 10 20 31 41 52 62 74 84 94 105 116 126 136 147 159 169 CB1 2; CB2 1; CB3CB4 97 CS5322 - Groupe 6

98. Controlled-Diffusion IdVal.OB 10 20 31 41 52 62 74 84 94 105 116 126 136 147 159 169 CB1 2; 3; CB2 1; CB3CB4 98 CS5322 - Groupe 6

99. Controlled-Diffusion IdVal.OB 10 20 31 41 52 62 74 84 94 105 116 126 136 147 159 169 CB1 2; 3; CB2 1; 4; CB3CB4 99 CS5322 - Groupe 6

100. Controlled-Diffusion IdVal.OB 10 20 31 41 52 62 74 84 94 105 116 126 136 147 159 169 CB1 2; 3; CB2 1; 4; CB3 5; 6; 8 CB4 7; 9; 100 CS5322 - Groupe 6

101. Controlled-Diffusion IdVal.OB 10 20 31 41 52 62 74 84 94 105 116 126 136 147 159 169 CB1 2; 3; 10; 13; CB2 1; 4; CB3 5; 6; 8 11; 12; CB4 7; 9; 101 CS5322 - Groupe 6

102. Controlled-Diffusion IdVal.OB 10 20 31 41 52 62 74 84 94 105 116 126 136 147 159 169 CB1 2; 3; 10; 13. CB2 1; 4; 14; 16. CB3 5; 6; 8 11; 12. CB4 7; 9; 15. 102 CS5322 - Groupe 6

103. Controlled-Diffusion IdVal.OB 10 20 31 41 52 62 74 84 94 105 116 126 136 147 159 169 CB1 2; 3; 10; 13. CB2 1; 4; 14; 16. CB3 5; 6; 8 11; 12. CB4 7; 9; 15. Range query: [3,5] 103 CS5322 - Groupe 6

104. 104

105. Data Figure 7: Uniform distrib.Figure 8: Normal distrib. 105 CS5322 - Groupe 6

106. Ratio of precision Figure 9: Uniform distrib.Figure 10: Normal distrib. 106 CS5322 - Groupe 6

107. Ratio of average standard deviation Figure 11: Uniform distrib.Figure 12: Normal distrib. 107 CS5322 - Groupe 6

108. Ratio of average entropy Figure 13: Uniform distrib.Figure 14: Normal distrib. 108 CS5322 - Groupe 6

109. Trade-off (precision vs std. dev.) Figure 15: Uniform distrib.Figure 16: Normal distrib. 109 CS5322 - Groupe 6

110. Trade-off (precision vs entropy) Figure 17: Uniform distrib.Figure 18: Normal distrib. 110 CS5322 - Groupe 6