Implementation (Group 6) Monika (A0066244H) Damien Forest (A0066246A) Rattanak Chhung (A0066240N) Yann-Loup Phan Van Song (A0066238B) 1 CS5322 - Groupe.

Slides:

Advertisements

Similar presentations

Ken C. K. Lee, Baihua Zheng, Huajing Li, Wang-Chien Lee VLDB 07 Approaching the Skyline in Z Order 1.

Advertisements

Querying Encrypted Data using Fully Homomorphic Encryption Murali Mani, UMFlint Talk given at CIDR, Jan 7,

A Privacy Preserving Index for Range Queries

Efficient Evaluation of k-Range Nearest Neighbor Queries in Road Networks Jie BaoChi-Yin ChowMohamed F. Mokbel Department of Computer Science and Engineering.

Query Optimization CS634 Lecture 12, Mar 12, 2014 Slides based on “Database Management Systems” 3 rd ed, Ramakrishnan and Gehrke.

Fast Algorithms For Hierarchical Range Histogram Constructions

Query Execution, Concluded Zachary G. Ives University of Pennsylvania CIS 550 – Database & Information Systems November 18, 2003 Some slide content may.

Outsourcing Search Services on Private Spatial Data Man Lung Yiu, Gabriel Ghinita, Christian Jensen, and Panos Kalnis Presenter: Uma Kannan 1.

Modeling and Analysis of Random Walk Search Algorithms in P2P Networks Nabhendra Bisnik, Alhussein Abouzeid ECSE, Rensselaer Polytechnic Institute.

Continuous Intersection Joins Over Moving Objects Rui Zhang University of Melbourne Dan Lin Purdue University Kotagiri Ramamohanarao University of Melbourne.

INTRODUCTION PROBLEM FORMULATION FRAMEWORK AND PRIVACY REQUIREMENTS FOR MRSE PRIVACY-PRESERVING AND EFFICIENT MRSE PERFORMANCE ANALYSIS RELATED WORK CONCLUSION.

Manufacturing Variation Plotting a Normal Distribution.

Subscription Subsumption Evaluation for Content-Based Publish/Subscribe Systems Hojjat Jafarpour, Bijit Hore, Sharad Mehrotra, and Nalini Venkatasubramanian.

Spatial Indexing I Point Access Methods.

Transforms What does the word transform mean?. Transforms What does the word transform mean? –Changing something into another thing.

Privacy and Integrity Preserving in Distributed Systems Presented for Ph.D. Qualifying Examination Fei Chen Michigan State University August 25 th, 2009.

Retrieval Evaluation. Introduction Evaluation of implementations in computer science often is in terms of time and space complexity. With large document.

Spatial Indexing I Point Access Methods. Spatial Indexing Point Access Methods (PAMs) vs Spatial Access Methods (SAMs) PAM: index only point data Hierarchical.

Research interest: Secure database outsourcing Presented by Alla Lanovenko Thesis Adviser: Professor Huiping Guo 599 A 11 December 2006.

Sorting and Query Processing Zachary G. Ives University of Pennsylvania CIS 550 – Database & Information Systems November 29, 2005.

Privacy-Preserving Data Mining Rakesh Agrawal Ramakrishnan Srikant IBM Almaden Research Center 650 Harry Road, San Jose, CA Published in: ACM SIGMOD.

Secure Cloud Database using Multiparty Computation.

Software Logic Mutation Testing Presented by Gary Kaminski.

Approximate Encoding for Direct Access and Query Processing over Compressed Bitmaps Tan Apaydin – The Ohio State University Guadalupe Canahuate – The Ohio.

Towards Robust Indexing for Ranked Queries Dong Xin, Chen Chen, Jiawei Han Department of Computer Science University of Illinois at Urbana-Champaign VLDB.

Executing SQL over Encrypted Data in Database-Service-Provider Model Hakan Hacigumus University of California, Irvine Bala Iyer IBM Silicon Valley Lab.

Cache-Conscious Performance Optimization for Similarity Search Maha Alabduljalil, Xun Tang, Tao Yang Department of Computer Science University of California.

Membership problem CYK Algorithm Project presentation CS 5800 Spring 2013 Professor : Dr. Elise de Doncker Presented by : Savitha parur venkitachalam.

Database Management COP4540, SCS, FIU Physical Database Design (ch. 16 & ch. 3)

The Sweet Spot between Inverted Indices and Metric-Space Indexing for Top-K–List Similarity Search Evica Milchevski , Avishek Anand ★ and Sebastian Michel.

Protection of outsourced data MARIA ANGEL MARQUEZ ANDRADE.

Privacy-preserving rule mining. Outline  A brief introduction to association rule mining  Privacy preserving rule mining Single party  Perturbation.

QED: A Novel Quaternary Encoding to Completely Avoid Re-labeling in XML Updates Changqing Li,Tok Wang Ling.

© 2002 Thomson / South-Western Slide 5-1 Chapter 5 Discrete Probability Distributions.

Wei-Shinn Ku Slide 1 Auburn University Computer Science and Software Engineering Query Integrity Assurance of Location-based Services Accessing Outsourced.

Answering Top-k Queries Using Views Gautam Das (Univ. of Texas), Dimitrios Gunopulos (Univ. of California Riverside), Nick Koudas (Univ. of Toronto), Dimitris.

Physical Database Design Purpose- translate the logical description of data into the technical specifications for storing and retrieving data Goal - create.

Presented By Amarjit Datta

Answering Top-k Queries with Multi-Dimensional Selections: The Ranking Cube Approach Dong Xin, Jiawei Han, Hong Cheng, Xiaolei Li Department of Computer.

Ohio State University Department of Computer Science and Engineering Servicing Range Queries on Multidimensional Datasets with Partial Replicas Li Weng,

KAIST TS & IS Lab. CS710 Know your Neighbors: Web Spam Detection using the Web Topology SIGIR 2007, Carlos Castillo et al., Yahoo! 이 승 민.

File Processing : Query Processing 2008, Spring Pusan National University Ki-Joune Li.

Query Processing – Implementing Set Operations and Joins Chap. 19.

An Interval Classifier for Database Mining Applications Rakes Agrawal, Sakti Ghosh, Tomasz Imielinski, Bala Iyer, Arun Swami Proceedings of the 18 th VLDB.

Secure Data Outsourcing

Indexing Structures Database System Implementation CSE 507 Some slides adapted from Silberschatz, Korth and Sudarshan Database System Concepts – 6 th Edition.

Privacy Preserving Outlier Detection using Locality Sensitive Hashing

Privacy-Preserving Data Aggregation without Secure Channel: Multivariate Polynomial Evaluation Taeho Jung 1, XuFei Mao 2, Xiang-Yang Li 1, Shao-Jie Tang.

Output Perturbation with Query Relaxation By: XIAO Xiaokui and TAO Yufei Presenter: CUI Yingjie.

”Map-Reduce-Merge: Simplified Relational Data Processing on Large Clusters” Published In SIGMOD '07 By Yahoo! Senthil Nathan N IIT Bombay.

No Free Lunch: Working Within the Tradeoff Between Quality and Privacy

Efficient Multi-User Indexing for Secure Keyword Search

Data Mining: Concepts and Techniques

CS411 Database Systems 08: Midterm Review Kazuhiro Minami 1.

The Advanced Encryption Standard: Rijndael

Sameh Shohdy, Yu Su, and Gagan Agrawal

Database Management Systems (CS 564)

Private and Secure Secret Shared MapReduce

A Privacy-Preserving Index for Range Queries

File Processing : Query Processing

File Processing : Query Processing

CS222P: Principles of Data Management Notes #11 Selection, Projection

EXAMPLE: The weight of a can of Coca Cola is supposed to have mean = 12 oz with std. dev.= 0.82 oz. The product is declared underweight if it weighs.

Efficient Cache-Supported Path Planning on Roads

Overview of Query Evaluation

Presented by : SaiVenkatanikhil Nimmagadda

CS222: Principles of Data Management Notes #11 Selection, Projection

Evaluation of Relational Operations: Other Techniques

A Privacy – Preserving Index

CS222/CS122C: Principles of Data Management UCI, Fall 2018 Notes #10 Selection, Projection Instructor: Chen Li.

Presentation transcript:

Implementation (Group 6) Monika (A H) Damien Forest (A A) Rattanak Chhung (A N) Yann-Loup Phan Van Song (A B) 1 CS Groupe 6 A Privacy-Preserving Index for Range Queries

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 CS Groupe 6 2

1 attribute CS Groupe 6 3

4 valuefreq Dataset of plain values Inputs find the bucketization that reduces the number of total false positives Our goal: Principle:

BC table CS Groupe 6 5 BC=

CS Groupe 6 6 valuefreq 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

CS Groupe 6 7 valuefreq Dataset of plain values Inputs Outputs BucketsBucketization cost [ ] 3.5 [ ] 3.6 [ ] 1.6 [ ] 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

CS Groupe 6 8 valuefreq 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

CS Groupe 6 9

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 ] Ind1Ind Dataset of plain values Partition attribute 1 Partition attribute 2 Encrypted table Inputs

CS 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 ] Ind1Ind Context To match the indexes and the buckets Our goal: How ? Working with cardinalities

CS 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 ] Ind1Ind 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…

CS 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 ] Ind1Ind First attack - BAA B11 = [ BAA :

CS 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 ] Ind1Ind First attack - BAA B11 = [ BAA :

CS 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 ] Ind1Ind First attack - BAA BAA : B11 = [73,

CS 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 ] Ind1Ind First attack - BAA BAA : B11 = [73,15 ]

CS 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 ] Ind1Ind 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 … 

CS 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 ] Ind1Ind 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 = [

CS 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

CS 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

CS 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

CS 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

CS 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

CS 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

CS 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

CS 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

CS 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

CS 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

CS 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 …  First attack - BAA2

CS 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 …  Ind1Ind

CS 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 …  Ind1Ind First attack - intersection

CS 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 & Ind1Ind First attack - intersection

CS 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 & Ind1Ind New identified indexes : 73, 15New identified indexes : First attack - intersection

CS 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 ] Ind1Ind New identified indexes : 73, 15New identified indexes : (73 ; [

CS 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 ] Ind1Ind New identified indexes : 73, 15New identified indexes : (73 ; [(45;1), B11 = 73 B12 = 15 Creation of couples of indexes

CS 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 ] Ind1Ind New identified indexes : 73, 15New identified indexes : (73 ; [(45;1), B11 = 73 B12 = 15 Creation of couples of indexes (20;1)])

CS 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 ] Ind1Ind New identified indexes : 73, 15New identified indexes : (73 ; [ (45;1), (20;1)]) (15 ; [ B11 = 73 B12 = 15 Creation of couples of indexes

CS 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 ] Ind1Ind New identified indexes : 73, 15New identified indexes : (73 ; [ (45;1), (20;1)]) (15 ; [ (9;2)]) B11 = 73 B12 = 15 Creation of couples of indexes

CS 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 ] Ind1Ind 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

CS 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 ] Ind1Ind 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

CS 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 ] Ind1Ind 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

CS 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 ] Ind1Ind 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)])

CS 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 ] Ind1Ind 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)])

CS 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 ] Ind1Ind 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)])

CS 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 ] Ind1Ind 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 !

CS 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 ] Ind1Ind 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

CS 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 ] Ind1Ind 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)])

CS 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 ] Ind1Ind 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

CS 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 ] Ind1Ind 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

CS 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 ] Ind1Ind 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)])

CS 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 ] Ind1Ind 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)])

CS 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 ] Ind1Ind 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

CS 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 ] Ind1Ind 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

CS 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 ] Ind1Ind 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

CS 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 Ind1Ind (20 ; [(79;1)]) Propagation 2 - identify the new index

CS 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 Ind1Ind (20 ; [(79;1)]) Propagation 2 - identify the new index

CS 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 Ind1Ind (20 ; [(79;1)]) Propagation 2 - identify the new index

CS 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 Ind1Ind (20 ; [(79;1)]) Propagation 2 - add the new index to the list

CS 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 Ind1Ind (20 ; [(79;1)]) Propagation 2 - remove deprecated data

CS 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 Ind1Ind (20 ; [(79;1)]) Propagation 2 - remove deprecated data

CS 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 Ind1Ind (20 ; [(79;1)]) Propagation 3 - look for new indexes

CS 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 Ind1Ind (20 ; [(79;1)]) Propagation 3 - look for new indexes

CS 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 Ind1Ind (20 ; [(79;1)]) Propagation 3 - identify the new index

CS 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 Ind1Ind (20 ; [(79;1)]) Propagation 3 - identify the new index

CS 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 Ind1Ind (20 ; [(79;1)]) Propagation 3 - identify the new index

CS 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)]) Ind1Ind (20 ; [(79;1)]) Propagation 3 - add the new index to the list

CS 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)]) Ind1Ind (20 ; [(79;1)]) Propagation 3 - remove deprecated data

CS 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)]) Ind1Ind (20 ; [(79;1)]) Propagation 3 - remove deprecated data

CS 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 Ind1Ind (20 ; [(79;1)]) Propagation 4 - look for new indexes

CS 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 Ind1Ind (20 ; [(79;1)]) Propagation 4 - look for new indexes

CS 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 Ind1Ind (20 ; [(79;1)]) Propagation 4 - identify the new index

CS 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 Ind1Ind (20 ; [(79;1)]) Propagation 4 - identify the new index

CS 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 Ind1Ind (20 ; [(79;1)]) Propagation 4 - identify the new index

CS 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)]) Ind1Ind (20 ; [(79;1)]) Propagation 4 - add the new index to the list

CS 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)]) Ind1Ind Propagation 4 - remove deprecated data

CS 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 ; [ ]) Ind1Ind Propagation 4 - remove deprecated data

CS 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 Ind1Ind Propagation 5 - look for new indexes

CS 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 Ind1Ind Propagation 5 - look for new indexes No way! Impossible to identify them

CS 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 Ind1Ind No other index: we have to stop!

CS 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 ] Ind1Ind Results B11 = 73 B12 = 15 B13 = 79 B14 = 30 B21 = [ 20, 45 ] B22 = 74 B23 = 9 B24 = [ 20, 45 ]

CS Groupe 6 81

Hilbert curve col1 col CS Groupe 6 Hilbert value Col1 value Col2 value

Hilbert curve col1 col CS Groupe 6 IdCol1Col2HV

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

Hilbert curve col1 col CS Groupe 6 IdCol1Col2HVB 1000B B2 7127B B B B3 B2B4 B1 B5

Hilbert curve col1 col CS Groupe 6 IdCol1Col2HVB 1000B B2 7127B B B B2B4 B1 B5 Range query on [1-1] for col1 … WHERE Col1 = 1 B3

Hilbert curve col1 col CS Groupe 6 IdCol1Col2HVB 1000B B2 7127B B B B3 B2B4 B1 B5 Range query on [1-2] for col2 … WHERE Col2 in [1-2]

Hilbert curve CS Groupe 6 88 Range query? col1 col2

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 CS Groupe 6 89

CS Groupe 6 90

[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 , New York, NY, USA, 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 , New York, NY, USA, 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 VLDB Endowment, [2] Eclipse. [4] Hilbert curves in more (or fewer) than two dimensions. [6] Hilbert Space-Filling Curves. [7] JUnit. [8] Project Locker. [9] Subclise. [10] Gaussian distribution. [11] Sudoku. [12] Variance - Discrete case CS Groupe 6 References

CS Groupe 6 92

Annexes CS Groupe 6 93

CS Groupe 6 94

Controlled-Diffusion IdVal.OB CB1CB2 CB3CB4 95 CS Groupe 6

Controlled-Diffusion IdVal.OB CB1CB2 1; CB3CB4 96 CS Groupe 6

Controlled-Diffusion IdVal.OB CB1 2; CB2 1; CB3CB4 97 CS Groupe 6

Controlled-Diffusion IdVal.OB CB1 2; 3; CB2 1; CB3CB4 98 CS Groupe 6

Controlled-Diffusion IdVal.OB CB1 2; 3; CB2 1; 4; CB3CB4 99 CS Groupe 6

Controlled-Diffusion IdVal.OB CB1 2; 3; CB2 1; 4; CB3 5; 6; 8 CB4 7; 9; 100 CS Groupe 6

Controlled-Diffusion IdVal.OB CB1 2; 3; 10; 13; CB2 1; 4; CB3 5; 6; 8 11; 12; CB4 7; 9; 101 CS Groupe 6

Controlled-Diffusion IdVal.OB CB1 2; 3; 10; 13. CB2 1; 4; 14; 16. CB3 5; 6; 8 11; 12. CB4 7; 9; CS Groupe 6

Controlled-Diffusion IdVal.OB 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 CS Groupe 6

104

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

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

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

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

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

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