1. Private and Secure Secret Shared MapReduce
30th Annual IFIP WG 11.3 Conference on Data and Applications Security and Privacy (DBSec 2016), Trento, Italy
Private and Secure Secret Shared MapReduce
Shlomi Dolev1, Yin Li2, and Shantanu Sharma1
1 Ben-Gurion University of the Negev, Israel
2 Xinyang Normal University, China

2. Outline Introduction System Settings Overview of the Approach
Count Operation
Search and Fetch Operation
Other Operations
Conclusion

3. Introduction Why is it required to ensure privacy?
Users send data on the clouds
Curious mappers and reducers can
Store useful data
Know the given job
Where is it required?
Banking, financial, retail, and healthcare

4. Make information secure data
Introduction
What others do?
Work on encrypted data
Authentication & Compress + Encrypt data
Encrypt data-at-rest
Secure storage of data in HDFS
Provide authentication before using Hadoop cluster
They are making ‘computational secure’ data.
But, for how long is it secured??
Make information secure data

5. Outline Introduction System Settings Overview of the Approach
Count Operation
Search and Fetch Operation
Other Operations
Conclusion

6. System Settings Secret-shares of the database
Step3: Master Process M R M R
Step 2: send queries
Step 1: Distribute secret-shares M
Step 3: obtaining addresses of outputs
Step 4: Fetching outputs
Database
Secret-shares of the database
Step3: Master Process
Step 4: Interpolation and obtain the final results M R M R M
Data owner
User-side
Secret-shares of the database
Step3: Master Process M R
Notations:
M: Mapper
R: Reducer M R M

7. Adversarial Setting Honest-but-curious adversary
Wants to gain knowledge
But executes computations honestly

8. Parameters of Analysis
Communication cost
Computational cost
Number of rounds

9. Outline Introduction System Settings Overview of the Approach
Count Operation
Search and Fetch Operation
Other Operations
Conclusion

10. Overview of the Approach
Accumulating Automata*
Make shares of data (or input split)
Send these shares to mappers
Mappers do not know the computation and data
Mappers have a defined accumulating automata
Example: Search a pattern “LO” in the string “LOXLO”
*S. Dolev, N. Giboa, X. Li, “Accumulating Automata and Cascaded Equations Automata for Communicationless Information Theoretically Secure Multi-Party Computation: Extended Abstract,” pages 21—29, 2015.

11. Overview of the Approach
Example: Search a pattern “LO” in the string “LOXLO”
L = {v3,v4}
O = {v5,v10}
X ={v1,v1}
L = {v4,v5}
O = {v15,v20}
Mapper 1
𝑁 1 𝑀 𝑘+1 =𝑣0
𝑁 2 𝑀 𝑘+1 = 𝑁 1 𝑀 𝑘 . 𝑣1
𝑁 3 𝑚 𝑘+1 = 𝑁 3 𝑀 𝑘 +𝑁 2 𝑀 𝑘 . 𝑣2 N1 N2 N3
v140
L = {v5,v6}
O = {v10,v19}
X = {v2,v2}
L = {v6,v7}
O = {v20,v29}
Mapper 2 N1 N2 N3
v698
Reducer
LO, 2
L = {v7,v9}
O ={v15,v28}
X = {v3,v3}
Mapper 3 N1 N2 N3
v1964
L = {v9,v12}
O={v20,v37}
X = {v4,v4}
Mapper 4 N1 N2 N3
v4226

12. Creating Secret-Shares
Consider only English words
Represent an alphabet as:
‘A’ is represented as (11, 02, 03, . . ., 026)
Make secret-shares of every bit by selecting different polynomials of an identical degree
Since we use different polynomials for creating secret-shares of each bit, multiple occurrences of a word in a database have different secret- shares

13. Outline Introduction System Settings Overview of the Approach
Count Operation
Search and Fetch Operation
Other Operations
Conclusion

14. Count Operation String-matching based Two phases
Matches a value of a relation with a pattern, where the value and the pattern are of the form of secret-shares
Two phases
Phase 1: Privacy-preserving counting in the clouds
Phase 2: Result reconstruction at the user-side

15. Count Operation Working in the cloud: A mapper
Creates an automaton of x+1 nodes where x is the length of p
Initializes values of these nodes
The first node is assigned a value one (N1 = 1) and all the other nodes are assigned values zero (Ni = 0)

16. Count Operation Working in the cloud: Count ‘John’ v1 = J * J
Name
Adam
John
v1 = J * J
v2 = o * o
v4 = n * n
v1 = J * A
v2 = o * d
v3 = h * h
v4 = m * n
v3 = a * h v1 v1 v2 v3 v4
N1 = 1
N2 = 0
N3 = 0
N4 = 0
N5 = 0
N1 = 1
N2 = 0
N3 = 0
N4 = 0
N5 = 1
N1 = 1
N2 = 0
N3 = 0
N4 = 0
N5 = 2

17. Count Operation Working at the user side
Result construction – a simple interpolation operation

18. Outline Introduction System Settings Overview of the Approach
Count Operation
Search and Fetch Operation
Other Operations
Conclusion

19. Search and Fetch Operation
Working in the cloud: A mapper
PHASE 1: Finding addresses of tuples containing p
PHASE 2: Fetching all the tuples containing p

20. Search and Fetch Operation Unary Occurrence
Working in the cloud: A mapper
No need to know the address
Multiply
Results will be 0 or 1 of the form of secret-shares
Multiply the result with the tuple
Add the values of an attribute
Name
Department
Adam CS
John EC
Name
Department 1
Adam

21. Search and Fetch Operation Unary Occurrence
Working at the user side
A simple interpolation

22. Search and Fetch Operation Multiple Occurrences
Tradeoff
Number of rounds vs computational load at the user side
Naïve algorithm and a database partitioning algorithm

23. Search and Fetch Operation Multiple Occurrences
The first way: Naïve Algorithm
Requires a lot of computation at the user side while only 2 rounds are required
Now the user can know the address
Name
Department
Adam CS
John EC
Name 1
John
Multiply

24. Search and Fetch Operation Multiple Occurrences
The first way: Naïve Algorithm – But HOW TO FETCH
Say L occurrences are there
Create a matrix M of L*n
Name 1
Name
Department
Adam CS
John EC
Name
Department
John EC CS 1 * M

25. Search and Fetch Operation Multiple Occurrences
The second way
Requires less computation at the user side while more than 2 rounds are required
Partitions database and knows address
Then fetches tuples using the solution suggested in the naïve algorithm

26. Search and Fetch Operation Multiple Occurrences
Database
#Occurrence = 1
#Occurrences = 2
#Occurrence = 1
#Occurrences = 2
#Occurrence = 0
#Occurrences = 2
#Occurrence = 0
Q&A Round 3
Q&A Round 1
Q&A Round 2

27. Outline Introduction System Settings Overview of the Approach
Count Operation
Search and Fetch Operation
Other Operations
Conclusion

28. Other Operations Equijoin Range query
Use two layers of clouds, where the first layer performs fetch operation and the second layer performs equijoin operation
Range query
By using 2’s complement
Count the occurrence of number that lies in the range and then fetch those tuples

29. Outline Introduction System Settings Overview of the Approach
Count Operation
Search and Fetch Operation
Other Operations
Conclusion

30. Conclusion Privacy-preserving operations based on MapReduce
A way to create secret-shares
Count, search, and fetch operations
Equijoin and range quires

31. Presentation is available at
Shlomi Dolev1, Yin Li2, and Shantanu Sharma1
1 Department of Computer Science, Ben-Gurion University of the Negev, Israel
2 Department of Computer Science, Xinyang Normal University, China