1. Multiplicative data perturbation (2)

2. Multiplicative Perturbation: RASP
Random space perturbation

3. confidential query services in the cloud
framework
Data D D’ D’
D’=F(D)
Data owner q’
Query q
q’=Q(q)
H(q’,D’)
Authorized
Users
Result R’
Result R
R=G(R’)
Trusted client
Honest but curious cloud
RASP framework for
confidential query services in the cloud

4. Order preserving encryption
Agrawal2004, Boldyreva2009
The set of data is securely transformed so that the order is preserved but the distribution and domain are changed
Benefits: indexing/searching on OPE encrypted data
Weakness: once the original distribution is known, OPE is broken

5. Not attribute-wise order preserving
Order preserving encryption (OPE, Agrawal et al 2004) is not resilient to distribution-based attacks
Original Xi distribution is known
Transformed Xi’ distribution
OPE
Bucket based
Estimation

6. RASP perturbation
k-dimensional numeric data, n records, represented as a k x n matrix, x: a record RG: random number generator A: (k+2)x(k+2) random invertible matrix K_ope : key for Order preserving encryption

7. Properties Not an OPE Preserves convexity of the dataset
Convex dataset in Rk  another convex dataset in Rk+2.
Good for range query
Each range query in Rk
 hyperplane based query
 range query in Rk+2 .

8. RASP properties Convexity preserving
Queried range (hypercube) is convex
RASP transforms the range to another convex (polyhedron)
half space: wTx<=a
wTx=a
The intersection of convex sets is also convex.

9. illustration of convexity preserving
Perturbed space
Original space
OPE space
Xi < a
 E(Xi)<E(a)

10. Secure query transformation
A naïve solution
Based on the convexity preserving property
Problems: (1) A-1 can be probed
(2) is If a is known, the whole
dimension i is breached.

11. Secure query transformation
Enhanced solution
Xk+2 is always positive
(Xi-a)  0  (Xi-a)Xk+2  0
Correspondingly, in the encrypted space yTy  0,
Problems addressed:
(1) A-1 cannot be derived from 
(2) (Xi-a)Xk+2  0 contains the random component Xk+2 that protects
the condition (Xi-a)  0

12. Efficient two-stage query processing
illustrated
Stage2:
Filter out the junk records
Stage1:
Querying this bounding
box
Original space
Transformed space
A multidimensional tree index is been built on the encrypted data (in the
transformed space) in the server.

13. The client calculates the large bounding box;
Stage 1:
The client calculates the large bounding box;
The server uses the index to find the results.
Stage 2:
filter the initial results with the conditions yTiy  0 for 1…2m
Note: the two-stage strategy works, if the output of stage 1 is significantly smaller than the original database and can be fit into the memory.
Otherwise, use linear scan with stage 2 filtering.