Privacy Preserving Similarity Evaluation of Time Series Data
Haohan Zhu, Xianrui Meng, George Kollios
Abstract: Privacy preserving issues of time series databases
in financial, medical and transportation applications have
become more and more important recently. A key problem in
time series databases is to compute the similarity between
two different time series. Although, some work has been
done in the past few years on security problems for time
series data, there is very limited work on computing
securely the similarity between two time series. We consider
exactly this problem in a two party setting. In particular, we
want to compute the similarity between two time series, one
stored in one party and the other in the other, without
revealing the actual time series to the other party. The two
parties should learn only the value of the similarity,
according to a specific similarity function, and nothing more
about the time series of the other party. At the same time,
we want to do that as efficiently as possible. Therefore, we
propose protocols for computing the similarity (or distance)
for time series using two popular and well know functions:
Dynamic Time Warping and Discrete Frechet Distance.
Since both of these functions require dynamic programming
to be computed, our protocols not only protect the original
time series data, but also try to prevent the parties involved
in the computation to infer intermediate results, including the
matrix of the dynamic programming algorithm and the path
of the optimal solution. The protocols combine partial
homomorphic encryption and random offsets to minimize
the leakage of intermediate information and at the same
time provide efficient computation. The protocols are
scalable and easy to implement. We also provide an
experimental evaluation where we assess the efficiency and
practicality of our schemes.
Filling One Entry of the Matrix
A
Minimum(A, B, C) +. δ
B
C
Dynamic Time
Warping
Distance
Two-Phase Protocol
1.Homomorphic
Encription
Server sends
information
Client Evaluates
2.Radom Offset
Client sends
information
Server
Evaluates
Client computes
Distances Computed by Dynamic Programming
Experimental Results
Runtime is linear to 2 parameters respectively
Y
D(X1, Y3)
D(X2, Y3)
D(X3, Y3)
D(X4, Y3)
D(X1, Y2)
D(X2, Y2)
D(X3, Y2)
D(X4, Y2)
D(X1, Y1)
D(X2, Y1)
D(X3, Y1)
D(X4, Y1)
X
The Matrix Maintain
Cypertexts Only
Owner of Matrix
Owner of Key