THESIS
2013
Abstract
In this big data era, often a person (say Bob) needs another person (say Alice)
to perform processing on his data. But both Alice and Bob do not know each
other and do not trust each other. It would be desirable for Bob to send his
data in encrypted form to Alice and for Alice to perform all the processing of
Bob's data in the encrypted domain such that Bob would be able to decrypt
the processed data sent by Alice to obtain the desired results. This kind of
processing is called signal processing in the encrypted domain (SPED). Some simple operations such as integer addition and multiplication have been known
to be possible for some cryptosystems. In this thesis, we focus on two SPED
problems: (1) the feasibility of performing bitwise operations in the encrypted
domain and (2) s...[
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In this big data era, often a person (say Bob) needs another person (say Alice)
to perform processing on his data. But both Alice and Bob do not know each
other and do not trust each other. It would be desirable for Bob to send his
data in encrypted form to Alice and for Alice to perform all the processing of
Bob's data in the encrypted domain such that Bob would be able to decrypt
the processed data sent by Alice to obtain the desired results. This kind of
processing is called signal processing in the encrypted domain (SPED). Some simple operations such as integer addition and multiplication have been known
to be possible for some cryptosystems. In this thesis, we focus on two SPED
problems: (1) the feasibility of performing bitwise operations in the encrypted
domain and (2) solving a system of linear equations, Ax = b, in the encrypted
domain.
For (1), we examine the basic bitwise operations and pose the question of
whether these can be perform in the encrypted domain. We show that such
bitwise operations are not possible for some cryptosystems.
For (2), we focus on a common iterative method called the Gauss-Seidel
method to solve Ax = b that is computationally feasible even when the dimension of A is large. The motivation is that the Gauss-Seidel requires only
addition and multiplication and thus should be possible to be performed in
the encrypted domain. However, problems occur when A, x or b contain non-integer numbers as the encrypted domain cannot handle non-integers. In this
thesis, we propose some integer approximation for the problem and show that
it can solve the problem with high accuracy.
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