Title: Efficient Hidden Vector Encryptions and Its Applications,
Abstract: Predicate encryption is a new paradigm of public key encryption that enables
searches on encrypted data. Using the predicate encryption, we can search
keywords or attributes on encrypted data without decrypting the ciphertexts. In
predicate encryption, a ciphertext is associated with attributes and a token
corresponds to a predicate. The token that corresponds to a predicate $f$ can
decrypt the ciphertext associated with attributes $x$ if and only if $f(x)=1$.
Hidden vector encryption (HVE) is a special kind of predicate encryption. In
this thesis, we consider the efficiency, the generality, and the security of
HVE schemes. The results of this thesis are described as follows.
The first results of this thesis are efficient HVE schemes where the token
consists of just four group elements and the decryption only requires four
bilinear map computations, independent of the number of attributes in the
ciphertext. The construction uses composite order bilinear groups and is
selectively secure under the well-known assumptions. The second results are
efficient HVE schemes that are secure under any kind of pairing types. To
achieve our goals, we proposed a general framework that converts HVE schemes
from composite order bilinear groups to prime order bilinear groups. Using the
framework, we convert the previous HVE schemes from composite order bilinear
groups to prime order bilinear groups. The third results are fully secure HVE
schemes with short tokens. Previous HVE schemes were proven to be secure only
in the selective security model where the capabilities of the adversaries are
severely restricted. Using the dual system encryption techniques, we construct
fully secure HVE schemes with match revealing property in composite order
groups.