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embedding in grayscale images with squared error distortion in the present
communication.
For example, we use simple least significant bit (LSB) embedding for digital
images in which the set of least significant bits (LSBs) of all pixels is the array of
binary cells. The LSBs of secret message-carrying pixels (the selection channel)
are regarded as functioning cells, while the LSBs of unused pixels correspond
to stuck cells. The challenge is to embed secret messages with nonshared selec-
tion channels so that the recipient, who has no information about the stuck cells
(the selection channel), can still correctly extract the embedded messages.
The most important attribute influencing steganographic security of mes-
sage embedding schemes is embedding efficiency [8,9], which is defined as
the average number of secret bits embedded per embedding change. In steg-
anography, embedding efficiency is used to quantify how effectively a given
message embedding scheme embeds secret messages. In general, fewer
changes during the embedding process mean a smaller chance that the
embedding modifications will be detected. However, the number of embed-
ding changes is not the only factor influencing security. In fact, for two mes-
sage embedding schemes using the same embedding operation, the one that
introduces fewer embedding changes will be harder to detect and thus will
provide greater security. As a result, it is desirable to increase embedding
efficiency in order to reduce the possibility of detection by a third party.
The disk modulo (DM) method [10,11] finds an approach to uniformly dis-
tribute files on multiple disks while maximizing parallel disk I/O access.
The DM uses the Hamming weight of a binary string (modulo operation)
to determine an appropriate disk for optimal match queries. To improve
security, we propose message embedding using a DM allocation method
that enables communication with nonshared selection channels. Moreover,
we also show that the DM allocation method can be applied to improve the
embedding efficiency of message embedding schemes.
To make this paper self-contained, in Section 10.2, we introduce the terminolo-
gies and the basic concepts of steganography necessary to explain the embedding
method. We also state known bounds on achievable embedding efficiency in the
same section. In Section 10.3, we review some traditional ±1 message embedding
techniques. The proposed method using the DM allocation method is explained
in Section 10.4. Performance analyses appear in Section 10.5 and the performance
is compared to theoretically achievable bounds.
10.2 Message Embedding
We assume that the grayscale cover image
C
= {
c
1
,
c
2
, …,
c
n
} is a vector of inte-
gers in the range [0,255] where
n
is the number of pixels. Let
M
= {
m
1
,
m
2
, …,
m
w
} be the embedded messages with a probability 1/
w
and independent of
C
.
