Cryptography Reference
In-Depth Information
8.4.2 Robust Embedding against the Visual Attack
Outline
The reason why BPCS is weak against the visual attack is to embed con-
jugation flags without using the complexity thresholding. Therefore, if both
secret data and the conjugation flags can be embedded by the complexity
thresholding, BPCS would be robust against it. To realize this idea, we em-
bed conjugation flags into each block.
Embedding
Let S be a mm squared binary image mapped from the bit sequences of
secret data. The conjugation flag, which takes on 0 or 1, of S can be
embedded within S if we make the value of a pixel on S correspond to the
flag. We call the pixel assigned the flag
a control pixel
. The value of the control
pixel represents whether the conjugation operation had been applied. In this
section we define that 1 of control pixel means the conjugate operation had
been applied to S.
First, the proposed method initializes the control pixel as 0, then makes
the bit sequences of secret data map on S except for the control pixel, next,
calculates the complexity. By the complexity, the method determines whether
the value of the control pixel should be changed form 0 to 1. In the
following, S
CP=0
and S
CP=1
represent that the value of the control pixel is
equal to 0 and 1.
We use one of the four corner of S as the control pixel. Because we consider
4 connectivity of pixels through this section, there are 2 adjacent pixels of the
control pixel. Thus, we can categorize adjacent-pixel patterns into 3 patterns :
the both values are 0, the both values are 1, and one is 0 and another is 1, and
vice versa. Each pattern is denoted by BB, WW and BW in the following.
As mentioned earlier section, conjugation flags are not needed for the S
whose complexity is within α
TH
and 1−α
TH
. In that case, it is better to
embed secret data to the control pixel to increase data hiding capacity. In the
extraction procedure, it is desirable that the meaning of the control pixel is
determined by the complexity of a block in which the control pixel is, that
is, when the complexity is greater than or equal to α
TH
and less than or
equal to 1−α
TH
, the control pixel represents secret data and, otherwise,
that represents conjugation flag. We can easily assign the meaning to the
control pixel in embedding, however, in some case, the meaning may change
in extraction because the complexity would be affected by changing the value
of the control pixel.
We show here an example of that case. Let β(S)beα(S)2m(m−1),
β
TH
be α
TH
2m(m−1), β
∗
TH
be (1−α
TH
)2m(m−1). We now consider
the case where β(S
CP=0
)=β
TH
−2 and the adjacent pixel pattern is BB. For
the S, we need to apply the conjugate operation because the complexity of S
