Cryptography Reference
In-Depth Information
the complexity histogram of the image with secret data embedded is, in gen-
eral, different from that of the original one. Here the complexity histogram
represents the relative frequency of occurrence of the various complexities in
the binary image. The unnatural distribution of complexity histogram, hence,
can be used as a signature or a distinguishing mark between natural images
and images with information embedded by BPCS. Since the term steganog-
raphy literally means covered writing, steganographic techniques should
not be distinguishable from cover images.
In this section, we discuss this possible attack to BPCS and present a
countermeasure that removes this distinguishing mark. The problem of BPCS
is that all bits in noise-like regions are used for secret data. This causes the
complexity of secret data to be different from that of the original noisy pattern
replaced with secret information. In the proposed method, only half of the bits
in noise-like regions are used for secret data. The remaining half of the bits
are used to adjust the complexity measure in those regions. The adjustment
of complexity is performed by changing the pixel values of the bits in the
noise-like regions that are not used for encoding secret data.
8.3.1 Changes in Complexity Histograms
Let P
ORG
be a block replaced with secret data and P
EMB
be a squared binary
pattern mapped from secret data. From a principle of embedding in BPCS,
the complexity of P
ORG
and P
EMB
satisfies the following conditions
α
TH
≤α(P
ORG
)andα
TH
≤α(P
EMB
)
(8.6)
where α(P
ORG
) means the complexity of P
ORG
and α
TH
represents the
threshold used to determine whether the subimage is noise-like or not. How-
ever the following equation is not always satisfied,
α(P
ORG
)=α(P
EMB
).
(8.7)
This causes a change in the shape of the complexity histogram. In order to
explain this fact, we will look at the complexity histogram in greater detail.
As mentioned above, the complexity histogram used in this section represents
the relative frequency of occurrence of the various complexities in a binary
pattern. Because the complexity of an original binary pattern is rarely equal
to that of a binary pattern mapped from secret data, a change in shape in
the complexity histogram will generally occur. Binary patterns having a com-
plexity value that exceeds the threshold are substituted for noise-like binary
patterns (secret data) having the complexity distribution described below.
One might assume that the complexities of random binary patterns of
size nn would follow a normal distribution, and indeed, this has been
experimentally verified [9]. Thus, for BPCS, patterns in bit-plane images that
are replaced by secret information generally have a normal distribution of
complexities, because the secret information is noise-like.
