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In this section we examine the security of our embedding system. In steganographic
applications there are two levels of security. The first is not allowing an
observer to detect the presence of a secret message. The other is not allowing the
attacker to read the original plain message after detecting the presence of secret
information. According to [12], a stego system is
called -secure if
Where represents the distribution of the cover object, represents the
distribution of the stego object and represents the relative entropy
between the two probability distributions [11]. For a perfectly secure
system we must have . To examine the security of our system we
compute the pdf of the cover image and the stego image in the transform domain. As
was shown before, the pdf of the cover signal follows a
Gaussian distribution. This distribution is determined by its mean and variance.
The mean of the distribution is approximately zero. Let
be the variance of the cover signal. To examine the
distribution of the stego image, we assume that the attacker knows the embedding
technique. This follows from kerckhoff's principle that security is not in the
technique but in the keys [7]. If the right key is not available then
the distribution of the stego in the transform domain will look exactly identical
to the original. Similarly the
mean of the transform of the stego image is also zero and it has a variance given
by . Figure 4 shows the distributions of the scrambled cover
and stego images in the transform domain. The ratio of the two pdf's is,
Both and are very close numerically.
Therefore, when we take their difference and divide the result by there product
the ratio . Therefore, the
two distributions are close which means . Hence the system
is extremely secure. The overall system security also depends on the security of
the encrypted hidden message, which is a cryptographic problem. In addition there
is the security of the scrambling key. Without this key no one can extract the
hidden information and decrypt it. The last level of security is related to
detection. The perceptual quality of the cover and stego images are identical.
Furthermore the statistical properties of the two images are also identical both
in the spatial and the transform domain. Therefore, it is very difficult for an
observer to detect any hidden information in the absence of the original image.
Figure:
Distributions in transform domain.
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Next: Example and Results
Up: SECURE HIGH DATA EMBEDDING
Previous: Embedding System
Muhammad Zubair Ikram
7/14/2000