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System Security

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
(11)
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,
(12)
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.


next up previous
Next: Example and Results Up: SECURE HIGH DATA EMBEDDING Previous: Embedding System
Muhammad Zubair Ikram
7/14/2000