Cryptography Reference
In-Depth Information
We can directly determine all difference values in Class 3 by using the
retrieval algorithm itself without any additional information according to
Fig. 13.14. We then collect the LSBs of all difference values in Class 3, and
form a binary bitstream B. The bitstream B is decompressed to restore
the location maps. That is, the lM ap and the pM ap by an arithmetic
decoder. Hence, by lM ap, we can differentiate between Class 1 and Class
2.
The original difference value h is restored as follows: for difference values
h in Class 1, h = h. For difference values
h in Class 2 and Class 3, h =
h
2
.
The original pixel values computing from h and l using Eq. (13.13) are next
obtained.
All watermarked bits including the hash function of the image blocks are
obtained by using the expression w =(h−2⌊
⌋) for Class 2 and Class 3.
This can be done for any value of k∈0, 1, 2, 3, provided the inequations
4h + k> min(2(255−l), 2l−1) satisfy, h in Class 2. This is classified
as the Flipping Class 2. Accordingly, the calculated binary numbers obtained
using the above expression are useless and discarded.
For the pixel values which are pseudo-randomly selected in the locating
decoding pattern, by the use of pM ap, we can identify the positions of the
changed pixel values. Then we can apply the invertible subtraction to restore
the original pixel value. For those unchanged pixel values, remain intact. All
the original image blocks are retrieved. We compare the extracted candidate
representing hash H
2
′
with hash H of the retrieved image. If they match, the
image is authentic. If H
′
= H, the image is deemed to be non-authentic.
Resisting on Collage Attack
A fragile watermark is designed to detect any small alternation to the pixel
values. The tampered areas can be easily detected by checking for the presence
of the fragile watermark. For the fragile watermark, it is very important to
precisely locate the maliciously tempered areas. A simple locating method is to
divide the image into blocks and embed the fragile watermark in each block.
However, this method is vulnerable to the collage attack which assembles
blocks of several authentic images or swaps blocks of the same image to forge
a new authentic image.
Our scheme, based on a block-wise fragile watermark, also suffers from
the collage attack. The attackers simulate our embedding method for another
arbitrary, interconnected image and visibly copy a portion of its watermarked
image to our watermarked image. During detection, since the retrieved hash
matches with the hash function of the restored fake image block, our method is
defeated. To resist collage attack, we utilize the method, proposed by Holliman
et al. [17]. The method resolves this problem by adding the image ID and block
index to the input of hash function.
