Chapter 4 A Fragile Authentication Method for Color Images
4.3 Authentication Signal Embedding Process
4.3.1 Embedding of Authentication Signals
Proposed Idea of Embedding Authentication Signals
In this section, the proposed idea for image authentication in color images is described. The relationship between the mother and child blocks is used to hide data.
The block size of the mother block used in the proposed method is chosen to be 3×3.
The mother block is chosen from a 9×9 block. The remaining blocks in the 9×9 block are regarded as child blocks. In this proposed method, authentication signals and embedding locations are generated by two keys. The first key is to choose the location of the mother block and assign the remaining blocks as the child blocks in each 9×9 block. And the second key is used to create authentication signals which contain 8 bits.
Authentication signals will be embedded in the child blocks and called authentication codes. The concept of edge direction described in Chapter 3 is also utilized to embed authentication signals. By modifying the degree of the edge direction of the child blocks, authentication codes can be embedded in them.
Authentication Signal Embedding Process
4.3.1 Embedding of Authentication Signals
An input image is first divided into non-overlapping 9×9 blocks. Then, each 9×9 block is divided further into nine non-overlapping 3×3 blocks. Figure 4.1 shows an example of a 9×9 block and its nine 3×3 blocks.
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(a) (b) Figure 4.1 An example of 9×9 image blocks. (a) A 9×9 block. (b) Each 3×3 block in
the 9×9 block.
A Selection of the location of the mother block and creation of the authentication signals using two keys.
In the proposed method, the two keys are used to enhance the security. The function of the first key K1 is used to select the location of the mother block and assign the remaining blocks as child blocks. There are only nine 3×3 blocks in a 9×9 block. And only one block can become the mother block and the others are the child blocks. Figure 4.2 shows an example of selecting the mother and child blocks. Figure 4.2(a) is the indices of the locations of a 3×3 block and (b) shows the selection of the block with index 2 to be the mother block, and the others are the child blocks.
The function of the second key K2 is used to create 8 bits of the authentication codes to be embedded in the child blocks. For instance, in Figure 4.2(b), if K2 creates 8 bits which are {1, 0, 1, 0, 1, 0, 1, 0}, then we embed these authentication codes into the child blocks with indices of {1, 3, 4, 5, 6, 7, 8, 9}, respectively. So, in our method, each child block can embed one authentication code.
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(a) (b) Figure 4.2 An example of selecting the mother and child blocks. (a) Indices of a
3×3 block. (b) The selection of the mother and child blocks.
B Authentication signal embedding process by edge direction.
The authentication signal embedding technique uses the edge direction. The definition of edge direction is described in Chapter 3 in detail. In short, we apply the Sobel operator to get an edge direction and then quantize it into 16 levels. The method to embed authentication signals is to adjust the edge direction according the input data.
The proposed method uses the relationship of the edge direction between the mother and the child block to embed an authentication code. We call the edge direction in the mother block to be Em, and the edge direction in the child block to be Ec. If the direction from Em to Ec is clockwise, it represents a “1;” otherwise, a “0.”
How to modify the edge direction in the child block is our main concern. If the direction from Em to Ec is counterclockwise and it is needed to embed a “1,” which is represented by a clockwise sign, we need to modify the gray values of the child block to make the edge direction rotate in the opposite direction. The opposite direction is the way to allow the edge direction to rotate in the clockwise direction. Figure 4.3 shows an illustration of changing the edge direction by modifying the gray values of
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pixels.
During the authentication process we only need to compare the difference between the authentication codes created by K2 and the extracted ones from the child blocks, and so verify the integrity of the stego-image. Figure 4.4 shows a flowchart of the proposed authentication embedding method.
According to our experiments, authentication signals can be embedded into the R channels without creating perceivable effects to human vision. And the gray values of the pixels in the blue and green channels are unchanged.
Degree=63.43
Figure 4.3 An illustration of changing the edge direction by modifying the grayvalues of pixels.
4.3.2 Detailed Algorithm
The input to the proposed authentication embedding process includes a color image I and two keys K1 and K2. The output is a stego-image S. The algorithm for the process can be briefly expressed as follows. Figure 4.3 shows a flowchart of the algorithm.
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Algorithm 1: authentication signal embedding.
Input: A given color image I and two keys K1 and K2. Output: A stego-image S.
Steps:
1 Divide I into non-overlapping 9×9 blocks.
2 For each 9×9 image block, divide it further into nine non-overlapping 3×3 blocks.
3 Select the mother block M and child blocks Ci by K1.
4 For M and each child block Ci, construct an edge direction in the following way.
4.1 Apply the Sobel masks and get an edge direction 4.2 Quantize the edge direction values into 16 levels.
5 Set the edge direction in the mother block to be Em, and the edge direction in the child block to be Ec.
6 For M and each child block Ci, embed authentication codes which are created by K2 into each child block by the following rule:
6.1 If the authentication code is “1”, then set the direction from Em to Ec to be clockwise.
6.2 If the authentication code is “0”, then the direction from Em to Ec to be counterclockwise.
7 Take the final result as the desired stego image S.
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