Kutter-Jordan-Bossen steganographic method
I decided to continue the cycle of articles on steganography, a primitive LSB algorithm has already been considered at Habré. I decided to write about the Kutter-Jordan-Bossen method (it is also called the “cross” method), which is used to embed information into images.
For embedding information in a container, one of the properties of the human visual system is used. This property lies in the fact that a person's susceptibility to changes in the brightness of blue in comparison with red and green is the least.
And so, for embedding information the blue color of the specified image container will be used.
The image will be viewed in the RGB color model .
B x, y is the blue brightness of a pixel with coordinates (x, y);
B x, y * - the altered brightness of the blue color of the pixel;
Y x, y - pixel brightness;
m i is the i-th bit of the message that we want to embed;
λ is the coefficient specifying the energy of the embedded data bit (given on the basis of the functional purpose and the particulars of the steganosystem);
σ is the size of the region over which the brightness will be predicted.
Information will be embedded in 1 bit of message in 1 pixel of the container. The secret key sets the coordinates of the pixels in which the embedding will be performed.
When embedding the brightness of red and green colors remain unchanged, and the brightness of blue - changes according to the following formula:
where λ = 0.1, Y x, y = 0.3 * R x, y + 0.59 * G x, y + 0.11 * B x, y
')
Since there is no original image on the receiving side, it’s guaranteed to know which way the brightness of the blue color has changed we cannot. Therefore, to extract the predicted brightness value of blue:
where σ = 1 ÷ 3.
I will illustrate with an example (σ = 2):
The pixel in the center is a pixel, the blue color of which we have to predict based on the pixels that are marked in light gray.
Finally, to extract the hidden message, use the formula:
High throughput;
High resistance to unauthorized familiarization;
High resistance to frequency detection;
High resistance to destruction of low bits of the container;
Resistance to compression attack;
The extraction is probabilistic in nature.
To reduce the likelihood of errors using robust coding.
1. Konakhovich GF, Puzyrenko A.Yu. “Computer steganography. Theory and practice"
2. Gribunin V.G., Okov I.N., Turintsev I.V. "Digital steganography"
For embedding information in a container, one of the properties of the human visual system is used. This property lies in the fact that a person's susceptibility to changes in the brightness of blue in comparison with red and green is the least.
And so, for embedding information the blue color of the specified image container will be used.
The image will be viewed in the RGB color model .
Designations
B x, y is the blue brightness of a pixel with coordinates (x, y);
B x, y * - the altered brightness of the blue color of the pixel;
Y x, y - pixel brightness;
m i is the i-th bit of the message that we want to embed;
λ is the coefficient specifying the energy of the embedded data bit (given on the basis of the functional purpose and the particulars of the steganosystem);
σ is the size of the region over which the brightness will be predicted.
Embedding
Information will be embedded in 1 bit of message in 1 pixel of the container. The secret key sets the coordinates of the pixels in which the embedding will be performed.
When embedding the brightness of red and green colors remain unchanged, and the brightness of blue - changes according to the following formula:
where λ = 0.1, Y x, y = 0.3 * R x, y + 0.59 * G x, y + 0.11 * B x, y
')
Extract
Since there is no original image on the receiving side, it’s guaranteed to know which way the brightness of the blue color has changed we cannot. Therefore, to extract the predicted brightness value of blue:
where σ = 1 ÷ 3.
I will illustrate with an example (σ = 2):
The pixel in the center is a pixel, the blue color of which we have to predict based on the pixels that are marked in light gray.
Finally, to extract the hidden message, use the formula:
Advantages and disadvantages
High throughput; High resistance to unauthorized familiarization; High resistance to frequency detection; High resistance to destruction of low bits of the container; Resistance to compression attack; The extraction is probabilistic in nature.To reduce the likelihood of errors using robust coding.
Literature
1. Konakhovich GF, Puzyrenko A.Yu. “Computer steganography. Theory and practice"
2. Gribunin V.G., Okov I.N., Turintsev I.V. "Digital steganography"
Source: https://habr.com/ru/post/115287/
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