Kutter-Jordan-Bossen Steganographic Method

    I decided to continue the series of articles on steganography, the primitive LSB algorithm has already been considered on the hub I decided to write about the Kutter-Jordan-Bossen method (it is also called the "cross" method), which is used to embed information in images.

    To embed information in a container, one of the properties of the human visual system is used. This property consists in the fact that a person’s susceptibility to changes in the brightness of blue compared 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 considered in the RGB color model .

    Designations


    B x, y - the brightness of the blue color of the pixel with coordinates (x, y);
    B x, y * - the changed brightness of the blue color of the pixel;
    Y x, y is the brightness of the pixel;
    m i - i-th bit of the message that we want to embed;
    λ is a coefficient that sets the energy of the embedded data bit (it is set based on the functional purpose and features of the steganosystem);
    σ is the size of the region over which brightness is predicted.

    Embedding


    Embedding information will be 1 bit message in 1 pixel container. The secret key sets the coordinates of the pixels to be embedded.
    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

    Extraction


    Since there is no original image on the receiving side, we cannot guarantee in which direction the brightness of the blue color has changed. Therefore, for extraction, the blue brightness value is predicted:

    where σ = 1 ÷ 3.
    I will illustrate with an example (σ = 2):

    The pixel in the center is the pixel whose blue brightness we must predict based on the pixels indicated by light gray.
    Finally, to retrieve a hidden message, use the formula:


    Pros and cons


    +High throughput;
    +High resistance to unauthorized familiarization;
    +High resistance to frequency detection;
    +High resistance to destruction of the least significant bits of the container;
    +Resistance to compression attack;
    -The extraction is probabilistic in nature.
    To reduce the likelihood of error, error-correcting coding is used.

    Literature


    1. Konakhovich G.F., Puzyrenko A.Yu. “Computer steganography. Theory and practice "
    2. Gribinin VG, Okov I.N., Turintsev I.V. Digital Steganography

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