**9. Conclusions**

The secrecy of steganographic systems is based on the assumption that the attacker is not aware of the fact of the information being introduced. In the event that this fact becomes publicly available, it will not be difficult for an unauthorized user to extract secret data or delete a given watermark. To solve this problem, it was proposed to use an additional container in the form of an algebraic fractal in the form of a Julia set.

Fractal generation is carried out using predefined secret parameters using the escape time algorithm (Escape time algorithm).

Embedding a digital watermark in a container was carried out in two stages. At the first stage, the watermark is added to the generated fractal. The resulting image is embedded in the original container in JPEG format. As a result, the original image has almost no visual distortion. The measurement of the values of the NMSE and PSNR metrics confirmed the high level of embedding quality and extraction of the watermark in the form of a QR code.

To confirm the high level of secrecy, an experiment was conducted, during which an attempt was made to replace the original secret key. The experiment

confirmed that it is impossible to extract the watermark without knowing the true parameters of the fractals.

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To assess the possibility of detecting the fact of embedding a watermark on the basis of fractals, the fractal dimension of intermediate containers was measured on the basis of the Julia set. Measurement of the dimension value was carried out before and after steganographic embedding. The results showed that the fractal dimension varies slightly, within the limits of the method error, and cannot be a sign that characterizes the presence of an integrated watermark.

The proposed technique allows for steganographic embedding with a high level of visual quality, as well as resistance to various steganographic attacks. As a result, it is possible to increase the level of secrecy of the watermark embedding algorithms and significantly reduce the likelihood of data theft.
