This paper addresses the task of developing a steganographic method to hide information, resistant to analysis based on the Rich model (which includes several different submodels), using statistical indicators for the distribution of the pairs of coefficients for a discrete cosine transform (DCT) with different values. This type of analysis implies calculating the number of DCT coefficients pairs, whose coordinates in the frequency domain differ by a fixed quantity (the offset). Based on these values, a classifier is trained for a certain large enough data sample, which, based on the distribution of the DCT coefficients pairs for an individual image, determines the presence of additional information in it.A method based on the preliminary container modification before embedding a message has been proposed to mitigate the probability of hidden message detection. The so-called Generative Adversarial Network (GAN), consisting of two related neural networks, generator and discriminator, was used for the modification. The generator creates a modified image based on the original container; the discriminator verifies the degree to which the modified image is close to the preset one and provides feedback for the generator.By using a GAN, based on the original container, such a modified container is generated so that, following the embedding of a known steganographic message, the distribution of DCT coefficients pairs is maximally close to the indicators of the original container.We have simulated the operation of the proposed modification; based on the simulation results, the probabilities have been computed of the proper detection of the hidden information in the container when it was modified and when it was not. The simulation results have shown that the application of the modification based on modern information technologies (such as machine learning and neural networks) could significantly reduce the likelihood of message detection and improve the resistance against a steganographic analysis