The article deals with the problem of masking hidden messages under natural noise in highly undetectable stegosystems ±1HUGO and ⊕HUGO. To ensure high resistance of stegosystems to hacking, a preliminary discrete chaotic transformation of the hidden message is performed according to the Arnold’s cat algorithm. Further, in their research, the authors effectively apply noise-resistant coding for the covering object and stego using a self-orthogonal noise-resistant code. To model the data transmission channel, the model of a binary synchronous communication channel with interference is used. The article also presents the results of simulation modeling, confirming the high resistance of the proposed stegosystems to hacking.