INDIRECT INFORMATION HIDING TECHNOLOGY ON A MULTIADIC BASIS

It is shown that the current direction of increasing the safety of information resources when transmitting information in info-communication systems is the use of methods of steganographic instruction in video imagery. The effectiveness of such methods is significantly increased when used in a complex of methods of concealment, which are based on the principles of inconsistent and cosmic communication. At the same time, existing methods of steganographic are used in the process of insertion of information mainly only laws, empty features of visual perception of video images. So, it is justified that the scientific and applied problem, which is to increase the density of embedded messages in the video container with a given level of their reliability, is relevant. The solution of this problem is based on the solution of the contradiction, which concerns the fact that increasing the density of embedded data leads to a decrease in the bit rate of the video container, steganalysis stability, reliability of special information, and video container. Therefore, the research aims to develop a methodology for the steganographic embedding of information, taking into account the regularities of the video container, which are generated by its structural and structural-statistical features. The solution to the posed problem of applying steganographic transformations is proposed to be realised by methods of indirectly embedding parts of the hidden message in certain conditions or functional relationships. The possibility of creating steganographic transformations regarding the indirect embedding and extraction of hidden information in a multiadic basis by modifying the underlying basis system within an admissible set is demonstrated. It is shown that the multiadic system, which is created in the spectral space of DCT transforms, has the potential to form a set of admissible modifications of basis systems.


Introduction
One of the actual directions for increasing the security of information resources during transmission in info-communication systems is the use of methods of steganographic embedding of information in video images. The efficiency of such methods significantly increases when used in a set of concealment methods, which are based on the principles of direct and indirect embedding of messages. It allows [1][2][3] to create conditions for localizing the imbalance between the timeliness of the delivery of hidden information (special information) and the indicator of its reliability [4,5,7,8].
At the same time, the existing methods of steganography are used in the process of embedding information mainly only the regularities generated by the features of visual perception of video images. In turn, this leads to the fact that with the use of modern telecommunication technologies and coding technology video container H26* creates conditions for the organization of the hidden message channel, which allows you to embed a message at 3 -20 Mpixels for PSNR in 20 dB. This accordingly creates conditions for hiding FullHD video images [9][10][11]. However, in this case, the level of PSNR is 20 dB, which means that there are significant distortions of the video container. So, such PSNR level does not satisfy the required level of video information fidelity in critical infrastructure management systems. On the contrary, for a given level of fidelity (the PSNR value reaches 40 dB) conditions are created for hiding messages with a bit volume of only 1.5 Mbytes. This allows hiding CIF and SD format video images. But this format of video images does not meet the requirements regarding the completeness of video information [12][13][14][15][16].
So, the scientific and applied problem, which is to increase the density of embedded messages in the video container with a given level of reliability, is relevant.
The solution to this problem is based on the solution of a contradiction, which concerns the fact that increasing the density of embedded data leads to a decrease in the bit rate of the video container, steganalysis stability, reliability of special information, and video container [15,17,18].
To resolve this contradiction, it is proposed to develop steganographic methods that allow message embedding under conditions of exclusion of necessity (or limitation) in the use of psychovisual regularities. That is, the process of message embedding should not be accompanied by additional distortions in the video container [19][20][21].
Therefore, the purpose of the study is the development of the methodology of steganographic information with the take into account the regularities of the video container, which are empty of its structural and structural-statistical characteristics.

The reasoning of the direction for creating steganographic systems with video container distortion exclusion
The solving of the formulated problem in the field of application of steganographic transformations is proposed to realize with the use of methods of indirect embedding of some condition or functional dependence to the bit of scrambled message [22][23][24][25][26].
But in turn, the existing methods of indirect steganographic transformations are characterized by a drawback, which is the insufficient value of the density of embedded data according to modern requirements [25,27,28].
To eliminate the disadvantages of indirect steganographic embedding, it is proposed to develop an approach that allows using not only psychovisual but also structural redundancy of video containers for concealment [6,[29][30][31][32][33].
To build a steganographic system under the conditions of fulfilling the requirements, it is proposed to use multiadic transformation [35][36][37]. In this case, the following is achieved.
1. The regularities appear adaptively for each data set with the structural-combinatorial origin and are described quantitatively in the form of estimates of the dynamic ranges of the data set elements. That is.
There is a possibility of restored data array elements to establish with given integrity of the appropriate conditional dependence. This provides a condition for extracting a hidden message without loss of information [38,39].
In this case, the process of removing hidden information will be carried out by analyzing the values of the initial and modified service information.
Modifications in the field of structural-combinator patterns create an opportunity to avoid its impact on the value of video elements. Therefore, there is potential relative to the avoidance of distortions in the masses of video data [40,41].
The data array is proposed to be considered as a container for indirect embedding information in the spectral region. This is because the DCT transformant creates conditions for identifying and reducing more structural and combinatorial redundancy than in the space-time domain [42,43]. Consequently, DCT transformants increase the potential for the embedding of the hidden message due to modification in the field of patterns according to dynamic ranges in the conditions of the presence of the corresponding amount of structural and combinatorial redundancy.
Thus, a selection of a multiadic system is substantiated to organize indirect hiding information in terms of avoidance of losses as built-in information, and additional distortion of the container.

Creation of methodology of the steganographic system of indirect hiding information.
Multiadic system (MAS)system ( ; ; ; 0) for sequences j A in multiadic space with the set system of bases  . Here j average deviation of elements of decoded multiadic number relative to elements of initial IODM number. This is described by the expression: mnumber of elements in multiadic number; ij -th item for  -th an option to recover the initial multiadic number  i оg n  will decrease. Therefore, the total bit volume of the compression representation of the data array (transformers) will be reduced as a result of the multiadic encoding of its columns.
It is clear that for the possibility of indirect concealment of information in a multiadic system at the level of structural meta-features, MAS must possess the following property (characteristic). To prove this property of MAS, we will formulate and then prove the following statement.

Property of MAS
To generalize the conclusions of the statement, we will carry out its examination without reference to a specific transformation or a set of video data. There is j A initial one-dimensional multiadic (IODM) number, There is At the same time, it should be taken into account that according to the technological requirements for digitization of full-color video images, the element values of each color component cannot exceed the value of 255. Then the dynamic range of each element will be in the following limits: At the same time, as practical studies show, the formation of a multiadic basis in the spectral space using the discrete cosine transform (DCT) provides the presence of patterns of such origin.
It follows that the multiadic system, which is created in the spectral space of the transformant DCT, has the potential for the formation of a set of admissible modifications of the systems of bases. In turn, this characteristic feature creates the possibility for the construction of indirect steganographic transformations on the multiadic basis based on a modification of structural meta-features 4. Conclusions 1. It has been proven that it is possible to create steganographic transformations to indirect embedding and removal of hidden information on a multiadic basis by modifying the basic system of bases within the permissible set. 2. There has been a proven existence of multiple permissible multiadic systems for the same continuity in a way that achieves mutually unambiguous (without erroneous) direct and reverse code transformation. This allows you to establish the conditions for modifying the system of multiadic space for which the recovery of the elements of the initial sequence without loss of information, namely:  selection of the system of bases, which is part of the permissible set of constructing options;  formation of the corresponding code values in allowable systems of bases. 3. It is substantiated that the multiadic system that is created in the spectral space transformant DCT has the potential for the formation of a set of permissible modifications of bases. In turn, such a characteristic feature creates an opportunity to build indirect steganographic transformations in a multiadic based on the modification of structural meta-features.