DEVELOPMENT OF A METHOD FOR ENSURING CONFIDENTIALITY AND AUTHENTICITY IN WIRELESS CHANNELS

post-quantum cryptosystems. The development of modern digital technologies ensures the transition to smart technologies and the formation of Next Generation Networks. The formation of smart technologies, as a rule, uses wireless communication channel standards IEEE 802.11X, IEEE 802.15.4, IEEE 802.16, which use only authentication protocols and pri- vacy mechanisms, which are formed on symmetric algorithms. In the condi- tions of the post-quantum period (the advent of a full-scale quantum com- puter), the stability of such algorithms is questioned. Such systems, as a rule, are formed on the basis of the synthesis of socio-cyber-physical systems and cloud technologies, which simplifies the conduct of Advanced Persistent Threat attacks, both on the internal circuit of execution systems and on external control systems. The creation of multi-circuit information protection systems allows for an objective assessment of the current state of the sys- tem as a whole and the formation of preventive measures to counter cyber threats. The proposed method of providing basic security services: confi- dentiality, integrity and authenticity based on crypto-code constructions takes into account the level of secrecy of information transmitted over wire- less channels and/or stored in data-bases of socio-cyber-physical systems. The use of post-quantum algorithms – McEliece/Niederreiter crypto-code constructions on elliptic/modified ellip-tic/lossy/Low-density parity-check code provides the necessary level of stability in the post-quantum crypto- period (crypto-stability at the level of 10 25 –10 35 group operations), speed and probability of information (Рerr not lower than 10 -9 –10 -12 ). The proposed method of information exchange using wireless communication channels ensures their practical implementation on resource-limited devices (creating of CCC on the GF field (2 4 –2 6 ) Keywords: crypto-code constructions of McEliece and Niederreiter, smart technologies, security concept, multi-contour


Introduction
The development of wireless technologies has significantly expanded the range of digital services based on services based on the synthesis of the Internet of things, mesh networks and smart technologies. The use of wireless communication channels can significantly increase the speed of information transfer and ensure the creation of socio-cyber-physical systems based on the of LTE, IEEE802.16, IEEE802.16e, IEEE802.15.4, IEEE802.11, Bluetooth standards. To provide security services in cyber-physical systems, as a rule, the KNX/ЕІВ (European Installation Bus) standard (ISO/IEC 14543) is used based on the use of virtual private network channels (encryption AES-128, -256) [1][2][3][4][5][6][7]. The KNX standard in IP Secure mode allows to provide confidentiality and authenticity services based on the use of an additional mechanism (protective shell) that protects all KNXnet/IP data traffic [8]. KNX Data Secure mode uses a longer KNX frame format based on CCM (Code Block Chain Message Authentication Counter) with 128-bit AES block symmetric cipher encryption to ensure information integrity. However, the security mechanisms of the KNX standard (ISO/IEC 14543) do not provide protection against IP networks channel monitoring, which allows an attacker based on a false server to intercept the traffic of the information flow. In addition, according to experts from the National Institute of Standards and Technology (NIST) of the United States, the use of symmetric algorithms with a key length of 128 bits does not provide the required level of security in the post-quantum period [9][10][11].
In the wireless channels of LTE technologies, only the 3A authentication service (AAA -authentication, authorization, accounting) is provided based on the Diameter protocol [12][13][14][15][16]. The Diameter protocol has a predefined set of common AVPs (Attribute-Value-Pair) between two Diameter nodes, allowing various combinations of the protocol to be used.
However, the absence of security mechanisms in wireless channels of mobile technologies does not allow confidentiality and integrity services to be provided. As practice shows, in networks based on the Diameter protocol, attacks aimed at denial of service, disclosure of information about subscribers and the operator's network, as well as fraud against the operator are possible [17,18]. In addition, an attacker can forcibly transfer the subscriber's device to 3G mode (third generation) -and carry out further attacks on the less secure SS7 system (signaling system, Signaling System No. 7) [18]. Table 1 shows the main characteristics of wireless mobile and computer networks and security services based on the KNX standard and the Diameter protocol.
Analysis of the Table 1 shows that in the context of the emergence of a full-scale quantum computer, hybridity and synergy of cyber-attacks, wireless channels partially provide privacy services, which requires new approaches to security based on post-quantum mechanisms.
Thus, a new concept of the security of systems formed on the basis of the synthesis of cyber-physical systems (CPS) and social networks -socio-cyber-physical systems (SCPS) is needed. Such systems are rapidly developing based on smart and Internet-of-things technologies and require a new approach to providing security services for wireless channels based on post-quantum cryptosystems. Niederreiter on algebrogeometric codes. The papers [29,30] present practical ways to reduce energy and computational costs, which makes it possible to use wireless CCC channels in the information security system to provide the required level of security services.
Thus, the analysis showed that the rapid growth of computing resources and mobile technologies determined the development vector of wireless channels of systems based on smart technologies. This approach makes it possible to integrate and form both CPS and SCPS, which significantly expands the range of digital services. Expanding the range of capabilities of wireless technologies makes it possible to form a smart-city system with functionality in various areas, on the one hand, on the other hand, the inability to resist APT attacks in the context of the emergence of a full-scale quantum computer significantly reduces the security level of such systems [31]. The lack of mechanisms for ensuring confidentiality and integrity services in 4G-6G technologies does not allow for their widespread implementation in the Next Generation Network and smart systems. A promising direction in the construction of IPS is the use of post-quantum algorithms -CCC on algebrogeometric codes and the formation of multicontour IPS.

The aim and objectives of the study
The aim of the study is to develop a method for ensuring confidentiality and authenticity in wireless channels. This approach will make it possible to form a dual-contour security system based on mobile and Internet technologies using wireless channels, and provide security services based on post-quantum algorithms.
To achieve the aim of the study, it is necessary to solve the following objectives: -to develop the conceptual foundations of the CPS dual-contour security system based on post-quantum algorithms; -to develop a mathematical model of a method for ensuring confidentiality and authenticity in wireless channels; -to develop an algorithm for the practical implementation of confidentiality and authenticity in wireless channels.

Research materials and methods
The object of research is the process of providing security services in wireless channels, which makes it possible to ensure the construction of multicontour security systems in the conditions of the post-quantum period.
The provision of security services in wireless channels is associated with a contradiction between the speed indicators of wireless channels and the need to use cryptographic algorithms to provide confidentiality and integrity services. In addition, in the post-quantum cryptoperiod, the requirements for symmetric cryptography algorithms increase significantly, which casts doubt on the possibility of providing a compromise between the amount of key data and the amount of memory of switching devices. Also, the possibility of offline encryption of various information flows based on symmetric cryptography.
To provide security services, it is proposed to use post-quantum algorithms -crypto-code constructions of McEliece and Niederreiter on algebrogeometric codes [28,29,31]. Both crypto-code constructions are based

Literature data analysis and problem statement
To provide security services and expand the range of digital services based on smart technologies, various approaches are proposed, based on classical symmetric and asymmetric mechanisms, and blockchain technologies. Thus, in [19] an analysis of threats to cyber-physical systems is carried out, and it is also proposed to use the modeling of information protection systems (IPS). Based on the business process models notation (BPMN), it is intuitively possible to describe various approaches to building information security systems. The proposed concept of building security systems allows taking into account the physical components of the CPS, as well as the control flows of the control system to the physical elements of the CPS. However, this does not take into account the actual separation of the physical and control subsystems of the CPS, which does not allow to objectively take into account the current state of security of the system as a whole. In [20], modeling approaches based on a multi-domain language for component-oriented modeling of CPS Modelica are proposed. This approach accurately captures the interaction between the physical and cyber components within the CPS. However, such models do not take into account the need to build multicontour information security systems. With this approach, the inner and outer contours provide not only an objective assessment of the current state of the system, but also allow to form the necessary tuple of IPS elements to provide security services. In [21], the authors proposed an authentication protocol, which, in their opinion, provides the required indicators of reliability and security and can be used in 5G technology. The proposed authentication approach is based on the use of smart cards for authentication using elliptic curve random number generators. However, the use of firmware authentication is subject to scream attacks and does not provide confidentiality and integrity services over wireless communication channels. To ensure the security of key data transmission, [22] presents a protocol based on an improved multi-server key agreement scheme with hash-based authentication and a standalone registration server (standalone RS). This approach ensures the use of a closed channel for the transmission of key data, but does not provide confidentiality and data integrity services. The work [23] presents an analysis of threats on CPS, as well as an analysis of the use of OTP passwords in various authentication schemes. However, it is proposed to use protocols and mechanisms to ensure the authenticity and integrity of classical computer networks as countermeasures for threats. This approach does not take into account the multicontour architecture of CPS, as well as the hybridity and synergy of APT attacks. The paper [24] presents an analysis of the 2-pass authentication and key agreement (AKA) protocol for 5G mobile communications (5G-AKA), which provides data confidentiality and authenticity based on the use of the A5 stream cipher [25,26]. The scheme of two-factor authentication and key agreement (AKA) for 5G mobile communications is analyzed. 5G-AKA has been proven to be vulnerable to Linkability of AKA Failure Messages (LFM) attacks, which does not allow for confidentiality. A modification of the AKA scheme is proposed, however, the use of a stream cipher for confidentiality will not allow providing the required level of security in the post-quantum period, taking into account the proposals in [27]. In [28,29], it is proposed to use post-quantum algorithms for providing security services -crypto-code constructs (CCC) McEliece and on the principle of using the theory of error-correcting coding and the orthogonality of the matrices G, the generating matrix of the linear code, and H, the check matrix of the linear code. Taking into account the orthogonality of matrices G and H (G×H Т =0), these cryptosystems have almost the same energy costs for encryption.
Concealment matrices are used as a key sequence in both crypto-code constructions: − X -masking nondegenerate randomly equiprobable k×k matrix formed by the source of keys with elements from GF(q); − P -permutation randomly equiprobably formed by the source of keys n×n matrix with elements from GF(q); − D -diagonal matrix formed by the n×n key source with elements from GF(q); In addition, a distinctive feature of Niederreiter's CCC is the preliminary use of equilibrium coding, which makes it possible to provide a practically relative coding rate equal to one. Table 2 shows the main characteristics of elliptic (EC) modified elliptic (MEC) codes. Notations: GF(q) -Galois finite field, X -smooth projective algebraic curve in a projective space P n over GF(q), g=g(X) -kind of curve, X(GF(q)) -the set of its points over a finite field, N=X(GF(q)) -their number. С -divisor class on X power α>g-1, C defines the mapping φ:X→P k-1 , where k≥α-g+1. The set y i =φ(x i ) specifies the code. Number of points in intersection φ(X) with the hyperplane is equal to α, i. e. n-d≤α. This construction allows building codes with parameters k+d≥n-g+1, length n of which is less than or equal to the number of points on the curve X.
(n, k, d) parameters of the code that is built through of the view φ:X→P r-1 Table 3 shows the main parameters of the McEliece cryptosystem.
The paper [31] presents the results of studies of the energy consumption of crypto transformations and cryptographic strength. The obtained results confirm the possibility of practical implementation and use of post-quantum algorithms (McEliece and Niederreiter CCC) in wireless channels in offline mode.

1. Development of the conceptual foundations of the two contour CPS security system based on post quan tum algorithms
When developing the conceptual foundations of the two-contour CPS security system based on post-quantum algorithms, the approach proposed in [31] was used. It is based on the concept of double-contour security based on crypto-code constructions. At the same time, it is proposed to use integrated solutions for the use of certain codes in crypto-code systems based on the gradation of the information secrecy degree in socio-cyber-physical systems. Table 4 shows the ratio of time and the degree of information secrecy. Table 4 The ratio of time and the degree of information secrecy  Fig. 1 shows a block diagram of the conceptual foundations of a dual-contour security system. For a formal description of the Concept, the approach in [31] will be used: to ensure the security of the entire protection system, it is necessary to take into account the threats of the internal and external contours for each of the platforms:  General assessment of threats of the internal contour, taking into account the form of ownership of the elements and technologies of the cyber-physical system ( Fig. 1 Overall assessment of threats of the internal contour, taking into account the form of ownership of the elements and technologies of the cyber-physical system (Fig. 1 -overall assessment of internal contour threats to the corporate property system. Based on expressions (3), (7), an assessment of threats in cyber-physical systems in the internal and external CPS security contours is formed, and on the basis of expressions (4), (8) -taking into account forms of ownership (separately). To provide a generalized assessment of a multicontour security system, the formula was used:

I Type A A A
Тype i -information asset type, described by a set of basic values: Тype i ={CI i , PD i , CD i , TS i , StR i , PubI i , ContI i , PI i }, where СI i -confidential information, PD i -payment documents, CD i -loan documents, TS i -commercial secret, StR i -statistical reports, PubI i -public information, ContI i -control information, PI i -personal data, β i -a metric of the ratio of time and degree of information confidentiality for an asset (critical -1.0; high -0.75; medium -0.5; low -0.25; very low -0.01).
Then the general (current) level of security of cyber-physical systems based on wireless mobile technologies is described by the expression: − for additive convolution: − for multiplicative convolution: Such an approach will allow to provide the required level of security in a timely manner, taking into account the degree of information secrecy and/or the security time that is necessary to provide confidentiality, integrity and authenticity services. To ensure the required security level, it is possible to combine various codes and CCC, both McEliece and Niederreiter.

2. Development of a mathematical model of a meth od for ensuring confidentiality and authenticity in wire less channels
The formation of a method for ensuring the confidentiality and authenticity of information based on a two-contour security system is proposed to be implemented at the CCC. The use of various error-correcting codes, defective and LDPC codes in McEliece and Niederreiter CCC allows to form various combinations, taking into account the level of secrecy (confidentiality), as well as the required time of information cryptographic strength. Fig. 2 shows a block diagram of the proposed approach. The main elements of the internal contour are various physical control devices (sensors, counters, tracking sensors, video cameras, etc.), as well as the server for dispatching and controlling the physical mechanisms of the CPS. The elements of the outer contour include a server for generating key sequences and storing long-term keys, as well as mobile applications (if necessary) for CPS users.
To provide security services, it is proposed to install McEliece CCC software and hardware encoders on the elements of the internal contour. In this case, on the basis of complexing and the level of circulating information secrecy, various noise-immune codes are established and used. The dependence of time and the degree of information secrecy is given in Table 4.
The relationship between the internal and external contours of the security system on the basis of the proposed method is provided by Niederreiter CCC, the relative coding rate is close to 1. At the same time, the use of two CCCs increases the security level by at least 2 times, and the use of various error-correcting codes integrated provides an increase in the error reliability. Long-term keys are formed in the external contour, the use of which allows to reset the CPS security system (in case of loss of gadgets control, compromise, etc.). As well as the formation of private keys for use in the CPS in the internal contour. To ensure security, long-term keys are stored in encrypted form by McEliece or Niederreiter CCC.

Fig. 1. Structural diagram of the conceptual foundations of a double-contour security system
This approach ensures the closure of all channels of information transmission both in the internal contour -the cyber-physical system, and in the external contour, as well as communication channels between the contours. In this case, post-quantum cryptosystems are used, which makes it possible to use this approach with the prospect of a full-scale quantum computer.
To form a mathematical model of the method for ensuring confidentiality and authenticity in wireless channels, the approaches of the works [29][30][31]  that is e i =0, ∀e i ∈h. Based on the equilibrium coding algorithm, the plaintext is converted into an error vector; -set of closed texts (codegrams) for McEliece CCC where X i -masking non-degenerate randomly equally probable generated by the key source k×k matrix with elements from GF(q); P i -permutable randomly equiprobably formed by the source of the keys n×n matrix with elements from GF(q); D i -diagonal formed by the source of the keys n×n matrix with elements from GF(q). Due to the fact that the diagonal matrix is equal to the identity matrix, the value can be neglected, which reduces the capacity and complexity of the calculation.
The public key is formed by multiplying the masking matrices by the generator/checking matrices: decodes the resulting vector using the Berle kamp-Massey algorithm [32]: i. e., gets rid of the second term and the factor ( ) in the first term on the right side of the equality, after which it removes the effect of the masking matrix X u . To do this, the result of decoding M i ×(X u ) T should be multiplied by (X u ) -1 : The resulting solution is the essence of plain text M i ; -for Niederreiter CCC. Next, an authorized user, using a set of matrices {X, P, D} u ={X u , P u , D u } forms a vextor: After substitution, getting the equality: An authorized user who has generated a vector has the ability to apply a fast (polynomial complexity) noise-correcting decoding algorithm and thus generate a vector Thus, the presented mathematical model makes it possible to use McEliece and Niederreiter CCC to provide confidentiality, integrity, and authenticity services and to practically implement the proposed method. Fig. 3 presents the main elements of the proposed method for providing basic security services in cyber-physical systems based on wireless communication channels. i Fig. 3. Block diagram of the proposed method for providing security services in wireless channels based on crypto-code constructions The main difference from the known approaches is, while maintaining the level of bandwidth of the wireless channel, to provide the required level of security (cryptostrength) of the channel in an integrated way (cryptosecurity based on post-quantum algorithms at the level of 10 25 -10 35 group operations), (Р err not less than 10 -9 -10 -12 ) [31].
The use of post-quantum algorithms -crypto-code structures on the MEC allows the formation of cryptosystems over the field GF (2 6 ), and when using defective codes, the formation of hybrid cryptosystems over the field GF (2 4 ), which allows their practical implementation on resource-limited chipsets. The conducted experimental studies have shown that the use of CCC in cyber-physical systems based on wireless channels requires the presence of a mobile Internet channel (broadband channel). This limitation is based on the existing multi-contour CPS model, where, as a rule, the control system is deployed in cloud technologies.
Thus, the proposed model for the use of McEliece and Niederreiter CCC is the basic component of the proposed method for the formation of cryptosystems to provide basic security services. Such an approach, taking into account the multi-contour CPS and an objective assessment of the current state of security, makes it possible to form a reliable information protection system in the post-quantum period, taking into account possible APT attacks with signs of hybridity and synergy.

3. Development of an algorithm for the practical implementation of confidentiality and authenticity in wireless channels
One of the variants of the proposed method for ensuring confidentiality and authenticity in outbred channels is the use of command transmission security based on two-way communication channels. For example, the connection between the key fob and the car's on-board computer. To form a "dialogue coding" that requires a two-way communication channel (the presence of a receiver and a transmitter, both in the main module and in the key fob), let's use McEliece CCC. In this case, the internal security contour is formed on the basis of encryption of the key fob authentication information package and information packages for the execution of various commands (unlocking the car, opening the driver's door, opening the trunk, etc.). The external contour (cyberspace platform) stores a long-term secret key that allows to reset the key sequences of the CCC and, at the request of the user, generates private keys and public keys of the CCC.
To ensure the service of authenticity -the authenticity of sending a command from the key fob of an authorized user, it is proposed to use a random number that is generated at each "appearance" by the on-board computer of the car, it generates a random number (session key) with a length of 76 bits.
As a pseudo-random number generator of length 76, it is proposed to use a pseudo-random number generator based on a linear recurrent feedback shift register (LFSR) modulo an irreducible polynomial of 76 degrees. These pseudo-random number generators generate sequences of the maximum period and are easily implemented both in hardware and software [33]. The general structural diagram of the LFSR is shown in Fig. 4. LFSR during the first k time counts, the key (switch) is in the upper position, and the shift register is filled with the key sequence K i =(K i0 , K i1 , …, K ik-1 ). During the following q k -1 time readings, the key (switch) is in the lower position and the values stored in the cells of the shift register are fed to the output of the device. At each time interval, it is in the lower position and the values stored in the cells of the shift register are fed to the output of the device. At each time interval, the information stored in the shift register moves one cell to the right, and the value stored in the rightmost cell is fed through the LRFSR feedback loop. The feedback function specifies a specific type of feedback circuit switching and ensures the formation of a pseudo-random sequence of the maximum period.
The resulting number of 76 bits is converted into an information sequence I 1×19 with elements from the field GF (2 4 ), due to the use of multiplexers according to the scheme presented in Fig. 5.
Let's consider the algorithm for ensuring the authenticity and confidentiality of the formation of "dialogue coding" based on McEliece CCC: Car key fob software: 1. Sends a request to execute a command.
4. Generation of an additional session key -е (error vector) -corresponding to some action) (number from 0 to 24). To form the error location, it is proposed to transform the sequence I 1×19 into a binary sequence and take the corresponding number in decimal number modulo 25.
6. c 1(1×19) enters the communication channel and is transmitted to the on-board computer of the car.
Vehicle on-board computer software: 1. At the request of the car key software, a random number of 76 bits is generated.
2. Converted to information sequence I 1x19 with elements from the field GF (2 4 ).
3. Transformation of the information sequence I 1×19 based on the use of McEliece CCC masking matrices Р 1(1×19) and diagonal matrix D 1(1×19) : 4. Transmission I 2(1×19) on a key fob. 5. Upon receipt c 1(1×19) based on the fast Berlekamp-Massey decoding algorithm, the error vector is found, which determines the command that came from the key fob. Table 5 presents the results of the analysis of the provision of security services: confidentiality, integrity and authenticity using various wireless channels. Table 5 Comparative characteristics of wireless channels Analysis of the Table 4 shows that the use of symmetric cryptosystems based on block and stream ciphers (used in the KNX standard) do not provide full confidentiality and integrity services in the post-quantum period.
Thus, the proposed algorithm ensures the closing of the wireless channel using a software and hardware complex. The use of a hardware solution for closing (encrypting) the execution command on the on-board computer of the car will counteract almost all threats of intercepting the code execution command and hacking the car's security system as a whole.

Discussion of the results of using the McEliece and
Niederreiter crypto code constructions to provide security services The developed method for ensuring the authenticity and confidentiality of information in wireless channels is based on the use of Grover and Shor, resistant to post-quantum threats, and makes it possible to provide a tunneling mode in open channels. Given in Table 4, the results of security service provision studies confirm that the proposed CCCs on the ECC provide basic security services. Parameters of noise-immune codes given in Table 1, and the parameters of asymmetric cryptosystems based on McEliece and Niederreiter CCCs provide their practical application. Table 6 shows the results of studies of the capacitive characteristic in software implementation on the power of the field.
The resulting Table 6 shows that the number of group operations of the software implementation of the CCC, depending on the field strength, is 4.5 times less when using the MEC. So, if for the implementation of McEliece's CCC in the field GF(2 10 ) it is needed 82,5×10 6 group operations, then the implementation of the CCC on the MEC in the field GF(2 6 ) requires 17.7 -18.6×10 6 group operations. Table 7 presents the results of studies of the capacitance characteristic in software implementation from the field strength when using defective codes and constructing hybrid crypto-code constructions (HCCC).
When using the HCCC, a significant increase in the speed of systems has been achieved (at least 20 times in terms of the speed of generating a cryptogram), which makes it possible to use resource-limited hardware devices for cryptographic information protection by such systems.
To conduct statistical studies of the stability of the studied cryptosystems, the package NIST STS 822 was used [31]. The research results are presented in Table 8.
Analysis of the Table 8 showed that despite the decrease in the power of the Galois field to GF (2 6 ) for CCC on МЕС and GF (2 4 ) for the HCCC, the statistical characteristics of such crypto-code structures turned out to be at least as good as the traditional McEliece CCC on GF (2 10 ). All cryptosystems passed 100 % of the NIST tests, and the best result was shown by the HCCC on shortened MECs: 155 out of 189 tests were passed at the level of 0.99, which is 82 % of the total number of tests. At the same time, the traditional McEliece CCC on GF (2 10 ) showed 149 tests at the level of 0.99. This approach confirms that the use of CCC makes it possible to provide basic security services in wireless channels without forming VPN channels, which greatly simplifies practical use in the formation of the architecture of smart-city networks. Thus, the proposed method on CCC with different ECCs makes it possible to provide not only security services, but also to increase the reliability of transmitted information flows in the channels of LTE technologies in an integrated manner. The use of a multi-loop information security system based on CCC also forms an objective assessment of threats, and the current state of security of the system as a whole. The main limitation of the proposed approach for providing security services in wireless communication channels is the use of either a tunnel mode for point-to-point connection, or the use of a mobile broadband Internet channel, in which there are "no" possible filters and limitations of various mobile communication providers. A promising direction for further research is to evaluate the effectiveness of using the proposed method and the Concept of multicontour information protection based on the use of McEliece and Niederreiter CCC with the formation of a control system based on a desktop server.

Conclusions
1. The formation of socio-cyber-physical systems based on the integration and synthesis of wireless technologies and mobile Internet technologies, with Internet of things, ensures the further development of digital services. The emergence and development of smart technologies determines not only the vector of further digitalization of services, but also requires a new approach to the formation of an objective assessment of security threats. At the same time, it is necessary to build multicontour information security systems that take into account not only the hardware/software elements of the CPS infrastructure, but also the physical location and form of ownership. In the context of the growth of APT-attacks, the formation of new foundations of the Security Concept is an objective necessity. The use of CCC in wireless channels allows to provide the required level of security, due to the formation of tunnel modes, when connecting point-to-point, or the use of broadband mobile Internet channels based on post-quantum algorithms -crypto-code constructions. The proposed approach allows not only to take into account signs of synergy and hybridity of threats, but also provides an objective assessment of both the threats themselves to critical elements of the CPS infrastructure and the assessment of CPS security as a whole.
2. The proposed mathematical model for constructing asymmetric cryptosystems based on McEliece and Niederreiter CCC makes it possible to provide the required level of confidentiality, integrity and authenticity services and to practically implement the proposed method. This approach provides the required level of protection of security services, and the use of various noise-immune codes allows, taking into account the level of information secrecy, to ensure its reduction in energy consumption and increase the efficiency of information transmission.
3. The proposed algorithm for the implementation of security services based on post-quantum algorithms of McEliece and Niederreiter asymmetric cryptosystems on various algebrogeometric and detrimental codes makes it possible to close the wireless channel and provides the possibility of expanding the range of commands and/or functionality.