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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>International
Journal of Computing 24(1) (2025) 35</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.1007/s10207-024-00930-z</article-id>
      <title-group>
        <article-title>network nodes⋆</article-title>
      </title-group>
      <contrib-group>
        <aff id="aff0">
          <label>0</label>
          <institution>Anatoliy Sachenko</institution>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Casimir Pulaski Radom University</institution>
          ,
          <addr-line>Malczewskiego St. 29 26-600 Radom</addr-line>
          ,
          <country country="PL">Poland</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Khmelnitsky National University</institution>
          ,
          <addr-line>Instytutska street 11 29016 Khmelnitsky</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff3">
          <label>3</label>
          <institution>Prigo University College European Research University Vítězslava Nezvala 801/1</institution>
          <addr-line>Havířov 736 01</addr-line>
          <country>Czech Republic European Union</country>
        </aff>
        <aff id="aff4">
          <label>4</label>
          <institution>West Ukrainian National University</institution>
          ,
          <addr-line>Lvivska Street 11 46009 Ternopil</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2025</year>
      </pub-date>
      <volume>9</volume>
      <fpage>281</fpage>
      <lpage>294</lpage>
      <abstract>
        <p>The current state of development of OS security subsystems is analyzed. Attention is paid to the principles of building centralized security systems for network OSes based on dynamic transfer of control between network nodes. This provides increased resistance to leaks of confidential information as a result of the destructive effects of malicious software and computer attacks. A description of the process of dynamic transfer of control between computer network nodes is presented, and mechanisms for forming centralized security resource bases are considered. The issue of optimizing security resources that are subject to centralized control by the current network control node when using dynamic transfer of control between computer network nodes is also considered. Strategies for forming global privilege bases, security policies, and network connections during each cycle of control transfer from the current computer network node to the next are presented. Several series of experiments were conducted with a network of virtual machines running the FreeBSD 13.1 operating system, the results of which confirmed theoretical calculations and mathematical modeling. A comparative analysis of the effectiveness of full centralization of security resources and their partial centralization with dynamic control transfer between computer network nodes was performed. The advantages of the proposed approach were manifested in a reduction in the time of control transfer between network nodes by 37 percent, a reduction in the attack surface due to the minimization of points of influence of malicious software on the security system.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;operating system</kwd>
        <kwd>computer networks</kwd>
        <kwd>centralized security systems</kwd>
        <kwd>security strategies</kwd>
        <kwd>centralization of security resources 1</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>The sphere of information technologies has become a defining path of development of mankind,
transforming not only the ways of its communication, but also the foundations of the world economy in all
its directions. Our world and its vital processes have become critically dependent on the stable functioning
of complex electronic systems and various software that processes, transmits and protects information. It is
already clear that this direction of development is not a temporary phenomenon, but an objective stage of
progress that has already determined the trajectory of the future, which has no turning back. We, as a
society, have finally entered the information era, in which the dominant value is not material resources,
but information.</p>
      <p>Technological achievements of mankind are faced with new large-scale challenges, threats to
information security, which today have become a constant background of digital life. Now success in any
field, beit science, economics, or security is determined by the level of access to reliable information, the
speed of its processing and the ability to protect it from external interference.</p>
      <p>The relevance of the task of ensuring information protection and increasing the resistance of
information systems to leaks of confidential information, despite the large-scale efforts of the planetary
economy, does not decrease. The analysis of the state of information systems protection shows that this
task remains extremely relevant today. Despite the fact that this problem is in the constant focus of
attention of the scientific community and the large number of methods and means of protecting
information systems proposed by it, it cannot be considered solved.</p>
      <p>This article is aimed at solving the problems of OS resistance to leaks of confidential information
processed in computer systems. Its purpose is to develop models of the process of random dynamic
transfer of control between network nodes, their study in the direction of optimizing the security
resources of the network OS, which are subject to centralized management, which in turn will allow
reducing the OS's time spent on transferring control between nodes and, thereby, ensuring the continuity
and stability of network management, which ultimately will lead to increasing the OS's resistance to
information leaks.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Analysis of known solutions</title>
      <p>OSs have gone through several technological stages in their development. Together with them, their
security systems have also overcome this path, until they have really reached a level that can guarantee
the protection of information processed in computer systems under their control. And all this in conditions
of constant, ever-growing influence of malicious software, which in turn is constantly being improved.
Developing under its continuous pressure, OS security systems today represent powerful control
subsystems that include a large range of highly effective protective mechanisms. The architecture of OS
security systems, especially network ones, has gone from decentralized to complexly organized centralized,
covering all the resources of a modern computer system with its control. Thus, in [1] a model is presented
that describes the interaction of protective mechanisms within the framework of a centralized security
system for the OS of a network node, which allows building a security architecture of a network OS that
minimizes the problem of leakage of confidential information during attacks on the system's RAM. The
search for a balanced architecture of the OS security system that effectively ensures the stability of the OS
is considered in [2].</p>
      <p>Many works are devoted to methods for improving the operation of network incident response systems
(IDS\IPS) and approaches that can be applied to increase the level of security in networks in terms of
counteracting the leakage of confidential information [3, 4]. In [5], a new IDS system based on a
combination of a multilayer perceptron network (MLP) is proposed. For software-defined networks (SDN),
a mechanism based on the entropy values of the source and destination IP addresses of flows observed by
the network controller is proposed [6]. In [7], an innovative approach is presented that provides proactive
protection against destructive DDoS attacks. It is based on the use of an echo state network (ESN),
specially designed for SDN. To detect DDoS traffic, in [8] a model is proposed that calculates its threshold
value for applications using the network. In real time, using a machine learning (ML) model, it is
determined whether this traffic is DDoS traffic. A new FLBC-IDS machine learning technique that
combines horizontal federated learning (HFL), Hyperledger blockchain, and EfficientNet for intrusion
detection is proposed in [9]. In [10], means for improving the efficiency of IDS systems that analyze and
cluster network traffic are proposed. A new metric for evaluating IDS systems that takes into account the
delay in detecting cyberattacks is presented in [11].</p>
      <p>Analysis of the performance of IDS based on machine learning has shown its dependence on the
implementation of functions, and the spatial and temporal correlation of network data attributes
complicates the manual design of functions. The proposed IDS [12] uses an optimized one-dimensional
convolutional neural network block and sufficient memory to automatically extract spatial and temporal
features from the input data. In addition, a knowledge transfer method is used to transfer features, which
allows detecting zero-day attacks.</p>
      <p>Also, much attention is paid to strategies and mechanisms for protecting network OSs in terms of
countering malicious software. A self-adaptive system based on SVM to ensure network resilience to
botnet cyberattacks called BotGRABBER is considered in [13, 14]. Another self-adaptive system in which
resilience is ensured by adaptive network reconfiguration is presented in [15]. In [16], a new method for
detecting DDoS botnets is proposed based on the analysis of their network characteristics, and in [ 17] on
the use of artificial immune system algorithms. A new step is the proposed distributed DDoS protection
scheme based on shared agents [18], which detects and prevents DDoS attacks within Internet service
providers (ISPs). The distributed security systems are reinforced by the genetic algorithm proposed in [19,
20], based on the selection and variations of search parameters. Another approach to ensuring network
security is data storage based on the architecture of a semi-network OS [21]. Integrated management
systems based on threat and risk models are proposed [22]. The idea of creating a secure OS with
controlled complexity is promising [23]. In [24], another research direction was initiated, based on
serverless security, which has a high potential for reliable protective measures.</p>
      <p>An interesting solution is to supplement the OS security system with a memory isolation mechanism
that does not allow bypassing it by virtualizing the memory management unit [25]. Also, works [26, 27]
are devoted to countering memory attacks (MCA), which change the contents of some memory areas in
order to disrupt the normal operation of computing systems, causing a leak of confidential data or
disruptions in current processes. In [28], attacks on modern heterogeneous embedded computing platforms
FPGA-SoC, which contain the most advanced memory and peripheral isolation mechanisms, are
investigated. In [29], a security model is proposed that provides a higher level of protection compared to
such existing approaches as recurrent neural networks and the support vector method. It is promising for
an active security control strategy for cyber-physical systems.</p>
      <p>OS security on various hardware platforms is a fundamental goal of current evaluation. Identifying and
evaluating OS security factors are essential components in OS design. In [30], a formal verification method
for the RIOT OS crypto module is proposed for software analysis of Frama-C code, in order to ensure its
security aspects. In [31, 32, 33], the causes of vulnerabilities are investigated, in particular for IoT, IIoT,
SCADA and Android systems for embedded systems, and the implementation of effective malware
detection strategies is proposed. The work [34] focuses on the problem of Kernel Address Space Allocation
Randomization (KASLR) violation on modern mobile devices without using cache memory, which is
related to the KASLR violation problem on ARM processors. In the search for OS architectures resistant to
information leaks, in [35] a tool is proposed for research and modeling of a prototype system with a
microkernel architecture that provides high reliability and scalability.</p>
      <p>An interesting authentication system is proposed in [36]. It is based on a protocol that includes the
Linux security module for user-based NAC. It requires neither user accounts nor a secure user space; it
loads signed rules and keys for the user from a USB security key, securely authenticates the user, and
controls network permissions directly from the Linux kernel.</p>
      <p>In [37], the issue of minimizing the provision of access privileges to resources is raised as a way to
increase resilience to information leaks. In particular, attackers can use vulnerabilities in file systems and
disk drivers to leak or manipulate the contents of program files. The key problem is that the cancellation of
the transfer of OS services privileges from the kernel level to the user level does not solve the problem. It is
proposed to use a special Mirage mechanism that deprives them of the right to access the contents of files,
while preserving the functions of manipulating them. In [38], the problem of the Windows Embedded OS,
which uses a security policy based on discretionary access control (DAC), which is vulnerable to external
hacker attacks, is raised. It is proposed to improve security by prohibiting the execution of files from
outside the white list.</p>
      <p>It is noted that traditional OS security systems based on static protection methods do not always cope
with increasingly complex attacks [39], where attackers gain an advantage by using even one vulnerability
to compromise the system, adapting to traditional protection measures. In order to overcome the problem,
the implementation of proactive and adaptive security systems is proposed [40, 41]. Another direction for
ensuring information protection in many computer systems is the change of the control center. A method
for determining the next centralization option without user intervention is proposed in [42].</p>
      <p>The integration of artificial intelligence into computer networks is one of the advanced technologies. It
is assumed that the concept of using artificial intelligence will solve the problems faced by computer
networks, especially with regard to the leveling of information leakage threats [43]. The fundamental idea
of using artificial intelligence is to move to a proactive OS security model that includes intelligent threat
detection, in-depth behavior analysis, and dynamic countermeasures against attackers [44], where
traditional methods, especially rule-based approaches, have encountered significant difficulties in
protecting confidential data from constantly changing threats, especially in conditions of increasing data
volumes.</p>
      <p>At the same time, it is noted [45] that artificial intelligence and machine learning methods are
increasingly used in cyberattacks. This means that, as in many other areas of our lives, there will be no
absolute victory, the struggle will continue and, as is customary, the more competent and experienced will
tend to win.</p>
      <p>The task of countering the leakage of confidential information in network OSes remains incompletely
solved. This includes incomplete centralization of access control to resources, countering multi-vector
threats, and the lack of a universal approach to coordinating policies from different formats and nodes,
which leads to gaps in protection.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Formulation of the problem</title>
      <p>The implementation of dynamic transfer of control between computer network nodes provides a number
of technical and organizational advantages, namely, improved flexibility of network management,
increased resistance to failures and counteraction to malicious software. However, obtaining maximum
efficiency of this method is closely related to many factors, the most important of which is the optimal
structuring and transfer of critical security resources to the new control node. The formation of an optimal
set of global security resources that must be transferred to the new control node at the time of a change in
the control center is a key aspect of the successful implementation of dynamic control of a computer
network. Solving this problem will avoid unnecessary duplication, reduce the volume of data to be
transferred and, accordingly, reduce the time for their synchronization.</p>
      <p>This set should include only those security resources of the network OS that directly affect the
integrity, availability and manageability of the computer network. As a rule, its minimum content includes
a global privilege database, security policies together with access policies to confidential data, a connection
database for managing network traffic. All other security resources that are mainly of local importance
(log files, local device drivers, etc.) should be left under the control of the corresponding network nodes,
which will ensure a reduction in the costs of transferring control. The formation of an excessively large set
of global resources will lead to an increase in the transfer time and, as a result, the risk of delays in control,
the emergence of data synchronization problems between nodes. Therefore, optimizing the volume of
security resources subject to centralization is a critically necessary condition for building an effective
partially centralized OS security management model. This work is devoted to an attempt to scientifically
solve this problem.</p>
      <p>Thus, the main task of this study is to solve the problem of ensuring maximum efficiency of dynamic
transfer of control between network nodes by optimizing security resources subject to centralized control.
This, in turn, should reduce the time spent on transferring control.</p>
    </sec>
    <sec id="sec-4">
      <title>4. The main part</title>
      <p>Transfer of control from one network node to another, randomly selected, is a rather complex and
resource-intensive process. One of the issues to be solved in this case is determining the volume of transfer
of security resources, or the degree of their centralization. The main resource is the global privilege base.
But to ensure stable and secure functioning of a computer network with dynamic random transfer of
control between its nodes, continuity of network control, it is necessary to transfer a number of critical
system data to the new control node, which ensure the integrity of security policies, fault tolerance during
the transfer of control.</p>
      <p>In addition to the global privilege base, this includes security policies, including sensitive information
labeling policies, network policies (Firewall operation, ACL), shared resource access policies, procedures
for transferring control between nodes, synchronization with privacy databases (e.g., DLP), local event logs
(audit.log), hardware configuration parameters (USB, ports, local drivers), local session caches (e.g.,
memory pages without sensitive data), background security services (local antivirus scanner,
selfmonitoring scripts), lists of authorized local processes, low-level drivers and the OS kernel of the network
node, and others.</p>
      <p>To reduce the overhead of random dynamic transfer of control between computer network nodes
without compromising security and ensuring continuity of control, it is proposed to leave part of the
security resources that are not critical for global decision-making; do not affect the consistency of the
entire security system; have a low probability of conflict or attack during local control, under the control
of local nodes, and centralize those of them that affect access, interaction between nodes, security policies
and transfer of control.</p>
      <p>The process of dynamic transfer of control between network nodes. To describe the process of dynamic
transfer of control between computer network nodes with the separation of centralized and local resource
management, notations for key aspects are required. The set of network nodes is denoted as:
N = {N 1 , N 2 , … , N n }, where N 1 , N 2 , … , N n are the computer network nodes.</p>
      <sec id="sec-4-1">
        <title>The set of node security resources is defined asRBR:</title>
        <p>RBR = {R1 , R2 , … , Rk }, where R1 , R2 , … , Rk are the security resources (privilege databases,
security policies, connection database, etc.).</p>
        <p>
          We define resources subject to centralized management as its subset Rcentr∈ R BR. Then the subset of
resources that can remain under local control can be defined as Rlocal, as one that is not intersecting with a
subset Rcentr . Let's define this as Rlocal= RBR / Rcentr , while their union forms a set RBR. To describe the
process of dynamic control transfer between computer network nodes, we will also introduce the
necessary notation. The current control node at time t is defined as CSMM t. At the same time CSMM t
belongs to a set of network nodes N : CSMM t ϵ N . Then the probability of transferring control from the
current network node CSMM t to the next CSMM t +1 that will take control of the network at time t + 1 can
be defined as:
(
          <xref ref-type="bibr" rid="ref1">1</xref>
          )
(
          <xref ref-type="bibr" rid="ref2">2</xref>
          )
        </p>
        <p>P ( CSMMt +1= N j|CSMMt = N i
where CSMM t and CSMM t +1 are the control nodes of the computer network at the points in time and,
respectively, from the set of network nodes N ; N i is the current control node at time t ; N j is the index of
the next control node from the set N at time t + 1, with the control transfer subject to constraint j ≠ i
(Figure 1, position 1).</p>
        <p>Based on the above, we can conclude that there is a uniform distribution of the probability of becoming
the network control node in the process of dynamic control transfer for each active network node, i.e. each
node has the same chance of becoming the central network control node. This can be represented by the
formula:</p>
        <p>P (CSMM t +1 = N j ) =</p>
        <p>, ∀ j ≠ i
1
n - 1
where N j is the index of the next control node CSMM t +1 from the set N at time t + 1; n – the total
number of active network nodes (currently working) in the set N ;. n - 1 takes into account that the
current control node cannot become the network control node again ( j ≠ i).</p>
        <p>The chosen law of distribution of probability of a network node becoming the central control node of
the network allows to guarantee randomness and uniformity of control transfer, allows to avoid overload
of the network node, increases resistance to attacks due to the difficulty for the attacker to predict who
will be the next control node, supports the idea of partial centralization - no node remains a permanent
center. Thus, it can be described as a Markov process, since the next state of the network is determined
only by its current state with a uniform probability of dynamic control transfer between nodes. The
transfer of control between network nodes itself actually means that the control of the network is
transferred from the central control module CSMM t of the centralized security service of the OS of the
current node to the same control module CSMM t +1 of the next active network node. The transfer process
is initiated by the current control node CSMM t by sending the control token T Governance to a randomly
selected active network node (Figure 1, position 1). After receiving the control token (Figure 1, position 2),
the new CSMM t +1 control node sends a request (Figure 1, position 3) to all active network nodes to
transfer security resources that require centralized management: a global privilege base - there must be
one consistent copy for all nodes, sensitive data labeling policies, they affect all access logic, network
policies is require a single security strategy, a control transfer schedule between nodes, its violation can
cause collisions in network management, security incident handling policies, also require centralized
response and analysis.</p>
        <p>Formation of global databases for centralized network management. In practice, this means that such
OS resources as /etc/security/policies.conf, /etc/firewall.rules, global_privileges.db are the minimum
possible set of them that require centralized management. Such delimitation of management allows you to
reduce traffic, accelerate the transfer of control between nodes, and at the same time maintain high
resistance to leaks of confidential information. However, it is necessary to take into account the nuances of
the mechanisms for forming centralized copies of these resources for the new CSMM t +1 control node. The
logic of ensuring the maximum level of resistance to leaks of confidential information dictates the methods
of their implementation.</p>
        <p>
          Thus, the current centralized privilege database global_privileges.db for the next control node
CSMM t +1 is obtained by combining the local privilege databases of active network nodes (Figure 1,
position 4). To represent this mechanism, we introduce the following notations: RBPlocal is the privilege
database of a local node. Then the global privilege database RG privileges can be represented as follows:
RG privileges=U i∈ A RBP local ( i )
(
          <xref ref-type="bibr" rid="ref3">3</xref>
          )
where RBP local (i) is the local privilege base of the i-th network node, where i belongs to the set A of
network nodes active at the time of control transfer, which in turn is a subset of the set of network nodes
N .
        </p>
        <p>In the process of implementing management actions by the current CSMM t module, all changes in the
global privilege base RG privileges are transactionally replicated on all relevant local bases of network nodes,
which allows, in the event of an incident with the current management node, to obtain a new up-to-date
global privilege base for the new CSMM t +1 management module, which increases the OS's resistance to
information leaks.</p>
        <p>Let us consider the formation of a global security policy database global_policies.conf which is another
centralized resource that is updated at each cycle of control transfer between nodes. For convenience of
description, we will introduce the following notations: RPi( x ) – security policy x i-th network node as a
security resource; RP local – security policy of some local node. It can be defined as the union of all security
policies of a given local node of a computer network:</p>
        <p>
          R Plocal=U in=1{R Pi (x )}
(
          <xref ref-type="bibr" rid="ref4">4</xref>
          )
where RPi(x) is the security policy of x i-th node; n is the number of network nodes.
        </p>
        <p>The next step is to obtain the global security policy base of the computer network. It should be noted
that when implementing the function of combining all local security policy bases, it is possible to use
several mechanisms that implement different access rules, lists of permitted actions, etc., and from which it
is necessary to choose the most optimal one that will ensure maximum system resistance to information
leakage. This may be a consensus approach, which is based on including in the global RG policies security
policy base all security policies present in the local security policy bases of active nodes. Another option
for the mechanism for forming a centralized policy base involves its implementation as an intersection of
security policies of all local bases of network nodes. It is also possible to use a mechanism that, when
forming a global RG policies policy base, takes into account the level of trust in nodes - a weighted union (for
example, taking into account their reliability, incident history, etc.), giving priority to including security
policies from local bases of nodes with a higher level of trust.</p>
        <p>Since we are talking about the formation of centralized databases of security resources of the network
OS security system, the most expedient and justified seems to be the use of a mechanism based on the
intersection of security policies of local databases of network nodes, since it is quite simple to implement
and at the same time provides a regime of the strictest rules for applying security policies from the central
control node, which in turn guarantees increased OS resistance to leaks of confidential information
processed in the system under its control.</p>
        <p>Then the global RG policies security policy database can be represented as follows:</p>
        <p>RG policies= ∩i∈ A {R p local ( i ) }
where R p local ( i ) is the local security policy base of the i-th node of the computer network, where i
belongs to the set of active nodes of the A network at the moment of control transfer.</p>
        <p>To form the global connection base RG firewall, we will use the same mechanism as when forming the
global security policy base RG policies, since connection management also, due to its importance, requires
the strictest control rules.</p>
      </sec>
      <sec id="sec-4-2">
        <title>Then RG firewall will be defined as follows:</title>
        <p>RG firewall= ∩i∈ A {RFW local ( i ) }
where RFW local ( i ) is the local connection base of the i-th node of the computer network, where i belongs
to the set of active nodes of the A network at the moment of control transfer.</p>
        <p>
          Justification of the effectiveness of partial centralization of security resources. To do this, we will
perform a comparative calculation of the costs of dynamic transfer of control between computer network
nodes for situations with complete centralization of all security resources of the network OS security
system and centralization of only privilege databases, security policies, and network connections.
(
          <xref ref-type="bibr" rid="ref5">5</xref>
          )
(
          <xref ref-type="bibr" rid="ref6">6</xref>
          )
        </p>
        <p>To mathematically represent the total costs of transferring control between network nodes, we will use
the previously introduced notations: RBR – set of network security resources; Rcentr∈ RBR – subset of
resources subject to centralized control for a partial centralization situation, and we will also introduce the
notation of comparative criteria: T fetch – time to poll all active network nodes and receive copies of the
resource Ri from them to form its current global database; T parse – time that the new control node spends
on parsing, unifying or confirming the compliance of the received data (checking the integrity of the
database, checking the consistency of security policies, building a generalized global version of the
resource); T aplying – time to restart a new global version of the resource on the new control node (activating
it in services or OS subsystems, transmitting confirmation to other network nodes if necessary).</p>
        <p>Then the total update time of the global version of some Ri security resource of the network OS can be
represented as the sum of all time periods of its formation:</p>
        <p>
          T G ( Ri) = T fetch ( Ri) + T parse ( Ri) + T ap plying ( Ri )
(
          <xref ref-type="bibr" rid="ref7">7</xref>
          )
where T fetch is the time to request local copies of the Ri resource from all active network nodes; T parse is
the time to form a global version of the Ri resource; T applying is the time to restart a new version of the
global Ri resource.
        </p>
        <p>
          The implementation of formula (
          <xref ref-type="bibr" rid="ref7">7</xref>
          ) is illustrated in (Figure 1, position 3, 4, 5) and (Figure 2, position 3, 4,
5), which present the processes of preparing global security resource bases for the next CSMM t +1 control
node of the OS security system with full (Figure 1) and partial (Figure 2) resource centralization.
        </p>
        <p>
          Now, for a situation with complete centralization of all security resources of the network OS, the time
of transfer of control to the new control node CSMM t +1, T F central can be represented as the sum of all
time periods required to form all global versions of all security resources of the OS according to the
scheme (Figure 1). Taking into account the above and (formula 7), it will take the form:
T F central = ∑ ( T fetch ( Ri) + T parse ( Ri) + T applying ( Ri)) (
          <xref ref-type="bibr" rid="ref8">8</xref>
          )
        </p>
        <p>i=1
where T fetch is the time to request local copies of the Ri resource from all active network nodes; T parse is
the time to form a global version of the Ri resource; T applying is the time to restart a new version of the
global Ri resource; n is the total number of OS security resources in the set RBP.</p>
        <p>
          The time of transfer of control to the new control node CSMM t +1 with partial centralization of security
resources T P central can be calculated using formula (
          <xref ref-type="bibr" rid="ref8">8</xref>
          ) with the only difference that the total number of OS
security resources n will correspond to the number of elements of the set Rcentr , which is a subset of the
set RBP. This feature of the construction of the model of dynamic control transfer is shown in (Figure 2).
With such a scheme of operation, part of the security resources remain in the local control of the network
node, respectively, they do not require the collection and centralization of data about them when
transferring control to the new central node CSMM t +1 , which significantly reduces the time spent on the
transfer of control itself. To minimize them, it is important that the number of elements of the set Rcentr be
as small as possible, but on the other hand such that the required level of OS resistance to leakage of
confidential information is ensured.
        </p>
        <p>Then the ratio of the time of transfer of control to a new control node with full centralization of
security resources T F central and the time of transfer of control with partial centralization of security
resources T P central greater than one will indicate a better efficiency of the OS security system with partial
centralization:</p>
        <p>Ecentral =</p>
        <sec id="sec-4-2-1">
          <title>T F central &gt; 1</title>
          <p>T P central
EP central =</p>
        </sec>
        <sec id="sec-4-2-2">
          <title>T F central - T P central × 100 %</title>
          <p>
            T F central
(
            <xref ref-type="bibr" rid="ref9">9</xref>
            )
(
            <xref ref-type="bibr" rid="ref10">10</xref>
            )
          </p>
          <p>
            To represent the value of EP central efficiency in percent, we present formula (
            <xref ref-type="bibr" rid="ref9">9</xref>
            ) in the following form:
where T F central is the time of transfer of control to a new control node with full centralization of security
resources; T P central is the time of transfer of control with partial centralization of security resources.
          </p>
          <p>A method for assessing the effectiveness of partial centralization of security resources during dynamic
transfer of control between network nodes in comparison with their full centralization has been developed
for use in the study of network OS security systems.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Experiments</title>
      <p>Experimental environment setup. In order to confirm the effectiveness of the network OS security system
with partial centralization of security resources during dynamic transfer of control between network
nodes, several series of experiments were conducted. For this purpose, a test environment was deployed
based on the use of a virtual computer network that includes virtual nodes VM01 - VM04, which served as
target machines during the experiments (Figure 3). All virtual machines operate under the control of the
Virtual Box hypervisor. With its help, virtual machines are combined into a separate local virtual network
necessary for conducting experiments. FreeBSD 13.1 is installed as a network OS on each virtual machine.</p>
      <p>Calculation of the efficiency of partial centralization of resources. As a result of experiments with a
virtual network with simulation of dynamic control transfer between its nodes, the data given in Table 1
were obtained.</p>
      <p>
        Substituting the data into formula (
        <xref ref-type="bibr" rid="ref8">8</xref>
        ) to calculate the control transfer time between computer network
nodes for a situation with complete centralization of security resources (taking into account Ri∈ RBP), we
obtain:
      </p>
      <p>n
T F central=∑ ( T fetch ( Ri )+T parse( R i)+ Tapplying ( Ri) )=(5.31+ 9.54+ 8.21+ 6.14+2.81+5.15)=37.16 sec
i =1</p>
      <p>
        As part of the next step, we calculate the time for control transfer between network nodes for a
situation with partial centralization of resources (formula (
        <xref ref-type="bibr" rid="ref8">8</xref>
        ) taking into account Ri∈ Rcentral) and obtain:
      </p>
      <p>E P central = T F cenTtraFl c-enTtraPl central ×100 % = 37.1367.-1263.06 × 100 % =37.9 %</p>
      <p>Calculations based on the results of the experiments confirmed the effectiveness of the method for
optimizing the centralization of network OS security resources during random dynamic transfer of control
between computer network nodes (Figure 4).</p>
      <p>The reduction in the time for transferring control between computer network nodes with partial
centralization of security resources was, as can be seen from the calculations, ≈ 38%, which was achieved
by excluding secondary security resources (log files, local device drivers, etc.) from centralized replication,
reducing the amount of data for synchronization, and reducing the overhead of data verification,
normalization, and logging.</p>
    </sec>
    <sec id="sec-6">
      <title>6. Conclusions</title>
      <p>The result of the proposed approach is the confirmation of a significant reduction in time (Figure 4) during
dynamic random transfer of control between network nodes, which, in turn, reduces the probability of
losing control of the network or reducing its security during the transition period. In addition, this
approach allows for better scaling of the system, since an increase in the number of nodes does not
proportionally affect the amount of data transferred to the new control node, due to the optimization of
the set of critical security resources.</p>
      <p>Another advantage of optimizing the set of global security resources is the reduction of the attack
surface, since the number of points through which an attacker could affect the security system during the
transfer of control is reduced. This is especially important in conditions where attacks can be coordinated
and aimed at the moments of maximum vulnerability of the system, namely at the moments of changing
the control node.</p>
      <p>Thus, the formation of an optimal set of global OS security resources for partially centralized network
management based on dynamic control transfer between its nodes is not only an engineering task, but also
a scientific tool for increasing the efficiency, reliability and security of the entire computer network. This
approach to building centralized OS security systems allows maintaining a balance between the flexibility
of dynamic management and the necessary rigidity of control over its critical aspects.</p>
    </sec>
    <sec id="sec-7">
      <title>Declaration on Generative AI</title>
      <p>The authors have not employed any Generative AI tools.
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