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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>Y. Kostiuk, et al., Information Protection and Secure Data Exchange in Wireless Mobile
Networks with Authentication and Key Exchange Protocols, Cybersecur. Educ. Sci. Technol.</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.28925/2663-4023.2024.25.229252</article-id>
      <title-group>
        <article-title>Architecture of the software system of confidential access to information resources of computer networks⋆</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Yuliia Kostiuk</string-name>
          <email>y.kostiuk@kubg.edu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Svitlana Rzaieva</string-name>
          <email>s.rzaieva@kubg.edu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Karyna Khorolska</string-name>
          <email>k.khorolska@kubg.edu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Nataliia Mazur</string-name>
          <email>n.mazur@kubg.edu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Nataliia Korshun</string-name>
          <email>n.korshun@kubg.edu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Borys Grinchenko Kyiv Metropolitan University</institution>
          ,
          <addr-line>18/2 Bulvarno-Kudriavska str., 04053 Kyiv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2024</year>
      </pub-date>
      <volume>1</volume>
      <issue>25</issue>
      <fpage>0000</fpage>
      <lpage>0001</lpage>
      <abstract>
        <p>The paper presents a formalized model of the architecture of a software system that provides confidential access to the information resources of computer networks amid the high dynamism of network infrastructures, the increasing complexity of the information environment, and the heightened requirements for protecting user privacy. The proposed architecture is grounded in the concepts of modularity, openness, and unified software interfaces, which together ensure compatibility with heterogeneous deployment environments. The functional subsystems integrate multi-level authentication, cryptographic encryption, attribute-based access control, anomaly detection in user behavior, and active access monitoring based on artificial-intelligence mechanisms. A mathematical model for assessing the degree of confidentiality of access has been developed, enabling quantification of the security level of information objects in accordance with Zero Trust Architecture standards. The practical significance lies in the architecture's applicability to information systems with stringent confidentiality demands while meeting institutional and regulatory oversight requirements.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;confidential access</kwd>
        <kwd>system architecture</kwd>
        <kwd>information security</kwd>
        <kwd>computer networks</kwd>
        <kwd>access control</kwd>
        <kwd>encryption</kwd>
        <kwd>multi-level security</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>The growing number of cybersecurity incidents accompanying the digital transformation of
enterprises requires new approaches to organizing secure access to the information resources of
computer networks. Traditional solutions based on centralized access control or classical
cryptographic schemes are insufficiently effective in distributed, multi-service environments,
where the volume, speed, and variability of traffic demand dynamic, flexible, and adaptive
protection.</p>
      <p>Of particular importance are software-based confidential-access systems that can provide not
only authenticated and authorized access but also preserve the confidentiality of user requests,
their sessions, and the history of interactions with network resources. In modern implementations,
such systems should support a multi-level security policy, automated access control, distributed
architecture, standardized encryption protocols, and interaction with other components of the
information infrastructure—including SIEM, VPN, and Zero-Trust environments. These systems
must offer open, unified interfaces; a flexible, modular architecture; and the capability to integrate
with SIEM, DLP, and VPN solutions, audit tools, digital-identity systems, and secure-transmission
protocols (TLS, IPsec, WireGuard, etc.).</p>
      <p>The purpose of this paper is to develop an architecture for a software system that enables
confidential access to the information resources of computer networks, integrates security
mechanisms with artificial-intelligence tools, supports information-security standards, and allows
access policies to adapt to the evolving risk landscape of IT infrastructures. The study proposes a
system model, a mathematical apparatus for assessing the level of confidentiality, and principles for
building an open architecture that accommodates third-party software components.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Literature review</title>
      <p>
        The issue of designing the architecture of software systems that enable confidential access to
information resources is a key topic in contemporary cybersecurity research, where special
attention is devoted to adaptive risk-management mechanisms, data protection, and dynamic
access control. Althar et al. [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ] present an automated risk-management model focused on
identifying and eliminating software vulnerabilities. The proposed solution integrates
riskassessment mechanisms directly into the secure-software development process, which is
particularly relevant for confidential-access architectures, where resistance to known and potential
threats must be ensured from the design stage.
      </p>
      <p>
        Wang, Ahmad, and Bakar [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ] conducted a systematic review of approaches to digital
transformation and risk management in small and medium-sized enterprises. The authors
emphasize the need to implement flexible and adaptive access-control systems in highly uncertain
environments. This conclusion aligns with modern requirements for confidential-access
architectures, which must deliver not only security but also scalability and adaptability.
      </p>
      <p>
        The study by Barraza de la Paz et al. [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ] offers a systematic review of risk-management
methodologies in complex Industry 4.0 and 5.0 organizations. In particular, the authors highlight
the importance of building intelligent information systems capable of self-organization, monitoring
user behavior, and analyzing threats in real time. This perspective directly corresponds to the
requirements of modern confidential-access software systems deployed in hybrid-cloud
environments and infrastructures with distributed access control.
      </p>
      <p>
        The review by Ahmad et al. [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] addresses security issues in software-defined networks (SDN).
The authors analyze key vulnerabilities in centralized network-management models and propose
dynamic routing and distributed authentication concepts that can be incorporated into
confidential-access system architectures. Given SDN’s capabilities for traffic control and the flexible
definition of security policies, such approaches can underpin the construction of confidential
network segments that isolate critical resources.
      </p>
      <p>
        Thus, contemporary scientific literature confirms the relevance of creating architectures that
support flexible interaction among security components, adaptive access control, and the
confidentiality of information processing—factors that collectively form the foundation for
developing effective software systems for confidential access in computer networks. Recent
research by Vakhula et al. [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] explores the implementation of policy-as-code frameworks for
rolebased and attribute-based access control, emphasizing automation and precision in managing
confidential access rights within complex network environments. Similarly, Susukailo and Lakh [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]
propose an innovative access control system leveraging encryption within QR-Code technology,
which enhances secure and user-friendly authentication methods suitable for confidential
information resource management.
      </p>
    </sec>
    <sec id="sec-3">
      <title>3. Research methods</title>
      <p>The research methods are grounded in the theory of algorithmic computational complexity, the
reliability of automated control systems, modern cryptographic primitives, distributed
programming, and the theory of multi-layer architectures. Additionally, risk-based modelling in
accordance with ISO/IEC 27005 and NIST SP 800-30, together with machine-learning techniques for
adaptive query analysis, were employed. Formal models of confidential access, fuzzy-logic
methods, Bayesian updating, and agent-based interaction within a distributed environment are
applied. The combined use of state-of-the-art cryptographic protocols (TLS 1.3, IPsec, SSH-2),
ZeroTrust concepts, and integration with SIEM and MFA systems provide an adaptive, scalable
architecture for confidential access to critical information resources.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Main material</title>
      <p>
        Modern software tools for protecting electronic information can be classified into the following
groups: cryptographic protection tools, access-control systems, tools enabling confidential access to
information resources, and security mechanisms deployed in financial, educational, and cloud
platforms [
        <xref ref-type="bibr" rid="ref1 ref2">1, 2</xref>
        ]. Analysis and comparison of such systems are necessary to create a unified
software-system architecture capable of ensuring both robust data protection and user privacy
within the digital environment.
      </p>
      <p>In this context, particular attention is devoted to data-protection solutions based on the IPsec
protocol, which provides confidential and authenticated exchanges in TCP/IP networks. Modern
mechanisms for building Virtual Private Networks (VPNs) are also examined; they allow secure
data exchange between distributed information systems while minimizing infrastructure costs and
simultaneously broadening the geographical reach of access [7, 8]. Notable effective
implementations include IPsec VPN, SSL VPN, and tunnelling with WireGuard.</p>
      <p>
        Figure 1 illustrates the deployment of the components of a software-based confidential-access
system designed in accordance with Zero Trust security principles and contemporary authorization
and encryption standards. The architecture comprises a client device, authorization and access
servers, a cryptographic gateway, a security-information and event-management (SIEM) system,
and cloud services hosting educational, financial, and other resources. The inter-component
connections demonstrate the flow of access requests, authorization decisions, cryptographic
protections, event logging, and configuration policies. The system supports scalability, adaptability,
and integration with external platforms through unified interfaces.
which no trust is granted to any user or device by default [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. Microsoft Windows systems employ
the Security Support Provider Interface (SSPI) for local authentication, and Linux uses PAM
(Pluggable Authentication Modules), which provides flexible management of credentials at the
OSkernel level.
      </p>
      <p>
        Typical architectures of such systems are characterized by modularity, where the key
components are: a module for collecting and analyzing event information, a decision-making
module based on security policies, a response module that implements blocking or allowing access,
a logging module that records the actions of access subjects for auditing, and a management
module that supports dynamic policy configuration in line with environmental changes [
        <xref ref-type="bibr" rid="ref10 ref11">10, 11</xref>
        ].
An important element is integration with monitoring systems (e.g., SIEM) and the use of
nextgeneration cryptographic protocols—TLS 1.3, SSH-2, and IPsec with Perfect Forward Secrecy (PFS)
[
        <xref ref-type="bibr" rid="ref12 ref13 ref14 ref4">4, 12–14</xref>
        ].
      </p>
      <p>The component architecture of the software system for confidential access to the information
resources of computer networks (Figure 2) is built with due regard for modern data-protection
requirements. It includes modules for multifactor authentication, policy-based authorization, and
access control in accordance with the Zero-Trust concept. The system features cryptographic
protection (IPsec, TLS, SSH-2, WireGuard), event logging, incident response, and monitoring
components through integration with SIEM platforms. Access to cloud resources—including
educational and financial services—is provided through secure confidential tunnels. The
architecture supports dynamic access-rights management, end-to-end encryption, user
identification, and traffic protection in accordance with industry information-security standards.</p>
      <p>
        Special attention is devoted to the construction of confidential communication channels. Their
organization includes key exchange via the IKEv2 protocol, the use of Encapsulating Security
Payload (ESP) for traffic encryption, and Authentication Header (AH) for source verification [
        <xref ref-type="bibr" rid="ref15 ref4 ref8">4, 8,
15</xref>
        ]. Together, these elements form end-to-end encryption and ensure the integrity of transmitted
data. Thus, the architecture of a confidential-access software system must meet the following
requirements: support for dynamic access control, scalability, compatibility with open protocols,
integration with cloud platforms, transparency of access without compromising security, and
preservation of the confidentiality of both data and user requests.
      </p>
      <p>
        The study examines algorithms and architectures for confidential access to information
resources, in particular technologies of anonymous virtual networks such as DC-net, Mix-net,
Crowds, Onion Routing, and Freedom Network [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ]. These systems implement traffic-protection
mechanisms, route obfuscation, and multi-level encryption, which make it impossible to track the
source of requests. Particular attention is paid to anonymous networks that are compatible with
the application layer of the TCP/IP stack, scalable, and capable of formally assessing the degree of
anonymity achieved using mathematical models such as entropy or differential anonymity.
The Mix-net architecture, whereby data are transmitted through mix servers that randomly route
and reorder messages to reduce the likelihood of correlating requests with responses, is also
investigated. Modern software-based confidential-access systems combine these approaches with
IPsec VPN, WireGuard, and the Zero Trust concept, in which no device or user is granted a priori
trust [
        <xref ref-type="bibr" rid="ref11 ref17">11, 17</xref>
        ].
      </p>
      <p>
        The generalized architecture of such systems includes modules for authentication,
authorization, response, logging, access-policy management, and traffic encryption using modern
cryptographic protocols (TLS 1.3, SSH-2, IPsec with PFS) [
        <xref ref-type="bibr" rid="ref12 ref13 ref15 ref18 ref19 ref8">8, 12, 13, 15, 18, 19</xref>
        ]. Interaction among
components is effected through unified interfaces, with integration into SIEM systems for
monitoring security events [
        <xref ref-type="bibr" rid="ref14 ref20">14, 20</xref>
        ]. This configuration enables the creation of a single dynamic
software-security framework that supports confidential access to cloud, financial, educational, and
corporate resources.
      </p>
      <p>
        The architecture of the anonymous Mix-net network was reviewed to deepen understanding of
the principles underlying confidential-access channels in distributed information environments
[
        <xref ref-type="bibr" rid="ref16">16</xref>
        ]. This approach facilitated the evaluation of practical mechanisms for protecting traffic at the
transport and network layers, including delayed routing, message shuffling, and multi-level
encryption. Analysis of the Mix-net architecture proposed by D. Chaum provided a foundation for
developing our own dynamic confidential-access system that accounts for anonymity, scalability,
and interaction with open TCP/IP protocols. The Mix-net system employs specialized mix servers
to transform incoming traffic, altering its sequence and encrypting data at each stage, thereby
significantly complicating the correlation between user requests and server responses.
      </p>
      <p>
        The practical value of this analysis lies in adapting the anonymization principles implemented
in Mix-net to the architecture of the system under development, which delivers confidential access
to information resources [
        <xref ref-type="bibr" rid="ref16 ref17 ref21">16, 17, 21</xref>
        ]. This adaptation enabled the inclusion of a route-obfuscation
module, the establishment of end-to-end encryption, and the assurance of privacy without
compromising functionality. Consequently, the study of the Mix-net architecture has supplied tools
and conceptual approaches that are integrated into a holistic software-security architecture to
enhance request anonymity, implement Zero Trust principles, and establish secure routes to critical
network resources.
      </p>
      <p>The diagram (Figure 3) depicts the complete sequence for routing an anonymous user request to
a secure resource over the Mix-net network, incorporating Java Anonymizer Proxy (JAP) as the
initial proxy service. In the first stage—Anonymous Request Routing—the user submits a request
through JAP, which applies the first layer of encryption. The request then proceeds to Mix Server
1, where it is re-encrypted (Layer 2), is forwarded to Mix Server 2 for another encryption layer
(Layer 3), and finally reaches Mix Server 3, which performs final processing and relays the request
to a secure resource, such as a financial, cloud, or educational system. The second stage—Response
Routing—traces the return path from the resource back to the user: the response travels through
Mix Server 3, where it is again encrypted, passes through Mix Server 2 and Mix Server 1 with
corresponding re-encryption layers, and is ultimately received and decrypted by JAP for the user.
The diagram illustrates the full cycle of request and response processing within a secure
environment that adheres to principles of end-to-end encryption, route obfuscation, multi-layer
encryption, and source-anonymity protection. The combination of these approaches in a single
scenario demonstrates the practical implementation of a confidential-access architecture that not
only safeguards traffic at every stage but also effectively counters correlation attacks and traffic
analysis, thereby maintaining the privacy and integrity of information exchange in computer
networks.</p>
      <p>
        The study proposes a formalized mathematical model and appropriate methods for
implementing confidential access in computer networks, focused on the protection of critical
information resources [
        <xref ref-type="bibr" rid="ref1 ref15 ref2 ref21 ref22 ref3">1–3, 15, 21, 22</xref>
        ]. The result of an information system vulnerability analysis
is a quantitative assessment of its information security level, which can be represented as a
function of time during which data is guaranteed to remain confidential, integral and accessible. All
requests are controlled by a security infrastructure that includes a security policy controller [
        <xref ref-type="bibr" rid="ref10 ref11 ref20">10, 11,
20</xref>
        ]. The model is easily scalable to any number of segments without losing generality.
      </p>
      <p>The information system is modeled as a set of objects:
(2)
(3)
(1)
(4)
where each oi is an information resource that stores or processes data. Set O represents all
objects of the information system, which can be either stored data or components that process
information (e.g., databases, services, files).</p>
      <p>Entities interacting with the system:
where each s j—user, device, or software agent. Set S describes the subjects of the information
system, i.e. everyone who can access objects: users, devices, processes, agents.</p>
      <p>Each object and subject is assigned a security rank from a partially ordered set:</p>
      <p>O = {o 1 , o 2 , … , o n},
S = {s1 , s2 , … , sn},
g : S × O →R ,</p>
      <p>Set R —are security ranks that are ordered by the degree of trust. They are used to categorize
both subjects and objects by level of sensitivity or trust. For example: r 0—public information, r k—
the highest level of confidentiality.</p>
      <p>As for the access control policy model, the access ranking function is used:
Function g ( s , o ) defines the level of security required for an entitys to gain access to an object o .
This mapping is used to determine the minimum subject rank required to access the corresponding
object in the system. In other words, it reflects the minimum rank that a subject must have in order
to access an information resource.</p>
      <p>Maximum access level of the subject:</p>
      <p>Determines the highest level of access that subject s has among all the objects that he or she can
access. This allows the system to determine the general level of privileges of this user.</p>
      <p>Minimum level for an external attacker:
rang ( s )= {g ( s , o )∨ o ∈ O },</p>
      <p>rang ( s attacker )= { R } =r 0,</p>
      <p>For an external attacker, the lowest possible access level is set to —r 0, which means no trust.
This is the starting point for analyzing potential threats.</p>
      <p>The access decision is formalized as a binary function:</p>
      <p>Access ( s , o )= { 1 , if rang ( s ) ≥ rang ( o ) 0 , otherwise ,
(7)
where rang ( s )= {g ( s , o )∨ o ∈ O }, а g : S × O →R is a ranking function. It is a binary
decisionmaking function for granting access. If the security level of the subject is not lower than the
security level of the object, access is allowed (1), otherwise—is denied (0).</p>
      <p>The model for assessing the level of confidentiality over time is based on the exponential
decrease in the probability of maintaining data confidentiality:
(5)
(6)
(8)</p>
      <p>C (t )= P secure (t )= e− λt,
where λ is the intensity of the risk or attack, and t is the time of data retention. The model
reflects that over time, the probability that information will remain confidential without additional
protection measures decreases exponentially. The presented function is an important tool for
formalized analysis of the loss of confidentiality in dynamic information systems. Thus, the
proposed model allows us to mathematically describe privacy dynamics, adapt access policies to
the time characteristics of data storage, and increase the efficiency of confidential access
architectures in computer networks.</p>
      <p>
        To build a more flexible protection system, the concept of a multilevel security model is
introduced, in which each component of the IT system is assigned a specific protection level [
        <xref ref-type="bibr" rid="ref10 ref3 ref4">3, 4,
10</xref>
        ]. This model enables the differentiation of access levels, the definition of security policies, the
formalization of privilege-granting principles, and the detection of violations based on a
comparison of the ranks of subjects and objects. The system supports the implementation of these
methods within the confidential-access architecture, which comprises modules for authentication,
authorization, encryption, monitoring, and auditing [
        <xref ref-type="bibr" rid="ref11 ref20 ref23">11, 20, 23</xref>
        ]. Consequently, the presented
mathematical model formalizes the processes of assessing information security and confidentiality,
ensuring the adaptive construction of access policies and their dynamic adjustment in response to
environmental changes [
        <xref ref-type="bibr" rid="ref1 ref21 ref3">1, 3, 21</xref>
        ]. This capability is fundamental to the deployment of
contemporary software architectures for secure access to computer networks.
      </p>
      <p>The diagram (Figure 4) illustrates the logic of the software system that provides confidential
access to the information resources of computer networks. The system performs access control by
comparing the security ranks of subjects and objects, which are determined during the ranking
process. Access requests are processed in accordance with established policies that incorporate
security parameters and current threat models. Decisions to grant or deny access are logged and
analyzed by the SIEM system to detect anomalies or unauthorized actions originating from either
legitimate users or potential attackers. The diagram depicts the interaction among the user, access
controllers, policies, data objects, and monitoring systems.</p>
      <p>
        The concept of a multi-level information-security model for automated data-processing systems
involves structuring system components according to their protection level and functional purpose.
This model enables clear delineation of areas of responsibility, minimizes the risk of compromise,
and supports the application of adaptive security policies at different logical tiers. In particular,
Level A encompasses users’ internal client devices; Level B protects an isolated information
resource (for example, a web application that processes confidential data); Level C comprises the
network infrastructure that supports internal interaction; and Level D represents external users
and the channels through which they access the system via public networks—most notably, the
Internet [
        <xref ref-type="bibr" rid="ref17 ref21 ref23">17, 21, 23</xref>
        ]. Such stratification facilitates flexible access control, well-reasoned security
zoning, and effective identification of potential attack vectors within each level.
      </p>
      <p>
        Within the confidential-access model, all system principals are divided into the following logical
groups: session initiators—users or devices that request resources; relay servers—nodes that
obfuscate traffic routes (e.g., Mix servers or Tor nodes) [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ]; receiving servers—components that
process user requests; information storage—a distributed database that holds anonymized data; and
third-party resources—services outside the architecture with which data are exchanged.
      </p>
      <p>
        In the proposed architecture of the confidential-access software system, data are transferred in
accordance with cryptographic-protection principles, ensuring confidentiality, integrity, and
authenticity at every stage of the route. Repeaters (intermediate nodes that relay encrypted packets
between the client and the target server) employ symmetric-encryption keys, enabling rapid
processing of large traffic volumes with minimal latency [24]. Symmetric encryption is effective for
tunnelling information when keys are pre-shared or transmitted over a secure channel. Receiving
servers (route endpoints) use asymmetric cryptography—specifically, public-key mechanisms—
which allows them to accept session keys or user requests securely without a pre-established
shared secret [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ]. This approach guarantees secure connection establishment even with previously
unknown clients. Users (request initiators) generate session-access keys, which are derived using a
cryptographic function:
      </p>
      <p>
        K session= F ( x , k ),
(9)
where x is the random variable (nonce or initialization vector) that ensures the uniqueness of
each connection, k is the encryption key, which can be symmetric or obtained by exchanging
through asymmetric methods (for example, through ECDH), F ( x , k ) is the cryptographic key
calculation function (e.g., HMAC, PBKDF2, or HKDF) [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. Thus, data confidentiality is ensured
through multi-level encryption, where each stage from the user to the target resource implements
the appropriate cryptographic mechanisms [
        <xref ref-type="bibr" rid="ref8">8, 24–26</xref>
        ]. This approach allows not only to preserve
the privacy of the transmitted data but also to ensure resistance to man-in-the-middle (MitM)
attacks, session replay, and correlation analysis of traffic.
      </p>
      <p>To build an anonymous channel, a route model in the form of a sequence of nodes is used:
where si are relay servers, g is the target receiving server [24, 27].</p>
      <p>The probability that user u was the source of the request through the confidential
communication system (CCS), in the absence of a priori information, is defined as:
where PS is the set of potential sources of the request. If the intruder has information about the
node through which the traffic passed, the set of possible routes decreases. In the case of building a
route without repetitions (without cycles), the number of possible options is calculated as a
combination of:
γ= 〈 s1 , s2 , … , sn , g 〉 ,</p>
      <p>,
C bj − 1= j ! ((bb−− 11−) ! j ) !</p>
      <p>,
N = ( b− 1 ) j,
(10)
(11)
(12)
(13)
where b is the number of available repeaters, j is the length of the route. If the use of
repetitions (loops) is allowed, then the number of possible route options is defined as:</p>
      <p>
        These mathematical models allow for a formalized assessment of the level of user anonymity
and the probability of channel compromise. The functional blocks of the system implement: access
control based on policies and the Zero Trust model [
        <xref ref-type="bibr" rid="ref17 ref23">17, 23</xref>
        ], route obfuscation through multi-stage
encryption, cryptographic traffic protection (TLS 1.3, IPsec, WireGuard) [
        <xref ref-type="bibr" rid="ref11 ref21 ref8">8, 11, 21, 25</xref>
        ], audit and
monitoring with support for SIEM systems, and dynamic adaptation of security policies [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ]. Thus,
the proposed confidential access architecture allows implementing anonymous data transmission
routes, following the principles of trust minimization and mathematical security verification. It is
scalable, integrates with cloud and enterprise environments, and provides flexible access control in
complex threat environments.
      </p>
      <p>In a situation where an attacker captures the first node of the route (or another part of the
request transmission path), he can partially exclude certain nodes from the set of potential request
sources, thereby reducing the degree of user anonymity. In this case, a model with filtering is used
to calculate the updated conditional probability that user u initiated the request:</p>
      <p>P (b , j , m, k )=</p>
      <p>
        1
| P S|− | NS|
,
(14)
where | P S| is the initial number of possible sources (potential users), | NS | is the number of
excluded (known or compromised) route nodes, b is the route length, j , m, k are route selection
parameters (e.g., depth, bypass strategies, number of mixes). The formula reflects the decrease in
anonymity: the more nodes an attacker can exclude (i.e. | NS | increases), the higher the probability
of correctly identifying the source of the request [
        <xref ref-type="bibr" rid="ref14 ref16 ref20">14, 16, 20, 27</xref>
        ]. Thus, the model allows us to
quantify the loss of anonymity under the influence of partial route compromise, which is important
for assessing the resistance of a confidential access system to correlation attacks.
Total probability of identity disclosure for a given route:
      </p>
      <p>b
P ( b )= ∑ P ( b , j , m , k ), (15)</p>
      <p>k =0</p>
      <p>
        In the case of an arbitrary access route length in a confidential communication system (CCS),
when all valid lengths have the same probability (uniform distribution), the total probability that
user uuu was the source of the request is calculated by the formula:
(16)
(18)
(19)
adv ( F )= | P ( AF = 1 )− P ( AU = 1 )|,
(17)
where AF is the attacker who has access to the function F , AU is the same attacker, but with
access to a random (ideal) generator U , P(⋅) is the probability of a successful attack [
        <xref ref-type="bibr" rid="ref13 ref8">8, 13</xref>
        ]. This
indicator determines the degree of difference between the function F from a random the point of
view of an attacker. The closer this value is to zero, the more secure the cryptographic function and
the entire system is considered to be. Thus, the combination of route anonymity and provable
cryptographic strength forms a comprehensive security assessment in modern CCS. The closer
adv ( F ) to zero, the more reliable the function F is in terms of cryptanalytic protection.
      </p>
      <p>The level of reliability of the cryptographic function F under the given conditions is defined as:
inse c F (t , q )= adv ( F ),
where A( t , q ) is the set of possible attacks that have no more than t computational steps and q
requests. The formalized value indicates the highest probability of successful hacking of the
function F under conditions of limited attacker resources. The lower the value of insec F , the higher
the cryptographic strength of the function in a particular environment.</p>
      <p>
        In the context of a cryptographic protocol E : K × R × P →C ,describing a probabilistic
encryption scheme, the security of the system against a Chosen Plaintext Attack (CPA) is evaluated
using the expression [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ]:
      </p>
      <p>P ( b )=</p>
      <p>
        1 b∑max ∑j P ( j , m , k ),
b max−b min+1 j =bmin k =0
where b min and b max are minimum and maximum route length, j is the specific route length,k
is the route parameter, such as the number of known nodes or the level of filtering, P ( j , m, k ) is
the conditional probability with fixed route parameters. The model takes into account the
variability of the data transmission route in a secure system and allows you to assess the degree of
user anonymity. The uniform distribution of lengths means that all possible routing scenarios are
considered equally likely, which is a typical assumption in systems such as Mix-net or Tor [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ]. At
the same time, an evidence-based approach is used to assess the cryptographic security of a
confidential access system. It is based on modeling cryptographic functions as a family of mappings
F : { 0,1 }* × { 0,1 }* →{ 0,1 }* , where the first argument is the input data, and the second is the
encryption key. The attacker A is represented as a probabilistic Turing machine with time and
number of calls to the function. Its attack capability is estimated by the difference between the
probability of successfully guessing the result when working with real function F and random
function U :
      </p>
      <p>adv CPA ( E )=| P ( A Ek =1 )− P ( AU =1 ) |,
where A is the attack algorithm (attacker), E k is the encryption with a secret key k, U is the
random function (the standard of complete unpredictability). The indicator reflects the difference
between the probability that an attacker will successfully distinguish encryption with a real
algorithm from a random function. The lower the value adv CPA, the more resistant the system is to
CPA attacks, meaning that an attacker cannot effectively distinguish between ciphertexts, even if
he can choose plaintexts.</p>
      <p>
        Accordingly, a system is considered CPA-resistant if:
insec CEPA ( t , q , l )=adv CPA ( E )&lt;ϵ ,
(20)
where ϵ is an acceptable level of cryptographic resistance. This formalized approach provides a
basis for building a software system that guarantees a high level of confidential access and can
adapt to modern information security requirements in computer networks. It combines theoretical
principles with practical cryptographic tools, allowing the implementation of attack-resistant
architectures with support for dynamic access policy, SIEM integration [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ], Zero Trust model [
        <xref ref-type="bibr" rid="ref17 ref23">17,
23</xref>
        ], and a multi-level resource hierarchy.
      </p>
      <p>To extend the formalized approach to building a software architecture for confidential access in
computer networks, mathematical models are used that take into account time dynamics,
multilevel trust, adaptability of access policies, and attack resistance. They are truly integrated with Zero
Trust mechanisms and analytical capabilities of SIEM systems, creating a flexible and secure
information processing platform. Dynamic privacy assurance feature:</p>
      <p>Aconf ( s , o , t )= α ∙ Access ( s , o )∙ e− λt,</p>
      <p>The formula estimates the level of confidential access of a subject s to an object o at the
moment of time t, where α is the weighting factor of the resource’s criticality, λ is the threat
intensity, Access ( s , o ) is the access permission (1 or 0). The exponential decay reflects the loss of
trust in the resource over time.</p>
      <p>Effective level of access of an entity:
where f ( u , t ) is the user behavior function u, β is the sensitivity of the SIEM algorithm. This
model takes into account changes in behavior to predict potential threats. Probability of anomaly
detection P anomaly ( u , t ) assesses how likely the system is to detect suspicious user behavior u at
the time t, taking into account the intensity of deviations f ( u , t ) and sensitivity of the SIEM
mechanism β .</p>
      <p>
        Assessment of user confidence [
        <xref ref-type="bibr" rid="ref14 ref20">14, 20</xref>
        ]:
      </p>
      <p>Q trust ( s )= ω 1 ∙ Aut h ( s )+ ω 2 ∙ Hist ( s )+ ω 3 ∙ SIEM ( s ),
(25)
τ policy ( t )=
dC ( t ) =− λ ∙ e−λt,</p>
      <p>dt</p>
      <p>P anomaly ( u , t )=1−e−β ∙ f ( u ,t ),
where δ ( s , o )=1, if access is allowed, and 0 otherwise, g ( s , o ) is the access rank. The formula
summarizes the subject’s access levels to all allowed objects, determining the subject’s real
influence in the system.</p>
      <p>Privacy loss rate:</p>
      <p>The rate of privacy loss τ policy ( t ) shows how quickly the probability of maintaining data
confidentiality decreases over time. This indicator is used to dynamically adjust access policies in
accordance with the rate of information security loss.</p>
      <p>
        Probability of anomaly detection [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ]:
(21)
(22)
(23)
(24)
Assessment of user confidenceQ trust ( s ) is a formalized indicator that allows to quantify the level
of trust to the subject s in the system. It combines three main components: the result of
authentication Auth ( s ), behavioral access history Hist ( s ) nd signals received from the SIEM
monitoring system SIEM ( s ). Each component has its own weight ω i, that reflects its importance
in the overall assessment. This model allows for adaptive decision-making to allow or restrict
access, especially in environments that use Zero Trust principles.
      </p>
      <p>Privacy gradient in parameter space:</p>
      <p>D adj ( p , t )=∇ p C ( p , t ),
(26)</p>
      <p>Privacy gradient in the parameter space D adj ( p , t ) reflects how the level of confidentialityC of
a resource changes at a certain point in time t depending on its characteristics. This indicator
allows you to determine in which direction you need to change access or security parameters to
ensure a stable level of confidentiality. It is a useful tool for dynamically adjusting security policies,
especially in a changing environment or at increased risk.</p>
      <p>
        System resistance to crypto attacks [
        <xref ref-type="bibr" rid="ref9">9, 26</xref>
        ]:
ζ resilience= min { insec F ( t , q ) , insec CEPA ( t , q , l ) },
(27)
      </p>
      <p>The system’s resistance to cryptoattacks ζ resilience determines the worst-case security scenario by
comparing the vulnerability to general probabilistic attacks insec F ( t , q ) and chosen plaintext
attacks (CPA) insec CEPA ( t , q , l ). The minimum value among them is selected, which indicates the
least resistant component. The lower this indicator is, the higher the cryptographic reliability of
the system as a whole. It allows you to formally evaluate the effectiveness of encryption algorithms
and justify their suitability for use in a secure access architecture.</p>
      <p>Average effective privilege:
(28)
(29)
1 n</p>
      <p>∑ Access ( s i , oi ) ∙ r ( oi ),
Φ access= n i=1</p>
      <p>Average effective privilege Φ access allows you to quantify the overall level of access in the
system, taking into account both the fact of access granted and the sensitivity of each object r ( oi ).
The formula calculates the average value of privileges for all active access sessions, where each
contribution is weighted according to the level of confidentiality of the resource. A high value of
the indicator may indicate the risk of excessive access to sensitive objects, which requires increased
control.</p>
      <p>Privacy entropy is a formalized metric that allows to assess the uniformity of privacy
distribution among information objects in a computer network. It is determined using the Shannon
formula:</p>
      <p>❑
H conf = − ∑ ❑ P ( oi ) ∙ lo g2 P ( oi ),</p>
      <p>
        i
where P ( oi ) is the probability that an object contains or processes confidential information.
This indicator allows you to quantify how well the confidential resources are distributed within the
network. If the entropy is high, this indicates an even distribution of confidentiality, when no
single object concentrates a significant amount of critical information. On the other hand, a low
entropy value means that there are objects with an excessive concentration of confidential data,
and these objects are critically vulnerable to attacks or information leaks. This situation requires an
immediate review of security policies in order to redistribute the load, strengthen control, or isolate
the most risky objects. Thus, the privacy entropy indicator plays an important role in making
decisions on adaptive risk management, developing security zones, and determining priority areas
for the application of cryptographic protection and monitoring [
        <xref ref-type="bibr" rid="ref10 ref23">10, 23</xref>
        ]. It is an integral element of
a formalized approach to building a flexible, dynamic and stable architecture of a software system
for confidential access to information resources of computer networks. The Zero Trust policy
application index, defined as:
⋀ zerotrust ( u )=1−Q trust ( u ) ⋅ P anomaly ( u , t ),
(30)
formalizes the principle of dynamic management of user trust u in systems based on the Zero
Trust model [
        <xref ref-type="bibr" rid="ref17 ref21 ref23">17, 21, 23</xref>
        ]. In this model, trust is not granted to any user or device by default, and
each request is verified in the context of current behavior, action history, and analytical monitoring
results. The value of Q trust ( u ) reflects the level of accumulated trust in the subject based on
multifactor authentication, analysis of past user behavior, access history, and SIEM system
responses [
        <xref ref-type="bibr" rid="ref14 ref20">14, 20</xref>
        ]. At the same time P anomaly ( u , t ) simulates the probability of detecting
anomalous user actions at a certain point in time t, calculated on the basis of behavioral patterns
and risk profiles [
        <xref ref-type="bibr" rid="ref20">20</xref>
        ]. Index ⋀ zerotrust ( u ) actually describes the degree to which restrictive measures
should be applied to the user. The lower the trust in the user and the higher the likelihood of
anomalies, the higher the index value, meaning that the system should act more cautiously,
restricting or blocking access, introducing additional layers of verification (for example, additional
MFA or contextual confirmation). In the case of Q trust ( u ) → 1 , P anomaly ( u , t ) → 0, value of
⋀ zerotrust ( u ) → 1, indicating that there is no need for additional control, as the user demonstrates
stable, trusted behavior.
      </p>
      <p>
        Thus, the formula allows to implement an adaptive security policy that automatically adjusts
according to the current user behavior and trust assessment, which is a key element in the
implementation of a modern architecture of confidential access to computer networks [
        <xref ref-type="bibr" rid="ref17 ref20 ref21 ref23">17, 20, 21,
23</xref>
        ]. Thanks to this mechanism, the system becomes capable not only of responding to incidents but
also of proactively preventing threats by forming a real-time access policy taking into account
many risk factors, which significantly increases the overall level of information security.
      </p>
      <p>
        According to contemporary digital-security requirements, the architecture of a software system
for confidential access to the information resources of computer networks must provide flexibility,
scalability, and resistance to a wide range of attacks [
        <xref ref-type="bibr" rid="ref1 ref12">1, 12, 24</xref>
        ]. The central element of this
architecture is a modular platform built on secure network protocols, modern cryptographic
algorithms, and adaptive access-control mechanisms. The system comprises the following
components: an administrative console, information probes (event sensors), security controllers,
SIEM components for centralized event analysis, secure entry points with multi-factor
authentication, traffic repeaters for tunnelling requests through isolated zones, and modules for
processing requests to the information-storage subsystem [
        <xref ref-type="bibr" rid="ref13 ref17 ref21 ref23">13, 17, 21, 23</xref>
        ]. All of these elements
interact through secure channels based on TLS 1.3, IPsec, or WireGuard, with support for Perfect
Forward Secrecy.
      </p>
      <p>
        The administrative console enables administrators to manage access policies, configure
modules, and monitor incidents in real time. It communicates with other system components—
including security controllers, SIEM modules, entry points, and traffic repeaters—to ensure
operational management and rapid incident response. In emergency situations, alternative
communication channels allow direct control of critical infrastructure elements without the need
for intermediate services. Information probes continuously monitor user actions and suspicious
requests, transmitting these data to SIEM systems for analysis and event correlation [
        <xref ref-type="bibr" rid="ref14 ref20">14, 20</xref>
        ].
Security controllers verify access rights to resources, block unauthorized requests, and maintain
security levels in accordance with assigned ranks.
      </p>
      <p>
        The architecture devotes special attention to organising confidential access to data repositories.
Requests to such repositories are routed through isolated paths created by virtual private networks
(VPNs) that employ tunnelling cryptography [
        <xref ref-type="bibr" rid="ref12 ref13 ref18 ref19 ref20 ref8">8, 12, 13, 18, 19, 20</xref>
        ]. This approach minimises the
risks of interception, modification, or replay of data within the transmission channel. The system is
integrated with the Zero Trust security model, which operates on the principle of distrusting every
component by default. Each resource access is independently validated through multi-level
authorisation that includes contextual verification of user behaviour, analysis of prior actions, and
interaction with incident-handling mechanisms. Acting as the analytical core, the SIEM aggregates
security events, classifies them, and detects anomalies on the basis of behavioural models.
      </p>
      <p>
        To verify the reliability of the architecture, a formalised approach grounded in cryptanalytic
models is employed to estimate the probability of information disclosure, privacy degradation over
time, and the effectiveness of the implemented protocols. The system incorporates mathematical
mechanisms for access ranking, dynamic risk analysis, and assessment of resistance to plaintext
attacks, thereby confirming its high level of cryptographic robustness [
        <xref ref-type="bibr" rid="ref20 ref22">20, 22, 25, 27, 28</xref>
        ].
      </p>
      <p>Figure 5 presents an extended sequence diagram of the system that protects confidential access
to information resources in computer networks, illustrating a typical interaction scenario among
key components while reflecting the principles of Zero Trust, multi-factor authentication (MFA),
user-behaviour analysis, and cryptographic traffic protection. The process begins when a user
submits an access request through an entry point that enforces MFA and Zero Trust verification.
After authentication, behaviour analysis is performed, generating a risk score that is forwarded to
the Access Controller. The Access Controller conducts contextual authorisation, evaluates
applicable access policies, and then issues a decision to allow or deny access. All actions are logged
in the SIEM, and a denial automatically triggers an incident notification for administrators. If
access is granted, a secure tunnel (WireGuard/IPsec) is established, through which data are
exchanged with the information resource (Storage/API). These data remain encrypted during
transit, are decrypted on the user’s side, and all access events are recorded for subsequent audit.
The diagram thus clearly depicts the phased execution of a secure-access scenario for confidential
information, encompassing dynamic access policy enforcement, anomaly response,
communication-channel protection, and centralised monitoring.
The proposed architecture is suitable for scaling and adaptation both in local area networks and in
complex distributed infrastructures using cloud solutions. It allows implementing an integrated
security system that maintains the confidentiality, integrity and availability of data at all levels of
operation, ensuring resistance to modern threats and compliance with international information
security standards.</p>
    </sec>
    <sec id="sec-5">
      <title>Conclusions</title>
      <p>The study has developed an architecture for a software system that enables confidential access to
the information resources of computer networks while addressing current digital-security
challenges and supporting effective interaction in highly dynamic network environments. The
proposed system combines the concepts of Zero Trust, multilevel authorization, cryptographic
traffic protection, and the analytical capabilities of SIEM solutions for anomaly detection and
incident response. A formalized access-control model based on security ranking has been
implemented, allowing the quantitative assessment of information-object security levels. The
integrated mathematical mechanisms let security policies adapt in real time, taking into account
risk-oriented approaches and user-behaviour factors. The incorporation of modern cryptographic
protocols—TLS 1.3, IPsec, and WireGuard—guarantees resistance to transport-layer attacks, while
support for multifactor authentication mechanisms ensures a high level of user trust.</p>
      <p>Particular attention has been devoted to implementing anonymous access routes to information
resources through Mix-net technology and multilevel encryption mechanisms, thereby minimizing
the risk of traffic de-anonymization. Owing to its flexible, modular structure, the system can be
scaled to a variety of deployment scenarios—ranging from local networks to cloud platforms—
while supporting open interfaces and external software components.</p>
      <p>The proposed architecture not only formalizes secure-access processes but also creates an
adaptive environment for executing information-security strategies in real time. The system’s
practical value lies in its capability to integrate with existing information infrastructures and
satisfy industry standards (ISO/IEC 27001, NIST SP 800-207, etc.), making it suitable for protecting
critical information assets in the public, financial, educational, and medical sectors.</p>
      <p>Thus, the study’s results indicate that the developed architecture for the confidential-access
software system provides a high level of information security, robust resistance to contemporary
cyber threats, and the capacity to evolve further as digital-environment risks continue to develop.</p>
    </sec>
    <sec id="sec-6">
      <title>Declaration on Generative AI</title>
      <p>While preparing this work, the authors used the AI programs Grammarly Pro to correct text
grammar and Strike Plagiarism to search for possible plagiarism. After using this tool, the authors
reviewed and edited the content as needed and took full responsibility for the publication’s content.</p>
    </sec>
  </body>
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