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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Adaptive Methods for Embedding Digital Watermarks to Protect Audio and Video Images in Information and Communication Systems⋆</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Pavlo Skladannyi</string-name>
          <email>p.skladannyi@kubg.edu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <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>Bohdan Bebeshko</string-name>
          <email>b.bebeshko@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-Kudryavska str., 04053 Kyiv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Institute of Mathematical Machines and Systems Problems of the National Academy of Sciences of Ukraine</institution>
          ,
          <addr-line>42 Ac. Glushkov ave., 03680 Kyiv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <fpage>13</fpage>
      <lpage>31</lpage>
      <abstract>
        <p>This paper introduces an adaptive approach for embedding digital watermarks into image, audio, and video files to protect multimedia content within modern information and communication systems. The proposed method leverages the host signal's spectral, statistical, and perceptual properties to ensure high perceptual fidelity and robustness against various attacks, including compression, filtering, and geometric distortions. A mathematical model for the watermarking process, based on a secret key, has been developed; this model formalizes the procedures for watermark embedding and extraction while ensuring minimal perceptual distortion. The system architecture is implemented as a multi-agent framework incorporating cryptographic protection, open Application Programming Interfaces (APIs), and automated integrity verification modules. Comprehensive testing conducted on real-world multimedia data has confirmed the effectiveness of this approach. The proposed solution is suitable for application in various domains, including digital forensics, copyright protection systems, streaming platforms, and digital archiving.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;adaptive embedding</kwd>
        <kwd>digital watermarks</kwd>
        <kwd>multimedia content protection</kwd>
        <kwd>perceptual transparency</kwd>
        <kwd>data integrity</kwd>
        <kwd>steganography</kwd>
        <kwd>digital identification</kwd>
        <kwd>digital forensics</kwd>
        <kwd>information and communication systems</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>Introduction</title>
      <p>The rapid proliferation of digital multimedia content within information and communication
systems has intensified the need for robust methods to protect such data from counterfeiting,
unauthorized distribution, and loss of authenticity. This challenge is particularly acute for video
and audio content transmitted over open communication channels or stored in cloud
environments. To address these issues, digital watermarking (DWM) technologies have become a
key solution, providing mechanisms for digital identification, authorship verification, data integrity
control, and the tracking of content distribution sources.</p>
      <p>Digital watermarks are imperceptible or minimally perceptible data structures embedded within
a media object that convey auxiliary information—identifiers, hash values, or digital certificates —
without degrading the user’s perceptual experience. In contrast to conventional watermarking
schemes, which rely on static rules and predetermined parameters, adaptive methods dynamically
configure the embedding algorithm based on a local analysis of a specific segment’s properties
within the media file. This approach enables the dynamic adjustment of watermark parameters,
such as embedding depth, spectral characteristics, spatial position, and intensity, in response to the
signal’s energy spectrum, local image contrast, and models of human perception.</p>
      <p>Therefore, adaptive digital watermarking algorithms provide high imperceptibility
(imperceptible to human sight or hearing) and robustness to a wide range of attacks and
transformations, including JPEG and MP3 compression, filtering, cropping, scaling, and
reencoding, while ensuring minimal degradation of the original signal quality. Furthermore, there is
a pressing need to counteract emerging forms of content manipulation, particularly deepfake
technologies, neural reconstruction, and other generative models to create synthetic audio and
video materials. Such fabricated content can be deployed for phishing, cyber blackmail,
disinformation campaigns, or evidence tampering in digital forensics.</p>
      <p>
        This study aims to develop and implement an adaptive method for embedding digital
watermarks designed to protect audio and video content within information and communication
systems. The proposed approach leverages spectral and perceptual analysis, in addition to
statistical and neural network models, to optimize embedding parameters according to the specific
characteristics of each media object (e.g., image, sound, video) [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. This methodology results in an
increased resilience of the watermark to attacks, improved accuracy of its detection and
identification, and the preservation of the visual and acoustic quality of the digital content [
        <xref ref-type="bibr" rid="ref2 ref3">2, 3</xref>
        ].
      </p>
      <p>This study also formalizes the architecture of an adaptive software framework that comprises
modules for preprocessing, watermark embedding, detection, quality assessment, and integration
with information and communication protocols. The architecture is founded upon the principles of
modularity, scalability, and compatibility with common multimedia standards (e.g., H.264, AAC,
JPEG2000), enabling the implementation of the proposed algorithms in on-premises environments
and in cloud infrastructure or real-time streaming systems.</p>
      <p>Consequently, the developed adaptive digital watermarking methods provide an effective
solution for protecting multimedia content from unauthorized use, distortion, and loss of
authenticity, while preserving high perceptual quality and ensuring suitability for integrating
modern information and communication technologies.
2.</p>
    </sec>
    <sec id="sec-2">
      <title>Literature review</title>
      <p>
        Modern research in digital watermarking increasingly incorporates adaptive and neural
networkbased methods to enhance robustness against attacks while preserving the quality of multimedia
content. For instance, Taha, Ngadiran, and Ehkan [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] proposed an adaptive image watermarking
algorithm that utilizes an efficient perceptual map to model the human visual system’s sensitivity
to luminance changes. This algorithm exhibits high resistance to JPEG compression and geometric
transformations, making it an effective solution for protecting visual content within information
and communication systems.
      </p>
      <p>
        Quan et al. [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] focused on embedding digital watermarks directly into the parameters of deep
neural networks (DNNs) used for image processing. The authors demonstrated that DNNs can be
protected from unauthorized use by embedding specially encoded watermarks into the model’s
parameters, which provides a mechanism for both model identification and proof of ownership.
      </p>
      <p>
        Li and Yue [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] conducted a security analysis of a dual watermarking structure for multimedia
data and proposed enhancements to the framework to protect privacy and authenticity. Their work
highlights the effectiveness of combining visible and invisible watermarks to create multi-level
protection systems for applications in digital archives and streaming services.
      </p>
      <p>
        Chen et al. [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] proposed an adaptive watermarking method based on wavelet entropy
optimization in the audio domain. Their approach considers the entropy characteristics of the
signal across different scales, which allows for the dynamic identification of optimal embedding
regions while minimizing the impact on perceptual audio quality.
      </p>
      <p>
        Naseem et al. [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ] integrated fuzzy logic into the watermark embedding process, proposing an
intelligent decision-making model to optimize the placement of watermarks within images. Their
method enhances information security by adapting to local content characteristics and considering
the probability of potential attacks.
      </p>
      <p>This research confirms that the most effective multimedia information protection systems are
based on integrating adaptive strategies, statistical signal analysis, and artificial intelligence. This
synergy ensures high robustness, transparency, and authenticity for digital watermarks within the
evolving digital information environment.
3.</p>
    </sec>
    <sec id="sec-3">
      <title>Methods and models</title>
      <p>This study integrates theoretical and applied methodologies, encompassing mathematical
modeling, information security principles, and digital signal processing. The attack model
incorporated a comprehensive set of transformations based on the discrete cosine transform (DCT)
and the Fast Fourier Transform (FFT), geometric distortions such as scaling and rotation,
StirMarktype benchmark attacks, and neural network-based reconstructions.</p>
      <p>The adaptive embedding algorithm leverages the entropy characteristics, frequency-domain
power, and texture features of the multimedia signal, which are extracted using techniques such as
Gabor filters and wavelet analysis. Embedding regions are determined based on perceptual
visibility models and weight functions derived from a trained convolutional neural network (CNN).</p>
      <p>A Monte Carlo simulation with 1000 independent iterations was conducted to validate the
method’s effectiveness. Each iteration involved the random selection of a multimedia container (in
JPEG or WAV format), the generation of a unique embedding configuration, the determination of a
random embedding location, a variable embedding density (from 1 to 6), and a specific attack
scenario. The digital watermark was embedded and subsequently extracted in each iteration, and
the results were evaluated.</p>
      <p>Performance was assessed using a suite of quality metrics: Peak Signal-to-Noise Ratio (PSNR),
Structural Similarity Index (SSIM), Quality Index (Q-index), Bit Error Rate (BER), Normalized
Cross-Correlation (NCC), and Learned Perceptual Image Patch Similarity (LPIPS). A successful
extraction was defined as an iteration in which the recovery accuracy, τ, met or exceeded a
threshold of 0.98.
4.</p>
    </sec>
    <sec id="sec-4">
      <title>Main material</title>
      <p>Modern security tools and methods for ensuring the integrity of multimedia information are
rapidly evolving in response to the escalating threats of unauthorized access, content modification,
and copyright infringement within digital communication channels. A significant limitation of
many existing solutions is their reliance on static architectures with fixed processing algorithms,
which fail to account for the dynamic nature of the transmission environment or the specific
content characteristics.</p>
      <p>
        A comprehensive system for controlling the integrity of multimedia objects is typically
implemented as a software-hardware architecture comprising several key functional modules.
These include: an integrity verification module for authenticating digital signatures, calculating
hash functions, and verifying embedded watermarks [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]; a watermark management module capable
of adapting to the properties of the multimedia container and prevailing threats [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ]; a secure
storage module for managing metadata, cryptographic keys, version history, and access rights [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ];
and a logging subsystem that records all system events in a secure, auditable format for subsequent
analysis [
        <xref ref-type="bibr" rid="ref10 ref11 ref12 ref4 ref5">4, 5, 10–12</xref>
        ]. Interaction among these components is coordinated via a management
interface or a multi-agent environment that facilitates integration with external security platforms,
such as Security Information and Event Management (SIEM) systems, Digital Rights Management
(DRM) frameworks, and blockchain-based storage solutions like Non-Fungible Tokens (NFTs).
      </p>
      <p>
        Fig. 1 presents a contextual and structural Data Flow Diagram (DFD) model of an adaptive
digital watermarking system designed to protect image, audio, and video content within
information and communication systems. The architecture comprises five key functional
subsystems: a control interface and API, a content analysis module, an adaptive embedding module,
a verification module, and a secure repository for service data and logs [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ]. The processing
workflow is initiated when user requests are received by a session manager, where they undergo
initial validation. Subsequently, the data is forwarded to the content analysis module, which
assesses the multimedia object’s entropy, frequency-domain, and perceptual characteristics. Based
on these parameters, the embedding module generates a digital watermark and adaptively inserts it
into optimal container regions [
        <xref ref-type="bibr" rid="ref14 ref4 ref5 ref7">4, 5, 7, 14</xref>
        ]. The corresponding watermark metadata is stored in the
secure repository, and all operational events are systematically logged.
      </p>
      <p>
        To verify content integrity or authenticity, a user can initiate the verification process, during
which the system extracts the embedded watermark, compares it against the reference value, and
generates a corresponding response [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ]. Within the diagram, data flows are denoted by symbolic
labels (e.g., DataX, LogX, ResponseX), and the functional modules are visually demarcated by
colorcoded zones for enhanced clarity [
        <xref ref-type="bibr" rid="ref16">16, 17</xref>
        ]. The proposed architecture integrates adaptability,
modularity, and a high level of information security, which are critical for operation within a
dynamic digital environment.
      </p>
      <p>
        The application of adaptive digital watermarking methods, which leverage perceptual analysis
[
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], wavelet transforms [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ], artificial neural networks—specifically Convolutional Neural Networks
(CNNs) [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] and Long Short-Term Memory (LSTM) networks—and fuzzy logic [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ], facilitates the
implementation of a context-aware, scalable, and flexible system for protecting multimedia
information. The proposed model is highly effective in domains such as digital broadcasting [18],
video streaming, digital forensics, digital archiving, and the protection of digital art. In contrast to
traditional centralized solutions, this system establishes a distributed, adaptive architecture where
watermarking, identification, authentication, and integrity control are cohesively integrated into a
singular digital information security ecosystem.
      </p>
      <p>
        The escalating cybersecurity threats [19] to multimedia information necessitate a
comprehensive risk analysis of unauthorized access, distortion, forgery, and illicit audio, video, and
graphic content copying. This study presents a systematic classification of threats into primary
categories and proposes a feature-based model [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] that enables the analysis of potential attacks
without a complete formal description. This approach accounts for environmental dynamics, the
variability of attack vectors, and the complexities of identifying threats within open information
and communication systems.
      </p>
      <p>Fig. 2 presents a generalized scheme of classification features for multimedia threats, illustrating
a hierarchical structure of risks that affect multimedia information security within information and
communication systems. The threats are categorized into four primary groups: by context of
occurrence (e.g., intentional attacks, unintentional distortions), by channel of influence (e.g.,
network interference, hardware failures), by attack vector (e.g., content modification, extraction of
hidden information, insertion of malicious watermarks), and by enabling technology (e.g.,
compression artifacts, AI-based reconstruction, format conversion). This classification framework
enables a systematic analysis of the risks associated with multimedia processing and transmission.
It facilitates the development of adaptive digital watermarking strategies capable of effectively
countering a wide range of attacks in the contemporary digital environment.</p>
      <p>A formalized steganography model is defined as a set of two basic functions—embedding and
extraction:
1. F : M ∙ B ∙ K → B ' is an embedding function that correlates a message m ∈ M , an empty
container b ∈ B, and a secret key k ∈ K with a modified container b ' ∈ B ' .
2. F ' : B ' ∙ K → M is an extraction function that, given the modified container b ' and key
k recovers the original message m.</p>
      <p>Thus, an adaptive steganographic system is defined as the five F , F ' , M , B , K , where M is a
set of messages, B is a set of containers, K is a set of keys, F and F ' are embedding and extraction
algorithms, respectively. This allows us to formally describe the stage for generating a protected
media object and the procedure for verifying integrity or authenticity. This approach ensures
generalization of processes at the model level, which is necessary for building universal software
solutions. In addition, the system structure allows you to set adaptation parameters depending on
the type of content and threats. The formalization based on sets and functions also facilitates
integration with cryptographic protocols and access control mechanisms.</p>
      <p>A comparative analysis of patented and published solutions in digital watermarking has
revealed several systemic limitations of traditional methods that restrict their practical application.
Key disadvantages include the introduction of significant visual or acoustic distortions, the
presence of detectable embedding artifacts vulnerable to steganalysis, the potential for extracting
hidden data without key knowledge if the modified container is compromised, and a lack of
robustness against watermark substitution or distortion resulting from minor edits to the
multimedia file.</p>
      <p>
        In contrast, modern adaptive embedding methods which leverage perceptual modeling [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ],
wavelet analysis [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ], deep neural networks (CNNs, LSTMs) [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], and fuzzy logic [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ] provide minimal
distortion, a high degree of imperceptibility, resilience to modification attempts, and the ability to
adapt based on the container’s intrinsic characteristics contextually. This paves the way for
developing reliable, invisible, and dynamically controlled digital watermarking systems suitable for
deployment in open networks, streaming services, blockchain-based authentication, and digital
forensics. The adaptability of such systems allows for the automatic adjustment of embedding
parameters to suit different content types without compromising quality. Furthermore, using
neural network models enables the system to learn from real-world data and incorporate complex
perceptual features of signal processing, significantly increasing the watermark’s reliability and
expanding its scope of application within information and communication environments.
      </p>
      <p>Effective digital multimedia watermarking systems must account for a wide range of potential
attacks targeting both the steganographic methods and the embedded watermarks. Threats from
passive (e.g., observation, steganalysis) and active (e.g., modification, deletion, substitution)
adversaries operating within a dynamic digital environment pose significant challenges.</p>
      <p>Fig. 3 illustrates the structural architecture of an adaptive digital watermark embedding system
designed to protect image, audio, and video content within information and communication
systems. The diagram outlines the primary stages of the watermarking lifecycle: message
encryption using the Advanced Encryption Standard (AES) symmetric block cipher; integrity tag
generation via a Hash-based Message Authentication Code (HMAC); adaptive embedding into the
multimedia container; transmission over a channel susceptible to potential threats; and subsequent
extraction, verification, and decryption on the recipient’s side. The architecture also accommodates
the integration of auxiliary components, including a Digital Rights Management (DRM) module, a
Security Information and Event Management (SIEM) system, and an event logging subsystem. All
data flows within the system are labeled with unique identifiers (e.g., Data1-Data11, Log1-Log4,
Auth1) to provide clear visibility into the interaction logic and enhance the transparency of
information process control. This comprehensive architecture ensures robust protection,
scalability, and ease of integration into modern digital environments.</p>
      <p>
        Assessing the resilience of such systems necessitates a comprehensive approach. This study
employs attack models based on extended threat matrices, encompassing various types of
interference, modification intensities, and access to keys and data [
        <xref ref-type="bibr" rid="ref4 ref5">4, 5</xref>
        ]. Evaluation methodologies
include classical metrics such as BER, NCC, and PSNR, modern metrics derived from perceptual
responses, receiver operating characteristic (ROC) curves, and simulation testing using adversarial
attacks generated by neural networks. Additionally, scenarios of subtle influence are considered,
where modifications do not directly lose the watermark but gradually degrade its detectability
under challenging conditions.
      </p>
      <p>
        As a result of this research, mathematical models and adaptive methods for monitoring the
integrity of multimedia information, based on the covert embedding and extraction of digital
watermarks, have been developed [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ]. The core element of this framework is a model of the
multimedia container’s “naturalness,” which provides a statistical assessment of changes
introduced by the embedded watermark. This model accounts for both the media file type (image,
audio, or video) and the specifics of its storage format, thereby enabling increased accuracy in
detecting unauthorized modifications without significantly impacting the perceptual quality of the
content.
      </p>
      <p>
        A key feature of the model is the concept of hiding space, a linearized sequence of elements of a
multimedia container suitable for marking, determined based on the signal’s type, format, and
perceptual significance [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ]. For each container, the hiding space is analyzed and described by a
parametric naturalness vector:
→
f =( f 0 , f 1 , … , f n ) , n ∈ N ,
      </p>
      <p>P ij = P ( s iH −s iL ) ,
n
P ( l i )= i , l i ∈ { 1,2 , … , 2k } .</p>
      <p>∑ n
P ( k i )= mi ,</p>
      <p>∑ m
where each parameter belongs to one of three groups.</p>
      <p>Statistical analysis of paired elements of the hiding space—evaluates the distribution of
differences between the high and low bits of the elements:
where ( s iH −s iL ) are the high and low bits of the elements, respectively.</p>
      <p>Frequency analysis of bit series—determines the probability of occurrence of a bit series of
length l in the hiding space:
(1)
(2)
(3)
(4)</p>
      <p>Analysis of the lengths of identical bit sequences—the probability of a series with identical bits:
where mi is the number of series of length i .</p>
      <p>Based on this model, adaptive methods for embedding and extracting digital watermarks have
been developed that depend on the secret key k ∈ K , which uniquely determines how the mark is
placed in the hiding space. The embedded bits are distributed according to the patterns generated
from the key sequence, ensuring uniformity and attack resistance. This approach makes it
impossible to reproduce or modify the mark without knowing the key and minimizes the likelihood
of an attacker localizing the marking structure. In addition, the dependence of the embedding
positions on the key ensures cryptographic reliability and makes it easy to scale the system to fit
different container sizes. In the event of an attempt to remove or edit the watermark, the system
reacts with a loss of correctness during authentication, which allows you to identify the fact of
interference quickly.</p>
      <p>The function describes the direct adaptive steganographic transformation:</p>
      <p>F : M ∙ B ∙ K → B ' , b'i = { mi , if k i−1=sh bi , otherwise ,
(5)
where F is an adaptive embedding function that may depend on spectral (DCT), wave (DWT), or
spatial (LSB) criteria, M is a set of messages to be embedded, B is a set of containers, K is a set of
keys, bi is the element of the original container’s hiding space, b'i are elements of the modified
container, mi are bits of the embedded message, k i are blocks of the key sequence generated from
the secret key, s h mask template that defines the places for embedding. Thus, the adaptive
steganographic system dynamically generates the space for embedding based on statistical and
structural features of the signal, while ensuring a high level of transparency, integrity, and
cryptographic strength when transmitting multimedia data in open networks.</p>
      <p>Fig. 4 shows a spatial vertical model of the embedding F and extraction F′, functions that
implement adaptive digital watermarking in multimedia containers. Visually, the diagram is
divided into three zones: input data (left), processing logic (center), and results (right). In the
process of embedding, a message m is hidden in the elements of a container bi using a key
sequence k i according to a template rule. The extraction of information follows a similar pattern,
with the message being recovered from the modified container b'i. Data and key flows are defined
and labeled for all stages, which ensures a transparent formalization of the process and increases
the system’s reproducibility.</p>
      <p>
        Integrity control is realized through adaptive embedding of digital watermarks, which allows
you to verify the authenticity of a multimedia container without the need to store separate control
hashes or reference copies. The method uses cryptographic hash functions that provide data
verification in the presence of only a modified container and a secret key [
        <xref ref-type="bibr" rid="ref13 ref8">8, 13</xref>
        ]. This approach
significantly reduces computational and resource costs, simplifies the integrity control procedure,
and increases the system’s adaptability to the dynamic conditions of the digital environment.
      </p>
      <p>
        Solving the problem of building a model for assessing the distortions introduced during the
embedding of a digital watermark and methods for their quantitative analysis is the content of a
separate research stage. The quality of a multimedia container is assessed using the distance metric
between the original (unmodified) container I and the modified (embedded) container O , which is
formalized as [
        <xref ref-type="bibr" rid="ref4">4, 20</xref>
        ]:
      </p>
      <p>q = K ( I , O ) ,
where K is the generalized similarity metric function (e.g., SSIM, PSNR, VMAF, NCC, etc.).</p>
      <p>The proposed quality model is presented as a set of indicators:</p>
      <p>S = { f i ( I , O ) ∨ i =1 , … , n } ,
(7)
where n is the model dimension, f i is the corresponding quality metric. For a specific type and
format of a multimedia container (image, audio, video), the optimal subset of relevant criteria is
selected:</p>
      <p>Θ = { f i ( I , O ) ∨ I , O ∈ B } ,
where B is a set of valid multimedia data formats.</p>
      <p>
        To ensure cryptographic security, a key function is used G [
        <xref ref-type="bibr" rid="ref13 ref6">6, 13</xref>
        ]:
      </p>
      <p>K → k = { k 1 , k 2 , … , k n } ,
k i = HMA C K ( i ||t ||UID ) , i ∈ N , t =timestamp , UID =user_id}.</p>
      <p>To guarantee confidentiality, the message m is encrypted before embedding using AES:
c = AES k ( m ) , c → is embedded instead of m .</p>
      <p>The pull function F ' : B ' ∙ K → M is defined as:</p>
      <p>mi = { F ( b'i ) ' , if k i−1=sh ⊥ , otherwise ,
where ⊥ is a marker indicating the absence of an embedded bit in this element.</p>
      <p>Verification is performed using the integrity function:</p>
      <p>Valid = { true ' , if HMAC K ( c )=stored_tag false, otherwis</p>
      <p>A composition of functions can describe the complete adaptive labeling process:
where Enc is a function of message encryption before embedding.</p>
      <p>After extracting the recovered message:
where Dec is an AES decryption.</p>
      <p>Reverse quality and compliance checks can be performed:</p>
      <p>W ( M , B , K , sh )= { b'1 , … , b'n } ,
b'i = F ( Enc ( mi ) , bi , k i ) ,
mi = Dec ( F ' ( b'i ) ) ,</p>
      <p>n
Match ( m , ^m)= ∑ δ ( mi =^mi ) /n ≥ τ ,
i=1
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
where τ is a threshold value of recovery accuracy (for example, 0.99).</p>
      <p>
        The proposed formalized approach provides a transparent mathematical model for operating an
adaptive digital watermarking system. It demonstrates its practical suitability for deployment in
dynamic information and communication systems [
        <xref ref-type="bibr" rid="ref5">5, 18, 21</xref>
        ]. Key application scenarios include
video streaming platforms, digital archives, and distributed authentication infrastructures. A
quantitative quality assessment model is essential for generating a comprehensive numerical
characterization of the embedding’s impact, which enables an objective determination of the
degree of degradation in the perceptual quality of the content and provides a feedback mechanism
for controlling the effectiveness of the adaptive watermarking process.
      </p>
      <p>
        An architecture for an adaptive software framework for maintaining the integrity of multimedia
information has been developed, founded upon a digital watermarking model [
        <xref ref-type="bibr" rid="ref10 ref9">9, 10, 22–24</xref>
        ]. This
architecture employs software agents to implement the embedding of digital watermarks and to
perform integrity verification, particularly in environments with an elevated risk of unauthorized
modifications, copying, or loss of content authenticity. The framework’s functional architecture is
based on the interaction of six specialized agents, each performing a distinct role in protecting
multimedia information [
        <xref ref-type="bibr" rid="ref11">11, 25</xref>
        ]. The Control and Management Agent coordinates the overall
system operation, configures parameters, and monitors subsystem status. The Information Storage
Agent provides secure storage for multimedia objects along with control signatures and metadata.
Communication, request routing, and centralized processing logic are implemented by the Control
Agent. The Registration Agent is responsible for registering new objects and embedding them with
watermarks and integrity codes, while the Cloning Agent creates uniquely identified copies to
track their distribution. The Integrity Analysis and Control Agent completes the architecture,
which audits containers in both internal storage and external environments by comparing
extracted watermarks with reference values to verify authenticity.
      </p>
      <p>
        Each agent is constructed using a modular architecture, comprising a main software module and
a set of functional components with a clear distinction between mandatory modules (required for
basic operation) and optional modules (which can be connected based on media type, security
policy, or user requirements) [
        <xref ref-type="bibr" rid="ref10">10, 17, 24, 26</xref>
        ]. This design ensures the framework’s flexibility,
scalability, and adaptability. Fig. 6 illustrates this component architecture, showing the six
functional agents distributed across logically isolated zones. Color zoning is used within the
diagram to visually demarcate each module’s functional roles.
      </p>
      <p>
        A software framework has been developed to ensure the integrity of multimedia information
using adaptive digital watermarking, with a focus on modern graphic (JPEG, PNG), audio (WAV,
MP3), and video (MP4, MKV) formats [
        <xref ref-type="bibr" rid="ref13">13, 17, 18, 25, 26</xref>
        ]. The architecture of this framework is
implemented using a modular approach and contemporary development tools, including Microsoft
Visual Studio Code, the C++17/20 and Python programming languages, and the OpenCV, FFmpeg,
and TensorFlow libraries [22, 23]. Scalability and flexibility are achieved through a containerized
architecture based on Docker with support for open REST APIs.
      </p>
      <p>
        Structurally, the framework is composed of four primary agents. A management and
monitoring agent coordinates inter-component interaction, configures security settings, and
maintains event logs supporting SIEM/SOAR systems [
        <xref ref-type="bibr" rid="ref11 ref14 ref9">9, 11, 14</xref>
        ]. The storage agent provides secure
storage for media containers using platforms such as Amazon S3 or MinIO and performs integrity
checks based on checksums [21]. A multimedia registration agent conducts the initial embedding of
the digital watermark, accounting for the container’s statistical characteristics, and generates
control hash codes [
        <xref ref-type="bibr" rid="ref14">14, 25–27</xref>
        ]. Finally, an integrity control agent performs regular audits of
content changes by comparing stored checksums with current ones using HMAC and SHA-256
algorithms [
        <xref ref-type="bibr" rid="ref13">13, 27</xref>
        ] and anomaly detection tools.
      </p>
      <p>
        A suite delivers the system’s functionality through specialized modules. A cryptographic
protection module (crypto_module) implements adaptive encryption based on AES-256 and
HMAC-SHA256, while a watermark insertion/extraction module (adaptive_stego) provides
adaptive embedding using DCT, FFT, and LSB methods [24]. A container naturalness evaluation
module (perceptual_model) analyzes perceptual quality using SSIM, PSNR, and the modern LPIPS
metric, while a distortion evaluation module (distortion_eval) determines acceptable modification
levels that do not compromise quality [
        <xref ref-type="bibr" rid="ref14 ref16">14, 16, 20</xref>
        ]. A key sequence generation module (keygen)
produces cryptographically secure keys based on user identifiers, timestamps, and random
variables. The entire system is engineered to ensure high stability, reliability, and adaptability for
security measures in digital information and communication systems.
      </p>
      <p>
        To evaluate the effectiveness of the developed method, a test sample was formed, comprising
1,000 JPEG images and 1,000 WAV audio files [
        <xref ref-type="bibr" rid="ref7">7, 17</xref>
        ]. Adaptive embedding of digital watermarks
was performed with a variable insertion density ranging from 1 to 6 bits per block. The
experimental results demonstrated that at an insertion density exceeding 4 bits per block, high
perceptual quality is maintained, with the Structural Similarity Index Measure (SSIM) surpassing
0.98 and the Perceptual Evaluation of Speech Quality (PESQ) exceeding 4.1 [ 25]. These findings
indicate that the embedded watermark has a minimal impact on the naturalness of the multimedia
content.
      </p>
      <p>
        The results of the experimental study confirm that the proposed method demonstrates high
efficacy with minimal impact on the perceptual quality of the multimedia content. This conclusion
is supported by stable values for the Structural Similarity Index Measure (SSIM) and Perceptual
Evaluation of Speech Quality (PESQ) metrics [20]. The adaptive approach facilitates an optimal
balance between watermark robustness against modifications and preserving the perceptual quality
of images, audio, and video [
        <xref ref-type="bibr" rid="ref13">13, 18</xref>
        ]. Consequently, the proposed methods provide reliable
protection for multimedia content within digital information and communication systems without
significantly degrading visual or auditory quality.
      </p>
      <p>
        Fig. 6 presents a Data Flow Diagram (DFD) of the adaptive multimedia integrity control
software framework, which is architected around the interaction of four specialized agents: a
control and monitoring agent, a storage agent, a multimedia registration agent, and an integrity
verification agent. The user initiates the configuration process via the control agent, which
orchestrates the interaction among all other system components [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]. The registration agent is
responsible for embedding a digital watermark using adaptive methods, including the discrete
cosine transform (DCT), the fast Fourier transform (FFT), and the least significant bit (LSB)
technique [
        <xref ref-type="bibr" rid="ref14 ref16">14, 16</xref>
        ]. The resulting control hash codes are transmitted to the storage agent, which
records them in a secure file environment, such as Amazon S3 or MinIO [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ]. The integrity
verification agent conducts periodic audits of multimedia objects, employing HMAC-SHA256
cryptographic algorithms and artificial intelligence models to detect anomalies [18]. The results of
these verifications are returned to the central management agent for analysis and subsequent
action. The system’s modular structure ensures flexibility, scalability, and automated quality
control, enabling it to adapt to various multimedia data formats within information and
communication systems.
      </p>
      <p>The implemented system validates the effectiveness of modern approaches to the embedding
and controlling digital watermarks, confirming its suitability for integration into information and
communication systems to ensure the digital authenticity, integrity, and protection of multimedia
objects.</p>
      <p>Within a simulation modeling framework implemented using the Monte Carlo method, a
comparative analysis was conducted to evaluate the effectiveness of the proposed adaptive
watermarking method against standard approaches, specifically those based on the least significant
bit (LSB) and static insertion using the discrete cosine transform [17, 19, 21, 26, 27]. The Monte
Carlo method was employed to simulate many random scenarios for embedding watermarks into
multimedia containers, which facilitated an assessment of the methods’ stability and quality under
variable input conditions. The container (JPEG or WAV), embedding density (from 1 to 6 bits per
block), watermark position, and attack type were selected randomly in each simulation. This
approach provides a statistically robust evaluation of effectiveness, enabling the determination of
average values for key metrics such as SSIM, PESQ, and BER, as well as their stability under
realworld conditions.</p>
      <p>Based on the simulation results, a heatmap was constructed to illustrate the dependence of the
Structural Similarity Index Measure (SSIM) on both the multimedia container format (JPEG or
WAV) and the digital watermark embedding density [22]. This visualization facilitates an
evaluation of the impact of these embedding parameters on perceptual content quality across a
wide range of conditions. The results indicate that at embedding densities up to 4 bits per block,
the proposed adaptive method maintains high imperceptibility (SSIM &gt; 0.98) and a low bit error
rate (BER &lt; 0.02), significantly outperforming classical LSB and static DCT-based watermarking
methods [25–27]. Furthermore, the average processing time remains within limits that are suitable
for practical implementation in real-time information and communication systems.</p>
      <p>
        Fig. 8 presents a heatmap illustrating the relationship between the Structural Similarity Index
Measure (SSIM), the multimedia container type (JPEG images and WAV audio), and the digital
watermark embedding density (ranging from 1 to 6 bits per element). The color scale represents the
degree of structural integrity preservation, where SSIM values approaching 1.000 signify nearly
imperceptible distortions introduced by the watermarking process. The results indicate that the
adaptive method maintains high perceptual quality (SSIM &gt; 0.98) at embedding densities up to 4
bits per element for both image and audio containers. A further increase in density to the 5–6 bit
range results in a slight decrease in SSIM values, indicating the emergence of noticeable perceptual
artifacts [
        <xref ref-type="bibr" rid="ref13">13, 17, 26, 27</xref>
        ]. These findings confirm the effectiveness of the proposed approach,
demonstrating that adaptive digital watermarking achieves an optimal balance between robustness
against modifications and the preservation of visual and acoustic quality in multimedia content.
      </p>
      <p>Fig. 9 presents a graph illustrating the dependence of the Structural Similarity Index Measure
(SSIM) on the digital watermark embedding density for two multimedia container formats: JPEG
(image) and WAV (audio). As the embedding density increases from 1 to 6 bits per element, a
gradual decrease in SSIM values is observed, corresponding to an increase in perceptual distortions.</p>
      <p>Despite a high embedding density of up to 6 bits per unit of information, testing demonstrates
that the SSIM values—an indicator of structural similarity between the original and watermarked
signals—remain high, exceeding a threshold of 0.95. This indicates that even with intensive data
embedding, the adaptive algorithm maintains high perceptual fidelity without compromising the
visual or acoustic quality of the content. This level of transparency is critical for applications in
information and communication systems, where multimedia data quality is crucial for the end user.</p>
      <p>Particular attention is given to a comparative analysis of watermarking effectiveness in
different container types, specifically graphic (JPEG) and audio (WAV) formats. The results show
that WAV audio containers provide greater robustness for embedded watermarks, particularly
against attacks such as re-encoding, filtering, and noise addition. This is attributable to the higher
internal redundancy and lossless nature of WAV files, which affords greater flexibility for
embedding data without a significant risk of corruption. Furthermore, the spectral characteristics
of audio signals in the WAV format are more stable and predictable than the high-frequency
components of JPEG images, which are highly susceptible to quantization during compression,
allowing the watermark to remain intact even after subsequent signal transformations.</p>
      <p>On the other hand, despite their ubiquity, JPEG graphic containers possess less redundancy,
especially in the high-frequency regions of an image that are often aggressively quantized or
distorted during compression. This creates significant challenges for preserving the embedded
watermark, as some data bits may be destroyed or altered. In this context, an adaptive
watermarking approach that analyzes the local properties of the container—such as texture
complexity, luminance, and contrast—enables the selection of optimal embedding regions that are
most resilient to alterations from digital processing.</p>
      <p>The built-in mechanism for the dynamic adjustment of parameters, including embedding depth,
masking coefficients, and spatio-spectral localization, allows the adaptive technique to demonstrate
high flexibility and stability in both the visual and acoustic domains. This not only preserves the
integrity of the watermark but also ensures that the content meets the requirements of perceptual
transparency and the absence of perceptible visual or auditory artifacts.</p>
      <p>The graph in Fig. 10 compares digital watermark stability in JPEG, WAV, and MP3 formats
when using classical versus adaptive methods. The results show that adaptive approaches provide
superior watermark preservation, particularly in the WAV format, which is attributed to the
container’s internal redundancy and stable spectral properties.</p>
      <p>The generalized results confirm the adaptive digital watermarking algorithm’s superiority in
protecting multimedia content within modern information and communication systems. Its
capacity to maintain high SSIM values even under aggressive embedding conditions, combined
with its enhanced stability in audio formats—particularly WAV—compared to JPEG graphics,
underscores the viability of this approach for practical applications in digital identification,
authorization, and media protection in open networks.</p>
    </sec>
    <sec id="sec-5">
      <title>Discussion</title>
      <p>Despite an intensive embedding density of up to 6 bits per data unit, experimental results confirm
that the media content’s high visual and acoustic quality is preserved. In particular, the Structural
Similarity Index Measure (SSIM), a metric used to assess the similarity between original and
modified image or video frames, remains consistently high, exceeding 0.95. This indicates that the
proposed adaptive method does not introduce significant distortions into the signal’s structure,
thereby preserving its naturalness and rendering the changes imperceptible to the user. This is a
critical feature for practical applications in information and communication systems where
perceptual quality is a priority.</p>
      <p>An additional comparative analysis of watermark robustness across different media container
types revealed that WAV audio files provide a more resilient environment for watermark
integration than JPEG graphic images. This can be attributed to several key factors. First, WAV
containers possess a significantly higher degree of internal redundancy, which provides
lowentropy regions suitable for inconspicuous embedding without disrupting the overall signal
structure. Second, the spectral characteristics of audio signals in the WAV format are more stable
and less sensitive to local alterations, allowing the embedded information to be preserved even
after subsequent processing or playback.</p>
      <p>In contrast, JPEG containers, despite their prevalence, are more vulnerable to watermark
information loss due to the inherent nature of lossy compression algorithms. This is particularly
true for high-frequency components, which are often aggressively quantized during encoding,
making it difficult to maintain a stable watermark. In this context, adaptive methods demonstrate
their advantages through their ability to dynamically select optimal embedding regions by
analyzing local signal properties such as energy, texture features, or spectral density. This allows
for an optimal balance between robustness, imperceptibility, and embedding capacity.</p>
      <p>Thus, adaptive methods of embedding digital watermarks demonstrate high efficacy for both
image and audio files, ensuring robustness against distortion, maintaining high SSIM values, and
proving their suitability for practical implementation in a wide array of digital content protection
systems, including multimedia platforms, streaming services, authorization systems, and digital
forensics.</p>
    </sec>
    <sec id="sec-6">
      <title>Conclusions</title>
      <p>This paper presents a comprehensive, adaptive method for embedding digital watermarks to
protect image, audio, and video files within information and communication systems. The
proposed approach is founded upon leveraging the multimedia signal’s statistical, spectral, and
perceptual characteristics, ensuring the embedding process’s dynamic adaptation according to the
content type and specific processing conditions.</p>
      <p>The developed mathematical model formally describes the watermark embedding and extraction
processes, ensuring their robustness against primary attack vectors, including compression,
geometric distortions, and neural network-based attacks. The proposed software architecture is
implemented as a scalable, multi-agent system featuring support for logging mechanisms,
cryptographic protection (AES, HMAC), SIEM/DRM infrastructure integration, and artificial
intelligence modules for assessing perceptual quality.</p>
      <p>The results of practical testing on a large sample of JPEG and WAV files demonstrate the high
efficacy of the approach. At an embedding density of up to 4 bits per block, the SSIM value exceeds
0.98, indicating that high perceptual quality is maintained while ensuring watermark integrity.
Importantly, the authentication procedure is blind, requiring only the watermarked container and
the secret key, thus obviating the need to store a reference copy.</p>
      <p>The proposed solution holds significant practical value for applications in digital forensics,
copyright protection, video streaming, and distributed digital authentication systems. Future work
will incorporate blockchain technologies to create an immutable audit trail of watermarking
events, extend support to modern video streaming formats such as HLS and MPEG-DASH, and
integrate Explainable AI (XAI) models for integrity verification within critical information
infrastructure environments.</p>
      <p>Despite the positive results, this study has several limitations. Specifically, the method’s
robustness against re-encoding into modern video formats like H.265 and AV1 and its efficacy in
the presence of active noise associated with transcoding or hardware recording artifacts were not
evaluated. Future research will be directed at overcoming these limitations and developing
intelligent, adaptive schemes for the real-time verification of digital watermarks.
Declaration on Generative AI
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.
[17] P. Kadian, S. M. Arora, N. Arora, Robust digital watermarking techniques for copyright
protection of digital data: A survey, Wireless Pers. Commun. 118(4) (2021) 3225–3249.
doi:10.1007/s11277-021-08177-w
[18] P. Aberna, L. Agilandeeswari, Digital image and video watermarking: Methodologies, attacks,
applications, and future directions, Multimed. Tools Appl. 83(2) (2023) 5531–5591.
doi:10.1007/s11042-023-15806-y
[19] A. Saini, S. Bhardwaj, A review on digital video watermarking security: Significance and
persistent challenges, in: Int. Conf. on Trends in Quantum Computing and Emerging Business
Technologies, Pune, India, 2024, 1–8, doi:10.1109/TQCEBT59414.2024.10545079
[20] Z. Wang, et al., Deep image steganography using transformer and recursive permutation,</p>
      <p>Entropy, 24, 2022, 878. doi:10.3390/e24070878
[21] R. R. Sunesh Kishore, A. Saini, Optimized image watermarking with artificial neural networks
and histogram shape, J. Inf. Optim. Sci. 41(7) (2020) 1597–1613. doi:10.1080/02522667.
2020.1802131
[22] Y. Kostiuk, et al., Information and intelligent forecasting systems based on the methods of
neural network theory, in: IEEE Int. Conf. on Smart Information Systems and Technologies
(SIST), 2023, 168–173. doi:10.1109/SIST58284.2023.10223499
[23] B. Jagadeesh, D. Praveen Kumar, Fuzzy-neuro based robust digital image watermarking
technique, Int. J. Adv. Res. Comput. Commun. Eng. 3(7) (2014) 7380–7385.
[24] A. Kumar, T. V. Narayana Rao, Digital image watermarking using fuzzy logic and genetic
algorithm, Int. J. Comput. Trends Technol. 41(2) (2016) 101–105.
[25] S. J. Horng, et al., An adaptive watermarking scheme for e-government document images,</p>
      <p>Multimed. Tools Appl. 72 (2014) 3085–3103. doi:10.1007/s11042-013-1579-5
[26] A. Attaullah Javeed, et al., Watermarking technique for copyright protection of digital images
using coupled differential equations, Multimed. Tools Appl. 84 (2025) 11027–11039.
doi:10.1007/s11042-024-19337-y
[27] P. Bhinder, N. Jindal, K. Singh, An improved robust image-adaptive watermarking with two
watermarks using statistical decoder, Multimed. Tools Appl. 79 (2020) 183–217.
doi:10.1007/s11042-019-07941-2</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <given-names>V.</given-names>
             
            <surname>Dudykevych</surname>
          </string-name>
          , et al.,
          <article-title>Detecting deepfake modifications of biometric images using neural networks</article-title>
          ,
          <source>in: Workshop on Cybersecurity Providing in Information and Telecommunication Systems (CPITS)</source>
          ,
          <volume>3654</volume>
          ,
          <year>2024</year>
          ,
          <fpage>391</fpage>
          -
          <lpage>397</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <given-names>B.</given-names>
             
            <surname>Zhurakovskyi</surname>
          </string-name>
          , et al.,
          <article-title>Modifications of the correlation method of face detection in biometric identification systems</article-title>
          ,
          <source>in: Cybersecurity Providing in Information and Telecommunication Systems</source>
          ,
          <volume>3288</volume>
          ,
          <year>2022</year>
          ,
          <fpage>55</fpage>
          -
          <lpage>63</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <given-names>Y.</given-names>
             
            <surname>Dreis</surname>
          </string-name>
          , et al.,
          <article-title>Restricted information identification model</article-title>
          ,
          <source>in: Cybersecurity Providing in Information and Telecommunication Systems</source>
          ,
          <volume>3288</volume>
          ,
          <year>2022</year>
          ,
          <fpage>89</fpage>
          -
          <lpage>95</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <given-names>T.</given-names>
             B. 
            <surname>Taha</surname>
          </string-name>
          ,
          <string-name>
            <surname>R.</surname>
          </string-name>
           Ngadiran,
          <string-name>
            <surname>P.</surname>
          </string-name>
           Ehkan,
          <article-title>Adaptive image watermarking algorithm based on an efficient perceptual mapping model</article-title>
          ,
          <source>IEEE Access 6</source>
          ,
          <year>2018</year>
          ,
          <fpage>66254</fpage>
          -
          <lpage>66267</lpage>
          . doi:
          <volume>10</volume>
          .1109/ACCESS.
          <year>2018</year>
          .2878456
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>Y.</given-names>
             
            <surname>Quan</surname>
          </string-name>
          , et al.,
          <article-title>Watermarking deep neural networks in image processing</article-title>
          ,
          <source>IEEE Trans. Neural Netw. Learn. Syst</source>
          .
          <volume>32</volume>
          (
          <issue>5</issue>
          ) (
          <year>2021</year>
          )
          <fpage>1852</fpage>
          -
          <lpage>1865</lpage>
          . doi:
          <volume>10</volume>
          .1109/TNNLS.
          <year>2020</year>
          .2991378
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <given-names>M.</given-names>
             
            <surname>Li</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Y.</given-names>
             
            <surname>Yue</surname>
          </string-name>
          ,
          <article-title>Security analysis and improvement of dual watermarking framework for multimedia privacy protection and content authentication</article-title>
          , Math.
          <volume>11</volume>
          (
          <issue>7</issue>
          ) (
          <year>2023</year>
          )
          <article-title>1689</article-title>
          . doi:
          <volume>10</volume>
          .3390/math11071689
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <given-names>S.</given-names>
             T. 
            <surname>Chen</surname>
          </string-name>
          , et al.,
          <article-title>Adaptive audio watermarking via the optimization point of view on the wavelet-based entropy</article-title>
          ,
          <source>Digit. Signal Process</source>
          .
          <volume>23</volume>
          (
          <year>2013</year>
          )
          <fpage>971</fpage>
          -
          <lpage>980</lpage>
          . doi:
          <volume>10</volume>
          .1016/j.dsp.
          <year>2012</year>
          .
          <volume>12</volume>
          .013
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <given-names>M.</given-names>
             T. 
            <surname>Naseem</surname>
          </string-name>
          , et al.,
          <article-title>Optimal secure information using digital watermarking and fuzzy rule base</article-title>
          ,
          <source>Multimed. Tools Appl</source>
          .
          <volume>78</volume>
          (
          <year>2019</year>
          )
          <fpage>7691</fpage>
          -
          <lpage>7712</lpage>
          . doi:
          <volume>10</volume>
          .1007/s11042-018-6501-8
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <given-names>Y.</given-names>
             
            <surname>Kostiuk</surname>
          </string-name>
          , et al.,
          <article-title>A system for assessing the interdependencies of information system agents in information security risk management using cognitive maps</article-title>
          ,
          <source>in: Cyber Hygiene &amp; Conflict Management in Global Information Networks</source>
          ,
          <volume>3925</volume>
          ,
          <year>2025</year>
          ,
          <fpage>249</fpage>
          -
          <lpage>264</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [10]
          <string-name>
            <given-names>Y.</given-names>
             
            <surname>Kostiuk</surname>
          </string-name>
          , et al.,
          <article-title>Integrated protection strategies and adaptive resource distribution for secure video streaming over a Bluetooth network</article-title>
          ,
          <source>in: Cybersecurity Providing in Information and Telecommunication Systems II 3826</source>
          ,
          <year>2024</year>
          ,
          <fpage>129</fpage>
          -
          <lpage>138</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          [11]
          <string-name>
            <given-names>Y.</given-names>
             
            <surname>Kostiuk</surname>
          </string-name>
          , et al.,
          <article-title>Models and algorithms for analyzing information risks during the security audit of personal data information system</article-title>
          ,
          <source>in: Cyber Hygiene &amp; Conflict Management in Global Information Networks</source>
          ,
          <volume>3925</volume>
          ,
          <year>2025</year>
          ,
          <fpage>155</fpage>
          -
          <lpage>171</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          [12]
          <string-name>
            <given-names>B.</given-names>
             
            <surname>Bebeshko</surname>
          </string-name>
          , et al.,
          <article-title>Application of game theory, fuzzy logic and neural networks for assessing risks and forecasting rates of digital currency</article-title>
          ,
          <source>J. Theor. Appl. Inf. Technol</source>
          .
          <volume>100</volume>
          (
          <issue>24</issue>
          ) (
          <year>2022</year>
          )
          <fpage>7390</fpage>
          -
          <lpage>7404</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          [13]
          <string-name>
            <given-names>M.</given-names>
             
            <surname>Mekhfioui</surname>
          </string-name>
          , et al.,
          <article-title>Optimized digital watermarking for robust information security in embedded systems</article-title>
          , Inf.
          <volume>16</volume>
          (
          <issue>4</issue>
          ) (
          <year>2025</year>
          )
          <article-title>322</article-title>
          . doi:
          <volume>10</volume>
          .3390/info16040322
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          [14]
          <string-name>
            <given-names>B. B.</given-names>
             
            <surname>Haghighi</surname>
          </string-name>
          , et al.,
          <string-name>
            <surname>WSMN:</surname>
          </string-name>
          <article-title>An optimized multipurpose blind watermarking in Shearlet domain using MLP and NSGA-II, Appl</article-title>
          . Soft. Comput.
          <volume>101</volume>
          (
          <year>2020</year>
          )
          <article-title>107029</article-title>
          . doi:
          <volume>10</volume>
          .1016/j.asoc.
          <year>2020</year>
          .107029
        </mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation>
          [15]
          <string-name>
            <given-names>S.</given-names>
             
            <surname>Sharma</surname>
          </string-name>
          , et al.,
          <article-title>A secure and robust color image watermarking using nature-inspired intelligence</article-title>
          ,
          <source>Neural Comput. Appl</source>
          .
          <volume>35</volume>
          (
          <year>2021</year>
          )
          <fpage>4919</fpage>
          -
          <lpage>4937</lpage>
          . doi:
          <volume>10</volume>
          .1007/s00521-020-05634-8
        </mixed-citation>
      </ref>
      <ref id="ref16">
        <mixed-citation>
          [16]
          <string-name>
            <given-names>J. P.</given-names>
             
            <surname>Dhar</surname>
          </string-name>
          , M. S. Islam,
          <string-name>
            <given-names>M.</given-names>
             A. 
            <surname>Ullah</surname>
          </string-name>
          ,
          <article-title>A fuzzy logic based contrast and edge sensitive digital image watermarking technique</article-title>
          ,
          <source>SN Appl. Sci. 1</source>
          (
          <year>2019</year>
          )
          <article-title>716</article-title>
          . doi:
          <volume>10</volume>
          .1007/s42452-019-0731-x
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>