1. Introduction
Modern communication systems underpinning
Industry 4.0 require high-capacity optical networks spanning local facilities, regional corridors, and transoceanic links. The latest backbone infrastructures, supporting data rates of 400 Gbps and above, rely on coherent technology enhanced by advanced digital signal processing and phase-sensitive detection [
1]. Such systems transmit terabits of data per second to serve the diverse, time-sensitive demands in industrial automation, robotics control, global financial transactions, and e-government databases. As reliance on these coherent networks grows, so does the urgency of addressing security vulnerabilities, especially in environments where interconnected machinery, sensors, and cloud-based analytics coexist [
2].
The evolution of network hardware design is driven by the surging throughput requirements typical of
smart factories and
robotic assembly lines. While earlier optical links depended primarily on upper-layer protocols, such as Transport Layer Security or IP security for data protection [
3], advanced Industry 4.0 applications increasingly employ Layer 2 solutions like Media Access Control Security (MACsec) to ensure confidentiality, integrity, and authenticity at the Ethernet layer. However, new technical challenges arise in coherent networks. Management interfaces bridging MACsec-enabled routers and optical modules, often using MDIO or I
2C protocols, lack robust security measures [
4]. Similarly, the overhead field-based structure of Optical Transport Unit level 4 framing is susceptible to interception or manipulation [
5]. The combined use of multiple protocols with different security assumptions can introduce unforeseen vulnerabilities, hampering the reliability required by fully automated manufacturing processes.
Recent research and development in quantum computing enhance security concerns. The distribution of keys for MACsec security uses cryptographic methods, which depend on finite mathematical assumptions. Modern quantum algorithms, notably Shor’s algorithm, threaten the security of classical cryptography once quantum computing matures to a sufficient level [
6,
7]. Adversaries can store intercepted ciphertexts now and decrypt them later, making the immediate adoption of quantum-safe measures critical. Modern data security demands the implementation of quantum-safe cryptographic approaches since attacks can happen while data is stored for later decryption. Although quantum key distribution (QKD) offers a theoretically unbreakable means of key exchange [
8], its integration with coherent optical networks has faced practical hurdles. Recent progress suggests that these hurdles are more surmountable than previously believed [
9].
Motivated by these challenges, the primary purpose of this research is to explore how coherent optical networks can be protected from both classical exploits and future quantum-based attacks, while preserving compatibility with existing networking standards. This work aligns with calls from the recent literature for quantum-safe encryption strategies in optical environments [
10,
11,
12]. The presence of management plane vulnerabilities in 400G ZR+ transceiver modules, as well as protocol weaknesses in OTU4 overhead fields, calls for rigorous investigation.
The specific gap in the current literature is that many proposed methods treat optical-layer security, MACsec, and quantum cryptography as separate domains. This fragmentation creates a scenario in which bridging them may introduce further security holes or degrade system performance. In this context, “quantum-resistant protocols” refer to cryptographic algorithms and key-exchange methods designed to remain secure even against adversaries equipped with large-scale quantum computing capabilities, typically by relying on mathematically hard problems that cannot be efficiently solved by known quantum algorithms. Therefore, this paper is guided by a research question that addresses the heart of this fragmentation: “How can coherent optical networks that rely on OTU4 framing and MACsec be enhanced to safeguard against emerging quantum threats while maintaining the throughput and latency requirements of existing infrastructure?”
This question captures the dual necessity of optical-layer protection and quantum key distribution in coherent environments. It targets the management plane vulnerabilities that arise in bridging router control planes with advanced optical modules and focuses on bridging the gap between classical cryptography, optical encryption, and emerging quantum technologies.
We implemented a qualitative security analysis that systematically probes each interface, protocol boundary, and cryptographic layer. This analysis systematically follows recognized risk assessment and critical infrastructure protection frameworks [
13,
14], ensuring the comprehensive identification of both classical and quantum vulnerabilities. This vulnerability analysis underpins this study’s creation and validation of a post-quantum security framework that merges spectral phase masking with multi-homodyne coherent detection at the physical layer and QKD key distribution for key management. By unifying these approaches in a single design, our solution delivers robust cryptographic strength, forward secrecy, and backward compatibility in coherent optical networks operating at 400 Gbps and above.
This research makes specific contributions through an original vulnerability analysis of coherent infrastructures and a novel design for post-quantum security. First, it systematically identifies overlooked weaknesses in bridge architectures that coordinate the router control plane with coherent modules. This includes close scrutiny of the management interfaces where protocol conversion and synchronization occur, as these seemingly routine operations can introduce timing discrepancies. Second, it classifies vulnerabilities in OTU4 framing, where overhead bytes and frame alignment can be manipulated to create covert channels or disrupt signal integrity. Third, it proposes a new approach that incorporates optical phase mask encoding with multi-homodyne coherent detection and quantum key distribution for holistic security. The theoretical findings indicate that such a layered strategy resists both contemporary classical attacks and future quantum-based decryption methods, particularly in the context of coherent optical transport at data rates of 400 Gbps and above.
We conclude that a concerted security strategy, one that bridges the physical encryption aspects of spectral phase encoding with post-quantum key distribution, can substantially mitigate vulnerabilities exposed at the interface between traditional data networking protocols and coherent optical platforms. This analysis provides a blueprint for researchers, network operators, and hardware vendors seeking to future-proof optical transport networks.
The structure of this manuscript proceeds as follows. First, a review of related work addresses classical encryption vulnerabilities, the integration of MACsec over OTU4, and the latest developments in quantum-resistant protocols. By cataloging vulnerabilities within and across architectural boundaries in
Section 4, this research provides a robust empirical foundation for the comparative and integrative frameworks that follow.
Section 5 reviews existing optical encryption approaches in the context of these vulnerabilities, while
Section 6 presents a cohesive post-quantum security framework designed to mitigate the weaknesses documented here. A discussion evaluates the significance of these findings, their limitations, and potential avenues for more advanced or large-scale implementations. The manuscript concludes by asserting the practicality and necessity of a post-quantum security framework for coherent optical networks, underscoring the benefits of layering quantum key distribution with optical encryption to protect critical data transmission over the long term.
4. Vulnerability Analysis
This section presents a detailed examination of vulnerabilities in coherent optical networks, grounded in a layered qualitative research methodology that ensures academic rigor. This study employed an iterative case-based framework [
32] to isolate individual subsystems, used methodological triangulation [
33] to confirm the presence and severity of potential threats, and aligned these findings with the CIA (confidentiality, integrity, availability) model’s [
30,
35] systematic vulnerability assessment guidelines. By applying ref. [
34]’s iterative validation process, the research team tested each vulnerability under simulated conditions mirroring real-world attack scenarios while accounting for both classical and quantum adversaries [
13,
14]. The results reveal that weaknesses often arise at the confluence of hardware design, protocol integration, and signal processing algorithms in 400G ZR+ coherent systems.
The analysis began by identifying the structural elements of a 400G ZR+ environment, specifically, the interfaces linking router control planes to coherent optical modules. Each interface and subsystem (bridge architecture, management plane protocols, DSP blocks, OTU4 framing, and physical-layer channels) was treated as a distinct case unit [
32]. This segmentation facilitated the close scrutiny of vulnerabilities in synchronization, timing control, overhead byte usage, and optical signal manipulation. Triangulating the data from component specifications, documented exploits, and real-time traffic simulations [
33] allowed the team to confirm that these vulnerabilities were neither hypothetical nor limited to a single test environment.
The focus then turned to systematically categorizing identified threats under the CIA (confidentiality, integrity, and availability) model. Confidentiality threats included the unauthorized interception of data streams, while integrity threats ranged from frame manipulation in OTU4 overhead bytes to the malicious reprogramming of DSP parameters. Availability threats spanned timing-based attacks on synchronization buffers, potentially degrading or halting network services. This classification clarified how each vulnerability affected the core security objectives in a coherent optical environment.
Drawing on systematic risk assessment, this study rated vulnerabilities by their likelihood, technical complexity, and potential damage [
35]. In parallel, an iterative validation approach ensured that the identified weaknesses were re-evaluated under multiple simulated threat profiles, including basic script-kiddie exploits, state-sponsored adversaries with quantum decryption capabilities, and insider threats [
34]. This repetition refined the accuracy of the impact ratings, revealing which attacks required minimal effort yet posed widespread danger (e.g., overhead byte manipulation) and which demanded advanced tools (e.g., manipulating phase estimation blocks).
Below is a comprehensive summary of these vulnerabilities in
Table 1, which maps architectural domains to potential exploit vectors and the resulting security implications. To enhance transparency, this Table also lists the primary vulnerability category (bridge architecture, DSP, OTU4 framing, management interfaces, or physical layer) and indicates whether post-quantum threats exacerbate each issue.
4.1. Bridge Architecture Vulnerabilities
The bridge architecture, which interconnects a router CPU to a 400G ZR+ optical module, emerged as a focal point of this study. A core vulnerability stems from synchronization gaps during protocol conversion, typically handled by PCIe Gen4 links and gearbox implementations. Following a case-based protocol, the research team analyzed buffer and clock domain interactions, detecting temporal windows of 1–2 nanoseconds in which data buffers could be surreptitiously modified [
32]. Triangulation methods confirmed that this was not a purely theoretical risk; documented hardware logs from high-speed data centers revealed suspicious traces in precisely these intervals [
33].
Furthermore, iterative testing showed that post-quantum vulnerabilities arise when classical key exchange protocols operate during the handshake phase [
34]. By employing timing analysis and advanced quantum decryption [
14], an adversary could potentially extract keys before they even protect the data. This elevated the severity rating in the framework from “medium” to “high,” underscoring that architecture-level solutions are essential for future-proofing coherent networks [
35].
The architectural complexity is compounded by the requirement to keep tight timing relationships across multiple clock domains, most typically at the interface boundaries between the router CPU and the optical subsystems. The clock frequencies and the phase relationships among the clocks need to be accommodated by the synchronization mechanisms at the input and output of protocol conversion points without compromising data integrity. Timing such critical operations may result in possible vulnerabilities at the protocol transition boundary. Specifically, various gearbox implementations, which manage the conversion between new data rates and protocols, are of particular concern. These must be buffered to provide data for rate matching operations, introducing temporal windows in which timing attacks can be performed. Protocol conversion to the electrical domain intensifies this vulnerability, making synchronization even more complex at the transition points between electrical and optical domains. Yet another layer of vulnerability is introduced within the management interface running on top of MDIO/I2C, providing configuration and monitoring capabilities that could be abused to manipulate timing parameters or inject malformed control sequences. Though crucial for proper functionality, these types of interfaces represent additional attack surfaces that must be properly secured. Architectural vulnerabilities go beyond simple timing considerations and encompass the entire chain of protocol conversion and synchronization mechanisms needed for coherent optical communications. Finally, each transition point between protocols and clock domains provides a potential attack surface that could cause timing relationships to be manipulated in order to compromise data integrity or provide covert channels.
The accompanying diagram shows the architecture of the CPU-ZR optical connection and the PCIe links, gearbox modules, and synchronization points. A detailed architecture diagram of a modern coherent optical module based on the OIF-400ZR implementation is shown in
Figure 4. This is shown in the data path from the router CPU out through PCIe interfaces, bridge functions, and the DSP core to coherent laser/modulator, and critical points of vulnerability to timing attacks are highlighted.
The bridge architecture binds the coherent optical module and the router control plane via critical interfaces such as PCIe Gen4 and gearbox implementations. The data rate conversion and synchronization tasks performed by these interfaces are critical to maintaining stable communication. The multiple clock domain and high-speed data flow management complexity, however, tends to lead to timing gaps when performing rate conversions (e.g., 8 × 53.125G to 4 × 106.25G lanes). These timing gaps could be used by an attacker to take advantage of the inherent latency discrepancies between clock domains during protocol conversion. During the conversion from 8 × 53.125G to 4 × 106.25G lanes, there is a brief temporal window (typically 1-2 nanoseconds) in which the gearbox buffer needs to support rate matching between the different clock domains. However, this vulnerability becomes exploitable when an attacker uses high-precision timing analysis equipment (e.g., a PCIe protocol analyzer) to uncover these conversion windows. An attacker can exploit race conditions in buffer management logic by injecting specially crafted packets that match the timing of these buffer transition periods. Consider, for instance, a data center interconnect that runs at 400G: an attacker could insert malicious packets in these windows that would be regarded as legitimate on both timing domains, as they coincide with the expected buffer transition periods. This technique allows the attacker to work around conventional buffer overflow protection mechanisms while staying in sync with both clock domains, making it difficult to detect with normal means of monitoring. Furthermore, classical key exchange protocols rely on presenting a clear post-quantum vulnerability. These protocols are based on mathematical algorithms that can be decrypted by a quantum computer. If an attacker has access to quantum computers, they could intercept key exchanges during the handshake phase, making encryption protection useless.
5. Comparative Analysis of Optical Encryption Methods
A comparative analysis of leading optical encryption techniques occurs in this section according to
Section 3’s identified weaknesses. This evaluation applies an iterative case-based approach [
32] and assesses the methods under classical and post-quantum circumstances. The research established findings about each method’s bandwidth abilities and operational constraints by assessing documented specifications together with laboratory test data and reported exploits [
33]. The evaluation validated by an iterative approach required several danger simulations that demonstrated each method’s performance against integrated hardware-based as well as protocol-level attacks, starting from minimal side-channel listening to quantum-aided codebreaking [
34]. A systematic methodology enables the establishment of which encryption approaches can handle vulnerabilities, including overhead byte manipulation, synchronization gaps, and advanced phase manipulations.
Improved cryptographic methods in optical networks have emerged because of rising security demands for data protection. The protection of high-speed data goes beyond conventional methods to use fundamental light physics and in certain instances depends on quantum mechanical principles. System encryption at the physical level eliminates specific attack routes that target overhead fields and DSP routines. Both approaches conform to the CIA model [
30] but share individual technical difficulties, as outlined in the systematic evaluation guidelines [
35].
Double Random Phase Encryption (DRPE) stands as one of the most researched optical encryption methods due to its wide scientific investigation. Two separate random phase masks serve as the core elements in DRPE and implement positioning in the input plane and the Fourier plane of an optical device. Previous research conducted used this technique within a specific case unit and executed the experiments to validate the findings in
Section 3 [
32]. The theoretical security level of DRPE depends on specific parameters, yet the validation [
34] showed that deep neural parameters [
36] utilized in advanced ciphertext-only attacks pose significant threats to the system. The attacks discover a method to reverse random phase transformations, leading to the unauthorized recovery of data while omitting necessary encryption keys. Official protocol descriptions with DRPE deployment reports to demonstrate DRPE phase masks fall victim to learning attacks, thus causing detrimental performance issues in fast networks [
1].
Block-based optical color image encryption, which solves several weaknesses of DRPE by conducting an independent block-based processing of data segments, was introduced in previous research [
37]. Systematic testing [
32] indicates that data block segmentation enables attackers to face greater challenges because each block introduces randomized features, which prevents some deep-learning attacks from succeeding. According to scenario analysis, the performance of block-based encryption remains stable for shorter times but fails to protect 400G network data at high transmission speed rates [
34]. Utilizing this method to reset phase parameters results in the accumulation of overhead, which restricts the scalability of coherent systems operating at a large scale.
According to current research, the optical phase mask encoding with multi-homodyne coherent detection (MHCD) method functions as a diagnostic test model for full assessment. Previous work [
38] demonstrated that MHCD shifts the signal into high levels of noise, which renders unauthorized decryption practically impossible.
Research has used metasurface-based methodologies as an additional method of investigation. The transformation of phase-change metasurfaces described in the previous work in [
39] delivers fast tuning capabilities through controlled manipulations of specialized materials to encrypt data. The security-enhancing capabilities of metasurfaces have been assessed [
40], yet these capabilities create manufacturing hurdles and thermal control problems that would pose substantial obstacles for widespread implementation. Reprogrammable meta-holograms offer nearly unlimited capabilities in creating dynamic encryption channels. Tests conducted showed that the sensitivity of metasurfaces depends strongly on perfect calibration during their iterative alignment trials. The theoretical bandwidth capacity is high yet the actual implementation of 400 Gbps or higher data transmission rates exists only in initial experimental stages [
40].
The research summary presented in
Table 2 showcases the technical principles and strengths and weaknesses alongside the confirmed bandwidth capacity of the examined methods. The table underwent modification to follow CIA model principles by explaining how each strategy deals with confidentiality, integrity, and availability risks [
31]. The research utilizes multiple reputable data sources that combine peer-reviewed research and vendor documentation and experimental network lab measures [
33].
Several findings emerged from iterative scenario modeling [
34]. First, methods that lack adaptability, such as traditional DRPE, are vulnerable to deep-learning-based analysis if the same phase mask is reused extensively. Second, purely classical approaches can excel at high data rates, but they risk eventual compromise if a sufficiently powerful quantum adversary emerges [
14]. The combination of advanced approaches using MHCD or meta-holograms presents potential solutions to unite classical–quantum security standards, although the necessary infrastructure must resolve precision and operational problems [
40].
6. Optical Network Security Framework
This final section synthesizes the vulnerabilities documented in
Section 3 with the comparative insights from
Section 4 to propose a layered security framework. Developed through an iterative case-based method [
32], this framework was first conceptualized as a theoretical design that combines physical-layer encryption (notably optical phase mask encoding with multi-homodyne coherent detection, MHCD) and quantum key distribution (QKD). The combination of advanced approaches using MHCD or meta-holograms presents potential solutions to unite classical–quantum security standards, although the necessary infrastructure must resolve precision and operational problems [
40].
The analysis shows that one method does not adequately tackle the vulnerabilities found in
Section 3 without being future-proof against quantum attacks. The current cryptographic methods demonstrate either strong throughput capabilities or post-quantum security but must compromise with hardware complication procedures. The analysis demonstrates why integrated architectures must be put into practice because
Section 5 builds upon this requirement. Networks become stronger by establishing a systematic union between physical-layer optical encryption and quantum key distribution because each method addresses different weaknesses and conceals other limitations [
13,
31]. This modification enhances the framework in a way that not only provides details of the most suitable physical layer implementation technique but does it within the context of the general hybrid security framework.
The proposed architecture in
Figure 8 has one major advantage, namely the two-tier security model. At the physical layer, MHCD offers a detailed data channel encryption mechanism suitable for high-speed optical networks while QKD establishes secure working keys through the principles of quantum mechanics. This integration achieves two critical objectives: the paper focuses on achieving the high efficiency of the optical networks in use today while at the same time enhancing their resilience to both classical and quantum attacks. Our framework presents a new way of integrating Layer 2 security on the direct link between MACsec-enabled encryption systems and optical transceivers. This configuration removes the risks that are usually associated with the use of conventional ZR modules as far as security and network performance are concerned. Integrating optical transceivers with MACsec provides strong encryption and integrity at Layer 2, while also being compliant with post-quantum cryptographic techniques without having an adverse impact on current security protocols.
The security architecture can be described as layered and based on several complementary mechanisms. Physical layer operations utilize spectral phase encoding to improve transmission speed through the implementation of specific distortion patterns that need correct phase detection equipment to be restored. During scenario testing [
34], it was proven that this method obstructs attackers from intercepting data since standard coherent receivers fail to retrieve concealed spectral patterns. Meanwhile, QKD runs in parallel but remains synchronized with the data channel to refresh encryption keys. From a case-based perspective [
32], each subsystem (MHCD, QKD, and MACsec) was scrutinized independently, then integrated to confirm that the layered security measures did not interfere with one another.
The framework’s quantum security is not derived by large numbers of computational operations but by its architectural design. In contrast to public key systems that hinge on the computational infeasibility of certain number-theoretic problems, the QKD approach ensures that any eavesdropping attempt alters the quantum state, thereby triggering alarms. The consistent detection of tampering validated that an attacker with advanced quantum capabilities would face a “double burden”: breaking the optical-layer security (MHCD) while simultaneously circumventing QKD’s tamper-evident exchanges.
By unifying these approaches in a single design, our solution delivers robust cryptographic strength, forward secrecy, and backward compatibility in coherent optical networks operating at 400 Gbps and above.
Although QKD theoretically guarantees tamper-evident key exchange, it does not resolve every vulnerability in a complex network. Specifically, QKD only addresses how keys are shared; it does not inherently secure the data plane or the control plane against attacks such as hardware tampering, management plane manipulation, or overhead exploitation. Additionally, practical QKD implementations may face distance and throughput constraints that necessitate fallback to conventional algorithms. Post-quantum cryptographic (PQC) methods, on the other hand, protect data against quantum-enabled adversaries at the encryption layer, regardless of how keys are generated or distributed. Consequently, a robust, layered security model includes both QKD for tamper-evident key distribution and PQC algorithms for data encryption. This dual approach fortifies the entire system, ensuring that even if one layer is compromised by sophisticated attacks, the other continues to provide protection.
Operation success depends heavily on the correct implementation of the classical–quantum interface. The research utilized an iterative refinement cycle [
34] to establish that the integration of classical signals alongside quantum channels on a single fiber does not degrade performance effectiveness between them. Lab tests confirmed that swift data encryption functions independently from slower quantum key distribution exchanges when these keys exist on different light frequencies or when time-based multiplexing occurs. The design methodology adopted by this system implements levels of modularity that allow the replacement or upgrade of individual components for future compatibility [
13].
Strong security characteristics emerge from the framework when it encounters advanced adversaries. QKD key exchanges become unreliable when man-in-the-middle attacks happen at the control plane, thus triggering immediate warnings, as documented in
Section 3. Side-channel attacks focused on physical implementation such as spectral phase state measurement and alteration become impossible because MHCD executes a near-real time randomization of optical signals. Real network logs combined with lab test data and theoretical analyses from validate the multiple security measures’ ability to make unauthorized network access highly difficult to detect [
33].
The system reacts to faults or noise by sophisticating its encryption level instead of shutting down service operations. According to the validation approach [
40], the encryption safety in the classical data plane remains functional despite QKD channel device errors or signal deterioration, which allows the baseline protection of data confidentiality and data corpus integrity to persist. The quantum layer makes continued efforts to rebuild secure keys, which stops the system from experiencing permanent failures. The risk model [
35] recommends that partial operational capability represents an acceptable approach for preventing the full compromise of systems and services.
The architects performed an analysis on upcoming quantum computing patterns to make their decisions. Physical-layer encryption together with QKD possesses physical principles that stay valid beyond all levels of computing capabilities. The necessary redesigns required to expand future capabilities such as quantum-safe algorithm updates and metasurface encryptor integration proved minimal. The approach demonstrates through its flexibility that it will endure over time.
The framework shows its main advantage through its capability to operate with current network foundations. The architecture enables invisible encryption changes to upper layers through a Layer 2 encryption boundary alignment. Upgrade procedures involving MHCD-compatible optical transceivers along with QKD system integration need significant action, yet they do not necessitate major changes to routing operations or data hardware equipment. Previous research [
33] established that incremental deployment is practical since networks can start QKD on particular links before expanding key distribution to all network links.
The precise calibration of spectral phase encoding generates minimal overhead and quantum key generation does not disrupt data flow if multiplexing techniques are properly used according to structured cases [
32]. The simultaneous operation of key refreshment with traffic ensures continuous encryption as the keys replace themselves. Multiple tests under different traffic loads showed that standard enterprise and carrier networks could smoothly implement the framework through measurement systems that met strict performance criteria [
34].
Due to its modular design structure, the architecture demonstrates an easy pathway for potential growth additions. The system architecture accepts new cryptographic methods, advanced DSP components, and MACsec firmware updates by integrating them into its current framework. The framework’s extensibility resulted from specific evaluations that involved examining hypothetical replacement mechanisms at the subsystem level (standard MHCD replacement with meta-hologram-based encryption). The study findings confirmed that system synergy would continue to exist because fundamental interface definitions, wavelength assignment, and synchronization schedules maintained their original state.
Scalability also formed part of the iterative validations. Distributed key management and synchronized encryption can handle complex topologies that feature multiple nodes or dynamic routing paths. Although more extensive coordination is required, especially if QKD is shared among numerous endpoints, the architecture’s underlying modularity supports expansions. Hence, large carriers or multinational enterprises can protect a wide-ranging set of optical links without incurring exponential complexity.
Author Contributions
Conceptualization, O.J. and I.A.; methodology, O.J. and I.A.; validation, O.J. and I.A.; formal analysis, O.J.; investigation, O.J.; data curation, O.J.; writing—original draft preparation, O.J. and I.A.; writing—review and editing, O.J. and I.A.; visualization, O.J.; supervision, I.A.; project administration, I.A. All authors have read and agreed to the published version of the manuscript.
Funding
This research received no external funding.
Institutional Review Board Statement
Not applicable.
Data Availability Statement
Data available on request due to privacy restrictions.
Acknowledgments
The authors extend their heartfelt gratitude to Eli Cohen, Ron Posti, Aviel Cohen, Eliran Barzilay, and Korin Dayan for their invaluable support. Their incisive feedback, constructive discussions, and unwavering encouragement significantly enriched the quality of this manuscript and were instrumental in bringing the project to fruition. Special thanks are also due to Irit Hadar, whose insightful guidance and meticulous supervision steered the research at every stage.
Conflicts of Interest
The authors declare no conflict of interest.
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