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<front>
<journal-meta>
<journal-id journal-id-type="pmc">CSSE</journal-id>
<journal-id journal-id-type="nlm-ta">CSSE</journal-id>
<journal-id journal-id-type="publisher-id">CSSE</journal-id>
<journal-title-group>
<journal-title>Computer Systems Science &#x0026; Engineering</journal-title>
</journal-title-group>
<issn pub-type="ppub">0267-6192</issn>
<publisher>
<publisher-name>Tech Science Press</publisher-name>
<publisher-loc>USA</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">24605</article-id>
<article-id pub-id-type="doi">10.32604/csse.2023.024605</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Neural Cryptography with Fog Computing Network for Health Monitoring Using IoMT</article-title><alt-title alt-title-type="left-running-head">Neural Cryptography with Fog Computing Network for Health Monitoring Using IoMT</alt-title><alt-title alt-title-type="right-running-head">Neural Cryptography with Fog Computing Network for Health Monitoring Using IoMT</alt-title>
</title-group>
<contrib-group content-type="authors">
<contrib id="author-1" contrib-type="author">
<name name-style="western"><surname>Ravikumar</surname><given-names>G.</given-names></name>
<xref ref-type="aff" rid="aff-1">1</xref>
</contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western"><surname>Venkatachalam</surname><given-names>K.</given-names></name>
<xref ref-type="aff" rid="aff-2">2</xref>
</contrib>
<contrib id="author-3" contrib-type="author">
<name name-style="western"><surname>AlZain</surname><given-names>Mohammed A.</given-names></name>
<xref ref-type="aff" rid="aff-3">3</xref>
</contrib>
<contrib id="author-4" contrib-type="author">
<name name-style="western"><surname>Masud</surname><given-names>Mehedi</given-names></name>
<xref ref-type="aff" rid="aff-4">4</xref>
</contrib>
<contrib id="author-5" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Abouhawwash</surname><given-names>Mohamed</given-names></name>
<xref ref-type="aff" rid="aff-5">5</xref>
<xref ref-type="aff" rid="aff-6">6</xref><email>abouhaww@msu.edu</email>
</contrib>
<aff id="aff-1"><label>1</label><institution>Department of Computer Science and Engineering, Coimbatore Institute of Engineering and Technology</institution>, <addr-line>Coimbatore, 641109</addr-line>, <country>India</country></aff>
<aff id="aff-2"><label>2</label><institution>Department of Applied Cybernetics, Faculty of Science, University of Hradec Kr&#x00E1;lov&#x00E9;</institution>, <addr-line>50003, Hradec Kr&#x00E1;lov&#x00E9;</addr-line>, <country>Czech Republic</country></aff>
<aff id="aff-3"><label>3</label><institution>Department of Information Technology, College of Computers and Information Technology, Taif University</institution>, <addr-line>P.O. Box 11099, Taif, 21944</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-4"><label>4</label><institution>Department of Computer Science, College of Computers and Information Technology, Taif University</institution>, <addr-line>P. O. Box 11099, Taif, 21944</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-5"><label>5</label><institution>Department of Mathematics, Faculty of Science, Mansoura University</institution>, <addr-line>Mansoura, 35516</addr-line>, <country>Egypt</country></aff>
<aff id="aff-6"><label>6</label><institution>Department of Computational Mathematics, Science, and Engineering (CMSE), Michigan State University</institution>, <addr-line>East Lansing, MI, 48824</addr-line>, <country>USA</country></aff>
</contrib-group><author-notes><corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Mohamed Abouhawwash. Email: <email>abouhaww@msu.edu</email></corresp></author-notes>
<pub-date pub-type="epub" date-type="pub" iso-8601-date="2022-05-24"><day>24</day>
<month>05</month>
<year>2022</year></pub-date>
<volume>44</volume>
<issue>1</issue>
<fpage>945</fpage>
<lpage>959</lpage>
<history>
<date date-type="received"><day>24</day><month>10</month><year>2021</year></date>
<date date-type="accepted"><day>24</day><month>1</month><year>2022</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Ravikumar et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Ravikumar et al.</copyright-holder>
<license xlink:href="https://creativecommons.org/licenses/by/4.0/">
<license-p>This work is licensed under a <ext-link ext-link-type="uri" xlink:type="simple" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</ext-link>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
</license>
</permissions>
<self-uri content-type="pdf" xlink:href="TSP_CSSE_24605.pdf"></self-uri>
<abstract>
<p>Sleep apnea syndrome (SAS) is a breathing disorder while a person is asleep. The traditional method for examining SAS is Polysomnography (PSG). The standard procedure of PSG requires complete overnight observation in a laboratory. PSG typically provides accurate results, but it is expensive and time consuming. However, for people with Sleep apnea (SA), available beds and laboratories are limited. Resultantly, it may produce inaccurate diagnosis. Thus, this paper proposes the Internet of Medical Things (IoMT) framework with a machine learning concept of fully connected neural network (FCNN) with k-nearest neighbor (k-NN) classifier. This paper describes smart monitoring of a patient&#x2019;s sleeping habit and diagnosis of SA using FCNN-KNN&#x002B; average square error (ASE). For diagnosing SA, the Oxygen saturation (SpO2) sensor device is popularly used for monitoring the heart rate and blood oxygen level. This diagnosis information is securely stored in the IoMT fog computing network. Doctors can carefully monitor the SA patient remotely on the basis of sensor values, which are efficiently stored in the fog computing network. The proposed technique takes less than 0.2 s with an accuracy of 95%, which is higher than existing models.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Sleep apnea</kwd>
<kwd>polysomnography</kwd>
<kwd>IOMT</kwd>
<kwd>fog node</kwd>
<kwd>security</kwd>
<kwd>neural network</kwd>
<kwd>KNN</kwd>
<kwd>signature encryption</kwd>
<kwd>sensor</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>The Internet of Medical Things (IoMT) is the amalgamation of medical applications using sensor devices to connect with health-related information. In this scenario, user health data are sensed by the IoMT and transferred to the chief physician through a modern communication system. Even without the physical presence of the patient, the doctor can naturally view his or her health condition to prescribe medication. Thus, transferring and storing the sensitive data must be secured.</p>
<p>Sleep is one of the fundamental daily needs and is significant for brain function. Any sleep disorder can naturally affect general health and cause serious health problems, such as brain stroke, high blood pressure, complicate daily activities, and risk safety. Experts use Polysomnography (PSG) to study sleep disorders. PSG is a collection of signals recorded from various sensors counting the Electroencephalogram (EEG), Electro oculography (EOG), Electromyogram (EMG), Electrocardiogram (ECG), airflow, thoracic and abdominal movements, and oximetry. Rechtschaffen and Kales standardized the sleep stage classification rules depending on EEG modifications and split Non-Rapid Eye Movement (NREM) in sleep is a natural relief of humans and prevents several diseases. Sleep apnea is a sleep disorder in which breathing problem occurs during sleep states. SA affects our health by decreasing the oxygen blood level, eventually leading to other diseases [<xref ref-type="bibr" rid="ref-1">1</xref>]. SA impacts our health, mentally and physically, causing diseases, such as stroke, cardio problems, and diabetes. Scientifically, based upon the international sleep expert&#x2019;s key observation, roughly one billion people worldwide have obstructive sleep apnea (OSA) [<xref ref-type="bibr" rid="ref-2">2</xref>].</p>
<p>IoMT collects significant health-related data and helps early diagnosis of diseases using machine learning techniques. Persons health data is considered extremely sensitive and confidential to users. Thus, IoMT must ensure user privacy [<xref ref-type="bibr" rid="ref-3">3</xref>] through a federated learning technique. This learning method trains the device to stop sharing the data outside the device [<xref ref-type="bibr" rid="ref-4">4</xref>]. For SA diagnosis, PSG test is needed, which produces electrical energy signals from sensor devices attached to the human body. The process of sleep monitoring people with SA is highly expensive and beds remain limited. Sometimes, a full night or two nights are required for monitoring in a well-equipped sleep laboratory. PSG-recorded values sometimes misguide health professionals, leading to inaccurate diagnosis.</p>
<p>However, monitoring a person&#x2019;s health condition continuously is extremely difficult. Nonetheless, IoMT makes this possible. Although data transfer is performed remotely, its security and privacy are not assured. Moreover, data are sensitive, and a need for authentication technology persists, given that various attacks can enter the IoMT environment through the internet. Some attackers easily acquire control over the medical device remotely. Malware in IoMT greatly affects its communication and control on the medical device. Moreover, traditional techniques are insufficient to highly secure IoMT communication. Recent attacks by Mirai botnets create distributed denial of service due to insecurity in the Internet of Things (IoT) environment. Hence, a strong security technique to detect attacks in the sensitive IoMT environment is warranted [<xref ref-type="bibr" rid="ref-5">5</xref>&#x2013;<xref ref-type="bibr" rid="ref-7">7</xref>].</p>
<p>This research contributes security features as follows:</p>
<p>1. Sleep apnea is monitored using health sensors, such as an oximeter, and stress is monitored on the basis of the heart rate. Data are collected and transmitted to fog nodes using the IoMT framework.</p>
<p>2. IoMT uses forward neural network to train the features and uses KNN to classify SA accurately. The classified data is stored in fog nodes using a signature encryption technique.</p>
<p>The rest of the article is structured as follows. <xref ref-type="sec" rid="s2">Section 2</xref> presents the survey on IoMT. <xref ref-type="sec" rid="s3">Section 3</xref> demonstrates the proposed architecture and apnea detection using IoMT. <xref ref-type="sec" rid="s4">Section 4</xref> discusses the result evaluation. <xref ref-type="sec" rid="s5">Section 5</xref> concludes.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>Literature Survey</title>
<p>The information or data is connected and communicated through the internet using the IoT. Smart devices of homes, cars, watches, and so on are connected to the internet to transfer real-time data from user to end user. Moreover, IoT produces Wireless Sensor Networks (WSN), smart technologies, cloud network, and so on [<xref ref-type="bibr" rid="ref-8">8</xref>]. Human to machine communication [<xref ref-type="bibr" rid="ref-9">9</xref>] is abruptly transferred to machine-machine communication. Recently the IoT became promising in smart applications, such as the health industry, smart city, and so on. Thus, this survey focused on intelligent monitoring of SA diagnosis continuously. The Internet of Intelligent Things (IoIT) [<xref ref-type="bibr" rid="ref-10">10</xref>&#x2013;<xref ref-type="bibr" rid="ref-12">12</xref>] blends the artificial intelligence in the healthcare system to analyze the data logically.</p>
<p>The main disadvantages of using the IoT is limited bandwidth processing, less memory, and small structure, which cause security attacks and privacy threats [<xref ref-type="bibr" rid="ref-13">13</xref>&#x2013;<xref ref-type="bibr" rid="ref-16">16</xref>]. These factors influence high research interest in IoT security. To address IoT security, various cryptographic frameworks and technology are suggested [<xref ref-type="bibr" rid="ref-17">17</xref>&#x2013;<xref ref-type="bibr" rid="ref-22">22</xref>]. Especially in the medical system, handling patient data is highly sensitive for the IoT [<xref ref-type="bibr" rid="ref-23">23</xref>,<xref ref-type="bibr" rid="ref-24">24</xref>]. Central cloud server requires high security structure for providing data authentication.</p>
<p>Some studies explored the adaptive architecture for IoMT architecture [<xref ref-type="bibr" rid="ref-25">25</xref>]. This work provides high security for health dataset using public and private key structures. However, the security of the system is not highly adaptive. Thus, this work explores whether the hybrid security system using a cyber security algorithm for the IoMT is implemented [<xref ref-type="bibr" rid="ref-26">26</xref>]. Streaming data is transmitted via nodes using high authentication [<xref ref-type="bibr" rid="ref-27">27</xref>] to secure the IoMT real-time data in networks. Previous research discussed the security of IoMT with different techniques [<xref ref-type="bibr" rid="ref-28">28</xref>].</p>
<p>This study discussed several SA surveys. The novel recurrent neural architecture is used to extract the apnea features from input dataset [<xref ref-type="bibr" rid="ref-29">29</xref>]. Machine learning classifiers, such as the support vector machine (SVM) [<xref ref-type="bibr" rid="ref-30">30</xref>], threshold-based detectors [<xref ref-type="bibr" rid="ref-31">31</xref>], and regression trees with Adaboost are used to classify SA from the input feature set. The health-based smart contracts [<xref ref-type="bibr" rid="ref-32">32</xref>,<xref ref-type="bibr" rid="ref-33">33</xref>] are used for IoMT to transfer health data [<xref ref-type="bibr" rid="ref-34">34</xref>&#x2013;<xref ref-type="bibr" rid="ref-38">38</xref>].</p>
</sec>
<sec id="s3">
<label>3</label>
<title>Proposed Methodology</title>
<p>Although SA syndrome is a common disease, patient diagnosis is difficult. Thus, smart monitoring of the sleeping habit of patients is presented. It monitors the variations in stress and observes the patient&#x2019;s heart rate and the blood oxygen level while asleep. The architecture of SA syndrome analysis is presented in <xref ref-type="fig" rid="fig-1">Fig. 1</xref>. The sensor transmits the values to the data analysis section. Here, SA is analyzed on the basis of the input SpO2 value. The forward neural network and KNN classifier is used to detect SA in patients.</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>Sleep apnea syndrome analysis</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_24605-fig-1.png"/>
</fig>
<sec id="s3_1">
<label>3.1</label>
<title>Visualizing of Sleep Disorder</title>
<p>During sleep state, the nervous system becomes inactive, and the relaxation of muscles forces the eyes to close. It is also associated with low movement, stress less posture, and consciousness becomes suspended involuntarily. To monitor the sleep disorder, patients must undergo five stages, which include rapid eye movement (REM) and non rapid eye movement (NREM). <xref ref-type="fig" rid="fig-2">Fig. 2</xref> shows the detailed sleeping stages categorically.</p>
<fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>Categorized sleep stages</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_24605-fig-2.png"/>
</fig>
<p>Human beings have five stages of sleep. Stages 1 and 2 are considered light sleep in which people can be easily awakened. Stage 3 is the deep sleep, Stage 4 represents very deep sleep, and Stage 5 is the REM. Each stage requires 5&#x2013;15 minutes to complete. After completion of five stages, it starts again from Stage 1. On average, 90 to 110 minutes are needed to complete a sleep cycle. Any irregularity that occurs within the five sleep stages is a sleep disorder. Thus, to maintain a good sound sleep, sufficient sleep in each stage and sleep cycle must be obtained. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> presents the sleep stages.</p>

</sec>
<sec id="s3_2">
<label>3.2</label>
<title>Monitoring Sleep Apnea</title>
<p>During the sleep state, some breathing-related disorder occurred is called SA. As shown in <xref ref-type="fig" rid="fig-3">Fig. 3</xref> for monitoring SA, SpO2 and heart rate variability(HRV) sensor devices are attached in various organs in the body. Electrical energy emitted by the body is collected from these sensors and transmitted as graphical representation and stored in the fog computing network. This procedure is the Polysomnogram diagnosis.</p>
<fig id="fig-3">
<label>Figure 3</label>
<caption>
<title>Sleep stages</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_24605-fig-3.png"/>
</fig>
</sec>
<sec id="s3_3">
<label>3.3</label>
<title>Proposed - IoMT-Fog Computing</title>
<p>IoMT sensor values, such as the heart rate, and oximetric values are collected and stored in the fog computing-based network. <xref ref-type="fig" rid="fig-4">Fig. 4</xref> shows the IoMT with the fog computing process. <xref ref-type="fig" rid="fig-4">Fig. 4</xref> contains two layers, namely, the IoMT section and the fog computing layer. In the IoMT layer, data are collected from sensor devices and are classified into sensitive data (confidential data) and non-sensitive data (non-confidential data). This classified data is transferred to the fog layer, which contains fog servers. Then, data encryption and authorization are performed by a hashing technique of Advanced Signature-Based Encryption (ASE) of Diffie-Hellman key exchange and digital signature. This algorithm is used to exchange information between IoMT devices securely.</p>
<fig id="fig-4">
<label>Figure 4</label>
<caption>
<title>IoMT with fog computing</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_24605-fig-4.png"/>
</fig>
<sec id="s3_3_1">
<label>3.3.1</label>
<title>IoMT Layer</title>
<p>The IoMT layer contains wearable sensor devices of SpO2, which extract the electrical energy signal of SpO2 and HRV. This combination of SpO2 levels and HRV is used to reduce the false detective cases and increases accuracy. This work implementation is focused on monitoring heart rate and oxygen blood level when SA transpires in the sleep state of a patient. When SA happens to the patient, the system will alarm the doctor and observe the readings stored in the fog node securely. The Apnea-Hypopnea Index (AHI) is used to measure SA severity. <xref ref-type="table" rid="table-1">Tab. 1</xref> displays the AHI value.</p>
<p><disp-formula id="eqn-1"><label>(1)</label>
<mml:math id="mml-eqn-1" display="block"><mml:mi>A</mml:mi><mml:mi>H</mml:mi><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:mi mathvariant="normal">T</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mspace width="thickmathspace" /><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">o</mml:mi></mml:mrow><mml:mo>.</mml:mo><mml:mtext>&#xA0;</mml:mtext><mml:mrow><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">f</mml:mi><mml:mspace width="thickmathspace" /><mml:mi mathvariant="normal">A</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mspace width="thickmathspace" /><mml:mi mathvariant="normal">E</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mi mathvariant="normal">T</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mspace width="thickmathspace" /><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">o</mml:mi></mml:mrow><mml:mo>.</mml:mo><mml:mrow><mml:mspace width="thickmathspace" /><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">f</mml:mi><mml:mspace width="thickmathspace" /><mml:mi mathvariant="normal">H</mml:mi><mml:mi mathvariant="normal">y</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mspace width="thickmathspace" /><mml:mi mathvariant="normal">E</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">A</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mspace width="thickmathspace" /><mml:mi mathvariant="normal">S</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mspace width="thickmathspace" /><mml:mi mathvariant="normal">T</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mspace width="thickmathspace" /><mml:mo>&#x00D7;</mml:mo><mml:mn>60</mml:mn></mml:mstyle></mml:math>
</disp-formula></p>
<table-wrap id="table-1"><label>Table 1</label>
<caption>
<title>Sleep apnea severity by AHI value</title></caption>
<table><colgroup>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>AHI value</th>
<th>Ratings</th>
</tr>
</thead>
<tbody>
<tr>
<td>&#x003C;5</td>
<td>Normal (No sleep apnea)</td>
</tr>
<tr>
<td>5 to 15</td>
<td>Mild sleep apnea</td>
</tr>
<tr>
<td>15 to 30</td>
<td>Moderate sleep apnea</td>
</tr>
<tr>
<td>&#x003E;30</td>
<td>Severe sleep apnea</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Algorithm 1 represents the patient&#x2019;s SA severity.</p>
<table-wrap id="table-20"><label>Algorithm 1</label>
<caption>
<title>Classification of data on the basis of the AHI value</title></caption>
<table><colgroup>
<col/>
</colgroup>
<tbody>
<tr>
<td><bold>Input:</bold> Monitor and collect the electrical energy signals of SpO2 and HRV.&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;</td>
</tr>
<tr>
<td><bold>Output:</bold> Analyze the sleep apnea level during sleep.</td>
</tr>
<tr>
<td><bold>Step 1:</bold> Read the total number of apnea and hypopnea events</td>
</tr>
<tr>
<td><bold>Step 2:</bold> Calculate AHI using <xref ref-type="disp-formula" rid="eqn-1">Eq. (1)</xref>.</td>
</tr>
<tr>
<td><bold>Step 3:</bold> Read AHI value from <xref ref-type="table" rid="table-2">Tab. 2</xref></td>
</tr>
<tr>
<td><bold>Step 4:</bold> If <inline-formula id="ieqn-1">
<mml:math id="mml-ieqn-1"><mml:mi>A</mml:mi><mml:mi>H</mml:mi><mml:mi>I</mml:mi><mml:mspace width="thickmathspace" /><mml:mo>&#x2264;</mml:mo><mml:mspace width="thickmathspace" /><mml:mn>5</mml:mn></mml:math>
</inline-formula> then display &#x201C;Normal&#x201D;</td>
</tr>
<tr>
<td><bold>Step 5:</bold> If <inline-formula id="ieqn-2">
<mml:math id="mml-ieqn-2"><mml:mo stretchy="false">(</mml:mo><mml:mn>5</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>A</mml:mi><mml:mi>H</mml:mi><mml:mi>I</mml:mi><mml:mspace width="thickmathspace" /><mml:mo>&#x2264;</mml:mo><mml:mspace width="thickmathspace" /><mml:mn>15</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula> then display &#x201C;Mild Sleep&#x201D;</td>
</tr>
<tr>
<td><bold>Step 6:</bold> If <inline-formula id="ieqn-3">
<mml:math id="mml-ieqn-3"><mml:mo stretchy="false">(</mml:mo><mml:mn>15</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>A</mml:mi><mml:mi>H</mml:mi><mml:mi>I</mml:mi><mml:mspace width="thickmathspace" /><mml:mo>&#x2264;</mml:mo><mml:mspace width="thickmathspace" /><mml:mn>30</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula> then display &#x201C;Moderate Sleep&#x201D;</td>
</tr>
<tr>
<td><bold>Step 7:</bold> If <inline-formula id="ieqn-4">
<mml:math id="mml-ieqn-4"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>A</mml:mi><mml:mi>H</mml:mi><mml:mi>I</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mspace width="thickmathspace" /><mml:mn>15</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> then display &#x201C;Severe Sleep&#x201D;</td>
</tr>
<tr>
<td><bold>Step 8:</bold> End.</td>
</tr>
<tr>
<td><bold>Step 9:</bold> End.</td>
</tr>
<tr>
<td><bold>Step 10:</bold> End.</td>
</tr>
<tr>
<td><bold>Step 11:</bold> End.</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>In the IoMT layer, data are collected and classified on the basis of the AHI value. The data are classified as sensitive information and non-sensitive information using FCNN and k-nearest neighbour (k-NN) classifier. <xref ref-type="fig" rid="fig-5">Fig. 5</xref> shows the FCNN diagram for SA classification.</p>
<fig id="fig-5">
<label>Figure 5</label>
<caption>
<title>FCNN of SA</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_24605-fig-5.png"/>
</fig>
<p>This FCNN has one input layer, two hidden layers, and one output layer with 20 neurons. This model is used to develop a relationship between AHI value and sleep stages. To obtain accurate classification after applying FCNN, KNN is implemented. In the KNN classification, the input value is the k-nearest neighbor, and the output value assigns the feature vector class membership. In the classification of KNN, Euclidean distance metric measures are used,</p>
<p><disp-formula id="eqn-2"><label>(2)</label>
<mml:math id="mml-eqn-2" display="block"><mml:mi>E</mml:mi><mml:mi>u</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>d</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msqrt><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:msqrt><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>+</mml:mo><mml:mspace width="thickmathspace" /><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>+</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>+</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:msqrt><mml:mo>.</mml:mo></mml:math>
</disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-2">Eq. (2)</xref>, classification is done by the majority votes of neighbourhood values that are grouped together. Here the value of k should be assigned only an odd number. That is, 1-NN, 3-NN, 5NN, and so on.</p>
</sec>
<sec id="s3_3_2">
<label>3.3.2</label>
<title>Fog Layer</title>
<p>In the fog layer, the classification of data is stored for promoting accuracy, security, and scalability. Fog servers are used to generate data encryption and decryption using Diffie-Hellman encryption in the fog node. Algorithms 2 and 3 are used to encrypt and decrypt the information.</p>
<table-wrap id="table-15">
<caption>
<title>Symbolic Notation</title></caption>
<table><colgroup>
<col/>
</colgroup>
<tbody>
<tr>
<td><inline-formula id="ieqn-5">
<mml:math id="mml-ieqn-5"><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mspace width="thickmathspace" /><mml:mo>:</mml:mo><mml:mi>S</mml:mi><mml:mi>l</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:mi>p</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>A</mml:mi><mml:mi>p</mml:mi><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>a</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-6">
<mml:math id="mml-ieqn-6"><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mspace width="thickmathspace" /></mml:mrow></mml:msub></mml:mrow><mml:mo>:</mml:mo><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mi>D</mml:mi><mml:mi>o</mml:mi><mml:mi>c</mml:mi><mml:mi>t</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>s</mml:mi></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-7">
<mml:math id="mml-ieqn-7"><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>I</mml:mi><mml:mi>o</mml:mi><mml:mi>M</mml:mi><mml:mi>T</mml:mi><mml:mo>:</mml:mo><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /><mml:mi>I</mml:mi><mml:mi>o</mml:mi><mml:mi>M</mml:mi><mml:mi>T</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>d</mml:mi><mml:mi>e</mml:mi><mml:mi>v</mml:mi><mml:mi>i</mml:mi><mml:mi>c</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-8">
<mml:math id="mml-ieqn-8"><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi><mml:mo>:</mml:mo><mml:mi>S</mml:mi><mml:mi>l</mml:mi><mml:mi>e</mml:mi><mml:mi>e</mml:mi><mml:mi>p</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>A</mml:mi><mml:mi>p</mml:mi><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>a</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msup><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup><mml:mi>s</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi></mml:math>
</inline-formula>&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="table-11"><label>Algorithm 2</label>
<caption>
<title>Reading data from IoMT devices to Fog Node</title></caption>
<table><colgroup>
<col/>
</colgroup>
<tbody>
<tr>
<td><bold>Input:</bold> Patients with SA &#x003D; <inline-formula id="ieqn-9">
<mml:math id="mml-ieqn-9"><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mspace width="thickmathspace" /><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mn>2</mml:mn><mml:mspace width="thickmathspace" /><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /></mml:mrow></mml:msub></mml:mrow><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mspace width="thickmathspace" /><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula>&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;</td>
</tr>
<tr>
<td>   Doctors: (<inline-formula id="ieqn-10">
<mml:math id="mml-ieqn-10"><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mspace width="thickmathspace" /></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mspace width="thickmathspace" /></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mn>3</mml:mn><mml:mspace width="thickmathspace" /></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula></td>
</tr>
<tr>
<td>   IoMT devices: <inline-formula id="ieqn-11">
<mml:math id="mml-ieqn-11"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>I</mml:mi><mml:mi>o</mml:mi><mml:mi>M</mml:mi><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>I</mml:mi><mml:mi>o</mml:mi><mml:mi>M</mml:mi><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>I</mml:mi><mml:mi>o</mml:mi><mml:mi>M</mml:mi><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><bold>Output:</bold> SA patient&#x2019;s PSG data</td>
</tr>
<tr>
<td><bold>While</bold><inline-formula id="ieqn-12">
<mml:math id="mml-ieqn-12"><mml:mspace width="thickmathspace" /><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>
</inline-formula> in <inline-formula id="ieqn-13">
<mml:math id="mml-ieqn-13"><mml:mi>P</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>
</inline-formula><bold>do</bold></td>
</tr>
<tr>
<td>Select <inline-formula id="ieqn-14">
<mml:math id="mml-ieqn-14"><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><bold>For</bold> each <inline-formula id="ieqn-15">
<mml:math id="mml-ieqn-15"><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>I</mml:mi><mml:mi>o</mml:mi><mml:mi>M</mml:mi><mml:mi>T</mml:mi></mml:math>
</inline-formula><bold>do</bold></td>
</tr>
<tr>
<td> <bold> IF</bold> doctor <inline-formula id="ieqn-16">
<mml:math id="mml-ieqn-16"><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mspace width="thickmathspace" /></mml:mrow></mml:msub></mml:mrow></mml:math>
</inline-formula> choose <inline-formula id="ieqn-17">
<mml:math id="mml-ieqn-17"><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>I</mml:mi><mml:mi>o</mml:mi><mml:mi>M</mml:mi><mml:mi>T</mml:mi><mml:mspace width="thickmathspace" /></mml:math>
</inline-formula><bold>then</bold></td>
</tr>
<tr>
<td>Retrieve <inline-formula id="ieqn-18">
<mml:math id="mml-ieqn-18"><mml:mi>P</mml:mi><mml:mi>S</mml:mi><mml:mi>G</mml:mi></mml:math>
</inline-formula>(<inline-formula id="ieqn-19">
<mml:math id="mml-ieqn-19"><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>I</mml:mi><mml:mi>o</mml:mi><mml:mi>M</mml:mi><mml:mi>T</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula></td>
</tr>
<tr>
<td>Store in the fog network</td>
</tr>
<tr>
<td><bold>End</bold></td>
</tr>
<tr>
<td><bold>End</bold></td>
</tr>
<tr>
<td><bold>End</bold></td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Algorithm 1 retrieves data from IoMT devices and transfers to fog nodes. In the fog node data from sensor devices of SoP2, HRV are stored securely. Algorithm 2 describes the data encryption and decryption using the Diffie-Hellman encryption during fog computation. ASE algorithm comprises asymmetric cryptographic operations, such as the Diffie-Hellman key exchange and digital signature.</p>
<table-wrap id="table-16">
<caption>
<title>Symbolic Notation</title></caption>
<table><colgroup>
<col/>
</colgroup>
<tbody>
<tr>
<td><inline-formula id="ieqn-20">
<mml:math id="mml-ieqn-20"><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>P</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi><mml:mi>y</mml:mi><mml:mi>s</mml:mi><mml:mi>o</mml:mi><mml:mi>m</mml:mi><mml:mi>n</mml:mi><mml:mi>o</mml:mi><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>p</mml:mi><mml:mi>h</mml:mi><mml:mi>y</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-21">
<mml:math id="mml-ieqn-21"><mml:mi>s</mml:mi><mml:mi>y</mml:mi><mml:mi>m</mml:mi><mml:mi>m</mml:mi><mml:mi>k</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>S</mml:mi><mml:mi>y</mml:mi><mml:mi>m</mml:mi><mml:mi>m</mml:mi><mml:mi>e</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>c</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>K</mml:mi><mml:mi>e</mml:mi><mml:mi>y</mml:mi></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-22">
<mml:math id="mml-ieqn-22"><mml:mi>p</mml:mi><mml:mi>u</mml:mi><mml:mi>b</mml:mi><mml:mi>l</mml:mi><mml:mi>k</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>p</mml:mi><mml:mi>u</mml:mi><mml:mi>b</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>c</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>k</mml:mi><mml:mi>e</mml:mi><mml:mi>y</mml:mi></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-23">
<mml:math id="mml-ieqn-23"><mml:mi>c</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>c</mml:mi><mml:mi>i</mml:mi><mml:mi>p</mml:mi><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>x</mml:mi><mml:mi>t</mml:mi></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-24">
<mml:math id="mml-ieqn-24"><mml:mi>c</mml:mi><mml:mi>i</mml:mi><mml:mi>k</mml:mi><mml:mi>e</mml:mi><mml:mi>y</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>c</mml:mi><mml:mi>i</mml:mi><mml:mi>p</mml:mi><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>k</mml:mi><mml:mi>e</mml:mi><mml:mi>y</mml:mi></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-25">
<mml:math id="mml-ieqn-25"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>u</mml:mi><mml:mi>b</mml:mi><mml:mi>l</mml:mi><mml:mi>k</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>g</mml:mi><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>p</mml:mi><mml:mi>u</mml:mi><mml:mi>b</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>c</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>k</mml:mi><mml:mi>e</mml:mi><mml:mi>y</mml:mi></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-26">
<mml:math id="mml-ieqn-26"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>v</mml:mi><mml:mi>k</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>g</mml:mi><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>v</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>k</mml:mi><mml:mi>e</mml:mi><mml:mi>y</mml:mi></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-27">
<mml:math id="mml-ieqn-27"><mml:mi>I</mml:mi><mml:mi>o</mml:mi><mml:mi>M</mml:mi><mml:mi>T</mml:mi><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>P</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi><mml:mi>y</mml:mi><mml:mi>s</mml:mi><mml:mi>o</mml:mi><mml:mi>m</mml:mi><mml:mi>n</mml:mi><mml:mi>o</mml:mi><mml:mi>g</mml:mi><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>p</mml:mi><mml:mi>h</mml:mi><mml:mi>y</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>g</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>f</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>m</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>I</mml:mi><mml:mi>o</mml:mi><mml:mi>M</mml:mi><mml:mi>T</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>d</mml:mi><mml:mi>e</mml:mi><mml:mi>v</mml:mi><mml:mi>i</mml:mi><mml:mi>c</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi></mml:math>
</inline-formula>&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;</td>
</tr>
<tr>
<td><inline-formula id="ieqn-28">
<mml:math id="mml-ieqn-28"><mml:mi>s</mml:mi><mml:mi>y</mml:mi><mml:mi>m</mml:mi><mml:mi>m</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>r</mml:mi><mml:mi>y</mml:mi><mml:mi>p</mml:mi><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>S</mml:mi><mml:mi>y</mml:mi><mml:mi>m</mml:mi><mml:mi>m</mml:mi><mml:mi>e</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>c</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>r</mml:mi><mml:mi>y</mml:mi><mml:mi>p</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-29">
<mml:math id="mml-ieqn-29"><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>y</mml:mi><mml:mi>m</mml:mi><mml:mi>m</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>r</mml:mi><mml:mi>y</mml:mi><mml:mi>p</mml:mi><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>a</mml:mi><mml:mi>S</mml:mi><mml:mi>y</mml:mi><mml:mi>m</mml:mi><mml:mi>m</mml:mi><mml:mi>e</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>c</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>r</mml:mi><mml:mi>y</mml:mi><mml:mi>p</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-30">
<mml:math id="mml-ieqn-30"><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>g</mml:mi><mml:mi>n</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>g</mml:mi><mml:mi>n</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>u</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>o</mml:mi><mml:mi>f</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>p</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-31">
<mml:math id="mml-ieqn-31"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>v</mml:mi><mml:mi>k</mml:mi><mml:mi>e</mml:mi><mml:mi>y</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>R</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>e</mml:mi><mml:mi>i</mml:mi><mml:mi>v</mml:mi><mml:mi>e</mml:mi><mml:msup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup><mml:mi>s</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>v</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>k</mml:mi><mml:mi>e</mml:mi><mml:mi>y</mml:mi></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-32">
<mml:math id="mml-ieqn-32"><mml:mi>p</mml:mi><mml:mi>u</mml:mi><mml:mi>b</mml:mi><mml:mi>k</mml:mi><mml:mi>e</mml:mi><mml:mi>y</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>R</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi><mml:mi>e</mml:mi><mml:mi>i</mml:mi><mml:mi>v</mml:mi><mml:mi>e</mml:mi><mml:msup><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2032;</mml:mi></mml:mrow></mml:msup><mml:mi>s</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>p</mml:mi><mml:mi>u</mml:mi><mml:mi>b</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>c</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>k</mml:mi><mml:mi>e</mml:mi><mml:mi>y</mml:mi></mml:math>
</inline-formula></td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="table-12"><label>Algorithm 3</label>
<caption>
<title>Diffie-Hellman Encryption in the Fog Node</title></caption>
<table><colgroup>
<col/>
</colgroup>
<tbody>
<tr>
<td><bold>Function</bold><inline-formula id="ieqn-33">
<mml:math id="mml-ieqn-33"><mml:mrow><mml:mspace width="thickmathspace" /><mml:mspace width="thickmathspace" /></mml:mrow><mml:mi>E</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>r</mml:mi><mml:mi>y</mml:mi><mml:mi>p</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mspace width="thickmathspace" /><mml:mi>D</mml:mi><mml:mi>H</mml:mi><mml:mi>E</mml:mi><mml:mi>B</mml:mi><mml:mspace width="thickmathspace" /><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>I</mml:mi><mml:mi>o</mml:mi><mml:mi>M</mml:mi><mml:mi>T</mml:mi><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></td>
</tr>
<tr>
<td>If the SA patient confirms <inline-formula id="ieqn-34">
<mml:math id="mml-ieqn-34"><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi></mml:math>
</inline-formula> store in fog node then</td>
</tr>
<tr>
<td>  Generate key of symmetric <inline-formula id="ieqn-35">
<mml:math id="mml-ieqn-35"><mml:mi>s</mml:mi><mml:mi>y</mml:mi><mml:mi>m</mml:mi><mml:mi>m</mml:mi><mml:mi>k</mml:mi></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><inline-formula id="ieqn-36">
<mml:math id="mml-ieqn-36"><mml:mi>c</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mo stretchy="false">&#x2190;</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>s</mml:mi><mml:mi>y</mml:mi><mml:mi>m</mml:mi><mml:mi>m</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>r</mml:mi><mml:mi>y</mml:mi><mml:mi>p</mml:mi><mml:mi>t</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>I</mml:mi><mml:mi>o</mml:mi><mml:mi>M</mml:mi><mml:mi>T</mml:mi><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mi>y</mml:mi><mml:mi>m</mml:mi><mml:mi>m</mml:mi><mml:mi>k</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula>   </td>
</tr>
<tr>
<td><inline-formula id="ieqn-37">
<mml:math id="mml-ieqn-37"><mml:mi>c</mml:mi><mml:mi>i</mml:mi><mml:mi>k</mml:mi><mml:mi>e</mml:mi><mml:mi>y</mml:mi><mml:mo stretchy="false">&#x2190;</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>y</mml:mi><mml:mi>m</mml:mi><mml:mi>m</mml:mi><mml:mi mathvariant="normal">&#x005F;</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>r</mml:mi><mml:mi>y</mml:mi><mml:mi>p</mml:mi><mml:mi>t</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>s</mml:mi><mml:mi>y</mml:mi><mml:mi>m</mml:mi><mml:mi>m</mml:mi><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>u</mml:mi><mml:mi>b</mml:mi><mml:mi>l</mml:mi><mml:mi>k</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula>   </td>
</tr>
<tr>
<td><bold>Else</bold></td>
</tr>
<tr>
<td> Do nothing</td>
</tr>
<tr>
<td><bold>End if</bold></td>
</tr>
<tr>
<td><bold>End function</bold></td>
</tr>
<tr>
<td><bold>Function</bold> <inline-formula id="ieqn-38">
<mml:math id="mml-ieqn-38"><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>g</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>I</mml:mi><mml:mi>o</mml:mi><mml:mi>M</mml:mi><mml:mi>T</mml:mi><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>g</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></td>
</tr>
<tr>
<td><bold>If</bold> the SA patient selects confidential data from the fog node then&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;</td>
</tr>
<tr>
<td>  Generate asymmetric key pair (<inline-formula id="ieqn-39">
<mml:math id="mml-ieqn-39"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>u</mml:mi><mml:mi>b</mml:mi><mml:mi>l</mml:mi><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mspace width="thickmathspace" /><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>v</mml:mi><mml:mi>k</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula></td>
</tr>
<tr>
<td>  Generate digital signature using <inline-formula id="ieqn-40">
<mml:math id="mml-ieqn-40"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>i</mml:mi><mml:mi>v</mml:mi><mml:mi>k</mml:mi></mml:math>
</inline-formula></td>
</tr>
<tr>
<td>  Share <inline-formula id="ieqn-41">
<mml:math id="mml-ieqn-41"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>u</mml:mi><mml:mi>b</mml:mi><mml:mi>l</mml:mi><mml:mi>k</mml:mi></mml:math>
</inline-formula> to the receiver</td>
</tr>
<tr>
<td><bold>End if</bold></td>
</tr>
<tr>
<td><bold>End function</bold></td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="table-13"><label>Algorithm 4</label>
<caption>
<title>Diffie-Hellman Decryption in the Fog Node</title></caption>
<table><colgroup>
<col/>
</colgroup>
<tbody>
<tr>
<td><bold>Function</bold> Decryption DHEB<inline-formula id="ieqn-42">
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</inline-formula>&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;&#x2003;</td>
</tr>
<tr>
<td><inline-formula id="ieqn-43">
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</inline-formula>   </td>
</tr>
<tr>
<td><inline-formula id="ieqn-44">
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</inline-formula>   </td>
</tr>
<tr>
<td><bold>End Function</bold></td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Algorithms 3 and 4 typically perform the encryption and decryption of the SA patient&#x2019;s data by using the digital signature of hash, and private key produces the Diffie-Hellman method for the exchange of the key among various mobile IoMT devices and fog nodes.</p>
</sec>
</sec>
</sec>
<sec id="s4">
<label>4</label>
<title>Results and Analysis</title>
<p>Independent analysis of SA is a breathing disorder that occurs during a person&#x2019;s sleep state. In this work, FCNN-KNN&#x002B;ASE uses two public datasets of Sleep-EDF-2013 and Sleep-EDF-2018. For evaluation, a 20-fold cross validation was applied to all 250 PSG data values of the dataset. The sleeping stages of R &#x0026; K standard of W, N1, N2, N3, N4, and REM are used to evaluate FCNN-KNN&#x002B;ASE. The parametric measures are given below.</p>
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</disp-formula></p>
<p><disp-formula id="eqn-8"><label>(8)</label>
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</disp-formula></p>
<p><disp-formula id="eqn-9"><label>(9)</label>
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</disp-formula></p>
<p><disp-formula id="eqn-10"><label>(10)</label>
<mml:math id="mml-eqn-10" display="block"><mml:mi>R</mml:mi><mml:mi>M</mml:mi><mml:mi>S</mml:mi><mml:mi>E</mml:mi><mml:mo>=</mml:mo><mml:msqrt><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mfrac></mml:mrow><mml:munderover><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mo>&#x221D;</mml:mo><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mo>&#x221D;</mml:mo><mml:mi>i</mml:mi><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>&#x2032;</mml:mo></mml:msup></mml:mrow></mml:msubsup></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:mstyle></mml:msqrt></mml:math>
</disp-formula></p>
<p>where TP-True Positive, TN-True Negative, FP-False Positive, FN-False Negative, and <inline-formula id="ieqn-45">
<mml:math id="mml-ieqn-45"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:mrow></mml:math>
</inline-formula> is Hypothetical probability. <xref ref-type="table" rid="table-2">Tabs. 2</xref> and <xref ref-type="table" rid="table-3">3</xref> shows that confusion matrix of Sleep-EDF-2013 dataset in FCNN-KNN&#x002B;ASE using 20-fold cross-validation.</p>
<table-wrap id="table-2"><label>Table 2</label>
<caption>
<title>Confusion matrix of the leep-EDF-2013 dataset using 20-fold cross validation</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th></th>
<th>W</th>
<th>N1</th>
<th>N2</th>
<th>N3</th>
<th>REM</th>
<th>Precision %</th>
<th>Recall%</th>
<th>F1-Score%</th>
</tr>
</thead>
<tbody>
<tr>
<td>W</td>
<td>7521</td>
<td>600</td>
<td>198</td>
<td>19</td>
<td>265</td>
<td>91.6</td>
<td>85.9</td>
<td>89.8</td>
</tr>
<tr>
<td>N1</td>
<td>475</td>
<td>1179</td>
<td>685</td>
<td>14</td>
<td>578</td>
<td>54.9</td>
<td>41.4</td>
<td>47.8</td>
</tr>
<tr>
<td>N2</td>
<td>110</td>
<td>292</td>
<td>16340</td>
<td>726</td>
<td>875</td>
<td>86.9</td>
<td>89.2</td>
<td>89.1</td>
</tr>
<tr>
<td>N3</td>
<td>7</td>
<td>3</td>
<td>821</td>
<td>4821</td>
<td>15</td>
<td>87.2</td>
<td>86.1</td>
<td>85.9</td>
</tr>
<tr>
<td>REM</td>
<td>75</td>
<td>154</td>
<td>598</td>
<td>1</td>
<td>6945</td>
<td>80.4</td>
<td>90.1</td>
<td>85.2</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="table-3"><label>Table 3</label>
<caption>
<title>Confusion matrix of the sleep-EDF-2018 dataset using 20-fold cross-validation</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th></th>
<th>W</th>
<th>N1</th>
<th>N2</th>
<th>N3</th>
<th>REM</th>
<th>Precision %</th>
<th>Recall %</th>
<th>F1-Score%</th>
</tr>
</thead>
<tbody>
<tr>
<td>W</td>
<td>61256</td>
<td>3278</td>
<td>377</td>
<td>16</td>
<td>589</td>
<td>91.8</td>
<td>92.9</td>
<td>91.8</td>
</tr>
<tr>
<td>N1</td>
<td>4181</td>
<td>9485</td>
<td>5668</td>
<td>141</td>
<td>1827</td>
<td>51.8</td>
<td>43.8</td>
<td>48.9</td>
</tr>
<tr>
<td>N2</td>
<td>612</td>
<td>3567</td>
<td>57891</td>
<td>3087</td>
<td>2521</td>
<td>84.2</td>
<td>86.7</td>
<td>85.2</td>
</tr>
<tr>
<td>N3</td>
<td>45</td>
<td>29</td>
<td>3225</td>
<td>9356</td>
<td>35</td>
<td>74.2</td>
<td>74.1</td>
<td>73.2</td>
</tr>
<tr>
<td>REM</td>
<td>880</td>
<td>1680</td>
<td>2013</td>
<td>78</td>
<td>21895</td>
<td>81.3</td>
<td>83.2</td>
<td>81.8</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="table" rid="table-4">Tab. 4</xref> shows the comparison of our proposed work with other machine learning algorithms in the parametric metric measures of kappa and MF1 score values using two different datasets of Sleep-EDF-2013 and Sleep-EDF-2018.</p>
<table-wrap id="table-4"><label>Table 4</label>
<caption>
<title>Comparison of sleep-EDF-2013 and sleep-EDF-2018 datasets</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th></th>
<th colspan="2">Sleep-EDF-2013 dataset</th>
<th colspan="2">Sleep-EDF-2018 dataset</th>
</tr>
</thead>
<tbody>
<tr>
<td><bold>Algorithm</bold></td>
<td><bold>Kappa</bold></td>
<td><bold>Melt Flow Index (MFI) (%)</bold></td>
<td><bold>Kappa</bold></td>
<td><bold>MFI (%)</bold></td>
</tr>
<tr>
<td>FCNN-ASE</td>
<td>0.76</td>
<td>79.34</td>
<td>0.79</td>
<td>81.12</td>
</tr>
<tr>
<td>KNN-ASE</td>
<td>0.72</td>
<td>75.12</td>
<td>0.76</td>
<td>78.45</td>
</tr>
<tr>
<td>FCNN-KNN &#x002B;ASE</td>
<td>0.7</td>
<td>81.37</td>
<td>0.8</td>
<td>84.65</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="table" rid="table-5">Tab. 5</xref> unveils that the evaluation of FCNN-KNN&#x002B;ASE was compared with FCNN-ASE and KNN-ASE. Our proposed work obtained better value in kappa of 0.7 in the Sleep-EDF-2013 dataset and obtained a kappa value of 0.8 in the Sleep-EDF-2018 dataset. Similarly, for the MF1 score value of the Sleep-EDF-2013 dataset obtained 81.37% and the Sleep-EDF-2018 dataset obtained 84.65% in our proposed work, FCNN-KNN&#x002B;ASE. <xref ref-type="table" rid="table-6">Tabs. 6</xref> and <xref ref-type="table" rid="table-7">7</xref> show the calculating error rate of the Sleep-EDF-2013 and Sleep-EDF-2018 datasets.</p>
<table-wrap id="table-5"><label>Table 5</label>
<caption>
<title>Error rate for the sleep-EDF-2013 dataset</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Algorithm</th>
<th colspan="2">Training data</th>
<th colspan="2">Testing data</th>
</tr>
</thead>
<tbody>
<tr>
<td></td>
<td><bold>RMSE</bold></td>
<td><bold>MAE</bold></td>
<td><bold>RMSE</bold></td>
<td><bold>MAE</bold></td>
</tr>
<tr>
<td>FCNN-ASE</td>
<td>0.336</td>
<td>0.387</td>
<td>0.323</td>
<td>0.265</td>
</tr>
<tr>
<td>KNN-ASE</td>
<td>0.310</td>
<td>0.292</td>
<td>0.245</td>
<td>0.145</td>
</tr>
<tr>
<td>FCNN-KNN &#x002B;ASE</td>
<td>0.016</td>
<td>0.036</td>
<td>0.018</td>
<td>0.012</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="table-6"><label>Table 6</label>
<caption>
<title>Error rate for the sleep-EDF-2018 dataset</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Algorithm</th>
<th colspan="2">Training data</th>
<th colspan="2">Testing data</th>
</tr>
</thead>
<tbody>
<tr>
<td></td>
<td><bold>RMSE</bold></td>
<td><bold>MAE</bold></td>
<td><bold>RMSE</bold></td>
<td><bold>MAE</bold></td>
</tr>
<tr>
<td>FCNN-ASE</td>
<td>0.386</td>
<td>0.387</td>
<td>0.323</td>
<td>0.265</td>
</tr>
<tr>
<td>KNN-ASE</td>
<td>0.310</td>
<td>0.292</td>
<td>0.245</td>
<td>0.145</td>
</tr>
<tr>
<td>FCNN-KNN &#x002B;ASE</td>
<td>0.016</td>
<td>0.036</td>
<td>0.018</td>
<td>0.012</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="table" rid="table-6">Tabs. 6</xref> and <xref ref-type="table" rid="table-7">7</xref> present tthat the error rate for our proposed work produces minimum error rate using two different datasets. <xref ref-type="table" rid="table-8">Tabs. 8</xref> and <xref ref-type="table" rid="table-9">9</xref> unveil that cost of communication and storage cost in bits of different algorithm with two different datasets are given.</p>
<table-wrap id="table-7"><label>Table 7</label>
<caption>
<title>Communication cost and storage cost in the sleep-EDF-2013 dataset</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Algorithm</th>
<th>Communication cost (bits)</th>
<th>Storage cost (bits)</th>
</tr>
</thead>
<tbody>
<tr>
<td>FCNN-ASE</td>
<td>5620</td>
<td>7350</td>
</tr>
<tr>
<td>KNN-ASE</td>
<td>4570</td>
<td>3275</td>
</tr>
<tr>
<td>FCNN-KNN &#x002B;ASE (Proposed)</td>
<td>2380</td>
<td>1350</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="table" rid="table-8">Tab. 8</xref> demonstrates that our proposed technique obtains minimum communication cost and storage cost compared with other techniques.</p>
<table-wrap id="table-8"><label>Table 8</label>
<caption>
<title>Communication cost and storage cost in the sleep-EDF-2018 dataset</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Algorithm</th>
<th>Communication cost (bits)</th>
<th>Storage cost (bits)</th>
</tr>
</thead>
<tbody>
<tr>
<td>FCNN-ASE</td>
<td>5820</td>
<td>7550</td>
</tr>
<tr>
<td>KNN-ASE</td>
<td>4790</td>
<td>3450</td>
</tr>
<tr>
<td>FCNN-KNN &#x002B;ASE (Proposed)</td>
<td>2180</td>
<td>1250</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="table" rid="table-9">Tab. 9</xref> presents that our proposed technique obtains minimum communication cost and storage cost compared with other techniques. <xref ref-type="table" rid="table-9">Tabs. 9</xref> and <xref ref-type="table" rid="table-10">10</xref> reveal that time analysis for encryption of PSG information with various file sizes and stored it in fog-node.</p>
<table-wrap id="table-9"><label>Table 9</label>
<caption>
<title>Encryption time analysis (ms) in the sleep-EDF-2013 dataset</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>File Size (MB)</th>
<th>FCNN-ASE</th>
<th>KNN-ASE</th>
<th>FCNN-KNN &#x002B;ASE (Proposed)</th>
</tr>
</thead>
<tbody>
<tr>
<td>5</td>
<td>13560</td>
<td>13270</td>
<td>12890</td>
</tr>
<tr>
<td>10</td>
<td>16350</td>
<td>15750</td>
<td>14780</td>
</tr>
<tr>
<td>20</td>
<td>19750</td>
<td>18890</td>
<td>15570</td>
</tr>
<tr>
<td>40</td>
<td>21450</td>
<td>20870</td>
<td>17670</td>
</tr>
<tr>
<td>100</td>
<td>33890</td>
<td>22450</td>
<td>21350</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="table" rid="table-10">Tab. 10</xref> shows that our proposed work obtained minimum time analysis for encryption using the Sleep-EDF-2013 dataset and the PSG information, which are collected from SoP2 and HRV sensor devices for diagnosis of SAS.</p>
<table-wrap id="table-10"><label>Table 10</label>
<caption>
<title>Encryption time analysis (ms) in the sleep-EDF-2018 dataset</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>File Size (MB)</th>
<th>FCNN-ASE</th>
<th>KNN-ASE</th>
<th>FCNN-KNN &#x002B;ASE</th>
</tr>
</thead>
<tbody>
<tr>
<td>5</td>
<td>13150</td>
<td>13350</td>
<td>12650</td>
</tr>
<tr>
<td>10</td>
<td>16550</td>
<td>15890</td>
<td>14250</td>
</tr>
<tr>
<td>20</td>
<td>19950</td>
<td>18450</td>
<td>15870</td>
</tr>
<tr>
<td>40</td>
<td>21650</td>
<td>20210</td>
<td>17770</td>
</tr>
<tr>
<td>100</td>
<td>34250</td>
<td>22350</td>
<td>21130</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="table" rid="table-10">Tab. 10</xref> demonstrates that our proposed work obtained minimum time analysis for encryption using the Sleep-EDF-2018 dataset and the PSG information, which are collected from SoP2 and HRV sensor devices for SAS diagnosis.</p>
<p>Our proposed work obtained minimum time analysis for decryption using the Sleep-EDF-2018 dataset and the PSG information, which are collected from SoP2 and HRV sensor devices for SAS diagnosis. <xref ref-type="fig" rid="fig-6">Fig. 6</xref> shows the average accuracy rate for FCNN-KNN&#x002B;ASE in the two datasets.</p>
<fig id="fig-6">
<label>Figure 6</label>
<caption>
<title>Accuracy</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_24605-fig-6.png"/>
</fig>
<p><xref ref-type="fig" rid="fig-6">Fig. 6</xref> presents that our proposed work gives high accuracy rate compared with other algorithms. <xref ref-type="fig" rid="fig-7">Fig. 7</xref> shows the computation time of our proposed work.</p>
<fig id="fig-7">
<label>Figure 7</label>
<caption>
<title>Computation time</title></caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="CSSE_24605-fig-7.png"/>
</fig>
<p>The figure shows that the computation of our proposed work obtained minimum time. It produces minimum execution time and minimum error rate.</p>
</sec>
<sec id="s5">
<label>5</label>
<title>Conclusion</title>
<p>This work provides reference for SA diagnosis using a fog computing-based IoMT in machine learning algorithms. It uses electrical energy signals that are carefully collected from SpO2 and HRV sensor devices and collected data stored in fog computing network. Thereafter, we implement a complex ASE algorithm for encryption and decryption for PSG values, which cannot be accessed by unauthorized users. This work uses two different public datasets of Sleep-EDF-2013and Sleep-EDF-2018. The advantages of the proposed work, FCNN-KNN &#x002B;ASE, are better security, faster access, minimal time execution, higher accuracy, more flexible, and more reliable compared with other existing algorithms. The overall accuracy performance of this work obtained 92.13% in the Sleep-EDF-2013 dataset and 93.32% in the Sleep-EDF-2018 dataset. Finally, our proposed work analysis provides effective monitoring for diagnosing people with the SA based on PSG values. Future work is upgraded by using various machine learning algorithms with edge computing. Energy efficiency must be calculated in future work to widely enhance fog computing the IoMT.</p>
</sec>
</body>
<back>
<ack>
<p>We would like to give special thanks to Taif University Research supporting Project Number (TURSP-2020/98), Taif University, Taif, Saudi Arabia.</p>
</ack><fn-group>
<fn fn-type="other">
<p><bold>Funding Statement:</bold> Taif University Researchers Supporting Project Number (TURSP-2020/98), Taif University, Taif, Saudi Arabia.</p>
</fn>
<fn fn-type="conflict">
<p><bold>Conflicts of Interest:</bold> The authors declare that they have no conflicts of interest to report regarding the present study.</p>
</fn>
</fn-group>
<ref-list content-type="authoryear">
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