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<front>
<journal-meta>
<journal-id journal-id-type="pmc">CMC</journal-id>
<journal-id journal-id-type="nlm-ta">CMC</journal-id>
<journal-id journal-id-type="publisher-id">CMC</journal-id>
<journal-title-group>
<journal-title>Computers, Materials &#x0026; Continua</journal-title>
</journal-title-group>
<issn pub-type="epub">1546-2226</issn>
<issn pub-type="ppub">1546-2218</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">32140</article-id>
<article-id pub-id-type="doi">10.32604/cmc.2023.032140</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>EsECC_SDN: Attack Detection and Classification Model for MANET</article-title>
<alt-title alt-title-type="left-running-head">EsECC_SDN: Attack Detection and Classification Model for MANET</alt-title>
<alt-title alt-title-type="right-running-head">EsECC_SDN: Attack Detection and Classification Model for MANET</alt-title>
</title-group>
<contrib-group content-type="authors">
<contrib id="author-1" contrib-type="author">
<name name-style="western"><surname>Vuyyuru</surname><given-names>Veera Ankalu</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>Alotaibi</surname><given-names>Youseef</given-names></name><xref ref-type="aff" rid="aff-2">2</xref></contrib>
<contrib id="author-3" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Veeraiah</surname><given-names>Neenavath</given-names></name><xref ref-type="aff" rid="aff-3">3</xref><email>neenavathveeru@gmail.com</email></contrib>
<contrib id="author-4" contrib-type="author">
<name name-style="western"><surname>Alghamdi</surname><given-names>Saleh</given-names></name><xref ref-type="aff" rid="aff-4">4</xref></contrib>
<contrib id="author-5" contrib-type="author">
<name name-style="western"><surname>Sirisha</surname><given-names>Korimilli</given-names></name><xref ref-type="aff" rid="aff-5">5</xref></contrib>
<aff id="aff-1"><label>1</label><institution>Department of Computer Science and Engineering, Koneru Lakshmaiah Education Foundation</institution>, <addr-line>Vaddeswaram, 522502, A.P</addr-line>, <country>India</country></aff>
<aff id="aff-2"><label>2</label><institution>Department of Computer Science, College of Computers and Information Systems, Umm Al-Qura University</institution>, <addr-line>Makkah, 21955</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-3"><label>3</label><institution>Department of Electronics and Communications, DVR &#x0026; DHS MIC Engineering College</institution>, <addr-line>Kanchikacharla, 521180, A.P</addr-line>, <country>India</country></aff>
<aff id="aff-4"><label>4</label><institution>Department of Information Technology, College of Computers and Information Technology, Taif University</institution>, <addr-line>Taif, 21944</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-5"><label>5</label><institution>Department of Electronics and Communications, BVC Institute of Technology &#x0026; Science</institution>, <addr-line>Amalapuram, 533221, A.P</addr-line>, <country>India</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Neenavath Veeraiah. Email: <email>neenavathveeru@gmail.com</email></corresp>
</author-notes>
<pub-date publication-format="print" date-type="pub" iso-8601-date="2022-12-15"><day>15</day>
<month>12</month>
<year>2022</year></pub-date>
<volume>74</volume>
<issue>3</issue>
<fpage>6665</fpage>
<lpage>6688</lpage>
<history>
<date date-type="received"><day>08</day><month>5</month><year>2022</year></date>
<date date-type="accepted"><day>16</day><month>6</month><year>2022</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Vuyyuru et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Vuyyuru 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_CMC_32140.pdf"></self-uri>
<abstract>
<p>Mobile Ad Hoc Networks (MANET) is the framework for social networking with a realistic framework. In the MANET environment, based on the query, information is transmitted between the sender and receiver. In the MANET network, the nodes within the communication range are involved in data transmission. Even the nodes that lie outside of the communication range are involved in the transmission of relay messages. However, due to the openness and frequent mobility of nodes, they are subjected to the vast range of security threats in MANET. Hence, it is necessary to develop an appropriate security mechanism for the data MANET environment for data transmission. This paper proposed a security framework for the MANET network signature escrow scheme. The proposed framework uses the centralised Software Defined Network (SDN) with an ECC cryptographic technique. The developed security framework is stated as Escrow Elliptical Curve Cryptography SDN (EsECC_SDN) for attack detection and classification. The developed EsECC-SDN was adopted in two stages for attack classification and detection: (1) to perform secure data transmission between nodes SDN performs encryption and decryption of the data; and (2) to detect and classifies the attack in the MANET hyper alert based Hidden Markov Model Transductive Deep Learning. Furthermore, the EsECC_SDN is involved in the assignment of labels in the transmitted data in the database (DB). The escrow handles these processes, and attacks are evaluated using the hyper alert. The labels are assigned based on the k-medoids attack clustering through label assignment through a transductive deep learning model. The proposed model uses the CICIDS dataset for attack detection and classification. The developed framework EsECC_SDN&#x2019;s performance is compared to that of other classifiers such as AdaBoost, Regression, and Decision Tree. The performance of the proposed EsECC_SDN exhibits &#x223C;3&#x0025; improved performance compared with conventional techniques.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>MANET</kwd>
<kwd>security</kwd>
<kwd>classifier</kwd>
<kwd>cryptography</kwd>
<kwd>attack</kwd>
<kwd>escrow</kwd>
<kwd>ECC</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1"><label>1</label><title>Introduction</title>
<p>Mobile Ad Hoc Network (MANET) comprises a vast range of mobile nodes to establish the network connection based on the demand in the network. Within the MANET environment, every packet in the network act as a router [<xref ref-type="bibr" rid="ref-1">1</xref>]. Furthermore, MANET has been widely utilized in a vast range of applications such as disaster management, military, personal area, networks, and so on. MANET environment comprises the dynamic or mobile environment with the estimation of failure point detection in the mobile ad-hoc environment [<xref ref-type="bibr" rid="ref-2">2</xref>]. However, the effective design of the protocol is involved in the transmission of packets in a dynamic environment between sender to receiver in topology. MANET environment comprises of the different categories such as the reactive, proactive, and hybrid environment. MANET environment provides connection-less, server, and permanent models in the centralized environment for dynamic access of data in a remote-control environment for improved security [<xref ref-type="bibr" rid="ref-3">3</xref>]. The functionality of MANET comprises the data blockage and time for the communication environment. MANET network offers a realistic framework with a broad range of social networking environments. The data transmission in the network is involved in information transmission based on reaction and query [<xref ref-type="bibr" rid="ref-4">4</xref>].</p>
<p>To improve the trusted user&#x2019;s privacy, needs to be maintained for effective maintenance of security. In a multi-hop MANET environment, explored packets need to be concerned about reaching the destination within the stipulated period. It is thought to be necessary for the construction of networks that connect nodes that are cooperative with one another [<xref ref-type="bibr" rid="ref-5">5</xref>]. In a MANET environment, data transmission routing is considered an effective parameter for the identification of optimal paths between nodes. The optimal performance of MANET is increased with spatial reusability of the nodes with increased throughput and end-to-end packet delivery [<xref ref-type="bibr" rid="ref-6">6</xref>]. Generally, the MANET is subjected to a vast range of security issues like the overflow of the routing table, wormhole, poisoning, snooping, packet replication, and denial of service (DoS).</p>
<p>The attacks affect the data transmission path between nodes to reach the destination without packet dropping [<xref ref-type="bibr" rid="ref-7">7</xref>&#x2013;<xref ref-type="bibr" rid="ref-9">9</xref>]. Those attacks can be either single or collaborative in the case of single; in which packets are dropped independently, those are forwarded to the neighbors. In collaborative attacks, malicious nodes cooperate with packet dropping with the elimination of detection time [<xref ref-type="bibr" rid="ref-10">10</xref>]. To achieve the desired security in MANET, secure data transmission needs to be achieved using the cryptographic method. A similar key distribution within the network needs to be achieved. However, key distribution is a challenging task in the MANET environment. Usually, key management is involved in key setting, distribution of keys, and reversals of keys. In addition, this cryptographic scheme is subjected to the challenge of load balancing for handling public keys [<xref ref-type="bibr" rid="ref-11">11</xref>].</p>
<p>This research concentrated on improving security in the MANET environment due to the mobility and openness of the network. To achieve security in the MANET environment, this paper incorporates the following things.
<list list-type="bullet">
<list-item><p>This paper incorporates SDN architecture to maintain the architecture of the MANET environment.</p></list-item>
<list-item><p>In this paper escrow-based, Elliptical Curve Cryptography (ECC) is applied for data encryption. The generated keys are updated in the SDN for MANET security.</p></list-item>
<list-item><p>To detect the attack transductive attacks integrated with Hidden Markov model (HMM) with hyper alerts.</p></list-item>
<list-item><p>Within the transductive matrix, k-centroids are implemented for examination of attacks in the network.</p></list-item>
<list-item><p>To classify the attack Intrusion Detection Evaluation Dataset (CIC-IDS2017) [<xref ref-type="bibr" rid="ref-12">12</xref>] is utilized for detection of attack in the MANET.</p></list-item>
<list-item><p>The performance of the proposed EsECC_SDN is evaluated under two scenarios with attackers and without attackers. Finally, the proposed EsECC_SDN is a classifier based on a Support Vector Machines (SVM) classifier for attack classification.</p></list-item>
</list></p>
<p>This paper is organized as follows: In Section 2, related works are presented. The proposed EsECC_SDN for MANET with hidden Markov model (HMM) and transductive model for security is presented in Section 3. The simulation setting and classification of attacks are presented in Section 4 followed by the overall conclusion in Section 5.</p>
</sec>
<sec id="s2"><label>2</label><title>Related Works</title>
<p>A MANET subjected to challenge of security to achieve desired communication performance of the network. This section provides the data transmission scheme between the nodes and the security scheme.</p>
<p>In [<xref ref-type="bibr" rid="ref-13">13</xref>], the authors developed a security scheme for MANET focused on DDoS attack prevention. The model involved in classification of DDoS attack with uses of dataset LIBSVM. The dataset for examination is generated through NS2 simulator for prediction accuracy. The testing and validation of the dataset s based on the consideration of bit rate, delay and packet delivery ratio PDR. The analysis expressed that the characteristics of the DDoS attack is minimal traffic network. However, the developed model involved in reduction of overall accuracy of the network.</p>
<p>In [<xref ref-type="bibr" rid="ref-14">14</xref>], the authors proposed a Diffie-Hellman method of key exchange and elliptic curve cryptography (HDHECC) for reliable data transmission with cryptography algorithm. Initially, the proposed HDHECC perform clustering with Low-energy adaptive clustering hierarchy (LEACH) protocol with selection of head with assigned weights in each node. Moreover, the proposed HDHECC incorporates trust mechanism for management of keys to retain public keys in the member node. With centralized key management public key are stored for estimation of packet loss, end-to-end delay and Packet delivery ratio. Similarly, in [<xref ref-type="bibr" rid="ref-15">15</xref>], the authors implemented multicast delay with cooperative multicast scheme for routing in MANET. The developed multicast algorithm with implementation of two-hop relay, where the packet transmitted between relay nodes to source node. The destination node involved in reception of packet from source node to the relay nodes. With implementation of multi-cast scheme cooperation and non-cooperation scheme is implemented for unicast algorithm with destination node those are equal to one. Furthermore, theoretical based Markov model cooperative multicast scheme for characterization of packet delivery.</p>
<p>To increase the overall security in the MANET network, in [<xref ref-type="bibr" rid="ref-16">16</xref>] the authors developed a modified ad-hoc on-demand multipath distance vector (AOMDV). The AOMDV model involved in detection of black hole attack in MANET for secure data transmission. In addition, AOMDV comprises of multi path message transmission for secure data with homomorphic encryption scheme. The examination of the results expressed that the PDR and throughput is higher. In [<xref ref-type="bibr" rid="ref-17">17</xref>], the authors examined the different MANET attacks for the security improvement than the conventional technique. The performance of the network is computed based on the estimation of routing table with minimal delay. The MANET efficiency is based on consideration of the different factors such as flow rate, mobility, traffic, attackers, and position of nodes. Similarly, in [<xref ref-type="bibr" rid="ref-18">18</xref>], the authors presented a decentralized traffic monitoring system based on optimization model. The optimization-based approach uses bio-inspired algorithm stated as Artificial Immune System Based Algorithm (AISBA).</p>
<p>The proposed AISBA algorithm incorporates Artificial Immune System (AIS) for estimation of selfish and genuine nodes. With implemented protocol design, PDR is achieved as 93.47&#x0025;. In [<xref ref-type="bibr" rid="ref-19">19</xref>], the authors focused on optimization and secure routing in MANET environment. The optimal routing in MANET is achieved through Ant Colony Optimization (ACO) for improved routing through estimation of difficulties in the network. To evaluate the network complexity, fuzzy logic model is implemented termed as Safety Aware Fuzzy Enhanced Ant Colony Optimization (SAFEACO) for effective routing in the network. The designed SAFEACO exhibits significant performance for the black hole, Sybil and inundation attacks in the network with computation of PDR and end-to-end delay.</p>
<p>In addition, in [<xref ref-type="bibr" rid="ref-20">20</xref>], the authors evaluated the MANET network performance based on Ad hoc On-Demand Distance Vector Routing (AODV), Dynamic Source Routing (DSR) reactive protocols. The evaluation is based on consideration of QoS matrices for guaranteed sensitivity level. The estimation is based on the consideration of node (PHY) layer. The estimation is based on the consideration of end-to-end delay, PDR and control overhead. In [<xref ref-type="bibr" rid="ref-21">21</xref>], computation is performed based on the peer-to-peer computing in the MANET. The performance is based on overlay participating peers (OPPs) for efficient processing in the MANET environment. With increase in node mobility overlay of protocol is minimized with increased maintenance, computation, control overhead, and lookup latency. In [<xref ref-type="bibr" rid="ref-22">22</xref>], the authors developed a AODV-BS protocol for prevention of black hole attack in MANET environment. The estimation is based on the consideration of different MANET model for normalization of the routing. The performance of the MANET is computed for the normalized routing, network delay and packet delivery ratio. <xref ref-type="table" rid="table-1">Tab. 1</xref> shows the summary of the literature.</p>
<table-wrap id="table-1"><label>Table 1</label><caption><title>Summary of literature</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Reference</th>
<th align="left">Published year</th>
<th align="left">Method</th>
<th align="left">Outcome</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">[<xref ref-type="bibr" rid="ref-13">13</xref>]</td>
<td align="left">2020</td>
<td align="left">Prevention of DDoS attack in MANET</td>
<td align="left">To prevent DDoS attack with improved performance</td>
</tr>
<tr>
<td align="left">[<xref ref-type="bibr" rid="ref-14">14</xref>]</td>
<td align="left">2020</td>
<td align="left">To design effective cryptographic scheme for MANET</td>
<td align="left">It offers desire key management scheme</td>
</tr>
<tr>
<td align="left">[<xref ref-type="bibr" rid="ref-15">15</xref>]</td>
<td align="left">2020</td>
<td align="left">To perform multi-cast secure data transmission</td>
<td align="left">Multi-cast scheme offers multi-cast communication</td>
</tr>
<tr>
<td align="left">[<xref ref-type="bibr" rid="ref-16">16</xref>]</td>
<td align="left">2020</td>
<td align="left">To develop secure algorithm for Ad-hoc demand protocol</td>
<td align="left">Developed a homomorphic scheme for security</td>
</tr>
<tr>
<td align="left">[<xref ref-type="bibr" rid="ref-17">17</xref>]</td>
<td align="left">2021</td>
<td align="left">Reviewed the security threats and challenges in MANET</td>
<td align="left">Reduced end-to-end delay and traffic load</td>
</tr>
<tr>
<td align="left">[<xref ref-type="bibr" rid="ref-18">18</xref>]</td>
<td align="left">2022</td>
<td align="left">To implement optimization-based security model for MANET</td>
<td align="left">Effectively identifies the selfish nodes</td>
</tr>
<tr>
<td align="left">[<xref ref-type="bibr" rid="ref-19">19</xref>]</td>
<td align="left">2020</td>
<td align="left">To develop secure optimization model</td>
<td align="left">Effectively prevents black hole, sybil and inundation</td>
</tr>
<tr>
<td align="left">[<xref ref-type="bibr" rid="ref-20">20</xref>]</td>
<td align="left">2021</td>
<td align="left">Self-configured secure routing scheme</td>
<td align="left">Improved throughput and PDR</td>
</tr>
<tr>
<td align="left">[<xref ref-type="bibr" rid="ref-21">21</xref>]</td>
<td align="left">2021</td>
<td align="left">Constructed routing model for MANET</td>
<td align="left">Routing overhead is minimal</td>
</tr>
<tr>
<td align="left">[<xref ref-type="bibr" rid="ref-22">22</xref>]</td>
<td align="left">2020</td>
<td align="left">Prevention of blackhole attack</td>
<td align="left">Provides security</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s3"><label>3</label><title>Security Scheme in MANET</title>
<p>The proposed escrow technique comprises the trustworthy SDN environment for security enhancement with the classification of attacks in the MANET [<xref ref-type="bibr" rid="ref-23">23</xref>&#x2013;<xref ref-type="bibr" rid="ref-32">32</xref>]. The SDN acts as a centralized environment for data transmission and reception between nodes. With the SDN, the environment performs encryption and decryption. The environment of MANET is focused on improving authentication, confidentiality, integrity, and availability [<xref ref-type="bibr" rid="ref-33">33</xref>&#x2013;<xref ref-type="bibr" rid="ref-42">42</xref>].
<list list-type="bullet">
<list-item><p>Authentication&#x2013;The legitimacy of the engaged data source that needs to be authenticated.</p></list-item>
<list-item><p>Confidentiality&#x2013;The system that involved in data processor execution in a devices.</p></list-item>
<list-item><p>Integrity&#x2013;The unauthorized user information is</p></list-item>
<list-item><p>modified or corrupted.</p></list-item>
<list-item><p>Availability&#x2013;The capability of a network involved in the provision of appropriate services.</p></list-item>
</list></p>
<p>The proposed EsECC_SDN comprises five phases. The five steps involved in the model are Setup Phase, Key Generation, Encryption, decryption of node phase and decryption of the head phase. The proposed escrow scheme uses third party identification with the SDN controller. With SDN architecture MANET, network environment involved in the provision of global, versatility, optimization, and process. The proposed EsECC_SDN incorporates limited availability of resources and an appropriate strategy for connectivity for an unfeasible environment. The constructed escrow comprises the networking scenario with a structured, hierarchical, configuration of the separate data in the control plane.</p>
<sec id="s3_1"><label>3.1</label><title>ESECC_SDN Cryptographic Scheme for Security</title>
<p>The proposed EsECC_SDN comprises the 5 phases those need to be encrypted and decrypted through ECC [<xref ref-type="bibr" rid="ref-43">43</xref>&#x2013;<xref ref-type="bibr" rid="ref-53">53</xref>]. The basic scenario in the encryption and decryption process is presented in <xref ref-type="disp-formula" rid="eqn-1">Eq. (1)</xref>
<disp-formula id="eqn-1"><label>(1)</label><mml:math id="mml-eqn-1" display="block"><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtext mathvariant="italic">setup</mml:mtext></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mtext mathvariant="italic">Encrypt</mml:mtext></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mtext mathvariant="italic">decrypt</mml:mtext></mml:mrow><mml:mo>,</mml:mo><mml:mi>S</mml:mi><mml:mi>D</mml:mi><mml:mi>N</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mtext mathvariant="italic">decrypt</mml:mtext></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>Consider the two prime numbers p and q with the bit size of k (i.e., <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:msup><mml:mn>2</mml:mn><mml:mrow><mml:mi>k</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>&#x003C;</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>&#x003C;</mml:mo><mml:msup><mml:mn>2</mml:mn><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula>). The generated random numbers are stated as <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mi>p</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>q</mml:mi></mml:math></inline-formula> with the random component value of <inline-formula id="ieqn-3"><mml:math id="mml-ieqn-3"><mml:mi>g</mml:mi><mml:mo>&#x2208;</mml:mo><mml:msub><mml:mi>Z</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and the order is stated as <inline-formula id="ieqn-4"><mml:math id="mml-ieqn-4"><mml:msub><mml:mi>g</mml:mi><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo>:=</mml:mo><mml:msup><mml:mi>g</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mi>m</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:msup><mml:mi>p</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. Based on the computed value hashing is performed <inline-formula id="ieqn-5"><mml:math id="mml-ieqn-5"><mml:mi>H</mml:mi><mml:mrow><mml:mo>:</mml:mo></mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>}</mml:mo></mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mo stretchy="false">&#x2192;</mml:mo><mml:msub><mml:mi>Z</mml:mi><mml:mrow><mml:mrow><mml:msup><mml:mn>2</mml:mn><mml:mrow><mml:mi>k</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mo>:</mml:mo></mml:mrow><mml:msub><mml:mi>Z</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">&#x2192;</mml:mo><mml:msup><mml:mrow><mml:mo>{</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>}</mml:mo></mml:mrow><mml:mrow><mml:mi>M</mml:mi></mml:mrow></mml:msup><mml:mo>&#x2217;</mml:mo><mml:msup><mml:mrow><mml:mo>{</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>}</mml:mo></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for the positive integer value of M. In this public key are generated as <inline-formula id="ieqn-6"><mml:math id="mml-ieqn-6"><mml:mi>P</mml:mi><mml:mi>K</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>,</mml:mo><mml:mi>g</mml:mi><mml:mo>,</mml:mo><mml:mi>H</mml:mi><mml:mo>,</mml:mo><mml:mi>G</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
<sec id="s3_1_1"><label>3.1.1</label><title>Key Generation</title>
<p>The input obtained with the random integer <italic>k</italic> is transmitted to the escrow for signature verification. The selected integer is stated as <inline-formula id="ieqn-7"><mml:math id="mml-ieqn-7"><mml:mi>k</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula> for <inline-formula id="ieqn-8"><mml:math id="mml-ieqn-8"><mml:mi>s</mml:mi><mml:mi>k</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msup><mml:mn>2</mml:mn><mml:mrow><mml:mi>k</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo>}</mml:mo></mml:mrow></mml:math></inline-formula> is computed as <inline-formula id="ieqn-9"><mml:math id="mml-ieqn-9"><mml:mi>p</mml:mi><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mi>g</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:msup><mml:mi>m</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>N</mml:mi></mml:math></inline-formula>.</p>
</sec>
<sec id="s3_1_2"><label>3.1.2</label><title>Encryption</title>
<p>The process of ECC in the encryption is involved in the computation of message as <inline-formula id="ieqn-10"><mml:math id="mml-ieqn-10"><mml:mi>m</mml:mi><mml:mtext>&#xA0;</mml:mtext><mml:mi>&#x03F5;</mml:mi><mml:msup><mml:mrow><mml:mo>{</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>}</mml:mo></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> with the public key generation of <inline-formula id="ieqn-11"><mml:math id="mml-ieqn-11"><mml:mi>p</mml:mi><mml:mi>k</mml:mi></mml:math></inline-formula> for the random integer <inline-formula id="ieqn-12"><mml:math id="mml-ieqn-12"><mml:mi>k</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula>. The ciphertext is computed as <inline-formula id="ieqn-13"><mml:math id="mml-ieqn-13"><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>B</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> with symmetric key encryption of <inline-formula id="ieqn-14"><mml:math id="mml-ieqn-14"><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mi>g</mml:mi><mml:mrow><mml:mi>H</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mi>m</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>N</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>B</mml:mi><mml:mo>=</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mo fence="false" stretchy="false">|</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
</sec>
<sec id="s3_1_3"><label>3.1.3</label><title>Decryption</title>
<p>The decryption of the encrypted data of the nodes in the MANET network is computed based on the secret key <inline-formula id="ieqn-15"><mml:math id="mml-ieqn-15"><mml:mi>s</mml:mi><mml:mi>k</mml:mi></mml:math></inline-formula> with the deciphering of the encrypted text as <inline-formula id="ieqn-16"><mml:math id="mml-ieqn-16"><mml:mi>C</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>B</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> with the computation of <inline-formula id="ieqn-17"><mml:math id="mml-ieqn-17"><mml:mi>m</mml:mi><mml:mo fence="false" stretchy="false">&#x2016;</mml:mo><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:mi>G</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>A</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:msup><mml:mi>m</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. As the proposed EsECC_SDN overall architecture of the encryption and decryption process are evaluated for analysis.</p>
<p>In MANET environment SDN estimated the escrow value for the estimation of the centralized environment. Upon the verification, the established trust between nodes is computed for data transmission and authentication. The computed network with SDN comprises the encryption and decryption for the classification of attacks in the network. The developed architecture process is presented in <xref ref-type="fig" rid="fig-1">Fig. 1</xref> and the Algorithm 1 is presented as follows.</p>
<statement id="st1" content-type="algorithm">
<label>Algorithm 1:</label>
<title>Steps: Encryption with EsECC_SDN</title>
<p><bold>Input:</bold> ECC points in the coordinates</p>
<p><bold>Output:</bold> Generated keys H and T</p>
<p>These are takes within the SDN of MANET
<list list-type="simple">
<list-item><p>1.&#x2002;&#x2002;Chooses coefficients to define the elliptical curve <inline-formula id="ieqn-18"><mml:math id="mml-ieqn-18"><mml:msup><mml:mi>y</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>a</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:mi>b</mml:mi></mml:math></inline-formula> over finite field Fn. In which, a and b define the rational integers or numbers.</p></list-item>
<list-item><p>2.&#x2002;&#x2002;Picks a based point <inline-formula id="ieqn-19"><mml:math id="mml-ieqn-19"><mml:mi>G</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> with a large order r and this gives us <inline-formula id="ieqn-20"><mml:math id="mml-ieqn-20"><mml:msup><mml:mi>G</mml:mi><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mi>E</mml:mi></mml:math></inline-formula> (where G is the binary form sequence of points in the elliptical curve for ciphertext and r is the positive integer)</p></list-item>
<list-item><p>3.&#x2002;&#x2002;Selects an integer m and m&#x2009;&#x003C;&#x2009;r.</p></list-item>
<list-item><p>4.&#x2002;&#x2002;Computes <inline-formula id="ieqn-21"><mml:math id="mml-ieqn-21"><mml:mi>B</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mi>G</mml:mi><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msup><mml:mi>m</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>q</mml:mi></mml:math></inline-formula></p></list-item>
</list>
</p>
<p>To encrypt any message w to a particular node in MANET, SDN does the following:
<list list-type="simple">
<list-item><p>1.&#x2002;&#x2002;Randomly chooses the secret integer k in which k is the secret key generated in the SDN.</p></list-item>
<list-item><p>2.&#x2002;&#x2002;Computes <inline-formula id="ieqn-22"><mml:math id="mml-ieqn-22"><mml:mi>H</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mi>G</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msup><mml:mi>m</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>n</mml:mi></mml:math></inline-formula> and <inline-formula id="ieqn-23"><mml:math id="mml-ieqn-23"><mml:mi>T</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mi>B</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msup><mml:mi>w</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>m</mml:mi><mml:mi>o</mml:mi><mml:mi>d</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>n</mml:mi></mml:math></inline-formula> in this H is the secret key generated by the sender and T is computed the receiver end along with the message sequence.</p></list-item>
<list-item><p>3.&#x2002;&#x2002;Produces the ciphertext (H, T).</p></list-item>
<list-item><p>4.&#x2002;&#x2002;SDN has the attribute values assigned for particular node A<sub>1</sub>, A<sub>2</sub>,&#x2026; An.</p></list-item>
<list-item><p>5.&#x2002;&#x2002;Computes <inline-formula id="ieqn-24"><mml:math id="mml-ieqn-24"><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>H</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi>H</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></p></list-item>
<list-item><p>6.&#x2002;&#x2002;Sends <inline-formula id="ieqn-25"><mml:math id="mml-ieqn-25"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi>H</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> to node those have data.</p></list-item>
</list>
</p>
<p><bold>Decryption</bold></p>
<p><bold>Input:</bold> Encryption points <inline-formula id="ieqn-26"><mml:math id="mml-ieqn-26"><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi>H</mml:mi></mml:math></inline-formula> and <inline-formula id="ieqn-27"><mml:math id="mml-ieqn-27"><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi>T</mml:mi></mml:math></inline-formula></p>
<p><bold>Output:</bold> Decryption of file W (file)</p>
<p>To decrypt the ciphertext <inline-formula id="ieqn-28"><mml:math id="mml-ieqn-28"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi>H</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> Alice needs to do the following:
<list list-type="order">
<list-item><p>Computes <inline-formula id="ieqn-29"><mml:math id="mml-ieqn-29"><mml:mrow><mml:mtext>R</mml:mtext></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mtext>&#xA0;A</mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mtext>n</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mtext>H</mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mtext>m</mml:mtext></mml:mrow></mml:mrow></mml:msup><mml:mrow><mml:mtext>mod n</mml:mtext></mml:mrow></mml:math></inline-formula>; R&#x2013;Encrypted message that is transferred to the receiver node</p></list-item>
</list>
</p>
<p>Recovers <inline-formula id="ieqn-30"><mml:math id="mml-ieqn-30"><mml:mrow><mml:mtext>w</mml:mtext></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mtext>A</mml:mtext></mml:mrow><mml:mrow><mml:mrow><mml:mtext>n</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mtext>T</mml:mtext></mml:mrow></mml:mrow><mml:mrow><mml:mtext>R</mml:mtext></mml:mrow></mml:mfrac></mml:mstyle><mml:mrow><mml:mtext>mod n</mml:mtext></mml:mrow></mml:math></inline-formula>; w&#x2013;Original data transmitted from the sender</p>
</statement>
<fig id="fig-1"><label>Figure 1</label><caption><title>Overall architecture of EsECC_SDN</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32140-fig-1.png"/></fig>
<p>The public keys of the system are formed by (G, B) and can be publicly in an open channel while the private key of ECC is represented as m.The encrypted data is available at the centralized SDN, the node those wants assess to within the network needs to get permission within the network that is performed in the revocation phase. The network revocation phase comprises the deep learning techniques AdaBoost integrated regression model that classifies whether the particular node is an attacker or a normal user.</p>
<p>The proposed EsECC_SDN uses <italic>Add<sub>DH</sub></italic> to denote the secure addition gate, which is given the ciphertext <italic>CT</italic><sub>1</sub> <italic>and CT</italic><sub>2</sub> of plaintext <italic>kp</italic><sub>1</sub> <italic>and kp</italic><sub>2</sub> under public key <italic>pk<sub>DH</sub></italic><sub>1</sub> <italic>and pk<sub>DH</sub></italic><sub>2</sub> respectively, the calculates the sum as <italic>c</italic>1&#x2009;&#x002B;&#x2009;<italic><sub>DH</sub> c</italic>2&#x2009;&#x003D;&#x2009;<italic>Add<sub>DH</sub></italic>(<italic>CT</italic><sub>1</sub>, <italic>CT</italic><sub>2</sub>). Similarly, MultiMF denotes the secure multiplication gate, the calculates the products as <italic>CT</italic><sub>1</sub>&#x2009;&#x00D7;&#x2009;<italic><sub>DH</sub>CT</italic><sub>2</sub>&#x2009;&#x003D;&#x2009;<italic>MultiMF</italic>(<italic>CT</italic><sub>1</sub>, <italic>CT</italic><sub>2</sub>). Similarly, MultiMF denotes the secure multiplication gate, the calculates the products as <italic>CT</italic><sub>1</sub>&#x2009;&#x00D7;&#x2009;<italic><sub>DH</sub>CT</italic><sub>2</sub>&#x2009;&#x003D;&#x2009;<italic>MultiMF</italic>(<italic>CT</italic><sub>1</sub>, <italic>CT</italic><sub>2</sub>). With the proposed EsECC_SDN transductive based HMM model is applied for the prevention and detection of attack in the MANET. As the HMM model belongs to the class of Bayesian network with computation of the probabilistics feature in the time-series analysis. The Hidden Markov model utilizes the sequences of the Hidden Markov chain in the hidden form for the computation of the different sequences randomly. In this paper the HMM is applied in the intrusion detection system for the temporal estimation of the undefined sequences in the network. The malicious within the network are computed based on the consideration of the multiple attacks with computation of the network characteristics to detect network accuracy. With estimation and identification of the temporal relationship attacks are computed and identified with consideration of the different states in the hidden layer for alerts transmits in the layer. Through application of the HMM in the malicious attack detection in the network cloud with transfer probabilities are presented in <xref ref-type="fig" rid="fig-2">Fig. 2</xref>. The state of HMM model is denoted as <italic>s</italic> with the time instances <italic>t</italic> with the node count of <italic>n<sub>i</sub></italic>. The HMM model applied in the MANET network are presented in <xref ref-type="disp-formula" rid="eqn-2">Eq. (2)</xref>
<disp-formula id="eqn-2"><label>(2)</label><mml:math id="mml-eqn-2" display="block"><mml:mi>&#x03BB;</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>B</mml:mi><mml:mo>,</mml:mo><mml:mi>H</mml:mi><mml:mo>,</mml:mo><mml:mi>C</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi><mml:mo>,</mml:mo><mml:mi>&#x03C0;</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<fig id="fig-2"><label>Figure 2</label><caption><title>HMM model for attack detection</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32140-fig-2.png"/></fig>
<p>As shown in <xref ref-type="fig" rid="fig-3">Fig. 3</xref>, the observation layer sequences are measured as <italic>N</italic>&#x2009;&#x003D;&#x2009;<italic>(n<sub>1,</sub>n<sub>2</sub>,&#x2026;, n<sub>T</sub>)</italic> with the attack intents represented as n<sub>t</sub>&#x003D; v<sub>i</sub>. At some instances, the intents within the hidden layer is presented as <inline-formula id="ieqn-31"><mml:math id="mml-ieqn-31"><mml:mi>H</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. At some times the instances can be <inline-formula id="ieqn-32"><mml:math id="mml-ieqn-32"><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> based on the attack sequence conditional probability for the vertical attacks is given as <inline-formula id="ieqn-33"><mml:math id="mml-ieqn-33"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:mi>a</mml:mi><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Also, with the intents with horizontal attack the conditional probability of the network scenario is defined as <inline-formula id="ieqn-34"><mml:math id="mml-ieqn-34"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> as <inline-formula id="ieqn-35"><mml:math id="mml-ieqn-35"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Generally, the application of HMM model comprises of the different challenges such as parameter estimation probability and decoding. The attack in the network at every stage are evaluated using transductive learning with transmission of sequence of hyper alerts with the random length of <inline-formula id="ieqn-36"><mml:math id="mml-ieqn-36"><mml:mi>L</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>M</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. In the network the positive integer value is denoted as <italic>M</italic> denoted as <inline-formula id="ieqn-37"><mml:math id="mml-ieqn-37"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>a</mml:mi><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>a</mml:mi><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mi>a</mml:mi><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. The intents of the hidden layer attack is stated as <italic>H</italic> and the probabilistic model values are represented in <xref ref-type="disp-formula" rid="eqn-3">Eq. (3)</xref>:
<disp-formula id="eqn-3"><label>(3)</label><mml:math id="mml-eqn-3" display="block"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:mi>N</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mi>&#x03BB;</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:munder><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>I</mml:mi></mml:mrow></mml:munder><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:mi>N</mml:mi><mml:mo>,</mml:mo><mml:mi>I</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mi>&#x03BB;</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:munder><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>I</mml:mi></mml:mrow></mml:munder><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:mi>N</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mi>I</mml:mi><mml:mo>,</mml:mo><mml:mi>&#x03BB;</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:mi>I</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mi>&#x03BB;</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<fig id="fig-3"><label>Figure 3</label><caption><title>Overall Architecture of ESECC_SDN</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32140-fig-3.png"/></fig>
<p>To reduce the intents for each attack both forwarding and backward operation are performed. The network hidden state is denoted as <inline-formula id="ieqn-38"><mml:math id="mml-ieqn-38"><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> with the observed node <inline-formula id="ieqn-39"><mml:math id="mml-ieqn-39"><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> with the forward probability of <inline-formula id="ieqn-40"><mml:math id="mml-ieqn-40"><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. For hidden state <inline-formula id="ieqn-41"><mml:math id="mml-ieqn-41"><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula> the corresponding state in the network is represented as <inline-formula id="ieqn-42"><mml:math id="mml-ieqn-42"><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> with the backward probability of <inline-formula id="ieqn-43"><mml:math id="mml-ieqn-43"><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> those are represented in the <xref ref-type="disp-formula" rid="eqn-4">Eqs. (4)</xref> and <xref ref-type="disp-formula" rid="eqn-5">(5)</xref>.
<disp-formula id="eqn-4"><label>(4)</label><mml:math id="mml-eqn-4" display="block"><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow><mml:mi>&#x03BB;</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-5"><label>(5)</label><mml:math id="mml-eqn-5" display="block"><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>&#x03BB;</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>The present state of intent probability is given in <xref ref-type="disp-formula" rid="eqn-6">Eq. (6)</xref>
<disp-formula id="eqn-6"><label>(6)</label><mml:math id="mml-eqn-6" display="block"><mml:msub><mml:mi>&#x03B3;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow><mml:mi>N</mml:mi><mml:mo>,</mml:mo><mml:mi>&#x03BB;</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:mi>N</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mi>&#x03BB;</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:mi>N</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mi>&#x03BB;</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:math></disp-formula></p>
<p>For backward probability, it is given in <xref ref-type="disp-formula" rid="eqn-7">Eq. (7)</xref>,
<disp-formula id="eqn-7"><label>(7)</label><mml:math id="mml-eqn-7" display="block"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:mi>N</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mi>&#x03BB;</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></disp-formula></p>
<p>Which provides,
<disp-formula id="eqn-8"><label>(8)</label><mml:math id="mml-eqn-8" display="block"><mml:msub><mml:mi>&#x03B3;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:munderover><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>j</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>j</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac></mml:math></disp-formula></p>
<p>With the defined states of model <inline-formula id="ieqn-44"><mml:math id="mml-ieqn-44"><mml:mi>&#x03BB;</mml:mi></mml:math></inline-formula>, the observation sequence <italic>N</italic>, the probabilities are computed for each states as <inline-formula id="ieqn-45"><mml:math id="mml-ieqn-45"><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-46"><mml:math id="mml-ieqn-46"><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> for the time instances <italic>t</italic> and <inline-formula id="ieqn-47"><mml:math id="mml-ieqn-47"><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula> given in <xref ref-type="disp-formula" rid="eqn-9">Eqs. (9)</xref>&#x2013;<xref ref-type="disp-formula" rid="eqn-11">(11)</xref>
<disp-formula id="eqn-9"><label>(9)</label><mml:math id="mml-eqn-9" display="block"><mml:msub><mml:mi>&#x03B4;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow><mml:mi>N</mml:mi><mml:mo>,</mml:mo><mml:mi>&#x03BB;</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow><mml:mi>N</mml:mi><mml:mo>,</mml:mo><mml:mi>&#x03BB;</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:mi>N</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mi>&#x03BB;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac></mml:math></disp-formula>
<disp-formula id="eqn-10"><label>(10)</label><mml:math id="mml-eqn-10" display="block"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:mi>N</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mi>&#x03BB;</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>j</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></disp-formula>
<disp-formula id="eqn-11"><label>(11)</label><mml:math id="mml-eqn-11" display="block"><mml:msub><mml:mi>&#x03B4;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>j</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:munderover><mml:msubsup><mml:mrow><mml:mo>&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>j</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac></mml:math></disp-formula></p>
<p>The simplified form of the equation is presented in <xref ref-type="disp-formula" rid="eqn-12">Eq. (12)</xref>,
<disp-formula id="eqn-12"><label>(12)</label><mml:math id="mml-eqn-12" display="block"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:mi>N</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mi>&#x03BB;</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:munderover><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:munderover><mml:msub><mml:mi>&#x03B1;</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>&#x03B2;</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>j</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>With the HM model the trained model is represented as <inline-formula id="ieqn-48"><mml:math id="mml-ieqn-48"><mml:mi>&#x03BB;</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>C</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi><mml:mo>,</mml:mo><mml:mi>&#x03C0;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>.</p>
</sec>
</sec>
<sec id="s3_2"><label>3.2</label><title>Transductive Transfer Learning Framework</title>
<p>In second phase of the proposed ESECC_SDN architecture transfer learning with the transductive (TL) is formulated for the attack prevention. The constructed TL model involved in binary classification process for the labelled instances represented as <inline-formula id="ieqn-49"><mml:math id="mml-ieqn-49"><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. The attack prevention can be denoted as <inline-formula id="ieqn-50"><mml:math id="mml-ieqn-50"><mml:msub><mml:mi>A</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math></inline-formula> with assignment of label classes in the label cluster. With the defined technique the soft label instances are computed for the threshold values those are involved in data transfer clustering process. The labels in the TL are evaluated and derived with the HMM model values without any attack stated as <inline-formula id="ieqn-51"><mml:math id="mml-ieqn-51"><mml:mi>&#x03BB;</mml:mi></mml:math></inline-formula>. As stated earlier the HM model uses the attack detection and prevention denoted as <inline-formula id="ieqn-52"><mml:math id="mml-ieqn-52"><mml:mi>&#x03BB;</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>C</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi><mml:mo>,</mml:mo><mml:mi>&#x03C0;</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:math></inline-formula> The <xref ref-type="fig" rid="fig-3">Fig. 3</xref> illustrates the overall architecture for the proposed ESECC_SDN model is presented.</p>
<sec id="s3_2_1"><label>3.2.1</label><title>Attack Prevention with ESECC_SDN</title>
<p>The attack prevention in the network is evaluated based on the domain capturing semantics with calculation of the HMM model ranking with consideration of the cluster group mean. The formulation of cluster is based on the consideration of the length of the cluster defined as <inline-formula id="ieqn-53"><mml:math id="mml-ieqn-53"><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mn>1</mml:mn><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup><mml:mtext>&#xA0;</mml:mtext><mml:mrow><mml:mtext>and</mml:mtext></mml:mrow><mml:mtext>&#xA0;</mml:mtext><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:msup><mml:mn>1</mml:mn><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> for the different domains. In the constructed cluster the similarity index is formulated as <inline-formula id="ieqn-54"><mml:math id="mml-ieqn-54"><mml:msubsup><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula>. In the cluster domain <italic>p</italic> and <inline-formula id="ieqn-55"><mml:math id="mml-ieqn-55"><mml:msup><mml:mi>i</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> offers the <italic>q</italic> value of 1. Similarly, with the domain <italic>p</italic> and <inline-formula id="ieqn-56"><mml:math id="mml-ieqn-56"><mml:mi>q</mml:mi></mml:math></inline-formula> for instances <inline-formula id="ieqn-57"><mml:math id="mml-ieqn-57"><mml:mo stretchy="false">(</mml:mo><mml:mi>i</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> and <inline-formula id="ieqn-58"><mml:math id="mml-ieqn-58"><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> the values are measured as 0.5 else it will be assigned as 0. Through source transformation domain the mapping function targeted to compute the latent space <italic>d</italic> for the different attack scenarios. Subsequently, the attack domain conversion is evaluated based on the label instances latent space for the classification of the target domain to prevent attacks. To perform attack prevention soft labelling is applied in the target instances with the appropriate training within the classifier. Through the derived HMM model the deep learning framework model uses the cluster score assignment for the attack prevention. Initially, the source cluster are assigned with labels either &#x201C;normal&#x201D; or &#x201C;attack&#x201D;. The network target domain is denoted as <inline-formula id="ieqn-59"><mml:math id="mml-ieqn-59"><mml:msubsup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> and <inline-formula id="ieqn-60"><mml:math id="mml-ieqn-60"><mml:msubsup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> based on source label Euclidean distance estimation and ranking as <inline-formula id="ieqn-61"><mml:math id="mml-ieqn-61"><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula>, the labelling process in the HMM model is defined in sequence of steps those are listed as follows:</p>
<p><bold>Step 1:</bold> Initially, all labels are stated as zero</p>
<p><bold>Step 2:</bold> If ranked as <inline-formula id="ieqn-62"><mml:math id="mml-ieqn-62"><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> in the source cluster then consider the attack <inline-formula id="ieqn-63"><mml:math id="mml-ieqn-63"><mml:mi>&#x03B1;</mml:mi></mml:math></inline-formula> is applied in the cluster else it eliminates form the cluster group</p>
<p><bold>Step 3:</bold> If the source cluster ranking is provided as <inline-formula id="ieqn-64"><mml:math id="mml-ieqn-64"><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula>, with the attack <inline-formula id="ieqn-65"><mml:math id="mml-ieqn-65"><mml:mfrac><mml:mi>&#x03B1;</mml:mi><mml:mn>2</mml:mn></mml:mfrac></mml:math></inline-formula> in the system else it will be eliminated from the group cluster.</p>
<p><bold>Step 4:</bold> For ranking as <inline-formula id="ieqn-66"><mml:math id="mml-ieqn-66"><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula> in source cluster, then attack <inline-formula id="ieqn-67"><mml:math id="mml-ieqn-67"><mml:mfrac><mml:mi>&#x03B1;</mml:mi><mml:mn>2</mml:mn></mml:mfrac></mml:math></inline-formula> is incorporated in the cluster else it will be removed in the cluster.</p>
<p>Finally, the target score is computed for the estimated attacks in the instances of the cluster group. The instances threshold values <inline-formula id="ieqn-68"><mml:math id="mml-ieqn-68"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> provided for the soft labels of &#x201C;attack&#x201D; else the network <inline-formula id="ieqn-69"><mml:math id="mml-ieqn-69"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> considered below the threshold and considered as &#x201C;normal&#x201D;. The instances target is defined as follows:
<disp-formula id="ueqn-1">
<mml:math id="mml-ueqn-1" display="block"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>&#x03B1;</mml:mi><mml:mtext>&#xA0;</mml:mtext><mml:mi mathvariant="normal">&#x2216;</mml:mi><mml:mi mathvariant="normal">&#x2216;</mml:mi><mml:mtext>&#xA0;</mml:mtext><mml:mrow><mml:mtext>Assign as attack</mml:mtext></mml:mrow></mml:math></disp-formula>
<disp-formula id="ueqn-2">
<mml:math id="mml-ueqn-2" display="block"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>&#x03B1;</mml:mi><mml:mtext>&#xA0;</mml:mtext><mml:mi mathvariant="normal">&#x2216;</mml:mi><mml:mi mathvariant="normal">&#x2216;</mml:mi><mml:mtext>&#xA0;</mml:mtext><mml:mrow><mml:mtext>Assign label as normal</mml:mtext></mml:mrow></mml:math></disp-formula></p>
<p>In those assigned labels the instances are classified and prevented in the network with generation of the soft labels. Within the cluster group the labels are assigned based consideration of different attack parts to perform classification. The cluster within the node are evaluated based on consideration of different factors such as conditional probability table (CPT), prior knowledge and edge probability. Through the causality the attacks are estimated in the HMM model with the transductive transfer learning. Hence, the unknown attack label instances are estimated and updated as given in <xref ref-type="disp-formula" rid="eqn-13">Eq. (13)</xref>
<disp-formula id="eqn-13"><label>(13)</label><mml:math id="mml-eqn-13" display="block"><mml:msubsup><mml:mrow><mml:mi>U</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left left left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mi>&#x03B4;</mml:mi><mml:mo>+</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>&#x03B4;</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msubsup><mml:mrow><mml:mi>U</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>,</mml:mo></mml:mtd><mml:mtd><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mtd><mml:mtd><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>&#x03B4;</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msubsup><mml:mrow><mml:mi>U</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>,</mml:mo></mml:mtd><mml:mtd><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mtd><mml:mtd><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msubsup><mml:mrow><mml:mrow><mml:mtext>U</mml:mtext></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mtext>ij</mml:mtext></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mtext>t</mml:mtext></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mtd><mml:mtd><mml:mrow><mml:mtext>otherwise</mml:mtext></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>Based on the assigned label instances for the unknown attack <inline-formula id="ieqn-70"><mml:math id="mml-ieqn-70"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-71"><mml:math id="mml-ieqn-71"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> instances with the CPT are denoted as <inline-formula id="ieqn-72"><mml:math id="mml-ieqn-72"><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow><mml:mi>U</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. In <xref ref-type="fig" rid="fig-4">Fig. 4</xref> the overall architecture process involved in proposed ESECC_SDN is presented for attack prevention and detection. The attack detected with the HMM model comprises of the transductive network model for the attack training and computational process.</p>
<fig id="fig-4"><label>Figure 4</label><caption><title>Overall Flow of ESECC_SDN</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32140-fig-4.png"/></fig>
<p>In the dataset the assigned label is evaluated with the elimination of the attacks represented as <inline-formula id="ieqn-73"><mml:math id="mml-ieqn-73"><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>}</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> through elimination of the data attack <inline-formula id="ieqn-74"><mml:math id="mml-ieqn-74"><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. The attack scenario in the HMM model is stated as <inline-formula id="ieqn-75"><mml:math id="mml-ieqn-75"><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. The Algorithm 2 provides the estimation of attack scenario in the network is presented below.</p>
<statement id="st2" content-type="algorithm">
<label>Algorithm 2:</label>
<title>Parameter Estimation</title>
<p>Input: Sequence of attack in network&#x2009;&#x003D;&#x2009;<inline-formula id="ieqn-76"><mml:math id="mml-ieqn-76"><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>a</mml:mi><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>a</mml:mi><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2026;</mml:mo><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>a</mml:mi><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>a</mml:mi><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2026;</mml:mo><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2026;</mml:mo><mml:mo>}</mml:mo></mml:mrow></mml:math></inline-formula></p>
<p>Output: <inline-formula id="ieqn-77"><mml:math id="mml-ieqn-77"><mml:msup><mml:mi>&#x03B4;</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>C</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:msup><mml:mi>J</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:msup><mml:mi>&#x03BB;</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></p>
<p>// Start</p>
<p>For n&#x2009;&#x003D;&#x2009;0 generate <inline-formula id="ieqn-78"><mml:math id="mml-ieqn-78"><mml:msubsup><mml:mrow><mml:mi>&#x03B4;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:math></inline-formula></p>
<p>For <inline-formula id="ieqn-79"><mml:math id="mml-ieqn-79"><mml:msubsup><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>&#x03B4;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:math></inline-formula> set <inline-formula id="ieqn-80"><mml:math id="mml-ieqn-80"><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>k</mml:mi><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></p>
<p>For unknown attack n&#x2009;&#x003D;&#x2009;0, 1, 2&#x2026;</p>
<p>&#x2002;&#x2002;do</p>
<p>Calculate using <xref ref-type="disp-formula" rid="eqn-11">Eq. (11)</xref></p>
<p>Calculate using <xref ref-type="disp-formula" rid="eqn-12">Eq. (12)</xref></p>
<p>&#x2002;&#x2002;End for</p>
<p>&#x2002;End for</p>
<p>Set values</p>
<p>Set comparison value</p>
<p>&#x2002;&#x2002;If <inline-formula id="ieqn-81"><mml:math id="mml-ieqn-81"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo><mml:msub><mml:mi>Z</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>|</mml:mo></mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003E;</mml:mo><mml:mrow><mml:mtext mathvariant="italic">trust Value</mml:mtext></mml:mrow></mml:math></inline-formula></p>
<p>&#x2002;&#x2002;&#x2002;then</p>
<p>Compare <inline-formula id="ieqn-82"><mml:math id="mml-ieqn-82"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-83"><mml:math id="mml-ieqn-83"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> with estimated value</p>
<p>&#x2002;&#x2002;End if</p>
<p>&#x2002;&#x2002;&#x2002;for <inline-formula id="ieqn-84"><mml:math id="mml-ieqn-84"><mml:mrow><mml:mtext mathvariant="italic">value</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>Z</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> compare attack value</p>
<p>&#x2002;&#x2002;&#x2002;&#x2002;If <inline-formula id="ieqn-85"><mml:math id="mml-ieqn-85"><mml:mrow><mml:mtext mathvariant="italic">value</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>Z</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003E;</mml:mo><mml:mrow><mml:mtext mathvariant="italic">trust Value</mml:mtext></mml:mrow></mml:math></inline-formula> then</p>
<p>&#x2002;&#x2002;&#x2002;&#x2002;Compute new set <inline-formula id="ieqn-86"><mml:math id="mml-ieqn-86"><mml:msub><mml:mi>Z</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></p>
<p>&#x2002;&#x2002;&#x2002;&#x2002;End if</p>
<p>&#x2002;&#x2002;&#x2002;End for</p>
<p>&#x2002;&#x2002;End for</p>
</statement>
<p>In transductive model the source mapping is generated for the targeted source with computation of the latent space in the domain. Through the conversion of the latent space the labels are assigned to the attack classifier. The soft label assignment provides the data accuracy process for the classifier training in the instances of the target. The assignment of the attack estimation is presented in Algorithm 3 for the prevention and classification.</p>
<p>The HMM based attack estimation computes the attack instances in the network through the calculated threshold values with the threshold label assignment and construction of the parameters. The developed model uses the transductive deep learning model for the training in which the attack are characterized as <inline-formula id="ieqn-87"><mml:math id="mml-ieqn-87"><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">attack</mml:mtext></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> and network real data is represented as <italic>D</italic>. In real-time data the training sequences are defined as <inline-formula id="ieqn-88"><mml:math id="mml-ieqn-88"><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> for the transductive layer value of 1. The maximization process in the transductive learning is given as <inline-formula id="ieqn-89"><mml:math id="mml-ieqn-89"><mml:mi>V</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mo>,</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> for the trained data <italic>D</italic> in the layer <italic>S</italic>. Similarly, with the minimization of the second order training in data <inline-formula id="ieqn-90"><mml:math id="mml-ieqn-90"><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> the attack prevention and detection is evaluated using <inline-formula id="ieqn-91"><mml:math id="mml-ieqn-91"><mml:mi>V</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mo>,</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> as <inline-formula id="ieqn-92"><mml:math id="mml-ieqn-92"><mml:munder><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:munder><mml:mo>&#x2061;</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:munder><mml:mrow><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:munder><mml:mo>&#x2061;</mml:mo><mml:mtext>&#x00A0;</mml:mtext><mml:mi>V</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>,</mml:mo><mml:mi>S</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">attack</mml:mtext></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mi>log</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>z</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>z</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>Z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo stretchy="false">[</mml:mo><mml:mi>log</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:math></inline-formula> The distributed data convergence is denoted as <italic>V (D, S)</italic> with the detection of attack in transductive learning process is computed as <inline-formula id="ieqn-93"><mml:math id="mml-ieqn-93"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>Z</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. The convergence in data is presented in <xref ref-type="disp-formula" rid="eqn-14">Eq. (14)</xref>.
<disp-formula id="eqn-14"><label>(14)</label><mml:math id="mml-eqn-14" display="block"><mml:msub><mml:mi>Z</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula>
In the TDL system the attacks are computed as presented in <xref ref-type="disp-formula" rid="eqn-15">Eqs. (15)</xref> and <xref ref-type="disp-formula" rid="eqn-16">(16)</xref>
<disp-formula id="eqn-15"><label>(15)</label><mml:math id="mml-eqn-15" display="block"><mml:munder><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:munder><mml:mo>&#x2061;</mml:mo><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:mi>g</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>Z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>
<disp-formula id="eqn-16"><label>(16)</label><mml:math id="mml-eqn-16" display="block"><mml:mo stretchy="false">&#x21D4;</mml:mo><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>Z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2248;</mml:mo><mml:mn>1</mml:mn></mml:math></disp-formula>
<disp-formula id="ueqn-3">
<mml:math id="mml-ueqn-3" display="block"><mml:mo stretchy="false">&#x21D4;</mml:mo><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2248;</mml:mo><mml:mi>x</mml:mi><mml:mo>&#x2208;</mml:mo><mml:mi>&#x03C7;</mml:mi><mml:mo>;</mml:mo></mml:math></disp-formula>In above condition the <inline-formula id="ieqn-94"><mml:math id="mml-ieqn-94"><mml:mi>&#x03C7;</mml:mi></mml:math></inline-formula> represets the dataset in real-time scenario. The training process in the HMM-TDL is given in <xref ref-type="disp-formula" rid="eqn-17">Eq. (17)</xref> as follows:
<disp-formula id="eqn-17"><label>(17)</label><mml:math id="mml-eqn-17" display="block"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:msup><mml:mi>S</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2264;</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:mi>S</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mi>S</mml:mi></mml:math></disp-formula></p>
<p>With incorporated HMM model with transductive deep learning attack is detection and those are subjected to constraints represented as in <xref ref-type="disp-formula" rid="eqn-18">Eqs. (18)</xref>&#x2013;<xref ref-type="disp-formula" rid="eqn-28">(28)</xref></p>
<p>Case 1: If <inline-formula id="ieqn-95"><mml:math id="mml-ieqn-95"><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">attack</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mo>&#x2248;</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> data used in the training process xConsider <inline-formula id="ieqn-96"><mml:math id="mml-ieqn-96"><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:mspace width="thinmathspace" /><mml:msup><mml:mi>S</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> for the minimal data value of
   <inline-formula id="ieqn-97"><mml:math id="mml-ieqn-97"><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">attack</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2264;</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></p>
<p>This will be<inline-formula id="ieqn-98"><mml:math id="mml-ieqn-98"><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">attack</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2264;</mml:mo><mml:msub><mml:mrow><mml:msup><mml:mi>A</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></p>
<disp-formula id="eqn-18"><label>(18)</label><mml:math id="mml-eqn-18" display="block"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:mi>S</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">attack</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>z</mml:mi></mml:math></disp-formula>
<disp-formula id="eqn-19"><label>(19)</label><mml:math id="mml-eqn-19" display="block"><mml:mo>=</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">attack</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi></mml:math></disp-formula>
<disp-formula id="eqn-20"><label>(20)</label><mml:math id="mml-eqn-20" display="block"><mml:mo>=</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">attack</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi></mml:math></disp-formula>
<disp-formula id="eqn-21"><label>(21)</label><mml:math id="mml-eqn-21" display="block"><mml:mo>=</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mn>1</mml:mn><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">attack</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003E;</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">attack</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi></mml:math></disp-formula>
<disp-formula id="eqn-22"><label>(22)</label><mml:math id="mml-eqn-22" display="block"><mml:mo>&#x2265;</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi></mml:math></disp-formula>
<p>Case 2: Consider <inline-formula id="ieqn-99"><mml:math id="mml-ieqn-99"><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:mspace width="thinmathspace" /><mml:msup><mml:mi>S</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> as minimal value for data</p>
<disp-formula id="ueqn-4"><mml:math id="mml-ueqn-4" display="block"><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">attack</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2265;</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula>
<p>This will be <inline-formula id="ieqn-100"><mml:math id="mml-ieqn-100"><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">attack</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2265;</mml:mo><mml:msub><mml:mrow><mml:msup><mml:mi>A</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
<disp-formula id="eqn-23"><label>(23)</label><mml:math id="mml-eqn-23" display="block"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:mi>S</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">attack</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>S</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>z</mml:mi></mml:math></disp-formula>
<disp-formula id="eqn-24"><label>(24)</label><mml:math id="mml-eqn-24" display="block"><mml:mo>=</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">attack</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi></mml:math></disp-formula>
<disp-formula id="eqn-25"><label>(25)</label><mml:math id="mml-eqn-25" display="block"><mml:mo>=</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mrow><mml:msup><mml:mi>G</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>p</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi></mml:math></disp-formula>
<disp-formula id="eqn-26"><label>(26)</label><mml:math id="mml-eqn-26" display="block"><mml:mo>=</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mn>1</mml:mn><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:mtext mathvariant="italic">attack</mml:mtext></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003E;</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:msup><mml:mi>G</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:msup><mml:mi>G</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi></mml:math></disp-formula></p>
<statement id="st3" content-type="algorithm">
<label>Algorithm 3:</label>
<title>Attack Estimation parameters</title>
<p>Input: Compute the target domain</p>
<p>Output: Assign the label for the attacks for the latent space in d-dimensions</p>
<p>&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;Construct the data node matrix <inline-formula id="ieqn-101"><mml:math id="mml-ieqn-101"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mtable columnalign="left left left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mn>0</mml:mn><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:mn>0</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x2026;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mn>0</mml:mn><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:mn>0</mml:mn></mml:mtd><mml:mtd><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
<list list-type="order">
<list-item><p>Compute matrix <inline-formula id="ieqn-102"><mml:math id="mml-ieqn-102"><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> for estimation of node distances as <inline-formula id="ieqn-103"><mml:math id="mml-ieqn-103"><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>.</mml:mo><mml:mi>j</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msup><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:msup></mml:math></inline-formula></p></list-item>
<list-item><p>Compute similarity indices in the matrix using Laplacian transformation <inline-formula id="ieqn-104"><mml:math id="mml-ieqn-104"><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></p></list-item>
<list-item><p>Compute the attack node using Laplacian matrix for attack computation <inline-formula id="ieqn-105"><mml:math id="mml-ieqn-105"><mml:mi>L</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mtable columnalign="left left left" rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mn>0</mml:mn><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:mn>0</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:mo>&#x2026;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mn>0</mml:mn><mml:mo>&#x2026;</mml:mo></mml:mtd><mml:mtd><mml:mn>0</mml:mn></mml:mtd><mml:mtd><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></p></list-item>
<list-item><p>Compute eigen vector dimensionality with mapping function <inline-formula id="ieqn-106"><mml:math id="mml-ieqn-106"><mml:mi>Z</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>&#x03B4;</mml:mi><mml:mi>L</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mi>Z</mml:mi><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mi>&#x03B4;</mml:mi><mml:mi>Z</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mi>Z</mml:mi><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mi>x</mml:mi></mml:math></inline-formula></p></list-item>
<list-item><p>Transform latent dimension of data as the target domain</p></list-item>
</list>
</p>
</statement>
<disp-formula id="eqn-27"><label>(27)</label><mml:math id="mml-eqn-27" display="block"><mml:mo>&#x2265;</mml:mo><mml:msub><mml:mo>&#x222B;</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mn>1</mml:mn><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003E;</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mrow><mml:msup><mml:mi>G</mml:mi><mml:mrow><mml:mo>&#x2217;</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>a</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi></mml:math></disp-formula>
<disp-formula id="eqn-28"><label>(28)</label><mml:math id="mml-eqn-28" display="block"><mml:mo>&#x2265;</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>M</mml:mi></mml:math></disp-formula>
</sec>
</sec>
<sec id="s3_3"><label>3.3</label><title>Dataset Description</title>
<p>The proposed EsECC_SDN concentrated on the attack classification mechanism for MANET environment. To estimate the attack detection and classification this paper uses CICICS 2020 dataset. The SDN mechanism focused on the attack classification and detection rate of the network. The proposed scheme uses the SVM classification model for attack detection. However, for efficient processing of data optimal subset features need to be processed with the elimination of irrelevant features without impact on the computational cost and accuracy. The attack classification model for MANET is presented in <xref ref-type="fig" rid="fig-5">Fig. 5</xref>. The developed EsECC_SDN uses the CICIDS dataset for training and testing the attack. Based on the attributes of the given dataset, attacks in the MANET are computed for training and testing of the attack sequences. The separation of the dataset for training and testing is presented in <xref ref-type="table" rid="table-2">Tab. 2</xref>.</p>
<fig id="fig-5"><label>Figure 5</label><caption><title>EsECC_SDN attack classification Model</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32140-fig-5.png"/></fig><table-wrap id="table-2"><label>Table 2</label><caption><title>Dataset distribution</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left"/>
<th align="left">Data distribution</th>
<th align="left">Training count</th>
<th align="left">Testing count</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left" rowspan="7">Attack distribution</td>
<td align="left">Normal activity</td>
<td align="left">67,343</td>
<td align="left">9,710</td>
</tr>
<tr>
<td align="left">Anomaly</td>
<td align="left">58,630</td>
<td align="left">12,834</td>
</tr>
<tr>
<td align="left">DoS</td>
<td align="left">45,927</td>
<td align="left">7,458</td>
</tr>
<tr>
<td align="left">Probe attack</td>
<td align="left">11,656</td>
<td align="left">2,422</td>
</tr>
<tr>
<td align="left">U2R (User to root) attack</td>
<td align="left">52</td>
<td align="left">67</td>
</tr>
<tr>
<td align="left">R2L (Root to local)</td>
<td align="left">995</td>
<td align="left">2,887</td>
</tr>
<tr>
<td align="left">Black hole attack</td>
<td align="left">12,945</td>
<td align="left">999</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>With the distribution of training and testing of the dataset, attacks are computed in the MANET network. The training of data comprises 70&#x0025; of data for training to achieve the desired accuracy with the remaining data is utilized for testing the performance of the network.</p>
</sec>
</sec>
<sec id="s4"><label>4</label><title>Simulation Results</title>
<p>The performance of the proposed EsECC_SDN is implemented in Network Simulator [<xref ref-type="bibr" rid="ref-3">3</xref>] attack detection and prevention in the MANET environment. <xref ref-type="table" rid="table-3">Tab. 3</xref> presents the simulation setting for the proposed EsECC_SDN. With SDN centralized architecture performance characteristics of EsECC_SDN are evaluated. The simulation is computed under two scenarios such as:
<list list-type="bullet">
<list-item><p>A varying number of nodes</p>
</list-item>
<list-item><p>Attackers Scenario</p></list-item>
</list></p>
<table-wrap id="table-3"><label>Table 3</label><caption><title>Simulation setting</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Simulation parameters</th>
<th align="left">Values</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Simulation software</td>
<td align="left">Phython</td>
</tr>
<tr>
<td align="left">Mobility of node</td>
<td align="left">4 (ms/s), 6 (ms/s) and 10 (ms/s)</td>
</tr>
<tr>
<td align="left">No.of nodes</td>
<td align="left">10, 20, 30, 40, and 50</td>
</tr>
<tr>
<td align="left">Channel</td>
<td align="left">Multi-path</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The performance characteristics of the proposed EsECC_SDN with the different parameters are computed those are Delay, Jitter, End-to-End delay, Packet Delivery Rate (PDR) and Throughput.</p>
<p>The performance of the proposed ESECC_SDN scheme performance is computed based on the varying mobility of nodes. The mobility of nodes is varied with respect to 4, 6 and 10 (ms/s). Similarly, for varying the mobility number of nodes are varied as 10, 20, 30, 40, and 50. <xref ref-type="table" rid="table-4">Tab. 4</xref> presented the performance of the network for varying mobility of nodes.The performance of the proposed EsECC_SDN is comparatively examined with the existing technique such as Dynamic Source Routing (DSR) [<xref ref-type="bibr" rid="ref-19">19</xref>], Three-Dimensional Clustered (TDC) [<xref ref-type="bibr" rid="ref-20">20</xref>] and Artificial Danger Theory (ADT) [<xref ref-type="bibr" rid="ref-17">17</xref>]. The performance of the proposed EsECC_SDN architecture involved in encryption and decryption of MANET data for analysis. The comparison of the performance is estimated based on the varying number of nodes and the attack nodes in the MANET environment.</p>
<table-wrap id="table-4"><label>Table 4</label><caption><title>Performance computation of MANET without attackers</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="center" colspan="5">Delay (s)</th>
</tr>
<tr>
<th align="left">No.of nodes</th>
<th align="left">DSR [<xref ref-type="bibr" rid="ref-19">19</xref>]</th>
<th align="left">Three-dimensional clustering (TDC) [<xref ref-type="bibr" rid="ref-20">20</xref>]</th>
<th align="left">Artificial danger theory (ADT) [<xref ref-type="bibr" rid="ref-17">17</xref>]</th>
<th align="left">EsECC_SDN proposed</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">10</td>
<td align="left">21</td>
<td align="left">18</td>
<td align="left">16</td>
<td align="left">8</td>
</tr>
<tr>
<td align="left">20</td>
<td align="left">27</td>
<td align="left">21</td>
<td align="left">20</td>
<td align="left">10</td>
</tr>
<tr>
<td align="left">30</td>
<td align="left">34</td>
<td align="left">26</td>
<td align="left">24</td>
<td align="left">13</td>
</tr>
<tr>
<td align="left">40</td>
<td align="left">39</td>
<td align="left">29</td>
<td align="left">28</td>
<td align="left">16</td>
</tr>
<tr>
<td align="left">50</td>
<td align="left">43</td>
<td align="left">32</td>
<td align="left">31</td>
<td align="left">19</td>
</tr>
<tr>
<td align="center" colspan="5">Loss &#x0025;</td>
</tr>
<tr>
<td align="left">No.of nodes</td>
<td align="left">DSR [<xref ref-type="bibr" rid="ref-19">19</xref>]</td>
<td align="left">Three-dimensional clustering (TDC) [<xref ref-type="bibr" rid="ref-20">20</xref>]</td>
<td align="left">Artificial danger theory (ADT) [<xref ref-type="bibr" rid="ref-17">17</xref>]</td>
<td align="left">EsECC_SDN proposed</td>
</tr>
<tr>
<td align="left">10</td>
<td align="left">33</td>
<td align="left">28</td>
<td align="left">21</td>
<td align="left">10</td>
</tr>
<tr>
<td align="left">20</td>
<td align="left">38</td>
<td align="left">31</td>
<td align="left">26</td>
<td align="left">13</td>
</tr>
<tr>
<td align="left">30</td>
<td align="left">42</td>
<td align="left">34</td>
<td align="left">29</td>
<td align="left">19</td>
</tr>
<tr>
<td align="left">40</td>
<td align="left">46</td>
<td align="left">38</td>
<td align="left">32</td>
<td align="left">23</td>
</tr>
<tr>
<td align="left">50</td>
<td align="left">52</td>
<td align="left">42</td>
<td align="left">36</td>
<td align="left">27</td>
</tr>
<tr>
<td align="center" colspan="5">PDR &#x0025;</td>
</tr>
<tr>
<td align="left">No.of nodes</td>
<td align="left">DSR [<xref ref-type="bibr" rid="ref-19">19</xref>]</td>
<td align="left">Three-dimensional clustering (TDC) [<xref ref-type="bibr" rid="ref-20">20</xref>]</td>
<td align="left">Artificial danger theory (ADT) [<xref ref-type="bibr" rid="ref-17">17</xref>]</td>
<td align="left">EsECC_SDN proposed</td>
</tr>
<tr>
<td align="left">10</td>
<td align="left">43</td>
<td align="left">58</td>
<td align="left">73</td>
<td align="left">99</td>
</tr>
<tr>
<td align="left">20</td>
<td align="left">40</td>
<td align="left">52</td>
<td align="left">69</td>
<td align="left">98</td>
</tr>
<tr>
<td align="left">30</td>
<td align="left">37</td>
<td align="left">48</td>
<td align="left">67</td>
<td align="left">97</td>
</tr>
<tr>
<td align="left">40</td>
<td align="left">34</td>
<td align="left">43</td>
<td align="left">64</td>
<td align="left">97</td>
</tr>
<tr>
<td align="left">50</td>
<td align="left">29</td>
<td align="left">38</td>
<td align="left">63</td>
<td align="left">96</td>
</tr>
<tr>
<td align="center" colspan="5">Control Overhead</td>
</tr>
<tr>
<td align="left">No.of nodes</td>
<td align="left">DSR [<xref ref-type="bibr" rid="ref-19">19</xref>]</td>
<td align="left">Three-dimensional clustering (TDC) [<xref ref-type="bibr" rid="ref-20">20</xref>]</td>
<td align="left">Artificial danger theory (ADT) [<xref ref-type="bibr" rid="ref-17">17</xref>]</td>
<td align="left">Esecc_SDN proposed</td>
</tr>
<tr>
<td align="left">10</td>
<td align="left">21.89</td>
<td align="left">10.67</td>
<td align="left">4.78</td>
<td align="left">1.49</td>
</tr>
<tr>
<td align="left">20</td>
<td align="left">19.73</td>
<td align="left">9.75</td>
<td align="left">5.34</td>
<td align="left">1.64</td>
</tr>
<tr>
<td align="left">30</td>
<td align="left">16.57</td>
<td align="left">8.56</td>
<td align="left">5.89</td>
<td align="left">1.93</td>
</tr>
<tr>
<td align="left">40</td>
<td align="left">13.47</td>
<td align="left">8.45</td>
<td align="left">6.35</td>
<td align="left">2.34</td>
</tr>
<tr>
<td align="left">50</td>
<td align="left">10.56</td>
<td align="left">7.89</td>
<td align="left">7.50</td>
<td align="left">2.96</td>
</tr>
<tr>
<td align="center" colspan="5">Throughput (kbps)</td>
</tr>
<tr>
<td align="left">No.of nodes</td>
<td align="left">DSR [<xref ref-type="bibr" rid="ref-19">19</xref>]</td>
<td align="left">Three-dimensional clustering (TDC) [<xref ref-type="bibr" rid="ref-20">20</xref>]</td>
<td align="left">Artificial danger theory (ADT) [<xref ref-type="bibr" rid="ref-17">17</xref>]</td>
<td align="left">EsECC_SDN proposed</td>
</tr>
<tr>
<td align="left">10</td>
<td align="left">43</td>
<td align="left">51</td>
<td align="left">59</td>
<td align="left">63</td>
</tr>
<tr>
<td align="left">20</td>
<td align="left">39</td>
<td align="left">48</td>
<td align="left">55</td>
<td align="left">60</td>
</tr>
<tr>
<td align="left">30</td>
<td align="left">36</td>
<td align="left">46</td>
<td align="left">53</td>
<td align="left">58</td>
</tr>
<tr>
<td align="left">40</td>
<td align="left">33</td>
<td align="left">43</td>
<td align="left">48</td>
<td align="left">55</td>
</tr>
<tr>
<td align="left">50</td>
<td align="left">28</td>
<td align="left">41</td>
<td align="left">44</td>
<td align="left">51</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="fig" rid="fig-6">Fig. 6</xref> shows the delay of the proposed EsECC_SDN compared with the DSR, TDC, and ADT. Simulation results show that the proposed method gives a minimum delay when the node count is from 10 to 50 nodes.</p>
<fig id="fig-6"><label>Figure 6</label><caption><title>Comparison of delay</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32140-fig-6.png"/></fig>
<p><xref ref-type="fig" rid="fig-7">Fig. 7</xref> shows the loss of the proposed EsECC_SDN compared with the DSR, TDC, and ADT. Simulation results show that the proposed method gives a minimum loss when the node count is from 10 to 50 nodes. <xref ref-type="fig" rid="fig-8">Fig. 8</xref> shows the packet delivery ratio of the proposed EsECC_SDN compared with the DSR, TDC, and ADT. Simulation results show that the proposed method gives a maximum packet delivery ratio when the node count is from 10 to 50 nodes.</p>
<fig id="fig-7"><label>Figure 7</label><caption><title>Comparison of loss</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32140-fig-7.png"/></fig><fig id="fig-8"><label>Figure 8</label><caption><title>Comparison of PDR</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32140-fig-8.png"/></fig>
<p><xref ref-type="fig" rid="fig-9">Fig. 9</xref> shows the control overhead of the proposed EsECC_SDN compared with the DSR, TDC, and ADT. Simulation results show that the proposed method required a minimum overhead when the node count is from 10 to 50 nodes. <xref ref-type="fig" rid="fig-10">Fig. 10</xref> shows the throughput of the proposed EsECC_SDN compared with the DSR, TDC, and ADT. Simulation results show that the proposed method gives a maximum throughput when the node count is from 10 to 50 nodes. The performance of the proposed EsECC_SDN expressed that with an increase in the number of nodes loss and delay is increases. Furthermore, the PDR and throughput of the MANET network are reduced compared with existing techniques.</p>
<fig id="fig-9"><label>Figure 9</label><caption><title>Comparison of control overhead</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32140-fig-9.png"/></fig><fig id="fig-10"><label>Figure 10</label><caption><title>Comparison of throughput</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32140-fig-10.png"/></fig>
<p>The performance of the proposed EsECC_SDN is significant exhibits minimal delay and loss. Moreover, the network PDR and throughput are higher but with the increase in the number of nodes is reduced. In addition, the mobility of nodes does not have a significant impact on the MANET performance. The proposed EsECC_SDN is involved in the classification of attacks in the network. The analysis is based on the consideration of the CICIDS dataset for attack classification and detection is shown in <xref ref-type="fig" rid="fig-11">Fig. 11</xref>. The model performance is classified based on the SVM classifier. As the proposed EsECC_SDN is involved in the detection of attacks in the MANET network. Based on the training data, attacks are classified in the network for consideration of different attacker&#x2019;s environments. The comparative analysis of results obtained for MANET with and without attackers&#x2019; environment expressed that with attacker&#x2019;s environment the performance is significantly reduced. The performance of the proposed EsECC_SDN for attack classification is presented in <xref ref-type="table" rid="table-5">Tab. 5</xref>.</p>
<fig id="fig-11"><label>Figure 11</label><caption><title>Confusion matrix for NSL-KDD dataset</title></caption><graphic mimetype="image" mime-subtype="png" xlink:href="CMC_32140-fig-11.png"/></fig><table-wrap id="table-5"><label>Table 5</label><caption><title>EsECC_SDN attack classification performance</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left"/>
<th align="left">Accuracy</th>
<th align="left">Precision</th>
<th align="left">Recall</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Normal activity</td>
<td align="left">97</td>
<td align="left">97</td>
<td align="left">98</td>
</tr>
<tr>
<td align="left">Anomaly</td>
<td align="left">98</td>
<td align="left">97</td>
<td align="left">98</td>
</tr>
<tr>
<td align="left">DoS</td>
<td align="left">95</td>
<td align="left">96</td>
<td align="left">96</td>
</tr>
<tr>
<td align="left">Probe Attack</td>
<td align="left">91</td>
<td align="left">91</td>
<td align="left">92</td>
</tr>
<tr>
<td align="left">U2R (User to root) attack</td>
<td align="left">91</td>
<td align="left">92</td>
<td align="left">91</td>
</tr>
<tr>
<td align="left">R2L (Root to local)</td>
<td align="left">94</td>
<td align="left">95</td>
<td align="left">95</td>
</tr>
<tr>
<td align="left">Black hole attack</td>
<td align="left">96</td>
<td align="left">96</td>
<td align="left">95</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The proposed EsECC_SDN scheme classifier performance for different attacks is computed for analysis. The analysis expressed that the proposed EsECC_SDN scheme exhibits a higher accuracy value of anomaly with 98&#x0025;. In the case of a black hole attack, the classification accuracy is estimated as 96&#x0025;. Similarly, in the estimation of precision DoS and Blackn hole attack, it is achieved as 96&#x0025;. The recall value is estimated higher value of 98&#x0025; for anomaly detection. The comparative analysis of the propised EsECC_SDN with the model is included in the accuracy with the consideration of the different attack scenario. The accuracy of the classification is computed as 97&#x0025; for the normal activity, anomaly as 98&#x0025;, DoS as 95&#x0025;, Probe atatck as 91&#x0025;, U2R as 91&#x0025;, R2L is 94&#x0025; and black hole attack as 96&#x0025;. In <xref ref-type="table" rid="table-6">Tab. 6</xref>, the attack classification performance of the proposed EsECC_SDN with conventional classifiers such as AdaBoost, ANN, and ensemble classifier is presented.</p>
<table-wrap id="table-6"><label>Table 6</label><caption><title>Comparative analysis of classifier</title></caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th align="left">Parameters</th>
<th align="left">AdaBoost</th>
<th align="left">ANN</th>
<th align="left">Ensemble classifier</th>
<th align="left">Proposed EsECC_SDN</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Accuracy &#x0025;</td>
<td align="left">93</td>
<td align="left">94</td>
<td align="left">95</td>
<td align="left">98</td>
</tr>
<tr>
<td align="left">Precision &#x0025;</td>
<td align="left">92</td>
<td align="left">92</td>
<td align="left">96</td>
<td align="left">97</td>
</tr>
<tr>
<td align="left">Recall &#x0025;</td>
<td align="left">91</td>
<td align="left">91</td>
<td align="left">91</td>
<td align="left">97</td>
</tr>
<tr>
<td align="left">F1&#x2013;score</td>
<td align="left">0.923</td>
<td align="left">0.936</td>
<td align="left">0.93</td>
<td align="left">0.965</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The attack classification performance expressed that the proposed EsECC_SDN scheme achieves an accuracy of 98&#x0025; while AdaBoost, ANN, and ensemble exhibit the accuracy of 97&#x0025;, 96&#x0025;, and 97&#x0025; respectively. This implies that the proposed EsECC_SDN scheme exhibits significant performance in attacks classification. Similarly, in the case of recall proposed EsECC_SDN achieves a higher percentage rather than AdaBoost, ANN, and ensemble classifiers. The recall of the proposed EsECC_SDN is 97&#x0025;, which is approximately 3&#x0025; higher than the conventional technique AdaBoost, ANN, and ensemble classifier</p>
</sec>
<sec id="s5"><label>5</label><title>Conclusion</title>
<p>MANET network subjected to vast range of security issues and challenges due to presence of higher node mobility scenario. This paper is presented a security scheme for the MANET network for attack prevention and classification using SDN architecture. The proposed EsECC_SDN scheme uses the data encryption and decryption using ECC scheme within the SDN network. In next stage, the attacks are prevented and detected using the model with transductive learning with computation of k-centroids with hyper alerts. The performance of the proposed EsECC_SDN evaluated for the attack detection and classification. The classification of the EsECC_SDN model uses the classifier for the classification of attacks. The proposed model achieves the overall accuracy of 98&#x0025; for the cryptography-based scheme in SDN model. The comparative analysis of the proposed EsECC_SDN with the conventional AdaBoost, ANN, and ensemble classifier exhibits improved performance for attack classification. Through analysis, it can be concluded that the proposed EsECC_SDN scheme is effective for secure data transmission in the MANET network. In the future, this work can be improved in a real-time attack detection scheme in an Intrusion Detection System (IDS).</p>
</sec>
</body>
<back>
<ack><p>The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: (22UQU4281768DSR05).</p>
</ack>
<fn-group>
<fn fn-type="other"><p><bold>Funding Statement:</bold> Deanship of Scientific Research at Umm Al-Qura University, Grant Code, funds this research: 22UQU4281768DSR05.</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">
<title>References</title>
<ref id="ref-1"><label>[1]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>K. N.</given-names> <surname>Dattatraya</surname></string-name> and <string-name><given-names>K.</given-names> <surname>Raghava Rao</surname></string-name></person-group>, &#x201C;<article-title>Hybrid based cluster head selection for maximizing network lifetime and energy efficiency in WSN</article-title>,&#x201D; <source>Journal of King Saud University-Computer and Information Sciences</source>, vol. <volume>34</volume>, no. <issue>3</issue>, pp. <fpage>716</fpage>&#x2013;<lpage>726</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-2"><label>[2]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>N. V.</given-names> <surname>Patil</surname></string-name>, <string-name><given-names>C. R.</given-names> <surname>Krishna</surname></string-name>, <string-name><given-names>K.</given-names> <surname>Kumar</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Behal</surname></string-name></person-group>, &#x201C;<article-title>E-Had: A distributed and collaborative detection framework for early detection of DDoS attacks</article-title>,&#x201D; <source>Journal of King Saud University-Computer and Information Sciences</source>, vol. <volume>34</volume>, no. <issue>4</issue>, pp. <fpage>1373</fpage>&#x2013;<lpage>1387</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-3"><label>[3]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>N.</given-names> <surname>Veeraiah</surname></string-name> and <string-name><given-names>B. T.</given-names> <surname>Krishna</surname></string-name></person-group>, &#x201C;<article-title>Trust-aware FuzzyClus-fuzzy NB: Intrusion detection scheme based on fuzzy clustering and Bayesian rule</article-title>,&#x201D; <source>Wireless Networks</source>, vol. <volume>25</volume>, pp. <fpage>4021</fpage>&#x2013;<lpage>4035</lpage>, <year>2019</year>.</mixed-citation></ref>
<ref id="ref-4"><label>[4]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>M. S.</given-names> <surname>Shaik</surname></string-name> and <string-name><given-names>F.</given-names> <surname>Mira</surname></string-name></person-group>, &#x201C;<article-title>A comprehensive mechanism of manet network layer based security attack prevention</article-title>,&#x201D; <source>International Journal of Wireless and Microwave Technologies</source>, vol. <volume>10</volume>, no. <issue>1</issue>, pp. <fpage>38</fpage>&#x2013;<lpage>47</lpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-5"><label>[5]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>M. N.</given-names> <surname>Malik</surname></string-name>, <string-name><given-names>H. H.</given-names> <surname>Khan</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Batool</surname></string-name>, <string-name><given-names>S.</given-names> <surname>ul Islam</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Suggestion mining from opinionated text of big social media data</article-title>,&#x201D; <source>Computers, Materials &#x0026; Continua</source>, vol. <volume>68</volume>, no. <issue>3</issue>, pp. <fpage>3323</fpage>&#x2013;<lpage>3338</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-6"><label>[6]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>N.</given-names> <surname>Veeraiah</surname></string-name> and <string-name><given-names>B. T.</given-names> <surname>Krishna</surname></string-name></person-group>, &#x201C;<article-title>An approach for optimal-secure multi-path routing and intrusion detection in MANET</article-title>,&#x201D; <source>Evolutionary Intelligence</source>, vol. 15, pp. 1313&#x2013;1327, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-7"><label>[7]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>N.</given-names> <surname>Veeraiah</surname></string-name> and <string-name><given-names>B. T.</given-names> <surname>Krishna</surname></string-name></person-group>, &#x201C;<article-title>Intrusion detection based on piecewise fuzzy C-means clustering and fuzzy na&#x00EF;ve Bayes rule</article-title>,&#x201D; <source>Multimedia Research</source>, vol. <volume>1</volume>, no. <issue>1</issue>, pp. <fpage>27</fpage>&#x2013;<lpage>32</lpage>. <year>2018</year>.</mixed-citation></ref>
<ref id="ref-8"><label>[8]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>P.</given-names> <surname>Bellavista</surname></string-name>, <string-name><given-names>C.</given-names> <surname>Giannelli</surname></string-name>, <string-name><given-names>L.</given-names> <surname>Thomas</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Panagiotis</surname></string-name></person-group>, &#x201C;<article-title>Multi-domain SDN controller federation in hybrid FiWi-MANET networks</article-title>,&#x201D; <source>EURASIP Journal on Wireless Communications and Networking</source>, vol. <volume>1</volume>, pp. <fpage>1</fpage>&#x2013;<lpage>19</lpage>, <year>2018</year>.</mixed-citation></ref>
<ref id="ref-9"><label>[9]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>J.</given-names> <surname>Maruthupandi</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Prasanna</surname></string-name>, <string-name><given-names>P.</given-names> <surname>Jayalakshmi</surname></string-name>, <string-name><given-names>V.</given-names> <surname>Mareeswari</surname></string-name> and <string-name><given-names>B.</given-names> <surname>Siva Kumar</surname></string-name></person-group>, &#x201C;<article-title>Route manipulation aware software-defined networks for effective routing in SDN controlled MANET by disney routing protocol</article-title>,&#x201D; <source>Microprocessors and Microsystems</source>, vol. <volume>80</volume>, pp. <fpage>103401</fpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-10"><label>[10]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>P.</given-names> <surname>Bellavista</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Dolci</surname></string-name> and <string-name><given-names>C.</given-names> <surname>Giannelli</surname></string-name></person-group>, &#x201C;<article-title>MANET-Oriented SDN: Motivations, challenges, and a solution prototype</article-title>,&#x201D; in <conf-name>2018 IEEE 19th Int. Symp. on &#x201C;A World of Wireless, Mobile and Multimedia Networks&#x201D; (WoWMoM)</conf-name>, <conf-loc>Chania, Greece</conf-loc>, pp. <fpage>14</fpage>&#x2013;<lpage>22</lpage>, <year>2018</year>.</mixed-citation></ref>
<ref id="ref-11"><label>[11]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>H. C.</given-names> <surname>Yu</surname></string-name>, <string-name><given-names>G.</given-names> <surname>Quer</surname></string-name> and <string-name><given-names>R. R.</given-names> <surname>Rao</surname></string-name></person-group>, &#x201C;<article-title>Wireless SDN mobile ad hoc network: From theory to practice</article-title>,&#x201D; in <conf-name>Proc. IEEE Int. Conf. on Communications (ICC)</conf-name>, <conf-loc>Paris, France</conf-loc>, pp. <fpage>1</fpage>&#x2013;<lpage>7</lpage>, <year>2017</year>.</mixed-citation></ref>
<ref id="ref-12"><label>[12]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>P.</given-names> <surname>Ranjit</surname></string-name> and <string-name><given-names>B.</given-names> <surname>Samarjeet</surname></string-name></person-group>, &#x201C;<article-title>A detailed analysis of CICIDS2017 dataset for designing intrusion detection systems</article-title>,&#x201D; <source>International Journal of Engineering &#x0026; Technology</source>, vol. <volume>7</volume>, pp. <fpage>479</fpage>&#x2013;<lpage>482</lpage>, <year>2018</year>.</mixed-citation></ref>
<ref id="ref-13"><label>[13]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>D.</given-names> <surname>Gautam</surname></string-name>, and <string-name><given-names>V.</given-names> <surname>Tokekar</surname></string-name></person-group>, &#x201C;<article-title>A novel approach for detecting DDoS attack in MANET</article-title>,&#x201D; <source>Materials Today: Proceedings</source>, vol. <volume>29</volume>, pp. <fpage>674</fpage>&#x2013;<lpage>677</lpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-14"><label>[14]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>V.</given-names> <surname>Alappatt</surname></string-name> and <string-name><given-names>P. J.</given-names> <surname>Prathap</surname></string-name></person-group>, &#x201C;<article-title>Hybrid cryptographic algorithm based key management scheme in MANET</article-title>,&#x201D; <source>Materials Today: Proceedings</source>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-15"><label>[15]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>B.</given-names> <surname>Yang</surname></string-name>, <string-name><given-names>Z.</given-names> <surname>Wu</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Shen</surname></string-name>, <string-name><given-names>X.</given-names> <surname>Jiang</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Shen</surname></string-name></person-group>, &#x201C;<article-title>On delay performance study for cooperative multicast MANETs</article-title>,&#x201D; <source>Ad Hoc Networks</source>, vol. <volume>102</volume>, pp. <fpage>102</fpage>&#x2013;<lpage>117</lpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-16"><label>[16]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>E.</given-names> <surname>Elmahdi</surname></string-name>, <string-name><given-names>S. M.</given-names> <surname>Yoo</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Kumar</surname></string-name></person-group>, &#x201C;<article-title>Secure and reliable data forwarding using homomorphic encryption against blackhole attacks in mobile ad hoc networks</article-title>,&#x201D; <source>Journal of Information Security and Applications</source>, vol. <volume>51</volume>, pp. <fpage>102425</fpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-17"><label>[17]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S. A.</given-names> <surname>Syed</surname></string-name></person-group>, &#x201C;<article-title>A systematic comparison of mobile Ad-hoc network security attacks</article-title>,&#x201D; <source>Materials Today: Proceedings</source>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-18"><label>[18]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>L. E.</given-names> <surname>Jim</surname></string-name>, <string-name><given-names>N.</given-names> <surname>Islam</surname></string-name> and <string-name><given-names>M. A.</given-names> <surname>Gregory</surname></string-name></person-group>, &#x201C;<article-title>Enhanced MANET security using artificial immune system based danger theory to detect selfish nodes</article-title>,&#x201D; <source>Computers &#x0026; Security</source>, vol. <volume>113</volume>, pp. <fpage>102538</fpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-19"><label>[19]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>N. C.</given-names> <surname>Singh</surname></string-name> and <string-name><given-names>A.</given-names> <surname>Sharma</surname></string-name></person-group>, &#x201C;<article-title>Resilience of mobile ad hoc networks to security attacks and optimization of routing process</article-title>,&#x201D; <source>Materials Today: Proceedings</source>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-20"><label>[20]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>T.</given-names> <surname>Ramya</surname></string-name>, <string-name><given-names>J. M.</given-names> <surname>Mathana</surname></string-name>, <string-name><given-names>R.</given-names> <surname>Nirmala</surname></string-name> and <string-name><given-names>R.</given-names> <surname>Gomathi</surname></string-name></person-group>, &#x201C;<article-title>Exploration on enhanced quality of services for MANET through modified lumer and Fai-eta algorithm with modified AODV and DSR protocol</article-title>,&#x201D; <source>Materials Today: Proceedings</source>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-21"><label>[21]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A.</given-names> <surname>Tahir</surname></string-name>, <string-name><given-names>N.</given-names> <surname>Shah</surname></string-name>, <string-name><given-names>S. A.</given-names> <surname>Abid</surname></string-name>, <string-name><given-names>W. Z.</given-names> <surname>Khan</surname></string-name> and <string-name><given-names>A. K.</given-names> <surname>Bashir</surname></string-name></person-group>, &#x201C;<article-title>A three-dimensional clustered peer-to-peer overlay protocol for mobile ad hoc networks</article-title>,&#x201D; <source>Computers &#x0026; Electrical Engineering</source>, vol. <volume>94</volume>, pp. <fpage>107364201</fpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-22"><label>[22]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>P.</given-names> <surname>Mohan</surname></string-name>, <string-name><given-names>N.</given-names> <surname>Subramani</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Alghamdi</surname></string-name>, <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Improved metaheuristics-based clustering with multihop routing protocol for underwater wireless sensor networks</article-title>,&#x201D; <source>Sensors</source>, vol. <volume>22</volume>, no. <issue>4</issue>, pp. <fpage>1618</fpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-23"><label>[23]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A.</given-names> <surname>Thakkar</surname></string-name> and <string-name><given-names>R.</given-names> <surname>Lohiya</surname></string-name></person-group>, &#x201C;<article-title>A review of the advancement in intrusion detection datasets</article-title>,&#x201D; <source>Procedia Computer Science</source>, vol. <volume>167</volume>, pp. <fpage>636</fpage>&#x2013;<lpage>645</lpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-24"><label>[24]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>R.</given-names> <surname>Rout</surname></string-name>, <string-name><given-names>P.</given-names> <surname>Parida</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Alghamdi</surname></string-name> and <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name></person-group>, &#x201C;<article-title>Skin lesion extraction using multiscale morphological local variance reconstruction based watershed transform and fast fuzzy C-means clustering</article-title>,&#x201D; <source>Symmetry</source>, vol. <volume>13</volume>, no. <issue>11</issue>, pp. <fpage>2085</fpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-25"><label>[25]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>N.</given-names> <surname>Subramani</surname></string-name>, <string-name><given-names>P.</given-names> <surname>Mohan</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Alghamdi</surname></string-name> and <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name></person-group>, &#x201C;<article-title>An efficient metaheuristic-based clustering with routing protocol for underwater wireless sensor networks</article-title>,&#x201D; <source>Sensors</source>, vol. <volume>22</volume>, pp. <fpage>415</fpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-26"><label>[26]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S.</given-names> <surname>Rajendran</surname></string-name>, <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Alghamdi</surname></string-name></person-group>, &#x201C;<article-title>MapReduce-based big data classification model using feature subset selection and hyperparameter tuned deep belief network</article-title>,&#x201D; <source>Scientific Reports</source>, vol. <volume>11</volume>, no. <issue>1</issue>, pp. <fpage>1</fpage>&#x2013;<lpage>10</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-27"><label>[27]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>U.</given-names> <surname>Srilakshmi</surname></string-name>, <string-name><given-names>N.</given-names> <surname>Veeraiah</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>S. A.</given-names> <surname>Alghamdi</surname></string-name>, <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>An improved hybrid secure multipath routing protocol for MANET</article-title>,&#x201D; <source>IEEE Access</source>, vol. <volume>9</volume>, pp. <fpage>163043</fpage>&#x2013;<lpage>163053</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-28"><label>[28]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A.</given-names> <surname>Alsufyani</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>A. O.</given-names> <surname>Almagrabi</surname></string-name>, <string-name><given-names>S. A.</given-names> <surname>Alghamdi</surname></string-name> and <string-name><given-names>N.</given-names> <surname>Alsufyani</surname></string-name></person-group>, &#x201C;<article-title>Optimized intelligent data management framework for a cyber-physical system for computational applications</article-title>,&#x201D; <source>Complex &#x0026; Intelligent Systems</source>, pp. <fpage>1</fpage>&#x2013;<lpage>13</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-29"><label>[29]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S.</given-names> <surname>Bharany</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Sharma</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Badotra</surname></string-name>, <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Energy-efficient clustering scheme for flying ad-hoc networks using an optimized LEACH protocol</article-title>,&#x201D; <source>Energies</source>, vol. <volume>14</volume>, no. <issue>19</issue>, pp. <fpage>6016</fpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-30"><label>[30]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>N.</given-names> <surname>Veeraiah</surname></string-name>, <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name>, <string-name><given-names>C. V. P. R.</given-names> <surname>Prasad</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Alsufyani</surname></string-name> <etal>et al.,</etal></person-group> <italic>&#x201C;</italic><article-title>Trust aware secure energy efficient hybrid protocol for manet</article-title>,&#x201D; <source>IEEE Access</source>, vol. <volume>9</volume>, pp. <fpage>120996</fpage>&#x2013;<lpage>121005</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-31"><label>[31]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name></person-group>, &#x201C;<article-title>A new database intrusion detection approach based on hybrid meta-heuristics</article-title>,&#x201D; <source>Computers, Materials &#x0026; Continua</source>, vol. <volume>66</volume>, no. <issue>2</issue>, pp. <fpage>1879</fpage>&#x2013;<lpage>1895</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-32"><label>[32]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name></person-group>, &#x201C;<article-title>A new secured E-government efficiency model for sustainable services provision</article-title>,&#x201D; <source>Journal of Information Security and Cybercrimes Research</source>, vol. <volume>3</volume>, no. <issue>1</issue>, pp. <fpage>75</fpage>&#x2013;<lpage>96</lpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-33"><label>[33]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>V.</given-names> <surname>Ramasamy</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name>, <string-name><given-names>P.</given-names> <surname>Samui</surname></string-name> and <string-name><given-names>J.</given-names> <surname>Jayabalan</surname></string-name></person-group>, &#x201C;<article-title>Prediction of groundwater table for chennai region using soft computing techniques</article-title>,&#x201D; <source>Arabian Journal of Geosciences</source>, vol. <volume>15</volume>, no. <issue>9</issue>, pp. <fpage>1</fpage>&#x2013;<lpage>19</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-34"><label>[34]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>D.</given-names> <surname>Anuradha</surname></string-name>, <string-name><given-names>N.</given-names> <surname>Subramani</surname></string-name>, <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Alghamdi</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Chaotic search-and-rescue-optimization-based multi-hop data transmission protocol for underwater wireless sensor networks</article-title>,&#x201D; <source>Sensors</source>, vol. <volume>22</volume>, no. <issue>8</issue>, pp. <fpage>2867</fpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-35"><label>[35]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name></person-group>, &#x201C;<article-title>A new meta-heuristics data clustering algorithm based on tabu search and adaptive search memory</article-title>,&#x201D; <source>Symmetry</source>, vol. <volume>14</volume>, no. <issue>3</issue>, pp. <fpage>623</fpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-36"><label>[36]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>J.</given-names> <surname>Jayapradha</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Prakash</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name> and <string-name><given-names>S. A.</given-names> <surname>Alghamdi</surname></string-name></person-group>, &#x201C;<article-title>Heap bucketization anonymity-an efficient privacy-preserving data publishing model for multiple sensitive attributes</article-title>,&#x201D; <source>IEEE Access</source>, vol. <volume>10</volume>, pp. <fpage>28773</fpage>&#x2013;<lpage>28791</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-37"><label>[37]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S. S.</given-names> <surname>Rawat</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Alghamdi</surname></string-name>, <string-name><given-names>G.</given-names> <surname>Kumar</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Infrared small target detection based on partial sum minimization and total variation</article-title>,&#x201D; <source>Mathematics</source>, vol. <volume>10</volume>, pp. <fpage>671</fpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-38"><label>[38]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name> and <string-name><given-names>A. F.</given-names> <surname>Subahi</surname></string-name></person-group>, &#x201C;<article-title>New goal-oriented requirements extraction framework for e-health services: A case study of diagnostic testing during the COVID-19 outbreak</article-title>,&#x201D; <source>Business Process Management Journal</source>, vol. <volume>28</volume>, no. <issue>1</issue>, pp. <fpage>273</fpage>&#x2013;<lpage>292</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-39"><label>[39]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>G.</given-names> <surname>Suryanarayana</surname></string-name>, <string-name><given-names>K.</given-names> <surname>Chandran</surname></string-name>, <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Alsufyani</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Accurate magnetic resonance image super-resolution using deep networks and Gaussian filtering in the stationary wavelet domain</article-title>,&#x201D; <source>IEEE Access</source>, vol. <volume>9</volume>, pp. <fpage>71406</fpage>&#x2013;<lpage>71417</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-40"><label>[40]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>G.</given-names> <surname>Li</surname></string-name>, <string-name><given-names>F.</given-names> <surname>Liu</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Sharma</surname></string-name>, <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Research on the natural language recognition method based on cluster analysis using neural network</article-title>,&#x201D; <source>Mathematical Problems in Engineering</source>, vol. <volume>2021</volume>, pp. <fpage>13</fpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-41"><label>[41]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>N.</given-names> <surname>Jha</surname></string-name>, <string-name><given-names>D.</given-names> <surname>Prashar</surname></string-name>, <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Alsufyani</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Blockchain based crop insurance: A decentralized insurance system for modernization of Indian farmers</article-title>,&#x201D; <source>Sustainability</source>, vol. <volume>13</volume>, no. <issue>16</issue>, pp. <fpage>8921</fpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-42"><label>[42]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A. F.</given-names> <surname>Subahi</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name> and <string-name><given-names>F.</given-names> <surname>Ajesh</surname></string-name></person-group>, &#x201C;<article-title>Packet drop battling mechanism for energy aware detection in wireless networks</article-title>,&#x201D; <source>Computers, Materials &#x0026; Continua</source>, vol. <volume>66</volume>, no. <issue>2</issue>, pp. <fpage>2077</fpage>&#x2013;<lpage>2086</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-43"><label>[43]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>H. H.</given-names> <surname>Khan</surname></string-name>, <string-name><given-names>M. N.</given-names> <surname>Malik</surname></string-name>, <string-name><given-names>R.</given-names> <surname>Zafar</surname></string-name>, <string-name><given-names>F. A.</given-names> <surname>Goni</surname></string-name>, <string-name><given-names>A. G.</given-names> <surname>Chofreh</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Challenges for sustainable smart city development: A conceptual framework</article-title>,&#x201D; <source>Sustainable Development</source>, vol. <volume>28</volume>, no. <issue>5</issue>, pp. <fpage>1507</fpage>&#x2013;<lpage>1518</lpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-44"><label>[44]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>N.</given-names> <surname>Veeraiah</surname></string-name> and <string-name><given-names>B. T.</given-names> <surname>Krishna</surname></string-name></person-group>, &#x201C;<article-title>Selfish node detection IDSM based approach using individual master cluster node</article-title>,&#x201D; in <conf-name>2018 2nd Int. Conf. on Inventive Systems and Control (ICISC)</conf-name>, <conf-loc>Coimbatore, India</conf-loc>, pp. <fpage>427</fpage>&#x2013;<lpage>431</lpage>, <year>2018</year>.</mixed-citation></ref>
<ref id="ref-45"><label>[45]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A.</given-names> <surname>Sundas</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Badotra</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Alghamdi</surname></string-name> and <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name></person-group>, &#x201C;<article-title>Modified bat algorithm for optimal vm&#x2019;s in cloud computing</article-title>,&#x201D; <source>Computers, Materials &#x0026; Continua</source>, vol. <volume>72</volume>, no. <issue>2</issue>, pp. <fpage>2877</fpage>&#x2013;<lpage>2894</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-46"><label>[46]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S.</given-names> <surname>Sennan</surname></string-name>, <string-name><given-names>K.</given-names> <surname>Gopalan</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>D.</given-names> <surname>Pandey</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Alghamdi</surname></string-name></person-group>, &#x201C;<article-title>EACR-LEACH: Energy-aware cluster-based routing protocol for WSN based IoT</article-title>,&#x201D; <source>Computers, Materials &#x0026; Continua</source>, vol. <volume>72</volume>, no. <issue>2</issue>, pp. <fpage>2159</fpage>&#x2013;<lpage>2174</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-47"><label>[47]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S. R.</given-names> <surname>Akhila</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Alghamdi</surname></string-name></person-group>, &#x201C;<article-title>Authentication and resource allocation strategies during handoff for 5G IoVs using deep learning</article-title>,&#x201D; <source>Energies</source>, vol. <volume>15</volume>, no. <issue>6</issue>, pp. <fpage>2006</fpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-48"><label>[48]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>P.</given-names> <surname>Kollapudi</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Alghamdi</surname></string-name>, <string-name><given-names>N.</given-names> <surname>Veeraiah</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Thotakura</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>A new method for scene classification from the remote sensing images</article-title>,&#x201D; <source>Computers, Materials &#x0026; Continua</source>, vol. <volume>72</volume>, no. <issue>1</issue>, pp. <fpage>1339</fpage>&#x2013;<lpage>1355</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-49"><label>[49]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>U.</given-names> <surname>Srilakshmi</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Alghamdi</surname></string-name>, <string-name><given-names>V. V.</given-names> <surname>Ankalu</surname></string-name>, <string-name><given-names>N.</given-names> <surname>Veeraiah</surname></string-name> and <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name></person-group>, &#x201C;<article-title>A secure optimization routing algorithm for mobile ad hoc networks</article-title>,&#x201D; <source>IEEE Access</source>, vol. <volume>10</volume>, pp. <fpage>14260</fpage>&#x2013;<lpage>14269</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-50"><label>[50]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S.</given-names> <surname>Palanisamy</surname></string-name>, <string-name><given-names>B.</given-names> <surname>Thangaraju</surname></string-name>, <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Alghamdi</surname></string-name></person-group>, &#x201C;<article-title>Design and synthesis of multi-mode bandpass filter for wireless applications</article-title>,&#x201D; <source>Electronics</source>, vol. <volume>10</volume>, pp. <fpage>2853</fpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-51"><label>[51]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>S.</given-names> <surname>Sennan</surname></string-name>, <string-name><given-names>D.</given-names> <surname>Pandey</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Alghamdi</surname></string-name></person-group>, &#x201C;<article-title>A novel convolutional neural networks based spinach classification and recognition system</article-title>,&#x201D; <source>Computers, Materials &#x0026; Continua</source>, vol. <volume>73</volume>, no. <issue>1</issue>, pp. <fpage>343</fpage>&#x2013;<lpage>361</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-52"><label>[52]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A. R.</given-names> <surname>Khaparde</surname></string-name>, <string-name><given-names>F.</given-names> <surname>Alassery</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Kumar</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>O. I.</given-names> <surname>Khalaf</surname></string-name> <etal>et al.,</etal></person-group> &#x201C;<article-title>Differential evolution algorithm with hierarchical fair competition model</article-title>,&#x201D; <source>Intelligent Automation &#x0026; Soft Computing</source>, vol. <volume>33</volume>, no. <issue>2</issue>, pp. <fpage>1045</fpage>&#x2013;<lpage>1062</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-53"><label>[53]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>H. H.</given-names> <surname>Khan</surname></string-name>, <string-name><given-names>M. N.</given-names> <surname>Malik</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Alotaibi</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Alsufyani</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Alghamdi</surname></string-name></person-group>, &#x201C;<article-title>Crowdsourced requirements engineering challenges and solutions: A software industry perspective</article-title>,&#x201D; <source>Computer Systems Science and Engineering</source>, vol. <volume>39</volume>, no. <issue>2</issue>, pp. <fpage>221</fpage>&#x2013;<lpage>236</lpage>, <year>2021</year>.</mixed-citation></ref>
</ref-list>
</back>
</article>
















