<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-discrete-mathematical-sciences-and-cryptography</journal-id>
      <journal-title-group>
        <journal-title>Journal of Discrete Mathematical Sciences and Cryptography</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-0065</issn>
      <issn publication-format="print">0972-0529</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JDMSC-2693</article-id>
      <title-group>
        <article-title>Discrete mathematical modeling–driven machine learning framework for secure encrypted DDoS attack detection in cloud and edge computing</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Sharma</surname>
            <given-names>Manmohan</given-names>
          </name>
          <aff>Department of Computer Science &amp; Engineering, Faculty of Science, Technology and Architecture (FoSTA), Manipal University Jaipur, Jaipur, Rajasthan, 303007, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Arora</surname>
            <given-names>Anudeep</given-names>
          </name>
          <aff>Department of Management, New Delhi Institute of Management (NDIM), Guru Gobind Singh Indraprastha University, Tughlakabad, New Delhi, 110062, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Mathur</surname>
            <given-names>Priya</given-names>
          </name>
          <aff>Department of Mathematics, Poornima Institute of Engineering &amp; Technology, Jaipur, Rajasthan, 302022, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Bhushan</surname>
            <given-names>Saloni</given-names>
          </name>
          <aff>Department of Computer Application, School of Humanities &amp; Sciences, D Y Patil Deemed to be University, Nerul, Navi Mumbai, Maharashtra, 400706, India</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Gupta</surname>
            <given-names>Amit Kumar</given-names>
          </name>
          <aff>Department of Computer Science &amp; Engineering, Faculty of Science, Technology and Architecture (FoSTA), Manipal University Jaipur, Jaipur, Rajasthan, 303007, India</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>8</issue>
      <fpage>3085</fpage>
      <lpage>3093</lpage>
      <pub-date date-type="pub">
        <day>14</day>
        <month>08</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>Distributed denial-of-service (DDoS) attacks causes significant threats in modern cloud and edge computing because of complex traffic patterns that intricate attack detection. Traditional methods have limitations in distinguishing attack strategies and extracting relevant information. This study retains machine learning and deep learning techniques to find DDoS attacks using the CICDDoS-2019 dataset, which has pre-processed to include 431,371 records and 78 features. The preprocessing intricate handling duplicates, missing values, and class imbalances using SMOTE. Various classifiers, including Logistic Regression, Decision Tree, Random Forest, XGBoost, and LightGBM, alongside One-Class SVM and Autoencoder-Bidirectional LSTM (AE–BiLSTM) models, were utilized. Assessments of metrics such as accuracy, precision, recall, F1-score, and ROC–AUC were employed to assess the models. Results indicated that ensemble methods like XGBoost and LightGBM achieved perfect ROC–AUC scores of 1.00, while AE–BiLSTM shows strong anomaly detection with a ROC–AUC of 0.9979. This framework gives a practical solution for improving network security within cloud and edge computing environments.</p>
      </abstract>
      <kwd-group>
        <kwd>DDoS attack</kwd>
        <kwd>Security</kwd>
        <kwd>Machine learning</kwd>
        <kwd>Deep learning</kwd>
        <kwd>Anomaly detection</kwd>
        <kwd>Edge computing</kwd>
      </kwd-group>
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        <custom-meta>
          <meta-name>access</meta-name>
          <meta-value>open</meta-value>
        </custom-meta>
        <custom-meta>
          <meta-name>retracted</meta-name>
          <meta-value>no</meta-value>
        </custom-meta>
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    </article-meta>
  </front>
</article>
