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<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-2812</article-id>
      <title-group>
        <article-title>Spectral security analysis of cryptographic Boolean functions using discrete mathematical modelling and machine learning</article-title>
      </title-group>
      <contrib-group>
        <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>Gupta</surname>
            <given-names>Pradeep</given-names>
          </name>
          <aff>Department of Computer Science and Engineering, Ajay Kumar Garg Engineering College, Ghaziabad, Uttar Pradesh, 201015, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Nandhini</surname>
            <given-names>K.</given-names>
          </name>
          <aff>Department of Computer Science and Engineering (AIML), Sridevi Women’s Engineering College, Hyderabad, Telangana, 500075, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Goel</surname>
            <given-names>Lipika</given-names>
          </name>
          <aff>Department of Computer Science and Engineering (AIML), Sridevi Women’s Engineering College, Hyderabad, Telangana, 500075, India</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Kushwaha</surname>
            <given-names>Satpal Singh</given-names>
          </name>
          <aff>Department of Computer Science &amp; Engineering, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Gupta</surname>
            <given-names>Amit  Kumar</given-names>
          </name>
          <aff>Department of Computer Science &amp; Engineering, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>8</issue>
      <fpage>3249</fpage>
      <lpage>3257</lpage>
      <pub-date date-type="pub">
        <day>14</day>
        <month>08</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>This study investigates how the structural and spectral properties of Boolean functions influence their susceptibility to machine learning–based cryptanalysis. A comprehensive framework is proposed, combining Boolean function generation, truth table representation, Walsh–Hadamard spectral analysis, and machine learning evaluation. Using a dataset of 2000 functions (linear, balanced, bent-like, and random), results show that higher nonlinearity reduces learnability, while linear functions remain predictable. A strong negative correlation (−0.6499) between nonlinearity and learning accuracy is observed. Functions with large Walsh coefficients are more easily approximated. The findings confirm that machine learning exploits inherent structural weaknesses, aiding the design of more secure, learning-resistant cryptographic primitives.</p>
      </abstract>
      <kwd-group>
        <kwd>Boolean functions</kwd>
        <kwd>Walsh spectrum</kwd>
        <kwd>Nonlinearity</kwd>
        <kwd>Machine learning cryptanalysis</kwd>
      </kwd-group>
      <custom-meta-group>
        <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>
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  </front>
</article>
