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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-3043</article-id>
      <title-group>
        <article-title>Modular forms and their role in cryptographic constructions</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Wani</surname>
            <given-names>Tanveer Ahmad</given-names>
          </name>
          <aff>Department of Physics, Noida International University, Greater Noida, Uttar Pradesh, 203201, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Bhuvaneswari</surname>
            <given-names>A. K.</given-names>
          </name>
          <aff>Department of Humanities and Sciences (Mathematics Division), Aarupadai Veedu Institute of Technology, Vinayaka Mission’s Research Foundation (Deemed to be University), Paiyanoor, Chennai, Tamil Nadu, 603104, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Shriyal</surname>
            <given-names>Swati Shivkumar</given-names>
          </name>
          <aff>Department of Artificial Intelligence, Vishwakarma University, Pune, Maharashtra, 411048, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <given-names>Tusha</given-names>
          </name>
          <aff>Quantum University Research Center, Quantum University, Roorkee, Uttarakhand, 247667, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Adhyaru</surname>
            <given-names>Yagna B.</given-names>
          </name>
          <aff>Faculty of Engineering, Gokul Global University, Sidhpur, Gujarat, 384151, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Baxrom</surname>
            <given-names>Abrayev</given-names>
          </name>
          <aff>Department of Information Technology and Exact Sciences, Termez University of Economics and Service, Termez, 190111, Uzbekistan</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>10-B</issue>
      <fpage>4189</fpage>
      <lpage>4199</lpage>
      <pub-date date-type="pub">
        <day>31</day>
        <month>10</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>The paper is concerned with the necessity of new cryptographic systems on classical assumptions and the issue of the secure, quantum resistant communication systems. It suggests a cryptography scheme based on modular forms and exploitation of the transformation invariance, Fourier structure and L-functions to generate strong keys and encrypt. It has been experimentally demonstrated that the performance is best with shorter encryption time (6.7 ms), decryption time (7.4 ms) and protection strength (192 bits) that is better than RSA and ECC. The novelty is that it is a combination of deep number-theoretic features and real world cryptography. It has a contribution of one mathematical-cryptographic framework. The plan proposes efficient and post quantum secure applications that are scalable in the existing digital communications systems.</p>
      </abstract>
      <kwd-group>
        <kwd>Modular forms</kwd>
        <kwd>Cryptography</kwd>
        <kwd>Hecke operators</kwd>
        <kwd>L-functions</kwd>
        <kwd>Public-key systems</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>
        </custom-meta>
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    </article-meta>
  </front>
</article>
