<?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-3032</article-id>
      <title-group>
        <article-title>Post-quantum cryptographic schemes using lattice problems</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Ali Khan</surname>
            <given-names>Mohammed Wahed</given-names>
          </name>
          <aff>Department of Cybersecurity, Versos - Unleash the Future, Riyadh, 11353, Kingdom of Saudi Arabia</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Khatoon</surname>
            <given-names>Afreen Rahmat</given-names>
          </name>
          <aff>Department of Electronics &amp; Communication Engineering, University College of Engineering, Osmania University, Hyderabad, Telangana, 500007, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Tariq</surname>
            <given-names>Hafiz Munaam Hussain</given-names>
          </name>
          <aff>Department of Computer Science and Information Technology, NED University of Engineering and Technology, Karachi, 75330, Pakistan</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Khan</surname>
            <given-names>Tahreem</given-names>
          </name>
          <aff>Department of Computer Science and Information Technology, NED University of Engineering and Technology, Karachi, 75330, Pakistan</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>10-A</issue>
      <fpage>4065</fpage>
      <lpage>4074</lpage>
      <pub-date date-type="pub">
        <day>31</day>
        <month>10</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>The quick progress of quantum computing is a considerable risk to the classical cryptography of the public key and, the creation of quantum-resistant analogs is necessary. This paper provides a generalized architecture of post-quantum cryptographic schemes, by using lattice problems, especially Learning with Errors (LWE) and Ring-LWE (RLWE). The suggested architecture combines the secure public-key encryption and key encapsulation mechanisms (KEMs) with the implementation in the IoT, blockchain, and cloud setup. An original lattice-based encryption design is developed that hybridizes with classical cryptographic primitives to improve security, efficiency and interoperability. It is a methodology that focuses on structured lattice formulations, noise based hardness models and parameter selection optimisation of real time performance. It is proved that experimental analysis has better resilience against quantum attacks and is computationally efficient. The outcomes confirm the high level of strength and scalability of the proposed solution, which can be implemented in the next generation secure communication systems.</p>
      </abstract>
      <kwd-group>
        <kwd>Post-quantum cryptography</kwd>
        <kwd>Lattice-based encryption</kwd>
        <kwd>LWE</kwd>
        <kwd>RLWE</kwd>
        <kwd>Key encapsulation mechanism</kwd>
        <kwd>Quantum-resistant security</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>
