<?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-2441</article-id>
      <title-group>
        <article-title>Mathematical foundations of secure AI : Homomorphic encryption for distributed learning systems</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Babbar</surname>
            <given-names>Nandini</given-names>
          </name>
          <aff>Department of IoT and Intelligent Systems, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Sharma</surname>
            <given-names>Amit Kumar</given-names>
          </name>
          <aff>Department of Computer and Communication Engineering, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Saini</surname>
            <given-names>Ravindra Kumar</given-names>
          </name>
          <aff>Department of Information Technology, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Verma</surname>
            <given-names>Neeraj Kumar</given-names>
          </name>
          <aff>Department of Data Science, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India</aff>
        </contrib>
      </contrib-group>
      <volume>28</volume>
      <issue>8</issue>
      <fpage>2967</fpage>
      <lpage>2975</lpage>
      <pub-date date-type="pub">
        <day>08</day>
        <month>12</month>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>Issues concerning the safety and privacy of facts are heightened with the upward push of new disbursed studying structures like federated getting to know. the extent of computation accomplished on encrypted information would require specific encryption, otherwise referred to as homomorphic encryption (HE) defends towards data decryption dangers. this article investigates how the arithmetic of HE lets in its application inside remote studying architectures. This examination carries superior modular mathematics structures, lattice frameworks, and polynomial encoding at the side of traditional framework HE systems. also, the paintings propose a relaxed structure for dispensed mastering that makes use of HE for version aggregation and personal gradient computation. Sectors forced below strict facts secrecy policies like in non-public healthcare, smart towns, and finance illustrate why those rules enforced look coverage freedom capitalism - why even more is wanted. This look at highlights the particular approaches HE can serve as a policy flexed surveillance capitalism- coverage that will become so much extra surveillance-centric to defend something in covered AI structures, therefore laying a coverage for research directed towards AI that prioritizes person privateness.</p>
      </abstract>
      <kwd-group>
        <kwd>Homomorphic encryption</kwd>
        <kwd>Federated learning security</kwd>
        <kwd>Encrypted computation</kwd>
        <kwd>Lattice-based cryptography</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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  </front>
</article>
