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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-2439</article-id>
      <title-group>
        <article-title>A private key cryptographic framework for preventing replay attacks and digital signature verification in securing blockchain networks </article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Upadhyay</surname>
            <given-names>Govind Murari</given-names>
          </name>
          <aff>Department of Computer Applications, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Joshi</surname>
            <given-names>Mukesh</given-names>
          </name>
          <aff>School of Computing, Graphic Era Hill University, Bhimtal, Uttarakhand, 263136, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Shanker</surname>
            <given-names>Surabhi</given-names>
          </name>
          <aff>Centre of Excellence-Cyber Security, School of Engineering and Technology, K. R. Mangalam University, Gurugram, Haryana, 122103, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <given-names>Anu</given-names>
          </name>
          <aff>Banarsidas Chandiwala Institute of Information Technology, Guru Gobind Singh Indraprastha University, Kalkaji, New Delhi, 110020, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Phogat</surname>
            <given-names>Ajay Kumar</given-names>
          </name>
          <aff>Maharaja Surajmal Institute, Guru Gobind Singh Indraprastha University, Janak Puri, Delhi, 110058, India</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Vats</surname>
            <given-names>Prashant</given-names>
          </name>
          <aff>Department of Computer Science &amp; Engineering, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India</aff>
        </contrib>
      </contrib-group>
      <volume>28</volume>
      <issue>8</issue>
      <fpage>2945</fpage>
      <lpage>2954</lpage>
      <pub-date date-type="pub">
        <day>08</day>
        <month>12</month>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>Blockchain technology is becoming a ground-breaking system for safe, decentralized transactions in a variety of industries. Assuring transaction integrity, validity, and non-repudiation is still a difficult task, nevertheless, particularly in settings vulnerable to hostile assaults. The architecture for private key cryptography presented in this study is intended to improve digital signature authentication to safeguard blockchain networks. The suggested framework creates a safe and effective way to verify the legitimacy of digital signatures by utilizing the fundamental advantages of private key cryptography. The framework employs a strong cryptographic structure to guarantee data integrity, secrecy, and resistance against manipulation. This research illustrates the efficacy of the architecture in minimizing common vulnerabilities including replay attacks, man-in-the-middle attacks, and key exposure through thorough security analysis and performance rating.</p>
      </abstract>
      <kwd-group>
        <kwd>Blockchain security</kwd>
        <kwd>Digital signature authentication</kwd>
        <kwd>Private key cryptography</kwd>
        <kwd>Decentralized networks</kwd>
        <kwd>Data integrity</kwd>
        <kwd>Non-repudiation</kwd>
        <kwd>Key management</kwd>
        <kwd>Transaction validation</kwd>
        <kwd>Tamper resistance</kwd>
        <kwd>SDG 9-secure digital innovation</kwd>
        <kwd>Computational efficiency</kwd>
        <kwd>Cryptographic protocols</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>
