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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-3076</article-id>
      <title-group>
        <article-title>Combinatorial game theory applications in cryptographic protocols</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Patil</surname>
            <given-names>Mahadev Kalyanrao</given-names>
          </name>
          <aff>School of Computer Science &amp; Engineering (SoCSE), RV University, Bengaluru, Karnataka, 560059, India</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Chaugule</surname>
            <given-names>Archana</given-names>
          </name>
          <aff>Department of Computer Engineering, PCET’S Pimpri Chinchwad College of Engineering &amp; Research, Ravet, Pune, Maharashtra, 412101, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Jawahire</surname>
            <given-names>Snehal Swapnil</given-names>
          </name>
          <aff>Department of Computer Engineering, Vishwakarma Institute of Technology, Pune, Maharashtra, 411037, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Patil</surname>
            <given-names>Varsha Kiran</given-names>
          </name>
          <aff>Department of Electronics &amp; Telecommunication Engineering, AISSMS Institute of Information Technology, Pune, Maharashtra, 411001, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Shirkande</surname>
            <given-names>Aparna Shrinivas</given-names>
          </name>
          <aff>Department of Electronics &amp; Telecommunication Engineering, S. B. Patil College of Engineering, Indapur, Pune, Maharashtra, 413106, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Gupta</surname>
            <given-names>Neeraj</given-names>
          </name>
          <aff>Department of Computer Engineering &amp; Applications, GLA University, Mathura, Uttar Pradesh, 281406, India</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>10-C</issue>
      <fpage>4595</fpage>
      <lpage>4610</lpage>
      <pub-date date-type="pub">
        <day>31</day>
        <month>10</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>These growing intricacy of cyber threats and the fast growth of interconnected digital systems have revealed the weaknesses of traditional cryptographic protocols basing their operation on fixed mathematical assumptions. The contemporary security landscapes require dynamic, intelligent and durable systems that can counter the dynamic adversarial behavior. Here, the paper discusses how combinatorics game theory can be applied to the design of cryptographic protocols to increase their effectiveness in providing better security and flexibility in their usage. The main goal of this work consists in creation of a new cryptographic framework in the form of combinatorial game which will represent the process of encryption and key generation as the strategies of the defender and adversary. The suggested methodology utilizes combinatorial frameworks, e.g., permutation spaces, transitions of the game states, and game-theoretic techniques, e.g., strategy optimization, and the minimax formulation, and equilibrium analysis. The mechanism of key generation is dynamic based on optimal game strategies and the process of encryption and decryption is motivated by the use of permutation based transformations and functions based on the strategies. There is also a feedback loop to enhance the continuous evolution of keys that the framework considers, and it enhances its flexibility and resistance to new threats. Measures that are used to perform the performance evaluation include encryption/decryption time, key space size, computational overhead and security strength. The findings show that the suggested model can attain a high degree of security with entropy being higher than what is available in the conventional schemes, with reasonable computational efficiency. The comparison to AES, RSA, and ECC shows that the given approach is more flexible, has a greater key space, and resistance to brute-force and analytical attacks. In general, this paper provides a strong and scalable cryptographic paradigm that could be used in the next-generation secure communication systems.</p>
      </abstract>
      <kwd-group>
        <kwd>Combinatorial game theory</kwd>
        <kwd>Cryptographic protocols</kwd>
        <kwd>Game-theoretic security</kwd>
        <kwd>Dynamic key generation</kwd>
        <kwd>Permutation-based encryption</kwd>
      </kwd-group>
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  </front>
</article>
