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A Cryptographic Framework Based on Graph Labeling and Max-Plus Algebra.

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Title: A Cryptographic Framework Based on Graph Labeling and Max-Plus Algebra.
Authors: Nurwan, Nurwan1 nurwan@ung.ac.id, Yahya, Nisky Imansyah2 nisky@ung.ac.id, Arsal, Armayani2 armayaniarsal@ung.ac.id, Muanalifah, Any2 any.muanalifah@walisongo.ac.id
Source: IAENG International Journal of Applied Mathematics. Jul2026, Vol. 56 Issue 7, p2473-2481. 9p.
Subjects: Data encryption, Graph theory, Cryptography, Matrix multiplications, Ordered algebraic structures, Data security, Digital communications
Abstract: This paper develops an encryption system that integrates graph theory with max-plus algebra to enhance data security and decryption reliability. The proposed method transforms plaintext into ciphertext by representing the message as a complete graph, where numerical values derived from an alphabet encoding scheme are used to label the edges. The encryption process applies substitution and permutation techniques based on max-plus algebra to generate complex ciphertext, thereby improving resistance against brute-force and frequency-based attacks. The algorithm follows a structured procedure that begins with numeric encoding, followed by complete graph construction, adjacency matrix generation, matrix modification, and max-plus algebraic transformation. The decryption process performs the inverse operations to recover the original plaintext accurately. Experimental results indicate that the proposed system achieves a high level of security while maintaining computational efficiency, making it suitable for protecting data in digital communication systems. [ABSTRACT FROM AUTHOR]
Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 195026879
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PubType: Academic Journal
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  Data: A Cryptographic Framework Based on Graph Labeling and Max-Plus Algebra.
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  Data: <searchLink fieldCode="AR" term="%22Nurwan%2C+Nurwan%22">Nurwan, Nurwan</searchLink><relatesTo>1</relatesTo><i> nurwan@ung.ac.id</i><br /><searchLink fieldCode="AR" term="%22Yahya%2C+Nisky+Imansyah%22">Yahya, Nisky Imansyah</searchLink><relatesTo>2</relatesTo><i> nisky@ung.ac.id</i><br /><searchLink fieldCode="AR" term="%22Arsal%2C+Armayani%22">Arsal, Armayani</searchLink><relatesTo>2</relatesTo><i> armayaniarsal@ung.ac.id</i><br /><searchLink fieldCode="AR" term="%22Muanalifah%2C+Any%22">Muanalifah, Any</searchLink><relatesTo>2</relatesTo><i> any.muanalifah@walisongo.ac.id</i>
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Jul2026, Vol. 56 Issue 7, p2473-2481. 9p.
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  Data: <searchLink fieldCode="DE" term="%22Data+encryption%22">Data encryption</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Cryptography%22">Cryptography</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+multiplications%22">Matrix multiplications</searchLink><br /><searchLink fieldCode="DE" term="%22Ordered+algebraic+structures%22">Ordered algebraic structures</searchLink><br /><searchLink fieldCode="DE" term="%22Data+security%22">Data security</searchLink><br /><searchLink fieldCode="DE" term="%22Digital+communications%22">Digital communications</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: This paper develops an encryption system that integrates graph theory with max-plus algebra to enhance data security and decryption reliability. The proposed method transforms plaintext into ciphertext by representing the message as a complete graph, where numerical values derived from an alphabet encoding scheme are used to label the edges. The encryption process applies substitution and permutation techniques based on max-plus algebra to generate complex ciphertext, thereby improving resistance against brute-force and frequency-based attacks. The algorithm follows a structured procedure that begins with numeric encoding, followed by complete graph construction, adjacency matrix generation, matrix modification, and max-plus algebraic transformation. The decryption process performs the inverse operations to recover the original plaintext accurately. Experimental results indicate that the proposed system achieves a high level of security while maintaining computational efficiency, making it suitable for protecting data in digital communication systems. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 9
        StartPage: 2473
    Subjects:
      – SubjectFull: Data encryption
        Type: general
      – SubjectFull: Graph theory
        Type: general
      – SubjectFull: Cryptography
        Type: general
      – SubjectFull: Matrix multiplications
        Type: general
      – SubjectFull: Ordered algebraic structures
        Type: general
      – SubjectFull: Data security
        Type: general
      – SubjectFull: Digital communications
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      – TitleFull: A Cryptographic Framework Based on Graph Labeling and Max-Plus Algebra.
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            – D: 01
              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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