A Key Exchange Protocol based on the Twin Conjugacy Search Problem over Tropical Algebra

Authors

  • A. Kashifa Begum Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur - 603203, Chengalpattu
  • V. Muthukumaran SRM Institute of Science and Technology
  • Vediyappan Govindan Department of Mathematics, Hindustan Institute of Technology and Science, Chennai
  • Haewon Byeon Convergence Department, Korea University of Technology and Education, Cheonan, South Korea

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.5888

Keywords:

Conjugacy Search Problem, Twin Conjugacy Probelm, Tropical Algebra

Abstract

In public key cryptography, the security of the data leans on the hardness of solving some mathematical problems over algebraic structures, such as groups, rings, etc. The first published key exchange protocol is by Diffie and Hellman in 1976, whose security hinges on the challenges in solving the Discrete Logarithm Problem (DLP) over any finite field. In this research article, we present a key exchange protocol based on the Twin Conjugacy Search Problem (TCSP), a variant of the well-known Conjugacy Search Problem (CSP), and Tropical Algebra as a platform for the TCSP. We have provided two variants of the key exchange protocol and also provided a toy example. The chosen platform, Tropical Algebra, is a new approach and is easy to implement and not computationally hard as with other non-abelian groups as a platform, since one doesn’t have to perform any complex multiplication or addition. The security and complexity analysis of the protocol have also been explored.

Author Biographies

  • A. Kashifa Begum, Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur - 603203, Chengalpattu

    Ph.D

  • Vediyappan Govindan, Department of Mathematics, Hindustan Institute of Technology and Science, Chennai

    Ph.D

  • Haewon Byeon, Convergence Department, Korea University of Technology and Education, Cheonan, South Korea

    Ph.D

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Algebra

License

Copyright (c) 2025 A. Kashifa Begum, V. Muthukumaran, Vediyappan Govindan, Haewon Byeon

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How to Cite

A Key Exchange Protocol based on the Twin Conjugacy Search Problem over Tropical Algebra. (2025). European Journal of Pure and Applied Mathematics, 18(3), 5888. https://doi.org/10.29020/nybg.ejpam.v18i3.5888