On Graph-Based Cryptography in Dynamical Systems

Authors

    Manouchehr Shahamat * Department of Mathematics‎, ‎Dezful branch‎, ‎Islamic Azad University‎, ‎Dezful‎, ‎Iran m.shahamat@iau.ac.ir

Keywords:

Shift space, Cryptography, Encoding, Decoding, Entropy, Graph

Abstract

For the purpose of data storage and transmission, constrained sets are required. Thus, to convert sequences from a full shift space to a sofic shift, certain constraints must be applied. One method to address this issue is the use of finite-type codes. An (X, n)-finite-type code can be used to transform sequences from a full n-shift into sequences from the shift space X. If X is a sofic space with entropy at least equal to the logarithm of n, then an (X, n)-finite-type code exists.

References

[1] P. Amudha and A.C. Charles Sagayaraj and A.C.Shantha Sheela, An Application of Graph Theory in Cryptography, Volume 119 No. 132018,375-383, International Journal of Pure and Applied Mathematics.

[2] W. Etaiwi, Encryption Algorithm Using Graph Theory, January 2014, Journal of Scientific Research and Reports, 3(19):2519-2527.

[3] D. Fiebig and U. Fiebig, Covers for coded systems, Contemporary Mathematics, 135, 1992, 139-179.

[4] D. Lind and B. Marcus, An introduction to symbolic dynamics and coding, Cambridge Univ. Press. 2005.

[5] K. Thomsen, On the ergodic theory of synchronized systems, Ergod. Th. Dynam. Sys. 356(2016)1235-1256.

[6] K. Thomsen, On the structure of a sofic shift space, American Mathematical Society, 356, Number 9(2014),

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Published

2025-03-20

Submitted

2025-02-03

Revised

2025-03-03

Accepted

2025-03-12

Issue

Section

Articles

How to Cite

Shahamat, M. (2025). On Graph-Based Cryptography in Dynamical Systems. The Decision Science and Intelligent Systems, 1(2), 94-110. https://dsisj.com/index.php/dsisj/article/view/16