Encoding-Decoding Algorithm Using the Catalan Transform of Weighted Tribonacci Sequence

Notice

This is an unedited manuscript accepted for publication and provided as an Article in Press for early access at the author’s request. The article will undergo copyediting, typesetting, and galley proof review before final publication. Please be aware that errors may be identified during production that could affect the content. All legal disclaimers of the journal apply.

Year : 2025 | Volume : | | Page :
    By

    bahar kuloglu,

  • Girma Wondale Gelagay,

  • Zerfie Teshome Yigzie,

  1. Assistant Professor, Department of Engineering Basic Sciences, Sivas, Turkey
  2. , Department of Mathematics Debre Tabor University Ethiopia, , Ethiopia
  3. , Department of Mathematics Debre Tabor University, , Ethiopia

Abstract

In order to improve information security, this paper presents a unique algorithm for encoding and decoding messages utilizing the Catalan Transform of a Weighted Tribonacci Sequence. Utilizing the Catalan and Tribonacci sequences, the methodology combines the concepts of number theory and combinatorics to create an effective encryption and decryption process. First, an array is created by mapping each character in the plaintext message to its corresponding ASCII value. The ASCII-weighted Tribonacci sequence is then obtained by first generating a similar Tribonacci sequence. The weighted Tribonacci sequence is encrypted by performing the Catalan Transform, which results in an encrypted message array. In order to recover the plaintext, the decryption method uses the inverse Catalan Transform to recreate the original ASCII values. The algorithm’s use is demonstrated by encrypting and decrypting the message “CODING” as an example. The method’s mathematical rigor is demonstrated by the computational steps that generate Catalan numbers, Tribonacci numbers, and their transformations. By changing the k-value, the algorithm’s versatility can be extended to k-Fibonacci sequences, providing more complexity and security. By fusing the structural characteristics of the Tribonacci and Catalan sequences, the method offers a fresh take on encryption methods. Results indicate that the suggested technique can improve secure communication in a number of applications, especially in settings where strong data security is required.

Keywords: Catalan Transform, Inverse Catalan Transform, Tribonacci Sequence, Weighted Tribonacci Sequence

How to cite this article:
bahar kuloglu, Girma Wondale Gelagay, Zerfie Teshome Yigzie. Encoding-Decoding Algorithm Using the Catalan Transform of Weighted Tribonacci Sequence. Research & Reviews: Discrete Mathematical Structures. 2025; ():-.
How to cite this URL:
bahar kuloglu, Girma Wondale Gelagay, Zerfie Teshome Yigzie. Encoding-Decoding Algorithm Using the Catalan Transform of Weighted Tribonacci Sequence. Research & Reviews: Discrete Mathematical Structures. 2025; ():-. Available from: https://journals.stmjournals.com/rrdms/article=2025/view=195454


References

REFERENCES

  1. Amalraj, A. J., & Jose, J. R. (2016). A Survey Paper on Cryptography Techniques. International Journal of Computer Science and Mobile Computing, 5(8), 55-59.
  2. Eser, E., Kuloglu, B., & Özkan, E. (2024). An Encoding-Decoding Algorithm Based On Fermat and Mersenne Numbers. Applied Mathematics E-Notes, 24, 274-282.
  3. Stakhov, A. P. (2006). Fibonacci matrices, a generalization of the “Cassini formula”, and a new coding theory. Chaos, Solitons & Fractals, 30(1), 56-66.
  4. Prasad, B. (2016). Coding theory on Lucas p numbers. Discrete Mathematics, Algorithms and Applications, 8(04), 1650074.
  5. Sangeetha, V., Anupreethi, T., & Somanath, M. (2024). Cryptographic Application of Elliptic Curve Generated through Centered Hexadecagonal Numbers. Indian Journal of Science and Technology, 17(20), 2074-2078.
  6. Kuloğlu, B. (2024). Creating a New Coding and Decoding Algorithm Based on Violin Notes.
  7. Kuloglu, B., & Ozkan, E. (2024). Matrix representation of (d, k)-Fibonacci polynomials. Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science, 185-200.
  8. Mudiyanselage, T.R.S., & Ekanayake Emusb. (2024). A Cryptography Algorithm Using Laplace Transformation. International Journal of Integrative Sciences, 3(9), 1053-1066.
  9. Raghunandan, K. R., Shetty, R., & Aithal, G. (2017, July). Key Generation and Security Analysis of Text Cryptography using Cubic Power of Pell’s Equation. International conference on intelligent computing, instrumentation, and control technologies (ICICICT) (pp. 1496-1500). IEEE.
  10. Deveci, O., & Shannon, A. (2022). On the Complex-type Catalan Transform of the k-Fibonacci Numbers. Journal of Integer Sequences, 25(4), 1352-1367.
  11. Parthasarathy, M.B., & Srinivasan, B. (2015). Increased Security in Image Cryptography using Wavelet Transforms. Indian Journal of Science and Technology, 8(12), 1-8.
  12. Barry, P. (2005). A Catalan Transform and Related Transformations on Integer Sequences. Journal of Integer Sequences, 8.
  13. American Standard Code for Information Interchange, ASA X3.4-1963″. American Standards Association (ASA). 1963-06-17. Retrieved 2020-06-06.
  14. Tan, B., & Wen, Z. Y. (2007). Some Properties of the Tribonacci Sequence. European Journal of Combinatorics, 28(6), 1703-1719.
  15. Falcon, S. (2013). Catalan Transform of the κ-Fibonacci Sequence. Communications of the Korean Mathematical Society, 28(4), 827-832.
  16. Kilic E. (2008). Tribonacci Sequences with Certain Indices and Their Sums.
  17. Renault, M. (2013). The Period, Rank, and Order of the (a, b)-Fibonacci Sequence Mod m. Mathematics Magazine, 86(5), 372–380
Ahead of Print Subscription Original Research
Volume
Received 19/12/2024
Accepted 30/12/2024
Published 10/01/2025
491

Login


My IP

PlumX Metrics