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

Year : 2024 | Volume : 11 | Issue : 03 | Page : 12 16
    By

    Girma Wondale Gelagay,

  • Zerfie Teshome Yigzie,

  • bahar kuloglu,

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

[This article belongs to Research & Reviews: Discrete Mathematical Structures ]

How to cite this article:
Girma Wondale Gelagay, Zerfie Teshome Yigzie, bahar kuloglu. Encoding-Decoding Algorithm Using the Catalan Transform of Weighted Tribonacci Sequence. Research & Reviews: Discrete Mathematical Structures. 2025; 11(03):12-16.
How to cite this URL:
Girma Wondale Gelagay, Zerfie Teshome Yigzie, bahar kuloglu. Encoding-Decoding Algorithm Using the Catalan Transform of Weighted Tribonacci Sequence. Research & Reviews: Discrete Mathematical Structures. 2025; 11(03):12-16. Available from: https://journals.stmjournals.com/rrdms/article=2025/view=206348


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Regular Issue Subscription Original Research
Volume 11
Issue 03
Received 19/12/2024
Accepted 30/12/2024
Published 10/01/2025
Publication Time 22 Days
206

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