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Research & Reviews: Discrete Mathematical Structures Original Research

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

  1. Girma Wondale Gelagay Department of Engineering Basic Sciences, Sivas University of Science and Technology
  2. Zerfie Teshome Yigzie Department of Mathematics
  3. Bahar Kuloglu Department of Mathematics

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

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