Fractal Graphs-Based Representation of Tamil Numerals into Mathematical Numerals for Secure Encryption and Decryption Techniques

Abstract

In times of growing needs of secured information transfer, several innovative cryptosystems have been developed based on advanced mathematical systems. The aim of this work is to construct a graph representation of Tamil numerals based on fractal properties and using the representation model for encryption and decryption purposes. This approach relies on graph theory and fractal mathematics by linking the Tamil numbers to some graph characteristics such as fractal dimension, chromatic number, graph radius and union operation of graphs. The methodology involves the use of classical fractals such as the Cantor Set, Fractal Polygon Graph, Von-Koch Curve, Sierpinski Triangle and Von-Koch Snowflake. Numbers are then assigned to Tamil numerals depending on the graph characteristic, which creates a one-to-one correspondence between Tamil numbers and mathematical numbers. In this case, the encryption process is the transformation of the sequence of Tamil numerals into another sequence of other languages with an algorithm that is known to the sender of the message. In this approach, the input is mapped into mathematical numeral form and the output after encryption will be in mathematical numeral form too. In decryption, reverse mapping takes place. From the experimental study, it could be said that all 10 Tamil numerals were encoded with their unique fractal graph structures. As per the experiments, there was a direct and precise relationship between Tamil numerals and mathematical numerals, the precision of which was calculated to be 100%, both in encryption and decryption. All test cases have proved the reversibility of the framework and absence of data loss in the process. Unique mapping and conversions were confirmed by the performance evaluation studies carried out by the authors.