An Approach of Graph Theory on Cryptography

Abstract

In this paper, we discuss about the connection between graph theory and cryptography. We use the spanning tree concept of graph theory to encryption the message.

Introduction

I. INTRODUCTION

Cryptography is the art of protect information by transforming it to unreadable format called Cipher text. The process of converting plain text to cipher text called encryption, and the process of converting cipher text on its original plain text called decryption. The remainder of this paper is a discussion of intractable problem from graph theory keeping cryptography as the base.

Firstly we represent the given text as node of the graph. Every node represent a character of the data. Now every adjacent character in the given text will be represented by adjacent vertices in the graph.

II. APPLICATION

Example :1

We will encrypt the text or data, say RATE , which we will be sending to the receiver on the other end.

Now we change this text into graph by converting each letter to vertices of graph.

The label on each edge represents the distance between the connected two vertices from the encoding table. So the edge connecting vertex C with vertex O has a label which is distance between the two characters in the encoding table.

Distance = code (A)−code (H) = 1 − 8 = −7.

Similarly we can deduce the distances of other edges. Then we label the graph containing all the plaintext letters and we get weighted graph which is given below. After that, we keep adding edges to form a complete graph and each new added edge has a sequential weight starting from the maximum weight in the encoding table which is 26.Therefore we can add 27,28 and so on.

We suppose that the vertex 0 is A, and by using encoding table

Vertex 1 = code (A) + -19  = 18, which is character R

Vertex 2 = code (H) - 7 = 1, which is character A

Vertex 3 = code (A) + 19 = 20, which is character T

Vertex 4 = code (T) + −15 = 5, which is character E

Which gives us the original text R A T E

Acknowledgement

One of the author (Dr. V. Balaji ) acknowledges University Grants Commission, SERO,    Hyderabad and India for financial assistance (No.FMRP5766/15(SERO/UGC)).

References

[1] Corman TH, Leiserson CE, Rivest RL, Stein C. Introduction to algorithms 2nd edition, McGraw-Hill. [2] Yamuna M, Meenal Gogia, Ashish Sikka, Md. Jazib Hayat Khan. Encryption using graph theory and linear algebra. International Journal of Computer Application. ISSN:2250-1797, 2012. [3] Ustimenko VA. On graph-based cryptography and symbolic computations, Serdica. Journal of Computing, 2007, 131-156. [4] Uma Dixit,CRYPTOGRAPHY A GRAPH THEORY APPROACH, International Journalof Advance Research in Science and Engineering, 6(01), 2017, BVCNSCS 2017. [5] Wael Mahmoud Al Etaiwi , Encryption Algorithm Using Graph Theory, Journal of Scientific Research and Reports, 3(19), 2519-2527, 2014, Article no.

Copyright

Copyright © 2022 Indhu K, Rekha S. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.