Cryptographic Algorithm Based on Prime Assignment

Abstract

Cryptography is a concept of protecting information and conversations which are transmitted through a public source, so that the send and receiver only read and process it. There are several encryption and decryption algorithm which involves mathematical concepts to provide more security to the text which has to be shared through a medium. In this paper, an algorithm is provided for both coding and decoding using cyclic symmetric matrices. Also Euler totient function, prime numbers are employed here. Furthermore, algorithm using prime number in integers is extended to prime numbers in Gaussian integers. This concept increases the security of the text.

Introduction

1. INTRODUCTION

For centuries, people have sent secret messages by various means. But some messages were not maintained secretly as there was no proper security. In order to maintain secrecy, cryptography was developed. It is the process of converting ordinary plain text (message to be sent) into some unintelligible text and vice versa. It helps to transmit data in a particular form so that the intended persons can read and process it. It is also useful for user authentication.

In olden days, an algorithm in cryptography was based on concepts which are well- known by all. But now- a- days, it is mainly based on mathematical theory and computer applications. Especially, number theory is playing a vital role in it, which employs the concepts such as congruence, Euler’s theorem.

In modern days, one can make use of any mathematical concepts to make their algorithm. As much as mathematics imposed, as much as security increases. Motivated by [3], this work aims to propose an algorithm to improve the security based on things such as prime numbers, Euler phi function, cyclic symmetric matrices. By modifying the assignments of alphabets in [3], this work is developed. 

This paper involves two algorithms. First one uses integer prime assignment whereas second one uses Gaussian prime assignment. For the second case, Euler phi function on Gaussian integers φZ[i]  is employed.

Common notations and definitions:

II. ALGORITHM BASED ON INTEGER PRIMES

B. Algorithm for Encryption

Assign the first 26  prime numbers to the alphabets. i.e.,

III. ALGORITHM BASED ON GAUSSIAN PRIMES

Conclusion

In this paper, there are two algorithms. One involving integer primes and the other uses Gaussian primes. One can maintain comparatively more secrecy in second one than that of first one. To improve much more security, one can modify the assignment by taking large primes as well as Gaussian primes.

References

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Copyright

Copyright © 2022 M. Mahalakshmi, J. Kannan, Manju Somanath, K. Raja, K. Kaleeswari. 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.