Review on cyclic group and affine cryptosystem and its application on cryptography

Abstract

In this thesis, I have tried to briefly describe the concept of cryptography and group theory and the relation between them. In short, Cryptography is regarded as a medium which enables communications to take place under secure parameters. The process of encryption and decryption which uses algorithm and key to convert plain texts into encrypted ones and vice versa makes such secure communication possible even with the presence of malicious third parties. A major portion of the study of cryptography deals with Group Theory. Group theory, perhaps the primary algebraic structure to be studied abstractly, is one of the most fundamental structures. A group is a finite or infinite set of elements together with a binary operation that satisfies the four basic properties of closure, associability, the identity property and the inverse property. In this thesis, I have put the Diffie Hellman’s protocol to demonstrate an application in which an outside client can privately communicate with members of a particular company without running the risk of important facts getting leaked elsewhere. Affine cryptosystem is used to encrypt and decrypt messages which uses the ℤ26 is also included in this thesis by which the client can send encrypted messages to any specific member he wants, and the receiver can also decrypt the message.