A study of some problems in cryptography and image processing

Abstract

In this thesis, we have 13 chapters. Chapter 1 deals with the introduction. In this, after making some preliminary remarks about the evolution of the areas cryptography and image processing, we have mentioned the basic concepts related to the areas, and presented a survey of the relevant literature. Further, we have introduced some mathematical techniques applied in the thesis, and then mentioned the outlines of the thesis. In chapter 2, we have developed a block cipher with Feistel structure. In this the plaintext is consisting of 256 bits and the key is containing 128 bits. The process of encryption is carried out by using modular arithmetic and interlacing the plaintext at various rounds of the iterative process. The avalanche effect and the cryptanalysis firmly indicate that the cipher is a strong one and it cannot be broken by any cryptanalytic attack. In chapter 3, we have developed a block cipher wherein the plaintext is represented in the form of a pair of square matrices in which each is of size m. In this, the key is also a square matrix of size m and it is used to multiply one of the plaintext matrices on both the sides. Here, we have followed Feistel iterative process in which number of iterations is n (=16). From the avalanche effect and the cryptanalysis, it is concluded that the cipher is a strong one and it cannot be broken by any cryptanalytic attack. In chapter 4, following Feistel, we have developed a symmetric block cipher wherein the XOR operation in the modified Feistel cipher is replaced by + operation. In this, a portion of the plaintext is multiplied on both the sides by a key matrix and mod operation is utilised. The avalanche effect and the cryptanalysis, carried out in this chapter, clearly indicate that the cipher is a potential one.