CHAPTER 13 CONCLUSIONS AND SCOPE FOR FUTURE WORK

Transcription

1 189 CHAPTER 13 CONCLUSIONS AND SCOPE FOR FUTURE WORK

2 Conclusions This thesis is devoted to the study of the following problems in cryptography and image processing. 1. A modified Feistel cipher involving modular arithmetic and interlacing. 2. A modified Feistel cipher involving modular arithmetic and a key on both the sides of the plaintext matrix. 3. A novel block cipher involving Feistel structure and modular arithmetic. 4. A block cipher involving a key applied on both the sides of the plaintext. 5. A block cipher having a key on one side of the plaintext matrix and its inverse on the other side. 6. A large block cipher involving a key applied on both the sides of the plaintext. 7. A large block cipher having a key on one side of the plaintext Matrix and its inverse on the other side as multiplicants. 8. Cryptography of a gray level image using a modified Feistel cipher. 9. Cryptography of a gray level image using a novel block cipher involving Feistel structure and modular arithmetic. 10. Cryptography of a binary image using a modified Hill cipher. 11. Cryptography of a gray level image using a modified Hill cipher. These problems 1 11 are presented in chapters Chapter 2 deals with the study of a block cipher based upon Feistel structure. This involves modular arithmetic and interlacing in each round of the iteration process.

3 191 In chapter 3, we have developed a block cipher by using Feistel structure. In this, the plaintext matrix is multiplied on both the sides by a key matrix K, and modular arithmetic is used appropriately. In chapter 4, we have extended the analysis of the chapter 3 by replacing the XOR operation with + operation. Chapter 5 includes a block cipher wherein we have multiplied the plaintext matrix P on both the sides by a key matrix K. In this, all the elements of P and K are binary bits and hence mod 2 operations are carried out. In chapter 6, we have extended the analysis in the previous chapter, by including a key matrix K on one side of the plaintext matrix P and its inverse on the other side as multiplicants. In chapters 7 and 8, we have presented the extended versions of the problems discussed in chapters 5 and 6 respectively. In chapters 9 12, we have investigated some problems related to cryptography of images. In chapter 9, we have used the cipher presented in chapter 3 and studied the cryptography of a gray level image. Chapter 10 deals with the cryptography of a gray level image wherein we have used a novel block cipher discussed in chapter 4. In chapter 11, we have analysed the cryptography of a binary image by using the cipher presented in chapter 6. Chapter 12 contains the cryptography of a gray level image. This analysis is carried out by using the cipher presented in chapter 8. In Table 13.1, we have presented the salient features of the various ciphers which are investigated in the problems 1 7 (Chapters 2 8).

4 192 Here, we have also mentioned the avalanche effect which can be considered as benchmark for block ciphers. However in the following Table, we have not mentioned the time required for each cipher, as it is a few milli seconds in the case of each block of a block cipher. Here, it is to be noted that all the ciphers are very strong as the avalanche effect is quite significant. Problem No. Cipher No. of bits in Avalanche effect Plaintext Key Plaintext Change Key Change 1 A modified Feistel cipher involving modular arithmetic and interlacing 2 A modified Feistel cipher involving modular arithmetic and a key on both the sides of the plaintext matrix 3 A novel block cipher involving Feistel structure and modular arithmetic 4 A block cipher involving a key applied on both the sides of the plaintext 5 A block cipher having a key on one side of the plaintext matrix and its inverse on the other Side 6 A large block cipher involving a key applied on both the sides of the plaintext 7 A large block cipher having a key on one side of the plaintext matrix and its inverse on the other side as multiplicants Table13. 1 Parameters of the various ciphers

5 Scope for Future Work Here it is fascinating to note that several extensions of the research work carried out in this thesis are possible. In chapter 2, we can vary the key from round to round of the iteration process. In chapters 3 and 4, we can introduce the modular arithmetic inverse of the key K and develop the corresponding ciphers. The work in chapters 5 and 7, can be extended to image cryptography.