Non-associative Structures for the Development and Application of Cryptosystems

Abstract

The absolute achievements of information sciences in last few decades are extensive deployment of soft and small computing devices in general public along with the speedy communication channel. An easy approach to valuable digital data had to face some security apprehensions. Frequent transmission and communication of information bears problems like copyright protection, false ownership claims and alteration in valued information, integrity, confidentiality, non-repudiation, access control and authenticity. All of these and many more of this type of security issues are the matter of concern for researchers as well as for officials. The security of data is preserved in such vulnerable situations by making use cryptography. Cryptography works generally on mechanisms of converting meaningful information into non readable form and vice versa. There are two main types of cryptography are symmetric and asymmetric key cryptography. These two types bifurcated on the basis of keys. Same key is used for encryption and decryption in a symmetric key cryptography whereas different set of keys are used in both these procedures in asymmetric key cryptosystems. Stream ciphers and block ciphers are the two broad categories of symmetric key cryptography. In block cryptograms, the procedure of enciphering is done for blocks of data with different sizes. The only nonlinear and complex part of block cryptosystem capable of generating hurdles for cryptanalysts is the substitution box (S-box). After the development of advanced encryption standard, the need of new encryption standard is diminished because of its robustness and strength against cryptanalyses. However, its security can be enhanced by using chaos based S-boxes instead of algebraic S-boxes. S-box is the nonlinear component of block cipher responsible for creating confusion in the systems. It can have different dimensions depending upon the need of algorithm. It is produced in the form of square matrix from a mathematical structure. Nonlinear mathematical systems are suitable candidates for the generation of S-boxes. In literature, large number of articles are available expressing research work of scientists related to cryptography and chaos. But they are more vulnerable to cyber threats like brute force and linear attacks due to the low key space, small chaotic range and involvement of fewer number of variables. These drawbacks motivated many cryptographers to use nonlinear algebraic systems, which hamper all such deficiencies and threats. This thesis primarily focuses on the generation of S-boxes from non-associative structures and the second aim is to design encryption and watermarking techniques by using these nonlinear components of block cipher. At the first stage of this thesis, block ciphers and non-associative structures are mainly discussed. Moreover, important properties of S-box on the perspective of mathematics are also discussed. A new non-associative structure power associative loop is used for the construction of S-boxes are introduced in chapter second of this thesis. This scheme is used for the construction of highly non-linear components of block ciphers. This scheme provides both confusion and diffusion characteristics. Investigational conclusions authenticate the competence of the predicted algorithms. Chapter 3 introduces the construction of the S-box from another type of non-associative structure. Compared with other complex structure-based constructions, this method of developing a strong encryption S-box utilizes a simple and single transformation. The main advantage of using a non-associative structure in stable communication is that it can provide you with more unpredictable and random data. An application of image encryption and watermarking are discussed in chapter four. In chapter five of this thesis, a new cryptographic scheme is proposed whose model is the same as presented in Rijndael algorithm by Joan Daemen and Vincent Rijmen. In the design of this cipher, we have used inverse property loop instead of extended binary Galois field. The complete description of encryption and decryption of this cryptographic scheme is given in this chapter. In chapter six of this thesis, another transformation that is Mobius transformation is applied on a non-associative structure for the construction of highly non-linear substitution boxes. This transformation helps us to achieve maximum nonlinearity of substitution boxes over non-associative structures. A novel image encryption scheme is presented in chapter seven. For this scheme, an encryption standard is proposed whose model is the same as presented by Eli Biham, Ross Anderson, and Lars Knudsen. The proposed method is simple and speedy in terms of computations, meanwhile, it affirms higher security and sensitivity. All the standard analyses were found promising in analysing the suggested scheme of encryption. This thesis has been ended with chapter eight which includes the conclusions and the future directions