Design of Symmetric Key Cryptosystems Based on Chaos and Algebra: Applications in Image Processing

Abstract

With the evolution of communication, digital media is now widely used throughout the world. Digital libraries containing a huge amount of information have been formed. These libraries contain digital data (books, images, magazines, even video and audio information) that can be accessed by anyone in the world. Due to free access of multimedia data throughout the internet and other accessible sources, the security of information has encouraged researchers to develop secure schemes for transmission as well as for copyright protection. Digital images are one of the major portions of communication happening around the globe. Generally, secure communication is when two individuals are communicating in such a way that no one in the path of communication can have any access to alter the data. There are many schemes available in literature to address this issue, but there is still a large room available for the development of secure, robust, and hassle-free cryptosystems. The only nonlinear element of the block cipher is the traditional expansion of Boolean functions from sole output to numerous outputs. The role of S-boxes in cryptosystems is to create confusion, which is achieved through substitution operations. The alteration of plaintext values by the S-box certifies resistance to any attempt at cryptanalysis. Constructions of S boxes based on finite fields are commonly used in literature. Many other algebraic structures, like groups or rings, are also used for such constructions. Cryptography and steganography are the two most important data hiding fields. The former is used to alter the original data into a bogus one, while the latter one is used to hide secret messages in a carrier. The importance of image encryption in the field of multimedia security is an established fact. Image encryption techniques transform information into an unreadable form to avoid unauthorized access. To improve multimedia security and guarantee secure communication, we in this thesis, emphasize on the construction of dynamical S-boxes from dynamical systems. The aim of this research is to build secure S-boxes with the additional property of diffusing the data. Based on these S-boxes, new cryptosystems are to be proposed for their practical utilization. With the advancement of computer technology, cryptanalytic schemes are also being designed to either alter the data or to recover secret messages. Therefore, the robustness of a cryptosystem is the ultimate target to be achieved. In this thesis, three constructions of robust S-boxes are proposed to enhance the security of block ciphers. The first method of construction is based on a newly designed 3D chaotic map. The suggested method can produce several types of S-boxes with admirable statistical and algebraic properties. In comparison to other algebraic techniques, the proposed technique is constraint free and simple. Moreover, it generates a large number of S-boxes having the property of confusion and diffusion as well. In the second method of construction, we designed chaotic S-boxes based on a 3D mixed chaotic map. This construction procedure guarantees many constraint-free, highly non-linear, and simple S-boxes. These S-boxes possess the unique property of diffusion along with confusion. These S-boxes yield the same algebraic analyses but different statistical analyses which is the motivation of our work to obtain a large number of highly non-linear S-boxes. These properties of S-boxes are very helpful for improving the multimedia security. In the third construction, we utilized linear fractional transformation for the construction of S-boxes. These S-boxes also preserve all cryptographic properties. The designed algebraic S-boxes and dynamic S-boxes are utilized in multimedia security through image encryption. Various schemes of image encryption utilizing algebraic and dynamic S-boxes have been designed. These schemes are capable of inducing confusion and diffusion at the same time. Moreover, in these encryption schemes, pixel values of the image are scrambled utilizing algebraic and dynamic S-box transformations to puzzle the connection between the plain and the encrypted image. Their security linked with differential and linear cryptanalysis has also been confirmed. These schemes are robust and have shown excellent outcomes