Algebraic and Chaotic Schemes to Synthesis S-boxes and their Applications in Multimedia Security

Abstract

Rapidly increasing use of international networking offers various new openings for the design and demonstration in the form of digital data. Easy availability and access to digital contents like electronic advertising, video, audio, digital repositories, electronic libraries, web designing etc. arise many security concerns. In this era, digital images are counted as one of the major communication sources as there is excessive application of multimedia knowledge and techniques. Generally, multimedia security is number of methods or techniques which ensures the security of multimedia data. For this reason, many researchers initiated working in developing different security techniques. Although there are certain methods for data security, but lot of improvement is required to guarantee the data security. The strength of substitution box ensures the strength of block ciphers which have very important role in symmetric key cryptography. The main purpose of Substitution box is to create confusion, secure the original data from cryptanalysis and hide it in cipher text. It is noticed that mostly substitution boxes are constructed on Galois field. The other algebraic structures like groups, finite commutative ring can also be utilized for the construction of substitution box. The methodologies for two multimedia security techniques i.e., for cryptography and steganography are different but they both are used for information hiding. In cryptography, data is transformed into an unintelligible arrangement called cipher text which is decrypted by receiver end into plaintext. On the other hand, steganography is an art of embedding surreptitious material into an unsuspicious carrier. Another multimedia security technique is watermarking. Watermarking provides copyright protection of digital content. Copyright violations and plagiarism indicate that current copyright rules are vulnerable to be used for the digital data transfer on Internet. Keeping in view, the importance of copyright protection of digital contents, robustness of watermarking techniques, we in this thesis, initiated working for the construction of algebraic and chaotic high nonlinearity substitution boxes which has strong cryptographic properties. These Substitution boxes are then utilized in the field of multimedia security specifically in watermarking and steganography (spatial and frequency domain) techniques. The basic purpose is to enhance the security and robustness against malicious attacks. The first construction of substitution box depends on the action of a projective general linear group over the set of units of the finite commutative ring. The strength of substitution box and ability to create confusion is assessed with different analyses and equated with well-known substitution boxes. In the next step, we suggest that the choice of the background irreducible polynomial, used for the construction of the Galois field 􀀁�(28) has a deep influence on the highly desirable features on an Substitution box. We therefore propose that the performance of a substitution box is not just depending on the nature of the bijective Boolean function, however, it is affected by the degree 8 irreducible polynomial 􀀇(􀀈) as well, which generates the maximal ideal of the principal ideal domain �􀀉[􀀈]. A unique nonlinear combination of two chaotic maps give a chaotic Tent-Sine system. This arrangement of chaotic maps shows brilliant complex chaotic properties. The chaotic range of Tent-Sine system is increased throughout the domain and the output sequences are distributed uniformly. We propose a chaotic substitution box with the help of this chaotic map. This Substitution box is capable of providing confusion ability by achieving the substitution operation. This Substitution box is helpful against linear and differential attacks. After that, the chaotic logistic map is employed for locating embedding positions of chaotic watermark generation and a novel watermarking scheme is proposed. Simulation results reveal that the proposed technique is feasible and watermarks are indiscernible. In the next two frequency domain watermarking techniques, chaotic and algebraic substitution boxes are used. In the first case, the system of non-linear ordinary differential equations which defines a continuous-time dynamical system is used to construct chaotic box. In the second case, the algebraic box which develops one-one correspondence between the multiplicative group of units of the local ring ℤ51􀀄 and the Galois field 􀀅􀀄56. is used. The watermark is substituted with substitution boxes and then embedded into host image which give additional security to our proposed techniques. For application of substitution box in digital steganography, we engage a specific high nonlinearity Substitution box along with some chaotic systems, possessing enhanced chaotic range, to embed information in the least significant bits of the host image. At the end, we have proposed a high capacity and robust steganographic algorithm based on an effective application of chaos and substitution box. The speciality of the proposed method lies, on one hand, in the process of embedding secret information using some stronger chaotic systems with enhanced chaotic range. While, on the other, high embedding-capacity level and robustness is attained due to the combination of the spatial domain steganography approach along with the frequency domain transform.