Sir Padampat Singhania University

Abstract: In this paper, we propose a new loss-less symmetric image cipher based on the widely used substitution–diffusion architecture which utilizes chaotic standard and logistic maps. It is specifically designed for the coloured images, which are 3D arrays of data streams. The initial condition, system parameter of the chaotic standard map and number of iterations together constitute the secret key of the algorithm. The first round of substitution/confusion is achieved with the help of intermediate XORing keys calculated from the secret key. Then two rounds of diffusion namely the horizontal and vertical diffusions are completed by mixing the properties of horizontally and vertically adjacent pixels, respectively. In the fourth round, a robust substitution/confusion is accomplished by generating an intermediate chaotic key stream (CKS) image in a novel manner with the help of chaotic standard and logistic maps. The security and performance of the proposed image encryption technique has been analyzed thoroughly using various statistical analysis, key sensitivity analysis, differential analysis, key space analysis, speed analysis, etc. Results of the various types of analysis are encouraging and suggest that the proposed image encryption technique is able to manage the trade offs between the security and speed and hence suitable for the real-time secure image and video communication applications.

Abstract: A novel and robust chaos-based pseudorandom permutation–substitution scheme for image encryption is proposed. It is a loss-less symmetric block cipher and specifically designed for the color images but may also be used for the gray scale images. A secret key of 161-bit, comprising of the initial conditions and system parameter of the chaotic map (the standard map), number of iterations and number of rounds, is used in the algorithm. The whole encryption process is the sequential execution of a preliminary permutation and a fix number of rounds (as specified in the secret key) of substitution and main permutation of the 2D matrix obtained from the 3D image matrix. To increase the speed of encryption all three processes: preliminary permutation, substitution and main permutation are done row-by-row and column-by-column instead of pixel-by-pixel. All the permutation processes are made dependent on the input image matrix and controlled through the pseudo random number sequences (PRNS) generated from the discretization of chaotic standard map which result in both key sensitivity and plaintext sensitivity. However each substitution process is initiated with the initial vectors (different for rows and columns) generated using the secret key and chaotic standard map and then the properties of rows and column pixels of input matrix are mixed with the PRNS generated from the standard map. The security and performance analysis of the proposed image encryption has been performed using the histograms, correlation coefficients, information entropy, key sensitivity analysis, differential analysis, key space analysis, encryption/decryption rate analysis etc. Results suggest that the proposed image encryption technique is robust and secure and can be used for the secure image and video communication applications.

Abstract: Recently Patidar et al. [Commun Nonlinear Sci Numer Simulat 14;2009:3056–75] proposed a new substitution–diffusion image cipher using chaotic standard and logistic maps, which is very fast and possess all the confusion and diffusion properties that any good cryptosystem should have. Soon after the proposal, Rhouma et al. [Commun Nonlinear Sci Numer Simulat 2010;15:1887–92.] proposed an equivalent description of the PPS09 cryptosystem which facilitated them in the cryptanalysis of the original cipher in terms of chosen plainext and known plaintext attacks. In this paper, we propose modifications in the Patidar et al.’s image cipher to make it robust against these two cryptanalytic attacks. The security analysis shows that the modified image cipher preserves all the good properties of the original cipher and is also capable to stand against the aforesaid attacks.

Abstract: In this paper, an encryption algorithm for gray images using a secret key of 128-bits size is proposed. Initially, visual quality of image is degraded by the mixing process. Resultant image is partitioned into key dependent dynamic blocks and, further, these blocks are passed through key dependent diffusion and substitution processes. Total sixteen rounds are used in the encryption algorithm. Proposed technique is simple to implement and has high encryption rate. Simulation experiment results have been given to validate the high security features and effectiveness of proposed system.

Abstract: In this communication, the two-well Duffing oscillator with non-linear damping term proportional to the power of velocity is considered. We mainly focus our attention on how the damping exponent affects the global dynamical behaviour of the oscillator. In particular, we obtain analytically the threshold condition for the occurrence of homoclinic bifurcation using Melnikov technique and compare the results with the computational results. We also identify the major route to chaos and the regions of the 2D parameter space (consists of external forcing amplitude and damping coefficient) corresponding to the various types of asymptotic dynamics under linear (viscous or friction like) and nonlinear (drag like) damping. We also attempt to analyze how the basins of attraction patterns change with the introduction of nonlinear damping. We also present our analysis for the physically less-interesting cases where damping is proportional to the 3rd and 4th power of velocity for the sake of generalizing our findings and establishing firm conclusion.