Abstract
Most of chaos-based cryptosystems utilize stationary dynamics of chaos for the permutation and diffusion, and many of those are successfully attacked. In this paper, novel models of the image permutation and diffusion are proposed, in which chaotic map is perturbed at bit level on state variables, on control parameters or on both. Amounts of perturbation are initially the coordinate of pixels in the permutation, the value of ciphered word in the diffusion, and then a value extracted from state variables in every iteration. Under the persistent perturbation, dynamics of chaotic map is nonstationary and dependent on the image content. The simulation results and analyses demonstrate the effectiveness of the proposed models by means of the good statistical properties of transformed image obtained after just only a single round.
Highlights
For recent decades, chaos has been discovered in natural, human, and engineering models [1]
Dynamics of any chaotic system is degraded to periodic orbits due to the round-off errors by the limited number of bits represented for values of state variables and control parameters [16,17,18]
Fixed-point representation is suitable for most chaotic maps because the value of state variables and of control parameters are in the narrow ranges
Summary
Chaos has been discovered in natural, human, and engineering models [1]. For most of chaos-based image cryptosystems, a chaotic system is used for generating chaotic sequences for the permutation and diffusion processes. Along with the use of hyperchaotic, time-delay, fractional order, and spatiotemporal chaotic systems, complicated dynamics can be obtained by mixed of various chaotic systems such as References [40,41,42,43,44,45] In such the chaos-based cryptosystems, chaotic systems work with fixed values of control parameters and with non-disturbed chaotic orbits. As presented in Reference [42], the initial value and the value of parameter of chaotic system are generated with the use of image content for whole encryption, but the parameter of chaotic map deciding the manner of the permutation and diffusion is dependent on the image content of blocks.
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