Biblio

Chaotic dynamics is widely used to design pseudo-random number generators and for other applications, such as secure communications and encryption. This paper aims to study the dynamics of the discrete-time chaotic maps in the digital (i.e., finite-precision) domain. Differing from the traditional approaches treating a digital chaotic map as a black box with different explanations according to the test results of the output, the dynamical properties of such chaotic maps are first explored with a fixed-point arithmetic, using the Logistic map and the Tent map as two representative examples, from a new perspective with the corresponding state-mapping networks (SMNs). In an SMN, every possible value in the digital domain is considered as a node and the mapping relationship between any pair of nodes is a directed edge. The scale-free properties of the Logistic map's SMN are proved. The analytic results are further extended to the scenario of floating-point arithmetic and for other chaotic maps. Understanding the network structure of a chaotic map's SMN in digital computers can facilitate counteracting the undesirable degeneration of chaotic dynamics in finite-precision domains, also helping to classify and improve the randomness of pseudo-random number sequences generated by iterating the chaotic maps.

The objective of this paper was to propose a 5D combined chaotic system used for image encryption by scrambling and DNA encryption. The initial chaotic values were calculated with a set of equations. The chaotic sequences were used for pixel scrambling, bit scrambling, DNA encryption and DNA complementary function. The average of NPCR, UACI and entropy values of the 6 images used for testing were 99.61, 33.51 and 7.997 respectively. The correlation values obtained for the encrypted image were much lower than the corresponding original image. The histogram of the encrypted image was flat. Based on the theoretical results from the tests performed on the proposed system it can be concluded that the system is suited for practical applications, since it offers high security.

Image encryption takes been used by armies and governments to help top-secret communication. Nowadays, this one is frequently used for guarding info among various civilian systems. To perform secure image encryption by means of various chaotic maps, in such system a legal party may perhaps decrypt the image with the support of encryption key. This reversible chaotic encryption technique makes use of Arnold's cat map, in which pixel shuffling offers mystifying the image pixels based on the number of iterations decided by the authorized image owner. This is followed by other chaotic encryption techniques such as Logistic map and Tent map, which ensures secure image encryption. The simulation result shows the planned system achieves better NPCR, UACI, MSE and PSNR respectively.