Novel two dimensional fractional-order discrete chaotic map and its application to image encryption

A novel fractional two-dimensional triangle function combination discrete chaotic map is proposed by use of the discrete fractional calculus. The chaos behaviors are then discussed when the differe...

Fractional two-dimensional discrete chaotic map and its applications to the information security with elliptic-curve public key cryptography:

A new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM) with the discrete fractional difference is proposed. We observe the bifurcation behaviors and draw the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits of the proposed map, respectively. On the application side, we apply the proposed discrete fractional map into image encryption with the secret keys ciphered by Menezes-Vanstone Elliptic Curve Cryptosystem (MVECC). Finally, the image encryption algorithm is analysed in four main aspects that indicate the proposed algorithm is better than others.

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Image Encryption Technology Based on Fractional Two-Dimensional Triangle Function Combination Discrete Chaotic Map Coupled with Menezes-Vanstone Elliptic Curve Cryptosystem

First this paper constructs a 3-dimensional discrete chaotic map. The dynamic behaviors of the chaotic map display chaotic attractor characteristics. Second a 6-dimensional chaotic generalized synchronic system is introduced based on the chaotic map and a chaos generalized synchronization (GS) theorem. Third using the chaotic generalized synchronic system and a transformation T form ℝ to an integer set {0, 1, ... , 255} designs a chaos-based pseudorandom number generator (CPRNG). Furthermore, some statistical tests of the CPRNG have been given. The outputs of the CPRNG are all passed the FIPS 140-2 criteria. Numerical simulation examples show that for the perturbations of the keys of the CPRNG which are larger than 10-14, the corresponding keystreams have an average 99.61% different codes which are different from the codes generated by unperturbed keys. The result suggests that the key stream of the CPRNG has sound pseudorandomness.

http://ieeexplore.ieee.org/iel7/6558541/6568023/06568135.pdf

A novel chaotic system and design of pseudorandom number generator

Amultitude of physical, chemical, or biological systems evolving in discrete time can be modelled and studied using difference equations (or iterative maps). Here we discuss local and global dynamics for a predator-prey two-dimensional map. The system displays an enormous richness of dynamics including extinctions, coextinctions, and both ordered and chaotic coexistence. Interestingly, for some regions we have found the so-called hyperchaos, here given by two positive Lyapunov exponents. An important feature of biological dynamical systems, especially in discrete time, is to know where the dynamics lives and asymptotically remains within the phase space, that is, which is the invariant set and how it evolves under parameter changes. We found that the invariant set for the predator-prey map is very sensitive to parameters, involving the presence of escaping regions for which the orbits go out of the domain of the system (the species overcome the carrying capacity) and then go to extinction in a very fast manner. This theoretical finding suggests a potential dynamical fragility by which unexpected and sharp extinctions may take place.

/pdf/on-dynamics-and-invariant-sets-in-predator-prey-maps-2xcazudr26.pdf

On dynamics and invariant sets in predator-prey maps

This paper introduces one new novel 2-dimensional quadric polynomial discrete chaotic map and seven novel triangle function combination discrete chaotic maps (2D-TFCDM) The 2D-TFCDMs have at least one positive Lyapunov exponent Extensive numerical simulations display the orbits of the 2D-TFCDMs to have different chaotic attractors

Pei Li

Papers

Novel two dimensional discrete chaotic maps and simulations