Narrow Results

This work proposes a generalization of the family of chaotic maps without fixed points, proposed by Jafari et al.; 2016 and termed the Vertigo maps. The original map family is parameterized by four control parameters, which can be used to scale the function used as a seed and control its domain. Several theoretical results are provided regarding the existence of the fixed points, the periodic cycles, and the Lyapunov exponents of the maps. Furthermore, two map examples are provided based on the logistic and tent seed functions, which are then studied using a series of numerical tools, like phase portraits, bifurcation diagrams, and Lyapunov exponent diagrams. Finally, an application to a Pseudo-Random Bit Generator is considered. The generator utilizes an exponential-based hash function in combination with the remainder operator.

A novel multiple-output pseudo-random-bit generator (PRBG) based on a coupled map lattice (CML) consisting of skew tent maps, which generates spatiotemporal chaos, is presented. In order to guarantee PRBG highly effective, avoiding synchronization among the sites in the CML is discussed. The cryptographic properties, such as probability distribution, auto-correlation and cross-correlation, of the PRBG with various parameters, are investigated numerically. The randomness of the PRBG is verified via FIPS 140-2. In addition, as compared with the PRBG based on the CML consisting of the logistic maps, which are often used in chaos-based PRBGs by many other researchers, the ranges of the parameters within which this multiple-output PRBG have good cryptographic properties are much bigger in terms of their cryptographic properties. It lays a foundation for designing a faster and more secure encryption.

A chaotic map which is realized on a computer will suffer dynamical degradation. Here, a coupled chaotic model is proposed to reduce the dynamical degradation. In this model, the state variable of one digital chaotic map is used to control the parameter of the other digital map. This coupled model is universal and can be used for all chaotic maps. In this paper, two coupled models (one is coupled by two logistic maps, the other is coupled by Chebyshev map and Baker map) are performed, and the numerical experiments show that the performances of these two coupled chaotic maps are greatly improved. Furthermore, a simple pseudorandom bit generator (PRBG) based on coupled digital logistic maps is proposed as an application for our method.