Reducing the Dynamical Degradation by Bi-Coupling Digital Chaotic Maps

2018 ◽  
Vol 28 (05) ◽  
pp. 1850059 ◽  
Author(s):  
Lingfeng Liu ◽  
Bocheng Liu ◽  
Hanping Hu ◽  
Suoxia Miao
Keyword(s):  
Chaotic Maps ◽  
Chaotic Map ◽  
Coupled Model ◽  
The Other ◽  
Coupled Models ◽  
Digital Map ◽  
State Variable ◽  
Chebyshev Map ◽  
Chaotic Model ◽  
Dynamical Degradation

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.

scholarly journals An Iteration-Time Combination Method to Reduce the Dynamic Degradation of Digital Chaotic Maps

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yao Wu ◽  
Lingfeng Liu
Keyword(s):  
Chaotic Maps ◽  
Control Function ◽  
Chaotic Map ◽  
Combination Method ◽  
Control Parameters ◽  
Improved Method ◽  
Dynamical Degradation ◽  
Dynamic Degradation ◽  
Number Of Iterations ◽  
Iteration Time

A new and improved method based on the number of iterations is proposed to reduce the dynamical degradation of the digital chaotic map in this study. We construct a control function by introducing iteration time instead of external systems, thereby replacing the control parameters in the original chaotic map. Experimental results show that the chaotic map based on the iteration-time combination method is more complicated and effective. The period is extended without completely destroying the phase space, which indicates that our method is effective and can compete with other proposed techniques. A type of pseudorandom bit generator based on the iteration-time combination method is proposed to demonstrate its simple application.

DESIGN OF PSEUDO-RANDOM BIT GENERATOR BASED ON CHAOTIC MAPS

2012 ◽  
Vol 26 (32) ◽  
pp. 1250208 ◽  
Author(s):  
XING-YUAN WANG ◽  
LEI YANG
Keyword(s):  
Cycle Length ◽  
Stream Cipher ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
The Other ◽  
One Dimensional ◽  
Random Bit Generator ◽  
Dynamical Properties ◽  
Finite States

In order to solve the problem of degradation of dynamical properties caused by finite states of computer, a new binary stream-cipher algorithm based on dual one-dimensional chaotic maps is proposed in this paper. In the process of generation, we employ a parameter of one chaotic map to perturb the other chaotic map's trajectory to lengthen the cycle-length of the other chaotic map's trajectory. In addition, we design a nonlinear principle to generate a pseudo-random chaotic bit sequence as key stream. Statistic proprieties show that the sequence is of high randomness.

scholarly journals Speech encryption by multiple chaotic map with fast fourier transform

2020 ◽  
Vol 10 (6) ◽  
pp. 5658
Author(s):  
Yahia Alemami ◽  
Mohamad Afendee Mohamed ◽  
Saleh Atiewi ◽  
Mustafa Mamat
Keyword(s):  
Social Communication ◽  
Data Security ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Logistic Map ◽  
The Other ◽  
Mathematical Structures ◽  
Multiple Encryption ◽  
Encryption Algorithms ◽  
Speech Encryption

There are various ways of social communication including writing (WhatsApp, Messenger, Facebook, Twitter, Skype, etc), calling (mobile phone) and voice recording (record your voice and then send it to the other party), but there are ways to eavesdropping the calls and voice messages, One way to solve this problem is via cryptographic approach. Chaos cryptography build on top of nonlinear dynamics chaotic system has gained some footstep in data security. It provides an alternative to conventional cryptography built on top of mathematical structures. This research focuses on the protection of speech recording by encrypting it with multiple encryption algorithms, including chaotic maps (Logistic Map and Sine Maps).

scholarly journals The Design and FPGA-Based Implementation of a Stream Cipher Based on a Secure Chaotic Generator

2021 ◽  
Vol 11 (2) ◽  
pp. 625
Author(s):  
Fethi Dridi ◽  
Safwan El Assad ◽  
Wajih El Hadj Youssef ◽  
Mohsen Machhout ◽  
René Lozi
Keyword(s):  
Stream Cipher ◽  
Chaotic Maps ◽  
Statistical Tests ◽  
Chaotic Map ◽  
Logistic Map ◽  
Tent Map ◽  
First Order ◽  
Recursive Filters ◽  
Weakly Coupled ◽  
Chebyshev Map

In this study, with an FPGA-board using VHDL, we designed a secure chaos-based stream cipher (SCbSC), and we evaluated its hardware implementation performance in terms of computational complexity and its security. The fundamental element of the system is the proposed secure pseudo-chaotic number generator (SPCNG). The architecture of the proposed SPCNG includes three first-order recursive filters, each containing a discrete chaotic map and a mixing technique using an internal pseudo-random number (PRN). The three discrete chaotic maps, namely, the 3D Chebyshev map (3D Ch), the 1D logistic map (L), and the 1D skew-tent map (S), are weakly coupled by a predefined coupling matrix M. The mixing technique combined with the weak coupling technique of the three chaotic maps allows preserving the system against side-channel attacks (SCAs). The proposed system was implemented on a Xilinx XC7Z020 PYNQ-Z2 FPGA platform. Logic resources, throughput, and cryptanalytic and statistical tests showed a good tradeoff between efficiency and security. Thus, the proposed SCbSC can be used as a secure stream cipher.

scholarly journals Reducing the Dynamical Degradation of Digital Chaotic Maps with Time-Delay Linear Feedback and Parameter Perturbation

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Bocheng Liu ◽  
Hongyue Xiang ◽  
Lingfeng Liu
Keyword(s):  
Time Delay ◽  
Chaotic Maps ◽  
Complexity Analysis ◽  
Chaotic Map ◽  
Logistic Map ◽  
Numerical Results ◽  
Linear Feedback ◽  
Parameter Perturbation ◽  
Dynamical Degradation ◽  
Baker Map

Digital chaotic maps are not secure enough for cryptographic applications due to their dynamical degradation. In order to improve their dynamics, in this paper, a novel method with time-delay linear feedback and parameter perturbation is proposed. The delayed state variable is used to construct the linear feedback function and parameter perturbation function. This method is universal for all different digital chaotic maps. Here, two examples are presented: one is 1D logistic map and the other is 2D Baker map. To show the effectiveness of this method, we take some numerical experiments, including trajectory and phase space analysis, correlation analysis, period analysis, and complexity analysis. All the numerical results prove that the method can greatly improve the dynamics of digital chaotic maps and is quite competitive with other proposed methods. Furthermore, a simple pseudorandom bit generator (PRBG) based on digital Baker map is proposed to show its potential application. The proposed PRBG is completely constructed by the digital chaotic map, without any other complex operations. Several numerical results indicate that this PRBG has good randomness and high complexity level.

scholarly journals A Novel S-Box Dynamic Design Based on Nonlinear-Transform of 1D Chaotic Maps

Electronics ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 1313
Author(s):  
Wenhao Yan ◽  
Qun Ding
Keyword(s):  
Chaotic Systems ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Logistic Map ◽  
Sample Entropy ◽  
One Dimension ◽  
Linear Combinations ◽  
Dynamic Design ◽  
Construction Methods ◽  
Low Dimensional

In this paper, a method to enhance the dynamic characteristics of one-dimension (1D) chaotic maps is first presented. Linear combinations and nonlinear transform based on existing chaotic systems (LNECS) are introduced. Then, a numerical chaotic map (LCLS), based on Logistic map and Sine map, is given. Through the analysis of a bifurcation diagram, Lyapunov exponent (LE), and Sample entropy (SE), we can see that CLS has overcome the shortcomings of a low-dimensional chaotic system and can be used in the field of cryptology. In addition, the construction of eight functions is designed to obtain an S-box. Finally, five security criteria of the S-box are shown, which indicate the S-box based on the proposed in this paper has strong encryption characteristics. The research of this paper is helpful for the development of cryptography study such as dynamic construction methods based on chaotic systems.

scholarly journals The Linear Response of ENSO to the Madden–Julian Oscillation

2005 ◽  
Vol 18 (13) ◽  
pp. 2441-2459 ◽  
Author(s):  
J. Zavala-Garay ◽  
C. Zhang ◽  
A. M. Moore ◽  
R. Kleeman
Keyword(s):  
Large Fraction ◽  
Surface Wind ◽  
Low Frequency ◽  
Coupled Model ◽  
Cumulative Effect ◽  
Enso Event ◽  
Kelvin Waves ◽  
Madden Julian Oscillation ◽  
Coupled Models ◽  
Stochastic Forcing

Abstract The possibility that the tropical Pacific coupled system linearly amplifies perturbations produced by the Madden–Julian oscillation (MJO) is explored. This requires an estimate of the low-frequency tail of the MJO. Using 23 yr of NCEP–NCAR reanalyses of surface wind and Reynolds SST, we show that the spatial structure that dominates the intraseasonal band (i.e., the MJO) also dominates the low-frequency band once the anomalies directly related to ENSO have been removed. This low-frequency contribution of the intraseasonal variability is not included in most ENSO coupled models used to date. Its effect in a coupled model of intermediate complexity has, therefore, been studied. It is found that this “MJO forcing” (τMJO) can explain a large fraction of the interannual variability in an asymptotically stable version of the model. This interaction is achieved via linear dynamics. That is, it is the cumulative effect of individual events that maintains ENSOs in this model. The largest coupled wind anomalies are initiated after a sequence of several downwelling Kelvin waves of the same sign have been forced by τMJO. The cumulative effect of the forced Kelvin waves is to persist the (small) SST anomalies in the eastern Pacific just enough for the coupled ocean–atmosphere dynamics to amplify the anomalies into a mature ENSO event. Even though τMJO explains just a small fraction of the energy contained in the stress not associated with ENSO, a large fraction of the modeled ENSO variability is excited by this forcing. The characteristics that make τMJO an optimal stochastic forcing for the model are discussed. The large zonal extent is an important factor that differentiates the MJO from other sources of stochastic forcing.

scholarly journals Impact of Resolution on the Tropical Pacific Circulation in a Matrix of Coupled Models

2009 ◽  
Vol 22 (10) ◽  
pp. 2541-2556 ◽  
Author(s):  
Malcolm J. Roberts ◽  
A. Clayton ◽  
M.-E. Demory ◽  
J. Donners ◽  
P. L. Vidale ◽  
...  
Keyword(s):  
Coupled Model ◽  
Walker Circulation ◽  
Ocean Model ◽  
Tropical Pacific ◽  
Coupled Models ◽  
Model Stability ◽  
The Mean ◽  
The Impact ◽  
Mean State ◽  
The Tropical Pacific

Abstract Results are presented from a matrix of coupled model integrations, using atmosphere resolutions of 135 and 90 km, and ocean resolutions of 1° and 1/3°, to study the impact of resolution on simulated climate. The mean state of the tropical Pacific is found to be improved in the models with a higher ocean resolution. Such an improved mean state arises from the development of tropical instability waves, which are poorly resolved at low resolution; these waves reduce the equatorial cold tongue bias. The improved ocean state also allows for a better simulation of the atmospheric Walker circulation. Several sensitivity studies have been performed to further understand the processes involved in the different component models. Significantly decreasing the horizontal momentum dissipation in the coupled model with the lower-resolution ocean has benefits for the mean tropical Pacific climate, but decreases model stability. Increasing the momentum dissipation in the coupled model with the higher-resolution ocean degrades the simulation toward that of the lower-resolution ocean. These results suggest that enhanced ocean model resolution can have important benefits for the climatology of both the atmosphere and ocean components of the coupled model, and that some of these benefits may be achievable at lower ocean resolution, if the model formulation allows.

scholarly journals Developing a common, flexible and efficient framework for weakly coupled ensemble data assimilation based on C-Coupler2.0

2021 ◽  
Vol 14 (5) ◽  
pp. 2635-2657
Author(s):  
Chao Sun ◽  
Li Liu ◽  
Ruizhe Li ◽  
Xinzhu Yu ◽  
Hao Yu ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Data Exchange ◽  
Coupled Model ◽  
Earth System ◽  
Model Ensemble ◽  
Coupled Models ◽  
Weakly Coupled ◽  
Abstract Data ◽  
Global Communications ◽  
Earth System Models

Abstract. Data assimilation (DA) provides initial states of model runs by combining observational information and models. Ensemble-based DA methods that depend on the ensemble run of a model have been widely used. In response to the development of seamless prediction based on coupled models or even Earth system models, coupled DA is now in the mainstream of DA development. In this paper, we focus on the technical challenges in developing a coupled ensemble DA system, especially how to conveniently achieve efficient interaction between the ensemble of the coupled model and the DA methods. We first propose a new DA framework, DAFCC1 (Data Assimilation Framework based on C-Coupler2.0, version 1), for weakly coupled ensemble DA, which enables users to conveniently integrate a DA method into a model as a procedure that can be directly called by the model ensemble. DAFCC1 automatically and efficiently handles data exchanges between the model ensemble members and the DA method without global communications and does not require users to develop extra code for implementing the data exchange functionality. Based on DAFCC1, we then develop an example weakly coupled ensemble DA system by combining an ensemble DA system and a regional atmosphere–ocean–wave coupled model. This example DA system and our evaluations demonstrate the correctness of DAFCC1 in developing a weakly coupled ensemble DA system and the effectiveness in accelerating an offline DA system that uses disk files as the interfaces for the data exchange functionality.

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