ALGORITHM FOR EXACT LONG TIME CHAOTIC SERIES AND ITS APPLICATION TO CRYPTOSYSTEMS

2004 ◽  
Vol 14 (10) ◽  
pp. 3607-3611 ◽  
Author(s):  
SHUNJI KAWAMOTO ◽  
TAKESHI HORIUCHI
Keyword(s):  
Time Series ◽  
Logistic Map ◽  
Rational Numbers ◽  
Prime Numbers ◽  
Chaotic Time Series ◽  
High Dependency ◽  
Key Space ◽  
Long Time ◽  
Computer Environment ◽  
Numerical Generation

It is said that the numerical generation of exact chaotic time series by iterating, for example, the logistic map, will be impossible, because chaos has a high dependency on initial values. In this letter, an algorithm to generate them without the accumulation of inevitable round-off errors caused by the iteration is proposed, where rational numbers are introduced. Also, it is shown that the period of the chaotic time series depends on the rational numbers including large prime numbers, which are fundamentally related to the Mersenne and the Fermat prime ones. Since the time series are numerically regenerated by the proposed algorithm in an usual computer environment, it could be applied to cryptosystems which do not need the synchronization, and have a large key-space by using large prime numbers.

scholarly journals Double image multi-encryption algorithm based on fractional chaotic time series

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Zhenghong Guo ◽  
Jie Yang ◽  
Yang Zhao
Keyword(s):  
Time Series ◽  
Chaotic Time Series ◽  
Encryption Algorithm ◽  
Brute Force ◽  
Double Image ◽  
Key Space ◽  
Plain Image ◽  
Image Pixels ◽  
Brute Force Attack ◽  
The Relationship

AbstractIn this paper, we introduce a new image encryption scheme based on fractional chaotic time series, in which shuffling the positions blocks of plain-image and changing the grey values of image pixels are combined to confuse the relationship between the plain-image and the cipher-image. Also, the experimental results demonstrate that the key space is large enough to resist the brute-force attack and the distribution of grey values of the encrypted image has a random-like behavior.

CIPHER SYSTEMS BASED ON CONTROLLED EXACT CHAOTIC MAPS

2010 ◽  
Vol 20 (12) ◽  
pp. 4039-4053 ◽  
Author(s):  
ALI KANSO
Keyword(s):  
Time Series ◽  
Cycle Length ◽  
Chaotic Maps ◽  
Necessary Conditions ◽  
Logistic Map ◽  
Security Level ◽  
Encryption Scheme ◽  
Key Space ◽  
Suggested Technique ◽  
High Level

In this paper, we present a class of chaotic clock-controlled cipher systems based on two exact chaotic maps, where each map is capable of generating exact chaotic time series of the logistic map. This class is designed in such a way that one map controls the iterations of the second map. The suggested technique results in generating orbits possessing long cycle length and high level of security from the two periodic exact maps. In the first part of this paper, two keystream generators based on two exact chaotic logistic maps are suggested for use in cryptographic applications. The necessary conditions to generate orbits with guaranteed long enough cycle length are established. Furthermore, the generated keystreams are demonstrated to possess excellent randomness properties. In the second part, we suggest a clock-controlled encryption scheme related to Baptista's scheme and based on two exact chaotic logistic maps. This technique results in increasing the size of the key space, and hence may increase the security level against some existing cryptanalytic attacks. Furthermore, it leads to reducing the size of the ciphertext file and propably increasing the encryption speed.

Local Adaptive Nonlinear Filter Prediction Model with a Parameter for Chaotic Time Series

2010 ◽  
Vol 44-47 ◽  
pp. 3180-3184
Author(s):  
Fen Fang ◽  
Hai Yan Wang ◽  
Zhou Mu Yang
Keyword(s):  
Time Series ◽  
Prediction Model ◽  
Gradient Descent ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Logistic Map ◽  
Predictive Performance ◽  
Nonlinear Filter ◽  
Chaotic Time Series ◽  
Proposed Model

In order to improve the predictive performance for chaotic time series， we propose a novel local adaptive nonlinear filter prediction model. We use a function with a parameter to build an adaptive nonlinear filter in this model, and we train this model with an adaptive algorithm, deduced by the minimum square-root-error criterion and the steepest gradient descent rule. We evaluate the proposed model using four well-known chaotic systems, namely Logistic map, Henon map, Lorenz system and Rosslor system. All the results show a remarkable increase in predictive performance, comparing with the local adaptive nonlinear filter prediction model.

scholarly journals Constructing Digitized Chaotic Time Series with a Guaranteed Enhanced Period

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Chuanfu Wang ◽  
Qun Ding
Keyword(s):  
Time Series ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Approximate Entropy ◽  
Chaotic Time Series ◽  
Pseudorandom Sequence ◽  
Periodic Behavior ◽  
Experimental Implementation ◽  
Sequence Generator

When chaotic systems are realized in digital circuits, their chaotic behavior will degenerate into short periodic behavior. Short periodic behavior brings hidden dangers to the application of digitized chaotic systems. In this paper, an approach based on the introduction of additional parameters to counteract the short periodic behavior of digitized chaotic time series is discussed. We analyze the ways that perturbation sources are introduced in parameters and variables and prove that the period of digitized chaotic time series generated by a digitized logistic map is improved efficiently. Furthermore, experimental implementation shows that the digitized chaotic time series has great complexity, approximate entropy, and randomness, and the perturbed digitized logistic map can be used as a secure pseudorandom sequence generator for information encryption.

CLARIFYING CHAOS III: CHAOTIC AND STOCHASTIC PROCESSES, CHAOTIC RESONANCE, AND NUMBER THEORY

1999 ◽  
Vol 09 (05) ◽  
pp. 785-803 ◽  
Author(s):  
RAY BROWN ◽  
LEON O. CHUA
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Stochastic Processes ◽  
Prediction Models ◽  
Prime Numbers ◽  
Chaotic Time Series ◽  
Chaotic Dynamical Systems ◽  
Estimation And Prediction ◽  
The Relationship

In this tutorial we continue our program of clarifying chaos by examining the relationship between chaotic and stochastic processes. To do this, we construct chaotic analogs of stochastic processes, stochastic differential equations, and discuss estimation and prediction models. The conclusion of this section is that from the composition of simple nonlinear periodic dynamical systems arise chaotic dynamical systems, and from the time-series of chaotic solutions of finite-difference and differential equations are formed chaotic processes, the analogs of stochastic processes. Chaotic processes are formed from chaotic dynamical systems in at least two ways. One is by the superposition of a large class of chaotic time-series. The second is through the compression of the time-scale of a chaotic time-series. As stochastic processes that arise from uniform random variables are not constructable, and chaotic processes are constructable, we conclude that chaotic processes are primary and that stochastic processes are idealizations of chaotic processes. Also, we begin to explore the relationship between the prime numbers and the possible role they may play in the formation of chaos.

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