scholarly journals A Two-Parameter Modified Logistic Map and Its Application to Random Bit Generation

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 829 ◽  
Author(s):  
Lazaros Moysis ◽  
Aleksandra Tutueva ◽  
Christos Volos ◽  
Denis Butusov ◽  
Jesus M. Munoz-Pacheco ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Logistic Map ◽  
Coexisting Attractors ◽  
Key Space ◽  
Modified Logistic Map ◽  
Nist Tests ◽  
Two Parameter

This work proposes a modified logistic map based on the system previously proposed by Han in 2019. The constructed map exhibits interesting chaos related phenomena like antimonotonicity, crisis, and coexisting attractors. In addition, the Lyapunov exponent of the map can achieve higher values, so the behavior of the proposed map is overall more complex compared to the original. The map is then successfully applied to the problem of random bit generation using techniques like the comparison between maps, X O R , and bit reversal. The proposed algorithm passes all the NIST tests, shows good correlation characteristics, and has a high key space.

scholarly journals Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 474 ◽  
Author(s):  
Lazaros Moysis ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Jesus M. Munoz-Pacheco ◽  
Jacques Kengne ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Image Encryption ◽  
Fuzzy Numbers ◽  
Statistical Tests ◽  
Logistic Map ◽  
Simple Rule ◽  
Pseudorandom Number ◽  
Bifurcation Diagrams ◽  
Triangular Numbers ◽  
Pseudorandom Number Generation

A modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis. The map is then applied to the problem of pseudo random bit generation, using a simple rule to generate the bit sequence. The resulting random bit generator (RBG) successfully passes the National Institute of Standards and Technology (NIST) statistical tests, and it is then successfully applied to the problem of image encryption.

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

scholarly journals Coexisting Attractors and Multistability in a Simple Memristive Wien-Bridge Chaotic Circuit

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 678 ◽  
Author(s):  
Yixuan Song ◽  
Fang Yuan ◽  
Yuxia Li
Keyword(s):  
Chaotic System ◽  
Analog Circuit ◽  
Random Sequence ◽  
Mathematical Expression ◽  
Digital Signal ◽  
Approximate Entropy ◽  
Chaotic Circuit ◽  
Coexisting Attractors ◽  
Key Space ◽  
Sequence Generator

In this paper, a new voltage-controlled memristor is presented. The mathematical expression of this memristor has an absolute value term, so it is called an absolute voltage-controlled memristor. The proposed memristor is locally active, which is proved by its DC V–I (Voltage–Current) plot. A simple three-order Wien-bridge chaotic circuit without inductor is constructed on the basis of the presented memristor. The dynamical behaviors of the simple chaotic system are analyzed in this paper. The main properties of this system are coexisting attractors and multistability. Furthermore, an analog circuit of this chaotic system is realized by the Multisim software. The multistability of the proposed system can enlarge the key space in encryption, which makes the encryption effect better. Therefore, the proposed chaotic system can be used as a pseudo-random sequence generator to provide key sequences for digital encryption systems. Thus, the chaotic system is discretized and implemented by Digital Signal Processing (DSP) technology. The National Institute of Standards and Technology (NIST) test and Approximate Entropy analysis of the proposed chaotic system are conducted in this paper.

A fast hybrid image cryptosystem based on random generator and modified logistic map

2018 ◽  
Vol 78 (12) ◽  
pp. 16177-16193 ◽  
Author(s):  
Ayman M. Hemdan ◽  
Osama S. Faragallah ◽  
Osama Elshakankiry ◽  
Ahmed Elmhalaway
Keyword(s):  
Logistic Map ◽  
Random Generator ◽  
Modified Logistic Map ◽  
Image Cryptosystem

Efficient Cancelable Iris Recognition Scheme Based on Modified Logistic Map

2018 ◽  
Vol 90 (1) ◽  
pp. 101-107 ◽  
Author(s):  
Randa F. Soliman ◽  
Noha Ramadan ◽  
Mohamed Amin ◽  
HossamEldin H. Ahmed ◽  
Said El-Khamy ◽  
...  
Keyword(s):  
Iris Recognition ◽  
Logistic Map ◽  
Modified Logistic Map

scholarly journals Efficient error correcting scheme for chaos shift keying signals

2019 ◽  
Vol 9 (5) ◽  
pp. 3550
Author(s):  
Hikmat N. Abdullah ◽  
Thamir R. Saeed ◽  
Asaad H. Sahar
Keyword(s):  
Error Correction ◽  
Logistic Map ◽  
Chaotic Sequence ◽  
Chaos Communication ◽  
Shortest Distance ◽  
Correction Scheme ◽  
Shift Keying ◽  
Minimum Delay ◽  
Modified Logistic Map ◽  
Chaos Shift Keying

An effective error-correction scheme based on normalized correlation for a non coherent chaos communication system with no redundancy bits is proposed in this paper. A modified logistic map is used in the proposed scheme for generating two sequences, one for every data bit value, in a manner that the initial value of the next chaotic sequence is set by the second value of the present chaotic sequence of the similar symbol. This arrangement, thus, has the creation of successive chaotic sequences with identical chaotic dynamics for error correction purpose. The detection symbol is performed prior to correction, on the basis of the suboptimal receiver which anchors on the computation of the shortest distance existing between the received sequence and the modified logistic map’s chaotic trajectory. The results of the simulation reveal noticeable Eb/No improvement by the proposed scheme over the prior to the error- correcting scheme with the improvement increasing whenever there is increase in the number of sequence N. Prior to the error-correcting scheme when N=8, a gain of 1.3 dB is accomplished in E<sub>b</sub>/N<sub>o</sub> at 10<sup>-3 </sup>bit error probability. On the basis of normalized correlation, the most efficient point in our proposed error correction scheme is the absence of any redundant bits needed with minimum delay procedure, in contrast to earlier method that was based on suboptimal method detection and correction. Such performance would render the scheme good candidate for applications requiring high rates of data transmission.

scholarly journals An Inverse Pheromone Approach in a Chaotic Mobile Robot’s Path Planning Based on a Modified Logistic Map

Technologies ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 84
Author(s):  
Eleftherios K. Petavratzis ◽  
Christos K. Volos ◽  
Lazaros Moysis ◽  
Ioannis N. Stouboulos ◽  
Hector E. Nistazakis ◽  
...  
Keyword(s):  
Path Planning ◽  
Mobile Robots ◽  
Efficient Method ◽  
Chaotic Motion ◽  
Logistic Map ◽  
Autonomous Mobile Robots ◽  
Motion Pattern ◽  
Major Topic ◽  
Random Bit Generator ◽  
Modified Logistic Map

One major topic in the research of path planning of autonomous mobile robots is the fast and efficient coverage of a given terrain. For this purpose, an efficient method for covering a given workspace is proposed, based on chaotic path planning. The method is based on a chaotic pseudo random bit generator that is generated using a modified logistic map, which is used to generate a chaotic motion pattern. This is then combined with an inverse pheromone approach in order to reduce the number of revisits in each cell. The simulated robot under study has the capability to move in four or eight directions. From extensive simulations performed in Matlab, it is derived that motion in eight directions gives superior results. Especially, with the inclusion of pheromone, the coverage percentage can significantly be increased, leading to better performance.

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.

scholarly journals An Adaptive and Secure Holographic Image Watermarking Scheme

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 460 ◽  
Author(s):  
Chuying Yu ◽  
Xiaowei Li ◽  
Xinan Chen ◽  
Jianzhong Li
Keyword(s):  
Image Watermarking ◽  
Logistic Map ◽  
Suggested Method ◽  
Contourlet Transform ◽  
Schur Decomposition ◽  
Holographic Image ◽  
Computer Generated Hologram ◽  
Key Space ◽  
Watermark Embedding ◽  
Watermarking Scheme

A novel adaptive secure holographic image watermarking method in the sharp frequency localized contourlet transform (SFLCT) domain is presented. Based upon the sine logistic modulation map and the logistic map, we develop an encrypted binary computer-generated hologram technique to fabricate a hologram of a watermark first. Owing to the enormous key space of the encrypted hologram, the security of the image watermarking system is increased. Then the hologram watermark is embedded into the SFLCT coefficients with Schur decomposition. To obtain better imperceptibility and robustness, the entropy and the edge entropy are utilized to select the suitable watermark embedding positions adaptively. Compared with other watermarking schemes, the suggested method provides a better performance with respect to both imperceptibility and robustness. Experiments show that our watermarking scheme for images is not only is secure and invisible, but also has a stronger robustness against different kinds of attack.

scholarly journals Design of Positive, Negative, and Alternating Sign Generalized Logistic Maps

2015 ◽  
Vol 2015 ◽  
pp. 1-23 ◽  
Author(s):  
Wafaa S. Sayed ◽  
Ahmed G. Radwan ◽  
Hossam A. H. Fahmy
Keyword(s):  
Lyapunov Exponent ◽  
Bifurcation Diagram ◽  
Degrees Of Freedom ◽  
Chaotic Maps ◽  
Logistic Map ◽  
Maximum Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
Financial Modeling ◽  
Design Flexibility ◽  
Special Case

The discrete logistic map is one of the most famous discrete chaotic maps which has widely spread applications. This paper investigates a set of four generalized logistic maps where the conventional map is a special case. The proposed maps have extra degrees of freedom which provide different chaotic characteristics and increase the design flexibility required for many applications such as quantitative financial modeling. Based on the maximum chaotic range of the output, the proposed maps can be classified as positive logistic map, mostly positive logistic map, negative logistic map, and mostly negative logistic map. Mathematical analysis for each generalized map includes bifurcation diagrams relative to all parameters, effective range of parameters, first bifurcation point, and the maximum Lyapunov exponent (MLE). Independent, vertical, and horizontal scales of the bifurcation diagram are discussed for each generalized map as well as a new bifurcation diagram related to one of the added parameters. A systematic procedure to design two-constraint logistic map is discussed and validated through four different examples.

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