• Journal of the Korean Data and Information Science Society
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• v.28 no.6
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• pp.1565-1571
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• 2017

The standard logistic map is an iterative function, which forms a discrete-time dynamic system. The chaotic logistic map is a kind of ergodic map defined over the unit interval. In this paper we study the limiting behaviors on the several processes induced by the chaotic logistic map. We derive the law of large numbers for the process induced by the chaotic logistic map. We also derive the uniform law of large numbers for this process. When deriving the uniform law of large numbers, we study the role of bracketing of the indexed class of functions associated with the process. Then we apply the idea of DeHardt (1971) associated with the bracketing method to the process induced by the logistic map. We finally illustrate an application to Monte Carlo integration.

• Journal of Advanced Navigation Technology
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• v.17 no.6
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• pp.652-657
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• 2013

In this paper the design methode of a separated composition state machine based on the compositive map with two chaotic maps together and the result of that is proposed. The digital circuits of chaotic composition map for the use of chaotic binary stream generator are designed in this work. The discretized truth table of chaotic composition function which is composed of two chaotic functions - the saw tooth function and skewed logistic function - is made out, and also simplefied Boolean algebras of digital circuits are obtained as a mathematical model. Consequently, the digital circuits of the map for chaotic composition function are presented in this paper.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.1B
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• pp.99-104
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• 2000

In this paper, as a digital watermark we propose to use a chaotic sequence instead of the conventional Gaussian sequence. It is relatively easy to generate the chaotic sequence and is very sensitive to the change of initial value. The chaotic sequence adopted in this paper is a modified version of logistic map to give the sequence distribution of Chebyshev map. In the experiments, we applied the Gaussian sequence and chaotic sequence to wavelet coefficients of images to compare the similarity distribution. The results show that, as id the DCT-based watermarking system, the chaotic sequence is robust for various signal processing attacks, Moreover, the similarity variance is smaller than the Gaussian sequence for iterative experiments. It also shows a better performance for compression errors than the Gaussian sequence.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.23 no.3
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• pp.279-283
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• 2014

Recently, a topology algorithm based on the artificial bee colony algorithm (ABCA) has been proposed for static and dynamic topology optimization. From the results, the convergence rate of the algorithm was determined to be slightly slow. Therefore, we propose a new search method to improve the convergence rate of the algorithm using a chaotic map. We investigate the effect of the chaotic map on the convergence rate of the algorithm in static and dynamic topology optimization. The chaotic map has been applied to three cases, namely, employ bee search, onlooker bee search, and both employ bee as well as onlooker bee search steps. It is verified that the case in which the logistic function of the chaotic map is applied to both employ bee as well as onlooker bee search steps shows the best dynamic topology optimization, improved by 5.89% compared to ABCA. Therefore, it is expected that the proposed algorithm can effectively be applied to dynamic topology optimization to improve the convergence rate.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1997.10a
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• pp.154-159
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• 1997

In this paper, we describe the OGY method that convert the motion on a chaotic attractor to attracting time periodic motion by malting only small perturbations of a control parameter. The OGY method is illustrated by application to the control of the chaotic motion in chaotic attractor to happen at the famous Logistic map and Henon map and confirm it by making periodic motion. We apply it the chaotic motion at the behavior of the thin beam under periodic torsional base-excitation, and this chaotic motion is made the periodic motion by numerical experiment in the time evaluation on this chaotic motion. We apply the OGY method with the Jacobian matrix to control the chaotic motion to the periodic motion.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38A no.6
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• pp.479-485
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• 2013

Recently, interest for wireless communication technology with improved security and low eavesdropping probability is increasing rapidly recognizing that information security is an important. Chaos signal can be used encode information efficiently due to irregular phenomena. Chaotic signal is very sensitive to the initial condition. Chaos signal is difficult to detect the signal if you do not know the initial conditions. Also, chaotic signal has robustness to multipath interference. In this paper, we evaluate the performance of correlation delay shift keying (CDSK) modulation with different chaotic map such as Tent map, Logistic map, Henon map, and Bernoulli shift map. Also, we analyze the BER performance depending on the selection of spreading factor (SF) in CDSK. Through the theoretical analyses and simulations, it is confirmed that Henon map has better BER performance than the other three chaotic maps when spreading factor is 70.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.2
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• pp.1064-1079
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• 2019

Information security has become increasingly important with the rapid development of mobile devices and internet. An efficient encryption system is a key to this end. In this paper, we propose an image encryption method based on the cross diffusion of two chaotic maps. We use two chaotic sequences, namely the Logistic map and the Chebyshev map, for key generation which has larger security key space than single one. Moreover, we use these two sequences for further image encryption diffusion which decreases the correlation of neighboring pixels significantly. We conduct extensive experiments on several well-known images like Lena, Baboon, Koala, etc. Experimental results show that our algorithm has the characteristics of large key space, fast, robust to statistic attack, etc.

• Journal of Information Processing Systems
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• v.11 no.2
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• pp.310-324
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• 2015

The stream cipher Salsa20 and its reduced versions are among the fastest stream ciphers available today. However, Salsa20/7 is broken and Salsa20/12 is not as safe as before. Therefore, Salsa20 must completely perform all of the four rounds of encryption to achieve a good diffusion in order to resist the known attacks. In this paper, a new variant of Salsa20 that uses the chaos theory and that can achieve diffusion faster than the original Salsa20 is presented. The method has been tested and benchmarked with the original Salsa20 with a series of tests. Most of the tests show that the proposed chaotic Salsa of two rounds is faster than the original four rounds of Salsa20/4, but it offers the same diffusion level.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.12
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• pp.5963-5980
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• 2017

Image scrambling is an important technology in information hiding, where the Arnold transformation is widely used. Several researchers have proposed the application of $H{\acute{e}}non$ map in square image scrambling, and certain improved technologies require scrambling many times to achieve a good effect without resisting chosen-plaintext attack although it can be directly applied to non-square images. This paper presents a non-square image scrambling algorithm, which can resist chosen-plaintext attack based on a chaotic two-dimensional Sine Logistic modulation map and $H{\acute{e}}non$ map (2D-SLHM). Theoretical analysis and experimental results show that the proposed algorithm has advantages in terms of key space, efficiency, scrambling degree, ability of anti-attack and robustness to noise interference.

• Journal of Advanced Navigation Technology
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• v.17 no.3
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• pp.292-297
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• 2013

In this paper, The design of digital circuits for chaotic composition function which is used for the key-stream generator is studied in this work. The overall design concept and procedure due to the mathematical model of chaotic key-stream generator is to be the explained in detail, and also the discretized truth table of chaotic composition function is presented in this paper. consequently, a composition state machine based on the compositive map with connecting two types of one dimensional and two dimensional chaotic maps together is designed and presented.