• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.967-979
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• 2019

Chaotic dynamical systems, preferably on a Cantor-like space with some arithmetic operations are considered as good pseudo-random number generators. There are many definitions of chaos, of which Devaney-chaos and pos itive topological entropy seem to be the strongest. Let $A=\{0,1,{\dots},p-1\}$. We define a continuous map on $A^{\mathbb{Z}}$ using addition with a carry, in combination with the shift map. We show that this map gives rise to a dynamical system with positive entropy, which is also Devaney-chaotic: i.e., it is transitive, sensitive and has a dense set of periodic points.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.1
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• pp.123-131
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• 1995

다주파수 입력을 갖는 강한 비선형 시스템의 유사주기 (quasi-periodic) 해를 해석하기 위하여 개선된 고정 점법(FPA:Fixed Point Alogrithm)을 개발하였다. 안정성 및 천이 특성을 판별하기 위하여 사용되어지는 Floquest 지수인 해석적 자코비언을 구하기 위하여 Poincare 맵상에서 이산 적분법을 새로이 고안, 사용하였다. 본 방법의 우수성을 입증하기 위하여 2개의 주파수 입력을 갖는 선형 시스템과 비선형 시스템을 예로 사용하였다. 본 방법을 이용하여 비선형 시스템에서 발생한 복잡한 chaos 현상을 체계적으로 해석하였다.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.837-851
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• 2014

We consider ${\omega}$-chaos as defined by S. H. Li in 1993. We show that c-dense ${\omega}$-scrambled sets are present in every transitive system with two-sided limit shadowing property (TSLmSP) and that every transitive map on topological graph has a dense Mycielski ${\omega}$-scrambled set. As a preliminary step, we provide a characterization of dynamical properties of maps with TSLmSP.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.49 no.1
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• pp.29-38
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• 2012

Due to the rapid development of network environment and wireless communication technology, the distribution of digital video has made easily and the importance of the protection for digital video has been increased. This paper proposes the digital video encryption system based on multiple chaos maps for MPEG-2 video encoding process. The proposed method generates secret hash key of having 128-bit characteristics from hash chain using Tent map as a basic block and generates $8{\times}8$ lattice cipher by applying this hash key to Logistic map and Henon map. The method can reduce the encryption overhead by doing selective XOR operations between $8{\times}8$ lattice cipher and some coefficient of low frequency in DCT block and it provides simple and randomness characteristic because it uses the architecture of combining chaos maps. Experimental results show that PSNR of the proposed method is less than or equal to 12 dB with respect to encrypted video, the time change ratio, compression ratio of the proposed method are 2%, 0.4%, respectively so that it provides good performance in visual security and can be applied in real time.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.277-288
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• 2004

In this paper, we discuss a continuous self-map of an interval and the existence of an uncountable strongly chaotic set. It is proved that if a continuous self-map of an interval has positive topological entropy, then it has an uncountable strongly chaotic set in which each point is recurrent, but is not almost periodic.

• Speech Sciences
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• v.8 no.3
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• pp.149-157
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• 2001

Based on the chaos theory, a new method of presentation of speech signal has been presented in this paper. This new method can be used for pattern matching such as speaker recognition. The expressions of attractors are represented very well by the logistic maps that show the chaos phenomena. In the speaker recognition field, a speaker's vocal habit could be a very important matching parameter. The attractor configuration using change value of speech signal can be utilized to analyze the influence of voice undulations at a point on the vocal loudness scale to the next point. The attractors arranged by the method could be used in research fields of speech recognition because the attractors also contain unique information for each speaker.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.39A no.6
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• pp.303-309
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• 2014

Chaos communication system can improve a system security due to characteristics of non-periodic, non-predictability, broadband signal and easy implementation. Also, chaos signal is sensitive to initial conditions of chaos map. By these reasons, security of chaos communication system is superior to digital communication system. BER performance of COOK modulation system is better than other chaos modulation systems, even if COOK modulation system uses an asynchronous receiver. However, security and safety of COOK modulated signal are worse than other chaos modulation systems, because information bits can be easily predicted from COOK modulated signal. In this paper, for security improvement of COOK modulated signal, we propose a novel Scrambling COOK modulation system by applying the scrambling method. Conventional COOK modulated signal can be predicted, because chaos signal is generated when data is only 1. However, proposed system cannot be predicted, because chaos signal is generated when data is 0 or 1. Therefore, security and safety of transmitted signal in scrambling COOK modulation system is superior to conventional COOK modulation system.

• Journal of Multimedia Information System
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• v.8 no.2
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• pp.131-142
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• 2021

This paper traces the process of constructing a new one-dimensional chaotic map, and will provide a simple application in color image encryption. The use of Sarkovskii's theorem will make it possible to determine the existence of chaos and restrict all conditions to ensure the existence of this new sequence. In addition, the sensitivity to initial conditions will be proved by Lyapunov's index value. Similarly, the performance of this new chaotic map will be illustrated graphically and compared with other chaotic maps most commonly used in cryptography. Finally, a humble color image encryption application will show the power of this new chaotic map.

• 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.