• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.1067-1076
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• 2017

This paper considers the asymptotic behaviors of the processes generated by the classical ergodic tent map that is defined on the unit interval. We develop a sequential empirical process and get the uniform version of law of iterated logarithm for the tent map by using the bracketing entropy method.

• The Journal of the Korea Contents Association
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• v.8 no.4
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• pp.86-91
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• 2008

To present the design procedure of discretized 8-bit tent map executing the transformation of tent function which is one of the chaotic functions, first, the truth table of discretized tent map was written, and then according to the simplified Boolean algebra equations obtained from the truth table, the discretized map is implemented with the exclusive logic gate as a real hardware. The discretized tent map circuit which provides the feedback circuit for generating the period-8 states relevant to the 8-bit finite precision is also designed and presented in this paper. Furthermore, it might be used stream cipher system with a new key-stream circuit for generate of chaotic binary sequence.

• International Journal of Contents
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• v.11 no.4
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• pp.56-69
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• 2015

This paper proposes an efficient image encryption scheme based on quintuple encryption using two chaotic maps. The encryption process is realized with quintuple encryption by calling the encrypt(E) and decrypt(D) functions five times with five different keys in the form EDEEE. The decryption process is accomplished in the reverse direction by invoking the encrypt and decrypt functions in the form DDDED. The keys for the quintuple encryption/decryption processes are generated by using a Tent map. The chaotic values for the encrypt/decrypt operations are generated by using a Gumowski-Mira map. The encrypt function E is composed of three stages: permutation, pixel value rotation and diffusion. The permutation stage scrambles all the rows and columns to chaotically generated positions. This stage reduces the correlation radically among the neighboring pixels. The pixel value rotation stage circularly rotates all the pixels either left or right, and the amount of rotation is based on chaotic values. The last stage performs the diffusion four times by scanning the image in four different directions: Horizontally, Vertically, Principal diagonally and Secondary diagonally. Each of the four diffusion steps performs the diffusion in two directions (forward and backward) with two previously diffused pixels and two chaotic values. This stage ensures the resistance against the differential attacks. The security and performance of the proposed method is investigated thoroughly by using key space, statistical, differential, entropy and performance analysis. The experimental results confirm that the proposed scheme is computationally fast with security intact.

• The Journal of the Korea institute of electronic communication sciences
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• v.9 no.10
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• pp.1145-1152
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• 2014

The RFID (Radio-Frequency Identification) system is a technology to discern things by radio and an epoch-making new method to improve product management such as distribution, transport, mobilization, inventory control. However, RFID, which uses radio, is at risk for information leakage and falsification due to the vulnerability of security of the communication section. We designed the new authentication protocol by applying the tent map, which is the representative complex systems, to the RFID communication system. A more solid and simple authentication system was designed by applying the initial value sensitivity and irregularity, which are the representative characteristics of the complex system, to the reader and tag of RFID. The purpose of this paper is to verify the usability of the RFID authentication protocol design that uses the nonlinear system shown in this thesis by the new system differentiated from the authentication system that depends on the existing hash function or random numbers.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.13 no.5
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• pp.425-431
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• 2020

Recent advancements in industries and technologies have resulted in an increase in the volume of transportation, management, and distribution of logistics. Radio-frequency identification (RFID) technologies have been developed to efficiently manage such a large amount of logistics information. The use of RFID for management is being applied not only to the logistics industry, but also to the power transmission and energy management field. However, due to the limitation of program development capacity, the RFID device is limited in development, and this limitation is vulnerable to security because the existing strong encryption method cannot be used. For this reason, we designed a chaotic system for security with simple operations that are easy to apply to such a restricted environment of RFID. The designed system is a two-dimensional tent map chaotic system. In order to solve the problem of a biased distribution of signals according to the parameters of the chaotic dynamical system, the system has a cryptographic parameter(𝜇₁), a distribution parameter(𝜇₂), and a parameter(𝜃), which is the constant point, ID value, that can be used as a key value. The designed RFID authentication system is similar to random numbers, and it has the characteristics of chaotic signals that can be reproduced with initial values. It can also solve the problem of a biased distribution of parameters, so it is deemed to be more effective than the existing encryption method using the chaotic system.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.765-773
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• 2013

We show that for the logistic map, almost every x is a normal number mod 2 with respect to all intervals except for $[a,b]=[\frac{1}{4},1]\;or\;[a,b]=[\frac{1}{2}-\frac{\sqrt{3}}{4},\frac{1}{2}+\frac{\sqrt{3}}{4}]$.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.10 no.12
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• pp.3688-3693
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• 2009

In this paper the design methode of a separated composition state machine based on the compositive map with connecting two chaotic maps together - sawtooth map $S_2(x)$ and tent map $T_2(x)$ and the result of that is proposed. this paper gives a graph of the chaotic states generated by the composition state machine using the compositive logic of two different chaotic maps - sawtooth map and tent map and also shows that the period of pseudo-random states has the length according to the precision of the discreet truth table.

• The Mathematical Education
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• v.33 no.1
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• pp.137-146
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• 1994

• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.865-868
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• 1993

This paper describes a simple random signal generator employing by CMOS analog technology in current mode. The system is a nonlinear dynamical system described by a difference equation, such as x(t＋1) = f(x(t)) , t = 0,1,2, ... , where f($.$) is a nonlinear function of x(f). The tent map is used as a nonlinear function to produce the random signals with the uniform distribution. The prototype is implemented by using transistor array devices fabricated in a mass product line. It can be easily realized on a chip. Uniform randomness of the signal is examined by the serial correlation test and the $\chi$2 test.