• 한국산업정보학회논문지
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• 제6권4호
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• pp.75-80
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• 2001

본 논문에서는 복잡한 하이퍼카오스 신호를 발생시키는 HVPM(Hyperchaotic Volume Preserving Maps) 모델을 이용한 카오스 동기화 알고리즘을 제안하고자 한다. 제안한 HVPM 모델은 3차원 이산시간(discrete-time) 연립 차분방정식으로 구성되어 있으며, 비선형 사상(maps)과 모듈러(modulus) 함수를 사용하여 랜덤한 카오스 어트랙터(attractor)를 발생시킨다. Pecora와 Caroll은 최근 카오스 시스템이 카오스 신호를 이용하여 동기화가 가능하다고 보고하였다. 따라서 본 논문에서는 하이퍼카오스 신호를 발생시키는 HVPM 모델간의 동기화를 위하여 결합동기(coupled synchronization) 알고리듬을 제안하였다. 모의실험에서 카오스 시스템과 하이퍼카오스 신호를 결합하여 카오스 동기화 현상을 확인할 수 있었다.

• 대한수학회논문집
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• 제19권3호
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• pp.507-517
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• 2004

Let (2,2,2,2) be ramification indices for the Riemann sphere. It is well known that the regular branched covering map corresponding to this, is the Weierstrass P function. Lattes [7] gives a rational function R(z)= ${\frac{z^4+{\frac{1}{2}}g2^{z}^2+{\frac{1}{16}}g{\frac{2}{2}}$ which is chaotic on ${\bar{C}}$ and is induced by the Weierstrass P function and the linear map L(z) = 2z on complex plane C. It is also known that there exist regular branched covering maps from $T^2$ onto ${\bar{C}}$ if and only if the ramification indices are (2,2,2,2), (2,4,4), (2,3,6) and (3,3,3), by the Riemann-Hurwitz formula. In this paper we will construct regular branched covering maps corresponding to the ramification indices (2,4,4), (2,3,6) and (3,3,3), as well as chaotic maps induced by these regular branched covering maps.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권12호
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• pp.6188-6204
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• 2017

Over the years, more password-based authentication key agreement schemes using chaotic maps were susceptible to attack by off-line password guess attack. This work approaches this problem by a new method--new theorem of chaotic maps: $T_{a+b}(X)+T_{a-b}(X)=2T_a(X)T_b(X)$,(a>b). In fact, this method can be used to design two-party, three-party, even in N-party intelligently. For the sake of brevity and readability, only a two-party instance: a novel Two-party Password-Authenticated Key Agreement Protocol is proposed for resisting password guess attack in this work. Compared with the related literatures recently, our proposed scheme can be not only own high efficiency and unique functionality, but is also robust to various attacks and achieves perfect forward secrecy. For capturing improved ratio of security and efficiency intuitively, the paper firstly proposes a new parameter called security/efficiency ratio(S/E Ratio). The higher the value of the S/E Ratio, the better it is. Finally, we give the security proof and the efficiency analysis of our proposed scheme.

• ETRI Journal
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• 제30권1호
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• pp.170-172
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• 2008

A substitution box (S-box) plays a central role in cryptographic algorithms. In this paper, an efficient method for designing S-boxes based on chaotic maps is proposed. The proposed method is based on the mixing property of piecewise linear chaotic maps. The S-box so constructed has very low differential and linear approximation probabilities. The proposed S-box is more secure against differential and linear cryptanalysis compared to recently proposed chaotic S-boxes.

• 한국산학기술학회논문지
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• 제10권12호
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• pp.3688-3693
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• 2009

본 논문에서는 두 가지 혼돈맵들 -톱니맵 $S_2(x)$ 와 텐트맵 $T_2(x)-$ 을 연결시킨 하나의 합성맵을 기초로 사용하는 독립된 하나의 합성상태머신을 설계하는 방법 및 그 결과을 제시하였다. 두 가지 다른 혼돈맵들 -톱니맵과 텐트맵- 의 합성 논리를 이용하여 설계된 독립된 하나의 합성상태머신에서 발생하는 혼돈적인 상태들을 그래프적으로 보였으며, 발생하는 의사 난수적인 상태들의 주기는 이산화된 진리표의 정밀도에 따른 길이를 갖는다는 것도 보였다.

• 정보보호학회논문지
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• 제14권4호
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• pp.183-194
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• 2004

인터넷 이용의 폭발적인 증가와 유무선 통신기술의 발달로 인해 디지털 영상의 교환이 매우 빈번하게 일어나고 있는 현실에서 개인 사생활과 기업 및 기관의 기밀에 관련된 영상에 대한 보안이 매우 중요시 되어가고 있다. 또한 최근 카오스 이론과 암호와의 밀접한 관련성으로 인해 카오스 사상(Map)에 기반 한 새로운 암호기술 개발에 많은 연구가 진행되고 있다. 본 논문에서는 1차원 카오스 사상(Map)인 PLCM(Piecewise Linear Chaotic Map)과 2차원 카오스 사상인 Baker 사상을 이용한 정지영상 암호 시스템을 제안한다. 본 제안 시스템은 1차원 PLCM을 기반으로 한 섭동(Perturbance)기반 카오스 스트림(Stream)암호 기법과 2차원 Baker 사상을 기반으로 한 카오스 블록(Block)암호 기법이 결합된 구조로서 좋은 혼동(Confusion)특성과 확산(Diffusion)특성을 지닌 매우 안전하고 구현이 쉬운 암호시스템이다. 또한 본 논문에서는 실험 결과를 통해 통계적(Statistical) 공격에도 매우 강함을 보여주었다.

• Journal of Multimedia Information System
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• 제8권2호
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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 Multimedia Information System
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• 제2권2호
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• pp.193-206
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• 2015

In this paper a new approach for image encryption based on quadruple encryption with dual chaotic maps is proposed. The encryption process is performed with quadruple encryption by invoking the encrypt and decrypt routines with different keys in the sequence EDEE. The decryption process is performed in the reverse direction DDED. The key generation for the quadruple encryption is achieved with a 1D Circle map. The chaotic values for the encrypt and decrypt routines are generated by using a 2D Henon map. The Encrypt routine E is composed of three stages i.e. permutation, pixel value rotation and diffusion. The permutation is achieved by: row and column scrambling with chaotic values, exchanging the lower and the upper principal and secondary diagonal elements based on the chaotic values. The second stage circularly rotates all the pixel values based on the chaotic values. The last stage performs the diffusion in two directions (forward and backward) with two previously diffused pixels and two chaotic values. The security and performance of the proposed scheme are assessed thoroughly by using the key space, statistical, differential, entropy and performance analysis. The proposed scheme is computationally fast with security intact.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권2호
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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.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1996년도 추계학술대회논문집; 한국과학기술회관, 8 Nov. 1996
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• pp.288-294
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• 1996

In this paper, Chaotic motions of a curved pipe conveying oscillatory flow are theoretically investigated. The nonlinear partial differential equation of motion is derived by Newton's method. The transformed nonlinear ordinary differential equation is a type of Hill's equation, which have the parametric and external excitation. Bifurcation curves of chaotic motion of the piping systems are obtained by applying Melnikov's method. Poincare maps numerically demonstrate theoretical results and show transverse homoclinic orbit of the chaotic motion.