• 한국통신학회논문지
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• 제35권12C호
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• pp.977-983
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• 2010

카오스 함수의 출력 값은 예측 불가능하고 무작위처럼 보이며, 이러한 특성은 안전한 암호 시스템에서 요구하는 특성과 일치한다. 이러한 이유로 인해, 카오스 함수를 이용한 암호 시스템이 지금까지 다양하게 제안되어 왔다. 하지만 대부분의 카오스 암호 시스템은 매우 높은 수준의 연산 능력을 필요로 하기 때문에 경량의 시스템에 적용하지 못했다. 본 논문에서는 적은 연산 능력을 가진 시스템에서도 응용 가능한 경량의 카오스 암호 시스템을 제안하고, 제안된 암호 시스템의 연산량 및 안전도와 관련된 성능을 모의 실험을 통하여 제시한다.

• 한국항행학회논문지
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• 제17권3호
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• pp.292-297
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• 2013

본 논문에서는 혼돈 스트림 발생기에 사용되는 혼돈합성함수의 디지털 회로설계를 연구 하였다. 혼돈키 스트림 발생기의 수학적 모델에 기인하는 전반적인 설계 개념과 절차를 자세히 설명하였다. 또한 혼돈 함수에 대한 이진화 2진 진리표를 보였다. 결과로서 1차원과 2차원 두 종류의 혼돈맵들-텐트맵과 삐뚤어진 로지스틱 맵-을 연결시켜 합성맵으로 사용하는 합성상태머신의 설계를 제시하였다.

• International Journal of Contents
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• 제11권4호
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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.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2002년도 ITC-CSCC -3
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• pp.1882-1885
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• 2002

This paper shows design of maximal-period sequences with prescribed constant auto-correlation values based on one-dimensional (1-D) maps with (mite bits. We construct such 1-D maps based on piecewise linear onto chaotic maps. Theoretical analyses and some design examples are given.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제7권6호
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• pp.1492-1511
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• 2013

A novel, chaotic map that is based on concatenated torus automorphisms is proposed in this paper. As we know, cat map, which is based on torus automorphism, is highly chaotic and is often used to encrypt information. But cat map is periodic, which decreases the security of the cryptosystem. In this paper, we propose a novel chaotic map that concatenates several torus automorphisms. The concatenated mechanism provides stronger chaos and larger key space for the cryptosystem. It is proven that the period of the concatenated torus automorphisms is the total sum of each one's period. By this means, the period of the novel automorphism is increased extremely. Based on the novel, concatenated torus automorphisms, two application schemes in image encryption are proposed, i.e., 2D and 3D concatenated chaotic maps. In these schemes, both the scrambling matrices and the iteration numbers act as secret keys. Security analysis shows that the proposed, concatenated, chaotic maps have strong chaos and they are very sensitive to the secret keys. By means of concatenating several torus automorphisms, the key space of the proposed cryptosystem can be expanded to $2^{135}$. The diffusion function in the proposed scheme changes the gray values of the transferred pixels, which makes the periodicity of the concatenated torus automorphisms disappeared. Therefore, the proposed cryptosystem has high security and they can resist the brute-force attacks and the differential attacks efficiently. The diffusing speed of the proposed scheme is higher, and the computational complexity is lower, compared with the existing methods.

• 정보통신설비학회논문지
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• 제4권2호
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• pp.19-27
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• 2005

In this paper, we propose 128-bit chaotic block encryption scheme using a PLCM (Piecewise Linear Chaotic Map) having a good dynamical property. The proposed scheme has a block size of 128- bit and a key size of 128-bit. The encrypted code is generated from the output of PLCM. We show the proposed scheme is very secure against statistical attacks and have very good avalanche effect and randomness properties.

• 한국항행학회논문지
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• 제17권6호
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• pp.652-657
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• 2013

논문에서는 두 가지 혼돈맵들을 연결시킨 하나의 합성맵을 기초로 사용하는 독립된 하나의 합성상태머신을 설계하는 방법 및 그 결과를 제시하였다. 혼돈2진스트림발생기로 사용하기 위하여 혼돈합성맵에 관한 디지털회로를 설계하였다. 두 가지 혼돈함수들- 톱니함수와 비뚤어진 로지스틱 함수-로 구성되는 혼돈합성함수의 이산화 진리표를 작성하였고, 디지털회로의 수학적 모델로써 간략화 된 부울대수식들을 제시하였다. 결과로써 혼돈합성함수의 맵에 관한 디지털회로들을 제시하였다.

• Journal of Computing Science and Engineering
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• 제8권4호
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• pp.187-198
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• 2014

In this paper an efficient image encryption scheme based on cyclic rotations and multiple blockwise diffusions with two chaotic maps is proposed. A Sin map is used to generate round keys for the encryption/decryption process. A Pomeau-Manneville map is used to generate chaotic values for permutation, pixel value rotation and diffusion operations. The encryption scheme is composed of three stages: permutation, pixel value rotation and diffusion. The permutation stage performs four operations on the image: row shuffling, column shuffling, cyclic rotation of all the rows and cyclic rotation of all the columns. This stage reduces the correlation significantly among neighboring pixels. The second stage performs circular rotation of pixel values twice by scanning the image horizontally and vertically. The amount of rotation is based on $M{\times}N$ chaotic values. The last stage performs the diffusion four times by scanning the image in four different ways: block of $8{\times}8$ pixels, block of $16{\times}16$ pixels, principal diagonally, and secondary diagonally. Each of the above four diffusions performs the diffusion in two directions (forwards and backwards) with two previously diffused pixels and two chaotic values. This stage makes the scheme resistant to differential attacks. The security and performance of the proposed method is analyzed systematically by using the key space, entropy, statistical, differential and performance analysis. The experimental results confirm that the proposed method is computationally efficient with high security.

• 전산구조공학
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• 제10권4호
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• pp.239-249
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• 1997

랜덤하중 하에서의 구분적선형시스템이 갖는 노이즈의 영향으로 인해 그 특성이 많이 감소되거나 소멸된 응답거동으로부터 chaos거동을 검출하는 방법을 개발, 분석하였다. 해양에서 구조물이 받는 파력은 결정론적이 아닌 추계론적이다. 바람, 파도 그리고 조류 등에 의한 파력은 유한도의 랜던성을 갖으며, 이러한 파력은 지배적인 조화가진하중과 정규 백색노이즈를 더함으로써 표현할 수 있다. 외적 동요를 받는 시스템의 응답거동은 그 거동이 방해를 받으며, 이로 인해 chaos응답거동을 확인하기가 어려우며, 그 거동의 특성이 일반적인 랜덤거동과 다를 바가 없다. 이러한 경우, 평균 포인케어맵을 이용하여 랜덤노이즈에 의해 발견되지 않는 chaos응답거동을 식별할 수 있다. 본 연구에서는 직접수치시뮬레이션상에서 이러한 평균 포인케어맵을 만드는 방법을 개발하였으며, 얻어진 평균 포인케어맵의 적용범위에 대하여 분석하였다. 평균 포인케어맵은 노이즈가 포함된 조화가진하중을 받는 시스템의 chaos응답거동을 확인하는데 있어서 노이즈의 강도가 높을 때 일반적인 포인케어맵만으로는 놓칠 수 있는 chaos응답거동을 성공적으로 확인할 수 있음을 알아내었다. 또한 시스템의 응답거동에서 chaos의 특성이 완전히 사라지는 노이즈의 강도를 얻을 수 있음도 알아내었다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1993년도 추계학술대회논문집; 반도아카데미, 26 Nov. 1993
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• pp.77-83
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• 1993

In this paper, the dynamics of a 2-DOF not 1:1 resonant Hamiltonian system are studied. In the first part of the work, the behaviors of special periodic orbits called normal modes are examined by means of the harmonic balance method and their approximate stability ar analyzed by using the Synge's concept named stability in the kinematico-statical sense. Secondly, the global dynamics of the system for low and high energy are studied in terms of a perturbation analysis and Poincare' maps. In this part, one can see that the unstable normal mode generates chaotic motions resulting from the transverse intersections of the stable and unstable manifolds. Although there exist analytic methods for proving the existence of infinitely many periodic orbits, chaos, they cannot be applied in our case and thus, the Poincare' maps constructed by direct numerical integrations are utilized fot detecting chaotic motions. In the last part of the work, the existence of arbitrarily many periodic orbits of the system are proved by using a subharmonic Melnikov's method. We also study the possibility of the breakdown of invariant KAM tori only when h>h$_{0}$ (h$_{0}$:bifurcating energy) and investigate the generality of the destruction phenomena of the rational tori in the systems perturbed by stiffness and inertial coupling.