• Communications of the Korean Mathematical Society
• /
• v.21 no.4
• /
• pp.759-769
• /
• 2006

Let L : $C\;\rightarrow\;C$ be a hyperbolic automorphism. Then the hyperbolic toral automorphism $L_A\;T^2\;\rightarrow\;T^2$, induced by L, is a chaotic map ([2] pg.192). We characterize hyperbolic toral automorphisms by proving the converse of the above statement.

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

• Journal of the Institute of Electronics Engineers of Korea CI
• /
• v.43 no.3 s.309
• /
• pp.10-19
• /
• 2006

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 12n-bit and a key size of 125-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.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.2
• /
• pp.495-508
• /
• 1995

The self-excited vibrations of airfoil is related to the classical flutter problems, and it has been studied as a system with linear stiffness and small damping. However, since the actual aircraft wing and the many mechanical elements of airfoil type have various design variables and parameters, some of these could have strong nonlinearities, and the nonlinearities could be unexpectedly strong as the parameters vary. This abrupt chaotic behavior undergoes ordered routes, and the behaviors after these routes are uncontrollable and unexpectable since it is extremely sensitive to initial conditions. In order to study the chaotic behavior of the system, three parameters are considered, i.e., free-stream velocity, elastic distance and zero-lift angle. If the chaotic parameter region can be identified from the mathematically modeled nonlinear differential equation system, the designs which avoid chaotic regions could be suggested. In this study, by using recently developed dynamically system methods, and chaotic regions on the parameter plane will be found and the safe design variables will be suggested.

• 한국정보통신설비학회:학술대회논문집
• /
• 2005.08a
• /
• pp.406-414
• /
• 2005

In this paper, we propose 128bits chaotic block encryption scheme using a PLCM(Piece-wise Linear Chaotic Map) having a good dynamical property. The proposed scheme has a block size of 128 bits and a key size of 128 bits. In proposed scheme we use four 32bi1s sub-keys of session key and four 32bit sub-blocks of block to decide the initial value and the number of iteration of PLCM. The encrypted code is generated from the output of PLCM. With results of test and analyses of security we show the proposed scheme is very secure against statistical attacks and have very good Avalanche Effect and Randomness properties.

• Journal of Korea Multimedia Society
• /
• v.24 no.3
• /
• pp.406-415
• /
• 2021

The worldwide spread of the Internet and the digital information revolution have resulted in a rapid increase in the use and transmission of multimedia information due to the rapid development of communication technologies. It is important to protect images in order to prevent problems such as piracy and illegal distribution. To solve this problem, I propose a new digital color image encryption algorithm in this paper. I design a new pseudo-random number generator based on 1D five-neighborhood maximum length cellular automata (FN-MLCA) to change the pixel values of the plain image into unpredictable values. And then I use a 3D chaotic cat map to effectively shuffle the positions of the image pixel. In this paper, I propose a method to construct a new MLCA by modeling 1D FN-MLCA. This result is an extension of 1D 3-neighborhood CA and shows that more 1D MLCAs can be synthesized. The safety of the proposed algorithm is verified through various statistical analyses.

• Journal of Information Processing Systems
• /
• v.13 no.1
• /
• pp.68-82
• /
• 2017

Nowadays, geographic information system (GIS) is developed and implemented in many areas. A huge volume of vector map data has been accessed unlawfully by hackers, pirates, or unauthorized users. For this reason, we need the methods that help to protect GIS data for storage, multimedia applications, and transmission. In our paper, a selective encryption method is presented based on vertex randomization and hybrid transform in the GIS vector map. In the proposed algorithm, polylines and polygons are focused as the targets for encryption. Objects are classified in each layer, and all coordinates of the significant objects are encrypted by the key sets generated by using chaotic map before changing them in DWT, DFT domain. Experimental results verify the high efficiency visualization by low complexity, high security performance by random processes.

• Journal of Computing Science and Engineering
• /
• v.8 no.4
• /
• pp.187-198
• /
• 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.

• 제어로봇시스템학회:학술대회논문집
• /
• 1993.10a
• /
• pp.1234-1239
• /
• 1993

We study how to design conventional feedback controllers to drive chaotic trajectories of the well-known systems to their equilibrium points or any of their inherent periodic orbits. The well-known chaotic systems are Heon map and Duffing's equation, which are used as illustrative examples. The proposed feedback controller forces the chaotic trajectory to the stable manifold as OGY method does. Simulation results are presented to show the effectiveness of the proposed design method.

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