• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.239-247
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• 2016

In recent years, CA has been applied to image security due to its simple and regular structure, local interaction and random-like behavior. Since the initial state is regenerated after some iterations in the group CA, the receiver is able to decrypt by the same CA. Pries et al. showed that the all lengths of the cycles in the complemented group CA C with rules 195, 153, and 51 are equal to the order of C. Nandi et al. reported the encryption technique using C. These results can be made efficient use in cryptosystem by expanding the Nandi's key space. In this paper, we analyze the order of the complemented group CA derived from 90=150 group CA and show that all the lengths of the cycles in the complemented CA are equal to the order of the complemented CA.

• The Journal of the Korea institute of electronic communication sciences
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• v.11 no.3
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• pp.293-302
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• 2016

In this paper we analyze the CA formed by combining the uniform 102 CA $\mathbb{C}_u$ and the m-cell 90/150 hybrid CA $\mathbb{C}_h$ whose characteristic polynomial is $(x+1)^m$. We analyze cycle structures of complemented group CA derived from $\mathbb{C}_u$ and propose a condition of complemented CA dividing the entire state space into smaller cycles of equal lengths. And we analyze the cycle structure of complemented group CA $\mathbb{C}^{\prime}$ derived from the CA $\mathbb{C}$ formed by combining $\mathbb{C}_u$ and $\mathbb{C}_h$ with complement vector F such that $(T+I)^{q-1}F{\neq}0$ where $(x+1)^q$ is the minimal polynomial of $\mathbb{C}$.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.5 no.2
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• pp.365-370
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• 2001

In this paper, we analyze behavior of complemented CA derived from a linear Two-Predecessor MACA(TPMACA) and obtain the state-transition diagram of complemented CA by using a basic path in the 0-Dee of a linear TPMACA.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.14 no.6
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• pp.25-30
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• 2004

Linear cellular automata(CA) which generate maximum-length cycles, have wide applications in generation of pseudo-random patterns, signature analysis, cryptography and error correcting codes etc. Linear CA whose characteristic polynomial is primitive has been studied. In this paper Ive propose a effective method for generation of a variety of maximum-length CA(MLCA). And we show that the complemented CA's derived from a linear MLCA are all MLCA. Also we analyze the Properties of complemented MLCA. And we prove that the number of n-cell MLCA is ${\phi}(2^{n}-1)2^{n+1}$/n.

• The Journal of the Korea institute of electronic communication sciences
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• v.14 no.5
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• pp.1001-1008
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• 2019

A high-quality pseudorandom sequence generation is an important part of many cryptographic applications, including encryption protocols. Therefore, a pseudorandom number generator (PRNG) is an essential element for generating key sequences in a cryptosystem. A PRNG must effectively generate a large, high-quality random data stream. It is well known that the bitstreams output by the CA-based PRNG are more random than the bitstreams output by the LFSR-based PRNG. In this paper, we prove that the complemented CA derived from 90/150 maximum length cellular automata(MLCA) is a MLCA to design a PRNG that can generate more secure bitstreams and extend the key space in a secret key cryptosystem. Also we give a method for calculating the cell positions outputting a nonlinear sequence with maximum period in complemented MLCA derived from a 90/150 MLCA and a complement vector.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2001.05a
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• pp.688-691
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• 2001

By using basic paths in the 0-tree of a linear TPMACA C we obtain the state-transition diagram of complemented CA C'derived from C such that the complement vector is a nonzero attractor of C. Also we analyze the behavior of C'.

• Journal of Korea Multimedia Society
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• v.6 no.3
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• pp.549-555
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• 2003

CA is cost-effective to generate pseudorandom patterns than LFSR. Based on the effectiveness of a CA based pseudorandom pattern generator, CA have been employed successfully in several applications. Especially Nongroup CA is applied to efficient hash function generation, cryptography and image compression. In this paper we analyze the properties of TPNCA and by using basic paths in the 0-tree of a linear TPNCA we analyze the structure of the state-transition graph. Also by showing the structure of the complemented CA which have the acyclic state of the 0-tree as the complement vector is isomorphic to the structure of the original TPNCA, we reduce the time in analyzing the CA-states.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.6C
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• pp.361-367
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• 2011

In this paper, we propose encryption method to using complemented MLCA(Maximum Length Cellular Automata) based on NBCA(Null Boundary CA) and 2D CAT (Two-Dimensional Cellular Automata Transform) for efficient image encryption. The encryption method is processed in the following order. First, a transition matrix T is created using the Wolfram Rule matrix. Then, the transition matrix T is multiplied to the original image that is intended to be encrypted, which transfers the pixel values of the original image. Furthermore, the converted original image goes through a XOR operation with complemented vector F to convert into a complemented MLCA applied image. Then, the gateway value is set and 2D CAT basis function is created. Also, the 2D CAT is encrypted by multiplying the created basis function to the complemented MLCA applied image. Lastly, the stability analysis verifies that proposed method holds a high encryption quality status.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.1
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• pp.13-18
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• 2017

With the advancement of internet technology, the importance of data protection is gaining more attention. As a possible data protection solution, we propose a novel video encryption method using complemented maximum-length cellular automata (C-MLCA). The first step for encryption is to use 90/150 CA rule to generate a transition matrix T of a C-MLCA state followed by a 2D C-MLCA basis image. Then, we divide the video into multiple frames. Once, we perform exclusive-OR operation with the split frames and the 2D basis image, the final encrypted video can be obtained. By altering values of pixel, the fundamental information in visualizing image data, the proposed method provides improved security. Moreover, we carry out some computational experiments to further evaluate our method where the results confirm its feasibility.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2002.09a
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• pp.14-14
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• 2002