• 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.10 no.9
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• pp.1565-1572
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• 2006

Recently with the ever increasing growth of data communication, the need for security and privacy has become a necessity. The advent of wireless communication and other handheld devices like Personal Digital Assistants and smart cards have made the implementation of cryptosystems a major issue. The Cellular Automata(CA) can be programmed to implement hardware sharing between the encryption and decryption. In this paper, we give conditions for a linear hybrid cellular automata with 60, 102 or 204 to be a linear hybrid group cellular automata C. And we present the conditions which the complemented hybrid group cellular automata C' with complement vectors derived from C has maximum equal lengths in the state transition diagram of C' Also we analyze the relationship among cycles of C' These results generalize Mukhopadhyay's results.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• v.9 no.1
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• pp.315-318
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• 2005

Recently, the advent of wireless communication and other handhold devices like Personal Digital Assistants and smart cards have made in implementation of cryptosystems a major issue. One important aspect of modern day ciphers is the scope for hardware sharing between the encryption and decryption algorithm. The cellular Automata which have been proposed as an alternative to linear feedback shift registers(LFSRs) can be programmed to perform the operations without using any dedicated hardware. But to generalize and analyze CA is not easy. In this paper, we characterizes uniform/hybird complemented group CA with rules 195/153/51 that divide the entire state space into smaller spaces of maximal equal lengths. This properties can be useful in constructing key agreement algorithm.

• Annual Conference of KIPS
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• 2005.05a
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• pp.1063-1066
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• 2005

셀룰라 오토마타(Cellular Automata, 이하 CA)는 LFSR의 대안으로 제안되었으나 일반화와 분석이 어려워 거의 이뤄지지 않고 있다. 본 논문에서는 특별한 전이규칙을 가지는 그룹 CA에서 각각의 여원벡터에 대응하여 유도되는 여원 그룹 CA의 구조를 분석한다. 여기서 분석하는 그룹 여원 CA는 전체 상태가 그룹 CA의 최대 주기나 그것의 2배가 되는 같은 길이의 사이클들로 분리된다. 이러한 성질은 암호학에서 키 공유 프로토콜에 유용한 성질로 사용될 수 있다.