• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.05a
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• pp.264-267
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• 2008

Many researchers have studied synthesis method of 90/150 group CA. However, there is a lack of researches for synthesis method of 90/150 nongroup CA. In this paper we report some interesting properties of 90/150 multiple-attractor CA in which all of the cycles are of unit length. 90/150 multiple-attractor CA is a class of nongroup CA. And we propose a construction of 90/150 single-attractor CA. Also we construct 90/150 multiple-attractor CA derived from 90/150 single-attractor CA.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1331-1342
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• 2009

In this paper, we analyze the behavior of the state transition of nongroup CA with a single attractor over GF($2^p$)(p > 1), and propose the algorithm for the construction of the state transition diagram of a Single Attractor CA(SACA) over GF($2^p$) which is very different from the construction algorithm for the state transition diagram of GF(2) SACA.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.2
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• pp.105-111
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• 2005

Though GF(2) CA can only handle data with bit units GF(2p) CA can handle data with units more than bit units. In this paper we analyze the state-transition of nongroup cellular automata(CA) with a single attractor over GF(2p). And we propose the constructing method the state-transition diagram of a linear SACA over GF(2p) by using the concept of basic path. Also we propose the state-transition diagram of the nonlinear complemented SACA by using the state-transition diagram of a linear SACA.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.9
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• pp.1939-1946
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• 2011

Expander graphs are useful in the design and analysis of communication networks. Mukhopadhyay et. al introduced a method to generate a family of expander graphs based on nongroup two predecessor single attractor CA(Cellular Automata). In this paper we propose a method to generate a family of expander graphs based on 60/102 Null boundary CA(NBCA) which is a group CA. The spectral gap generated by our method is larger than that of Mukhopadhyay et. al [12]. As an application we give an algorithm which generate one-way functions whose security lies on the combinatorial properties of our expander graphs. the one-way function using d-regular graph generated by the 60/102 NBCA is based on the Goldreich's construction [5].

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2007.06a
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• pp.423-426
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• 2007

In this paper, we propose an algorithm for finding 90/150 Two Predecessor Nongroup Cellular Automata(TPNCA). Especially, we synthesize TPNCA for the minimal polynomial whose type is of the form xp(x) or x(x+1)p(x) using the proposed algorithm which is useful to study pseudorandom number generation, where p(x) is some primitive polynomial. Also we synthesize Two Predecessor Single Attractor CA and Two Predecessor Multiple Attractor CA which are useful to study hashing.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.6
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• pp.1047-1054
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• 2004

One of the fundamental problems in computer science is how to store information so that it can be searched and retrieved efficiently. Hashing is a technique which solves this problem. In this paper, we propose a tree construction algorithm using linear two-predecessor single attractor cellular automata C and its complemented cellular automata. Also by using the concept of MRT we give a perfect hasing algorithm based on C.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• v.9 no.1
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• pp.335-338
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• 2005

Though GF(2) CA can only handle data with bit units, GF(2$^{p}$) CA can handle data with byte units. In this paper we analyze the state-transition of nongroup cellular automata(CA) with a single attractor over GF(2$^{p}$). And we propose the constructing method of the state-transition diagram of a linear SACA over GF(2$^{p}$) by using the concept of basic path. Also we propose the state-transition diagram of the nonlinear complemented SACA by using the state-transition diagram of a linear SACA.