• The Journal of the Korea institute of electronic communication sciences
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• v.13 no.3
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• pp.593-600
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• 2018

Cellular automata (CA) have been applied to effective cryptographic system design. CA is superior in randomness to LFSR due to the fact that its state is updated simultaneously by local interaction. To apply these CAs to the cryptosystem, a study has been performed how to synthesize CA corresponding to given polynomials. In this paper, we analyze the recurrence relations of the characteristic polynomial of the 90 UCA and the characteristic polynomial of the 90/150 CA whose transition rule is <$00{\cdots}001$>. And we synthesize the 90/150 CA corresponding to the trinomials $x^{2^n}+x+1(n{\geq}2)$ satisfying f(x)=f(x+1) using the 90 UCA transition rule blocks and the special transition rule block. We also analyze the properties of the irreducible factors of trinomials $x^{2^n}+x+1$ and propose a 90/150 CA synthesis algorithm corresponding to $x^{2^n}+x^{2^m}+1(n{\geq}2,n-m{\geq}2)$.

• The Journal of the Korea institute of electronic communication sciences
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• v.14 no.1
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• pp.235-242
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• 2019

Self-reciprocal polynomials over finite fields are useful in several applications, including reversible codes with read-backward properties. This paper is a study on 90/150 CA with characteristic polynomials of maximal weight polynomials, which is one of the self-reciprocal polynomials. In this paper, we propose a decision method for determining the existence of 90/150 MWCA corresponding to the maximum weight polynomial of degree 2n using n-cell 90/150 CA with transition rule <$100{\cdots}0$>. The proposed method is verified through experiments.

• 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.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.23-35
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• 2019

Self-reciprocal polynomials are important because it is possible to specify only half of the coefficients. The special case of the self-reciprocal polynomial, the maximum weight polynomial, is particularly important. In this paper, we analyze even cell 90/150 cellular automata with linear rule blocks of the form < $a_1,{\cdots},a_n,d_1,d_2,b_n,{\cdots},b_1$ >. Also we show that there is no 90/150 CA of the form < $U_n{\mid}R_2{\mid}U^*_n$ > or < $\bar{U_n}{\mid}R_2{\mid}\bar{U^*_n}$ > whose characteristic polynomial is $f_{2n+2}(x)=x^{2n+2}+{\cdots}+x+1$ where $R_2$ =< $d_1,d_2$ > and $U_n$ =< $0,{\cdots},0$ >, and $\bar{U_n}$ =< $1,{\cdots},1$ >.

• 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 $\mathbb{C}$.

• The Journal of the Korea institute of electronic communication sciences
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• v.5 no.1
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• pp.10-16
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• 2010

90/150 CA is a CA completely specified by using rule 90 and rule 150. Since 90/150 CA whose minimal and characteristic polynomials are identical has outstanding randomness, this CA is more attractive than LFSR. Sarkar proposed a scheme based on the 90 uniform CA and the 150 uniform CA. That scheme provided authentication by digital signature and other basic security requirements like confidentiality. In this paper we analyze 90 or 150 uniform CA and give a synthesis method of 2n-cell uniform CA and (2n+1)-cell uniform CA using a special n-cell 90/150 CA. And we propose an effective method of computation of characteristic polynomial corresponding to uniform CA.

• The Journal of the Korea institute of electronic communication sciences
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• v.13 no.2
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• pp.383-390
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• 2018

Since cellular automata(CA) is superior to LFSR in randomness, it is applied as an alternative of LFSR in various fields. However, constructing CA corresponding to a given polynomial is more difficult than LFSR. Cattell et al. and Cho et al. showed that irreducible polynomials are CA-polynomials. And Cho et al. and Sabater et al. gave a synthesis method of 90/150 CA corresponding to the power of an irreducible polynomial, which is applicable as a shrinking generator. Swan characterizes the parity of the number of irreducible factors of a trinomial over the finite field GF(2). These polynomials are of practical importance when implementing finite field extensions. In this paper, we show that the trinomial $x^{2^n-1}+X+1$ ($n{\geq}2$) are CA-polynomials. Also the trinomial $x^{2^a(2^n-1)}+x^{2^a}+1$ ($n{\geq}2$, $a{\geq}0$) are CA-polynomials.

• The Journal of the Korea institute of electronic communication sciences
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• v.13 no.6
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• pp.1301-1308
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• 2018

90/150 CA which are used as key generators of the cipher system have more randomness than LFSRs, but synthesis methods of 90/150 CA are difficult. Therefore, 90/150 CA synthesis methods have been studied by many researchers. In order to synthesize a suitable CA, the analysis of the characteristic polynomial of 90/150 CA should be preceded. In general, the characteristic of polynomial ${\Delta}_n$ of n cell 90/150 CA is obtained by using ${\Delta}_{n-1}$ and ${\Delta}_{n-2}$. Choi et al. analyzed $H_{2^n}(x)$ and $H_{2^n-1}(x)$, where $H_k(x)$ is the characteristic polynomial of k cell 90/150 CA with state transition rule <$10{\cdots}0$>. In this paper, we propose an efficient method to obtain $H_n(x)$ from $H_{n-1}(x)$ and an efficient algorithm to obtain $H_{2^n+i}(x)$ and $H_{2^n-i}(x)$ ($1{\leq}i{\leq}2^{n-1}$) from $H_{2^n}(x)$ by using this method.

• The Journal of the Korea institute of electronic communication sciences
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• v.13 no.4
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• pp.819-826
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• 2018

The generalized Hamming weight is one of the important parameters of the linear code. It determines the performance of the code when the linear codes are applied to a cryptographic system. In addition, when the block code is decoded by soft decision using the lattice diagram, it becomes a measure for evaluating the state complexity required for the implementation. In particular, a bit-parallel multiplier on finite fields based on trinomials have been studied. Cellular automata(CA) has superior randomness over LFSR due to its ability to update its state simultaneously by local interaction. In this paper, we deal with the efficient synthesis of the pseudo random number generator, which is one of the important factors in the design of effective cryptosystem. We analyze the property of the characteristic polynomial of the simple 90/150 transition rule block, and propose a synthesis algorithm of the reversible 90/150 CA corresponding to the trinomials $x^2^n+x^{2^n-1}+1$($n{\geq}2$) and the 90/150 reversible CA(RCA) corresponding to the maximum weight polynomial with $2^n$ degree by using this rule block.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2006.05a
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• pp.393-396
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• 2006

In this paper, we analyze the characteristic polynomials of 90/150 cellular automata which uses only 90, 150 rules as state-transition rules. In particular, we propose the method which the characteristic polynomial is represented as the exponential type of a primitive polynomial by synthesizing 90/150 CA.