• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2006.06a
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• pp.376-377
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• 2006

This paper presents the characteristics of Ta-N thin film strain gauges that are suitable for harsh environemts, which were deposited on thermally oxidized Si substrates by DC reactive magnetronsputtering in an argon-nitrogen atmosphere (Ar-$N_2$ (4 ~ 16 %)). These films were annealed for 1 hr in $2{\times}10^{-6}$ Torr in a vacuum furnace with temperatures that ranged from 500 - $1000^{\circ}C$. The optimized deposition and annealing conditions of the Ta-N thin film strain gauges were determined using 8 % $N_2$ gas flow ratio and annealing at $900^{\circ}C$ for 1 hr. Under optimum formation conditions, the Ta-N thin film strain gauges obtained a high electrical resistivity, ${\rho}\;=\;768.93\;{\mu}{\Omega}{\cdot}cm$, a low temperature coefficient of resistance, $TCR\;=\;-84\;ppm/^{\circ}C$ and a high temporal stability with a good longitudinal gauge factor, GF=4.12. The fabricated Ta-N thin film strain gauges are expected to be used inmicromachined pressure sensors and load cells that are operable under harsh environments.

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.201-209
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• 2017

There exists already mass formula which is the number of self orthogonal codes in $GF(q)^n$, but not proof of it. In this paper we described some theories about finite geometry and by using them proved the mass formula when $q=p^m$, p is odd prime.

• International Journal of Contents
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• v.3 no.2
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• pp.40-43
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• 2007

This paper proposed a new modular inverse algorithm based on the right-shifting binary Euclidean algorithm. For an n-bit numbers, the number of operations for the proposed algorithm is reduced about 61.3% less than the classical binary extended Euclidean algorithm. The proposed algorithm implementation shows substantial reduction in computation time over Galois field GF(p).

• Honam Mathematical Journal
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• v.33 no.3
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• pp.381-391
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• 2011

One of the main interesting things of a matroid theory is the representability by a matroid from a matrix over some field F. The representability of uniform matroid $U_{m,n}$ over some field are studied by many authors. In this paper we construct a matrix representing $U_{3,6}$ over the field GF(4). Also we find out matrix of the affine matroid AG(2, 3) over the field GF(4).

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.7
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• pp.743-751
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• 1999

공개키 암호 시스템에서 모듈러 지수 연산은 주된 연산으로, 이 연산은 내부적으로 모듈러 곱셈을 반복적으로 수행함으로써 계산된다. 본 논문에서는 GF(2m)상에서 수행할 수 있는 Montgomery 알고리즘을 분석하여 right-to-left 방식의 모듈러 지수 연산에서 공통으로 계산 가능한 부분을 이용하여 모듈러 제곱과 모듈러 곱셈을 동시에 수행하는 선형 시스톨릭 어레이를 설계한다. 본 논문에서 설계한 시스톨릭 어레이는 기존의 곱셈기보다 모듈러 지수 연산시 약 0.67배 처리속도 향상을 가진다. 그리고, VLSI 칩과 같은 하드웨어로 구현함으로써 IC 카드에 이용될 수 있다.Abstract One of the main operations for the public key cryptographic system is the modular exponentiation, it is computed by performing the repetitive modular multiplications. In this paper, we analyze Montgomery's algorithm and design a linear systolic array to perform modular multiplication and modular squaring simultaneously. It is done by using common-multiplicand modular multiplication in the right-to-left modular exponentiation over GF(2m). The systolic array presented in this paper improves about 0.67 times than existing multipliers for performing the modular exponentiation. It could be designed on VLSI hardware and used in IC cards.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.3
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• pp.418-424
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• 1994

Like the Hermitian function field over GF(q), those subfields defined by y +y=x where s divides q+1 are also maximal, having the maximum number os places of degree one permissible by the Hasse-Weil bound. Geometric Goppa codes(or algebraic geometric codes) arising from these subfields of the Hermitian function field are studied in this paper. Their dimension and minimum distance are explicilty and completely presented for any m with m

• Journal of the Institute of Convergence Signal Processing
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• v.13 no.4
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• pp.194-200
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• 2012

In this paper we analyze the code sequence generating algorism defined on $GF(2^n)$ proposed by S.Bostas and V.Kumar[7] and derive the implementation functions of code sequence generator using Boolean functions which can map the vector space $F_2^n$ of all binary vectors of length n, to the finite field with two elements $F_2$. We find the code sequence generating boolean functions based on two kinds of the primitive polynomials of degree, n=5 and n=7 from trace function. We then design and implement the code sequence generators using these functions, and produce two code sequence groups. The two groups have the period 31 and 127 and the magnitudes of out of phase(${\tau}{\neq}0$) autocorrelation and crosscorrelation functions {-9, -1, 7} and {-17, -1, 15}, satisfying the period $L=2^n-1$ and the correlation functions $R_{ij}({\tau})=\{-2^{(n+1)/2}-1,-1,2^{(n+l)/2}-1\}$ respectively. Through these results, we confirm that the code sequence generators using boolean functions are designed and implemented correctly.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.1
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• pp.123-136
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• 2004

In this paper, complexity and regularity of polynomial multiplication over $GF({2^n})$ are defined by using Hamming weight of rows and columns of the matrix ever GF(2) which represents polynomial multiplication. It is shown experimentally that in order to construct the block cipher robust against differential cryptanalysis, polynomial multiplication of substitution layer and the permutation layer should have high complexity and high regularity. With result of the experiment, a way of constituting S box and G function is suggested in the block cipher whose structure is similar to SEED, which is KOREA standard of 128-bit block cipher. S box can be formed with a nonlinear function and an affine transform. Nonlinear function must be strong with differential attack and linear attack, and it consists of an inverse number over $GF({2^8})$ which has neither a fixed pout, whose input and output are the same except 0 and 1, nor an opposite fixed number, whose output is one`s complement of the input. Affine transform can be constituted so that the input/output correlation can be the lowest and there can be no fixed point or opposite fixed point. G function undergoes linear transform with 4 S-box outputs using the matrix of 4${\times}$4 over $GF({2^8})$. The components in the matrix of linear transformation have high complexity and high regularity. Furthermore, G function can be constituted so that MDS(Maximum Distance Separable) code can be formed, SAC(Strict Avalanche Criterion) can be met, and there can be no weak input where a fixed point an opposite fixed point, and output can be two`s complement of input. The primitive polynomials of nonlinear function affine transform and linear transformation are different each other. The S box and G function suggested in this paper can be used as a constituent of the block cipher with high security, in that they are strong with differential attack and linear attack with no weak input and they are excellent at diffusion.

• ETRI Journal
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• v.35 no.3
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• pp.523-529
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• 2013

Subquadratic space complexity multipliers for optimal normal bases (ONBs) have been proposed for practical applications. However, for the Gaussian normal basis (GNB) of type t > 2 as well as the normal basis (NB), there is no known subquadratic space complexity multiplier. In this paper, we propose the first subquadratic space complexity multipliers for the type 4 GNB. The idea is based on the fact that the finite field GF($2^n$) with the type 4 GNB can be embedded into fields with an ONB.

• 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.