• The KIPS Transactions:PartC
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• v.17C no.2
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• pp.145-152
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• 2010

In this paper, we first propose a fast division algorithm in GF($2^{163}$) using standard basis representation, and then it is mapped into divider for GF($2^{163}$) with iterative hardware structure. The proposed algorithm is based on the binary ExtendedGCD algorithm, and the arithmetic operations for modular reduction are performed within only one "while-statement" unlike conventional approach which uses two "while-statement". In this paper, we use reduction polynomial $f(x)=x^{163}+x^7+x^6+x^3+1$ that is recommended in SEC2(Standards for Efficient Cryptography) using standard basis representation, where degree m = 163. We also have implemented the proposed iterative architecture in FPGA using Verilog HDL, and it operates at a clock frequency of 85 MHz on Xilinx-VirtexII XC2V8000 FPGA device. From implementation results, we will show that computation speed of the proposed scheme is significantly improved than the existing two approaches.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.3
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• pp.283-308
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• 2018

'Divisor and multiple' is the topic included both in the elementary and in the secondary mathematics curriculum, but there has been lack of research on it. It has been reported that students have a difficulty in understanding the meaning of the greatest common divisor (GCD) and the least common multiple (LCM), while they can find out GCD and LCM. Against the lack of research on how to overcome this difficulty, this study designed teaching methods with a model for visualization to emphasize the meanings of divisor and multiple in finding out GCD and LCM, and implemented the methods in one fourth grade classroom. A questionnaire was developed to explore students' solution methods and interviews with focused students were implemented. In addition, fourth-grade students' thinking was compared and contrasted with fifth-grade students who studied divisor and multiple with the current textbook. The results of this study showed that the teaching methods with a specific model for visualization had a positive impact on students' conceptual understanding of the process to find out GCD and LCM. As such, this study provides instructional implications on how to foster the meanings of finding out GCD and LCM at the elementary school.

• Tribology and Lubricants
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• v.18 no.4
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• pp.299-304
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• 2002

This paper reports the studies on the wear-corrosion behavior of ductile cast iron in the acidic environment. In atmosphere and variety of pH solution, specific wear rate and wear-corrosion characteristics of GCD 60 with various sliding speed and distance were investigated. And electrochemical polarization test of GCD 60 was examined in the environment of various pH values. The main results are as following : As the contact pressure increases, the critical velocity of specific wear rate becomes transient at low sliding speed. As pH value becomes low, wear-corrosion loss increases in the aqueous solution. As the corrosion environment is acidified, corrosion potential of GCD 60 becomes noble and corrosion current density increases.

• Korean Journal of Mathematics
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• v.17 no.2
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• pp.189-196
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• 2009

Let D be an integral domain, and let U be a group of units of D. Let $D^*=D-\{0\}$ and ${\Gamma}=D^*/U$ be the commutative cancellative semigroup under aU+bU=abU. We prove that $Cl(D)=Cl({\Gamma})$ and that D is a PvMD (resp., GCD-domain, Mori domain, Krull domain, factorial domain) if and only if ${\Gamma}$ is a PvMS(resp., GCD-semigroup, Mori semigroup, Krull semigroup, factorial semigroup). Let U=U(D) be the group of units of D. We also show that if D is integrally closed, then $D[{\Gamma}]$, the semigroup ring of ${\Gamma}$ over D, is an integrally closed domain with $Cl(D[{\Gamma}])=Cl(D){\oplus}Cl(D)$; hence D is a PvMD (resp., GCD-domain, Krull domain, factorial domain) if and only if $D[{\Gamma}]$ is.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.473-482
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• 2004

Let D be an integral domain, I a proper ideal of D, and R =D[It, $t^{-1}$] a generalized Rees ring, where t is an indeterminate. For suitable conditions, we show that R satisfies the ACCP (resp., is a BFD, an FFD, a (pre-) Schreier domain, a G-GCD domain, a PVMD, a v-domain) if and only if D satisfies the ACCP (resp., is a BFD, an FFD, a (pre-) Schreier domain, a G-GCD domain, a PVMD, a v-domain).

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.965-989
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• 2015

Let p, ${\ell}$ be distinct odd primes, q be an odd prime power with gcd(q, p) = gcd(q,${\ell}$) = 1, and m, n be positive integers. In this paper, we determine all self-dual, self-orthogonal and complementary-dual negacyclic codes of length $2p^{n{\ell}m}$ over the finite field ${\mathbb{F}}_q$ with q elements. We also illustrate our results with some examples.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.355-364
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• 2023

In this paper, we investigate the sums of the elements in the finite set $\{x^k:1{\leq}x{\leq}{\frac{n}{m}},\;gcd_u(x,n)=1\}$, where k, m and n are positive integers and gcd_u(x, n) is the unitary greatest common divisor of x and n. Moreover, for some cases of k and m, we can give the explicit formulae for the sums involving some well-known arithmetic functions.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.12 no.5
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• pp.185-189
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• 2012

It is almost impossible to directly find the prime factor, p,q of a large semiprime, n=pq. So Most of the integer factorization algorithms uses a indirect method that find the prime factor of the p=GCD(a-b,n),q=GCD(a+b,n) after getting the congruence of squares of the $a^2{\equiv}b^2$(mod n). Many methods of getting the congruence of squares have proposed, but it is not easy to get with RSA number of greater than a 100-digit number. This paper proposes a fast algorithm to get the congruence of squares. The proposed algorithm succeeded in getting the congruence of squares to a 19-digit number.

• Journal of Ocean Engineering and Technology
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• v.17 no.5 s.54
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• pp.76-81
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• 2003

Friction welding of GCD45 spheroidal graphite cast iron and 2024 aluminum alloy has been studied, especially in terms of the joint faces and strength of friction welding. For appropriate results of the friction welding of GCD45 graphite cast iron and 2024 aluminum alloy, an insert of A1050 pure aluminum metal was used. The joint strength of the A1050 pure aluminum insert approached the maximum strength of 165.7Mpa, compared to 128MPa for the joint between GCD45 graphite cast iron and A1050 pure aluminum without the insert metal. Maximum strength, 165.7Mpa, was possible for the following optimum conditions: 20MPa for the friction pressure, P1, 60MPa for the upsetting pressure, P2, 1 second for the friction time, t1, 3000rpm for the rotation, N, and 0.3 seconds for the brake time, tB.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2002.05a
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• pp.96-102
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• 2002

This paper was studied on the wear-corrosion behavior of ductile cast iron in the acidic environment. In the dry atmosphere and variety of pH solution, wear-corrosion characteristics and friction coefficient of GCD 60 with various sliding speed and distance were investigated. And electrochemical polarization test of GCD 60 was examined in the environment of various pH value. The main results are as following : In the dry atmosphere, boundary friction appears below nearly 5 $kg_{f}$ of contact load, and it is considered that solid friction occurs over nearly 5 $kg_{f}$ of contact load. As pH value becomes low, wear-corrosion loss in the aqueous solution increases. As the corrosion environment is acidified, corrosion potential of GCD 60 becomes noble, polarization resistance becomes low, and corrosion current density increases.