• International Journal of Computer Science & Network Security
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• 제21권8호
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• pp.17-27
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• 2021

Non-abelian group based cryptosystems are a latest research inspiration, since they offer better security due to their non-abelian properties. In this paper, we propose a novel approach to non-abelian group based public-key cryptographic protocols using semidirect products of finite groups. An intractable problem of determining automorphisms and generating elements of a group is introduced as the underlying mathematical problem for the suggested protocols. Then, we show that the difficult problem of determining paths and cycles of Cayley graphs including Hamiltonian paths and cycles could be reduced to this intractable problem. The applicability of Hamiltonian paths, and in fact any random path in Cayley graphs in the above cryptographic schemes and an application of the same concept to two previous cryptographic protocols based on a Generalized Discrete Logarithm Problem is discussed. Moreover, an alternative method of improving the security is also presented.

• Proceedings of the Korea Society for Simulation Conference
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• 한국시뮬레이션학회 1994년도 춘계초청 강연회 및 임시총회
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• pp.0.1-0
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• 1994

• Honam Mathematical Journal
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• 제30권2호
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• pp.207-217
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• 2008

Digital geometry has strongly contributed to the study of a discrete topological space $X{\subset}{\mathbf{Z}}^n$ with k-adjacency of ${\mathbf{Z}}^n$. As a survey-type article, we review various utilities of digital geometry.

• Journal of Electrical Engineering and information Science
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• 제1권2호
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• pp.87-95
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• 1996

This paper presents a (k,n) threshold digital signature scheme with no trusted dealer. Our idea is to use the EIGamal signature scheme modified for group use. Among many digital signature schemes, our modification has a nice property for our purpose. We also show a (k.n) threshold fail stop signature scheme and two (k.n) threshold undeniable signature schemes. We use [10] as the original fail stop signature scheme, and use [3] and [2] as the original undeniable signature schemes. Since all these schemes are based on the discrete log problem, we can use the same technique.

• Communications of the Korean Mathematical Society
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• 제11권1호
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• pp.253-258
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• 1996

For a nonelementary discrete group $\Gamma$ of hyperbolic isometries acting on $B^m(m\geq2)$, we give a topological characterization of conical limit points using admissible pairs.

• Communications for Statistical Applications and Methods
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• 제17권1호
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• pp.127-140
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• 2010

In interim analysis, group sequential tests are widely used for the ethical, scientific, and economic reasons. In this paper, we propose the group sequential tests using both type I and type II error spending rate functions when the response variable is discrete, especially binomial distribution, in the interim analysis. In addition, we propose new error spending rate function which covers the formerly proposed. Our method has good property that is flexible, fast and easily applicable. A numerical simulations are carried out to evaluate our method and it shows good performance.

• Journal of Integrative Natural Science
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• 제10권2호
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• pp.110-114
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• 2017

The connected and simply connected four-dimensional matrix solvable Lie group $Sol^4_1$ is the four-dimensional geometry. A crystallographic group of $Sol^4_1$ is a discrete cocompact subgroup of $Sol^4_1{\rtimes}D(4)$. In this paper, we geometrically describe the crystallographic groups of $Sol^4_1$.

• The Pure and Applied Mathematics
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• 제17권4호
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• pp.275-288
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• 2010

A one-holed torus ${\Sigma}$(l, 1) is a building block of oriented surfaces. In this paper we formulate the matrix presentations of the holonomy group of a one-holed torus ${\Sigma}$(1, 1) by the gluing method. And we present an algorithm for deciding the discreteness of the holonomy group of ${\Sigma}$(1, 1).

• Journal of the Chungcheong Mathematical Society
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• 제23권4호
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• pp.749-755
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• 2010

We investigate biprojectivity of $C_{r}^{*}(G)$ as a $L^1(G)$-bimodule for a locally compact group G. The main results are the following. As a $L^1(G)$-bimodule$C_{r}^{*}(G)$ is biprojective if G is compact and is not biprojective if G is an infinite discrete group or G is a non-compact abelian group.

• Proceedings of the Korean Nuclear Society Conference
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• 한국원자력학회 1998년도 춘계학술발표회논문집(2)
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• pp.618-623
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• 1998

A shielding analysis was performed for the end shield of CANDU 6 reactor. The one-dimensional discrete ordinate code ANISN with a 38-group neutron-gamma library, extracted from DLC-37D library, was used to estimate the dose rate for the natural uranium CANDU reactor. For comparison MCNP-4B calculation was performed for the same system using continuous, discrete and multi-group libraries. The comparison has shown that the total dose rate of the ANISN calculation agrees well with that of the MCNP calculation. However, the individual dose rate (neutron and gamma) has shown opposite trends between AMISN and MCNP estimates, which may require a consistent library generation for both codes.