• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 1994.11a
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• pp.51-66
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• 1994

A divisible off-line electronic cash system based on cut-and-choose has first been proposed by [OO91] and recently more efficient single term divisible cash system was presented in [EO94] which is based on Brand's scheme [Bra93]. In this paper, we present a different type of single term divisible electronic cash system which is more efficient than previously proposed systems such as [OO91], [YLR93], and [EO94] in the standpoint of the amount of communication, the number of modular multiplications required in the payment transactions, and the storage requirement in the withdrawal protocol. Our scheme is a modified version of [LL93], where the major improvement has been made in its withdrawal transaction to introduce untraceability and multi-spendability. We have borrowed the idea of the withdrawal protocol of our scheme from [EO94] with minor modifications. Transferability in our scheme allows only a finite number of transfer. Our scheme satisfies an the desirable properties of an electronic cash system such as untraceability, divisibility and transferability. In addition, we present a n-spendable cash. The basic idea of extension to multi-spendability has been borrowed from [Bra93] with minor modifications.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1187-1198
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• 2019

Let R be a domain with its field Q of quotients. An R-module M is said to be weak w-projective if $Ext^1_R(M,N)=0$ for all $N{\in}{\mathcal{P}}^{\dagger}_w$, where ${\mathcal{P}}^{\dagger}_w$ denotes the class of GV-torsionfree R-modules N with the property that $Ext^k_R(M,N)=0$ for all w-projective R-modules M and for all integers $k{\geq}1$. In this paper, we define a domain R to be w-Matlis if the weak w-projective dimension of the R-module Q is ${\leq}1$. To characterize w-Matlis domains, we introduce the concept of w-Matlis cotorsion modules and study some basic properties of w-Matlis modules. Using these concepts, we show that R is a w-Matlis domain if and only if $Ext^k_R(Q,D)=0$ for any ${\mathcal{P}}^{\dagger}_w$-divisible R-module D and any integer $k{\geq}1$, if and only if every ${\mathcal{P}}^{\dagger}_w$-divisible module is w-Matlis cotorsion, if and only if w.w-pdRQ/$R{\leq}1$.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.1073-1085
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• 2023

A partition of n is called a t-core partition if none of its hook number is divisible by t. In 2019, Hirschhorn and Sellers [5] obtained a parity result for 3-core partition function a3(n). Motivated by this result, both the authors [8] recently proved that for a non-negative integer α, a3αm(n) is almost always divisible by an arbitrary power of 2 and 3 and at(n) is almost always divisible by an arbitrary power of pji, where j is a fixed positive integer and t = pa11pa22···pamm with primes pi ≥ 5. In this article, by using Hecke eigenform theory, we obtain infinite families of congruences and multiplicative identities for a2(n) and a13(n) modulo 2 which generalizes some results of Das [2].

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.419-424
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• 2009

Let J be the Jacobian variety of a hyperelliptic curve over $\mathbb{Q}$. Let M be the field generated by all square roots of rational integers over a finite number field K. Then we prove that the Mordell-Weil group J(M) is the direct sum of a finite torsion group and a free $\mathbb{Z}$-module of infinite rank. In particular, J(M) is not a divisible group. On the other hand, if $\widetilde{M}$ is an extension of M which contains all the torsion points of J over $\widetilde{\mathbb{Q}}$, then $J(\widetilde{M}^{sol})/J(\widetilde{M}^{sol})_{tors}$ is a divisible group of infinite rank, where $\widetilde{M}^{sol}$ is the maximal solvable extension of $\widetilde{M}$.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.661-666
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• 2001

In this paper we consider the properties of group divisible designs and triangular designs which belong to linked block designs. These designs have minimum number of experiments among the same average efficiency factor Optimal complete diallel cross designs are constructed by these designs. A list is prepared of all linked block designs in the class of group divisible designs and triangular designs enumerated by Clatworthy(1773).

• Journal of the Korean Data and Information Science Society
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• v.3 no.1
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• pp.47-63
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• 1992

Bechhofer and Tamhane(1981) proposed Balanced Treatment Incomplete Block (BTIB) desings for comparing p test treatments with a control treatment in blocks of size ${\kappa}$. Notz and Tamhane(1983) solved the problem about determination of the minimal complete class for ${\kappa}=3$. However there are a number of design parameters for which BTIB designs do not exist. We suggest a new class of designs called Group Divisible Treatment Desings(GDTD's) that is a larger class including BTIB designs as a subclass. In this paper we give the minimal complete classes of generator designs for GDTD's with ${\kappa}=2,\;p{\geq}4(except\;prime\;number)\;and\;{\kappa}=3,\;p=4(2)6$.

• 한국정보통신설비학회:학술대회논문집
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• 2005.08a
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• pp.382-387
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• 2005

There are many studies on arbitrarily divisible load scheduling problem in a distributed computing network consisting of processors interconnected through communication links. It is not efficient to arbitrarily distribute the load that comes into the system. In this paper, how to schedule in case that arbitrarily indivisible load comes into the system is studied. Also, the cases of the divisible load mixed with the indivisible load that come into network were dealt with optimal load distribution in parallel processing system by scheduling applied to linear programming.

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.7
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• pp.839-846
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• 1999

전자상거래에서 중요한 지불 수단으로 떠오르고 있는 전자화폐 시스템에 있어서 사용자에의 익명성 제공은 기존의 지불 시스템에서 제공하지 못하는 중요한 요소이다. 그러나 사용자 익명성을 악용하여 각종 범죄 활동에 이용하려는 시도가 발생할 수 있으며 전자화폐 시스템 도입시 이에 대한 대책도 함께 강구되어야 한다. 따라서 본 논문에서는 전자화폐의 효율적 사용을 위해 분할성 기능과 함께 화폐 추적과 사용자 추적 기능을 제공하는 효율적인 전자화폐 프로토콜을 제안한다.Abstract Electronic Cash System is an important payment method in Electronic Commerce. The anonymity of users is an important issue in such systems, but the issue has not been addressed by previous payment methods. User anonymity can lead to a system that is vulnerable to various criminal activities. Therefore, e-cash systems must consider ways to prevent such criminal activities. In this paper we suggest an efficient e-cash system that eliminates the vulnerability of the system by using the divisible ability of the system with the coin and owner tracing.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.7 no.4
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• pp.3-10
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• 1997

본 논문은 기존 비밀분산방식의 악세스 구조를 조합디자인 이론의 관점에서 해석함으로써 새로운 비밀분산방식이 구성될 수 있음을 보인다. 종래의 비밀분산방식으로서는 다항식보간을 이용하는 방법, 사영기하를 이용하는 방법등이 알려져 있으나 본 논문에서는 OA(orthogonal Arrary), t-(v,k l)디자인, 그룹분할 가능한 GD(Group Divisible)디자인이 갖는 행렬구조로부터 비밀분산방식의 악세스 구조를 정합시킴으로써 비밀분산방식을 새롭게 구성하고 있다. 이와같이 구성된 비밀분산방식은 기존 방식의 비밀 사이즈가 소수의 멱승 q에 의존하고 있는 반면 본 방식의 경우 조합디자인 파라메터에 관계하고 있으므로 비밀 사이즈 선택의 융통성이 있고 잘 알려진 조합적 구조를 이용함으로써 실현이 용이한 특징을 갖는다.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1237-1252
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• 2023

A fundamental problem in coding theory is to find n_q(k, d), the minimum length n for which an [n, k, d]_q code exists. We show that some q-divisible optimal linear codes of dimension 4 over 𝔽_q, which are not of Belov type, can be constructed geometrically using hyperbolic quadrics in PG(3, q). We also construct some new linear codes over 𝔽_q with q = 7, 8, which determine n₇(4, d) for 31 values of d and n₈(4, d) for 40 values of d.