• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.131-150
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• 2007

In this paper, we will define direct producted $W^*-porobability$ spaces over their diagonal subalgebras and observe the amalgamated free-ness on them. Also, we will consider the amalgamated free stochastic calculus on such free probabilistic structure. Let ($A_{j},\;{\varphi}_{j}$) be a tracial $W^*-porobability$ spaces, for j = 1,..., N. Then we can define the corresponding direct producted $W^*-porobability$ space (A, E) over its N-th diagonal subalgebra $D_{N}\;{\equiv}\;\mathbb{C}^{{\bigoplus}N}$, where $A={\bigoplus}^{N}_{j=1}\;A_{j}\;and\;E={\bigoplus}^{N}_{j=1}\;{\varphi}_{j}$. In Chapter 1, we show that $D_{N}-valued$ cumulants are direct sum of scalar-valued cumulants. This says that, roughly speaking, the $D_{N}-freeness$ is characterized by the direct sum of scalar-valued freeness. As application, the $D_{N}-semicircularityrity$ and the $D_{N}-valued$ infinitely divisibility are characterized by the direct sum of semicircularity and the direct sum of infinitely divisibility, respectively. In Chapter 2, we will define the $D_{N}-valued$ stochastic integral of $D_{N}-valued$ simple adapted biprocesses with respect to a fixed $D_{N}-valued$ infinitely divisible element which is a $D_{N}-free$ stochastic process. We can see that the free stochastic Ito's formula is naturally extended to the $D_{N}-valued$ case.

• Journal of KIISE:Information Networking
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• v.30 no.2
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• pp.207-221
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• 2003

A hash chain is highly efficient, attractive structure to use in electronic cash. Previous systems using hash chain were, however, either credit-based vendor-specific cash or debit-based general-purpose cash which lacks efficiency due to double spending problem. In this paper, we propose a new divisible cash system using hash chain. This newly proposed cash is general-purpose, debit-based, anonymous, and offline. The efficiency of the system results from its capacity to pay variable amounts with no additional costs. A client always performs a single blind signature in the withdrawal phase, independent of the length of the chain. During payment, a client performs a single challenge-and-response or generates a single signature, independent of the amount paid. This system provides a new refund mechanism, which uses a refund ticket, that allows clients to refund the unspent part of the chain without revealing any connection to the spent part.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.40 no.6
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• pp.106-113
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• 2003

The modified discrete cosine transform (MDCT) and inverse MDCT (IMDCT) are employed in subband/transform coding schemes as the analysis/synthesis filter bank based on time domain aliasing cancellation (TDAC). And the MDCT and IMDCT are the most computational intensive operations in layer III of the MPEG audio coding standard. In this paper, we propose a new efficient algorithm for the MDCT/IMDCT computation in various audio coding systems. It is based on the MDCT/IMDCT computation algorithm using the discrete cosine transforms (DCTs), and It employs two discrete cosine transform of type II (DCT-II) to compute the MDCT/IMDCT In addition, it takes advantage of ability in calculating the MDCT/IMDCT computation, where the length of a data block Is divisible by 4. The Proposed algorithm in this paper requires less calculation complexity than the existing method does. Also, it can be implemented by the parallel structure, therefore its structure is particularly suitable for VLSI realization

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38A no.2
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• pp.156-163
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• 2013

The use of an error-correcting code is essential in communication systems where the channel is noisy. When channel coding parameters are unknown at a receiver side, decoding becomes difficult. To perform decoding without the channel coding information, we should estimate the parameters. In this paper, we introduce a method to reconstruct the generator polynomial of BCH(Bose-Chaudhuri-Hocquenghem) codes based on the idea that the generator polynomial is compose of minimal polynomials and BCH code is cyclic code. We present a probability compensation method to improve the reconstruction performance. This is based on the concept that a random data pattern can also be divisible by a minimal polynomial of the generator polynomial. And we confirm the performance improvement through an intensive computer simulation.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.9 no.1
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• pp.103-114
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• 1999

Recently, various prototypes for electronic commerce are realized and its related researches are active under the present condition which it is increasing for the reality of its extended applications. First of all, actual demands are increasing for more secure and efficient electronic payment systems. Electronic cash, one of the Electronic payment systems, must have several properties like real money. Blind signature scheme by D. Chaum stands for the methods of obtaining privacy. In this paper, we propose a method for obtaining the blind signature based on the Elliptic Curve Cryptosystems, where the crytosystems are known as solving some problems of conventional crytosystems in views of computation time and key space. Also, we present a method for the divisibility of the electronic cash using our proposal by re-signing spare cash. Thus applying the proposed method, we can develop an efficient electronic payment systems.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.3
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• pp.93-100
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• 2007

Since Koblitz and Miller suggested the use of elliptic curves in cryptography, there has been an extensive literature on elliptic curve cryptosystem (ECC). The use of ECC is based on the observation that the points on an elliptic curve form an additive group under point addition operation. To realize secure cryptosystems using these groups, it is very important to find an elliptic curve whose group order is divisible by a large prime, and also to find a base point whose order equals this prime. While there have been many dramatic improvements on finding an elliptic curve and computing its group order efficiently, there are not many results on finding an adequate base point for a given curve. In this paper, we propose an efficient method to find a random base point on an elliptic curve defined over $GF(p^m)$. We first show that the critical operation in finding a base point is exponentiation. Then we present efficient algorithms to accelerate exponentiation in $GF(p^m)$. Finally, we implement our algorithms and give experimental results on various practical elliptic curves, which show that the new algorithms make the process of searching for a base point 1.62-6.55 times faster, compared to the searching algorithm based on the binary exponentiation.

• The Transactions of the Korea Information Processing Society
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• v.5 no.8
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• pp.2013-2026
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• 1998

In optical passive star interconnections, all packets are transmitted between nodes ina broadcast and-select manner. It is assumed that each node has a innable transmitter and a fixed-savelength receiver, ad that all packet lengths are equal so that each transmission can be done in a unit time. The tuning delay, denoted by $\delta$, means the amount of time for transmitter to change its wavelength to another one. The problec is , given ay value of the mumber of nodes N and the number of wavelengths $\kappa$ according to WDM implementations, to find transmission schedules with minimum cycle length for all-to all brondcaxt where no one sends any packet to itself. In this paper, we prove that the cycle length of optimal transcission schedules should be at least $max[[{\frac{N}{k}](N-1)}]$,$k\delta$$+N-1$. A novel algorithm for optimal transmission schedules is then presented when N-1 is divisible by $\kappa$. This algorithm also can be used for any values of N and $\kappa$ if the tuning delay $\delta$ does not affect strictly the cycle length of transmission schedules, i,e, $[\frac{N}{k}](N-1)$ > $\kappa\delta$+N-1.

• Journal of the Korean earth science society
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• v.40 no.1
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• pp.24-36
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• 2019

In the mid-eastern Yellow Sea, glacio-eustatic sea-level fluctuations and a regional tectonic subsidence have combined to represent an aggradational stacking pattern of sedimentary units during late Pleistocene-Holocene. The accumulated sediments are divisible into two-type units of Type-A and Type-B in high-resolution air-gun seismic profiles and the deep-drilled core of YSDP-105. Type-A unit largely comprises clast-rich coarse-grained sediments of non-marine to paralic origin, whereas Type-B unit consists mostly of tidal fine-grained sediments. Based on a bottom model of the sedimentary units, this study suggested a geoacoustic model of long-coring bottom layers at the YSDP-105 drilling site of the mid-eastern Yellow Sea. The geoacoustic model of 64-m depth below the seafloor with four-layer geoacoustic units was reconstructed in continental shelf strata at 45 m in water depth. For actual modeling, the geoacoustic property values of the models were compensated to in situ depth values below the seafloor using the Hamilton modeling method. We suggest that the geoacoustic model will be used for geoacoustic and underwater acoustic experiments of mid- and low-frequency reflecting on the deep bottom layers in the mid-eastern Yellow Sea.

• The Journal of Korean Philosophical History
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• no.32
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• pp.215-249
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• 2011

This essay reflects on the modernity of Korea by examining the transformation of the traditional knowledge system from a historico-semantic perspective with its focus on the opposition and collision of the old and the new conception occurred in the early period(1890~1910) of the acceptance of the Western modern civilization. With scientific success, trick of reason, Christianity and evolutionary view of history, the Western modernity regarded itself as a peak of civilization and forced the non-Western societies into the world system in which they came to be considered as 'barbarism(野蠻)' or 'half-enlightened(半開).' The East Asian civilization, which had its own history for several centuries, became degraded as kind of delusion and old-fashioned customs from which it ought to free itself. The Western civilization presented itself as exemplary future which East Asian people should achieve, while East Asian past traditions came to be conceived as just unnecessary vestiges which it was better to wipe out. It can be said that East Asian modernization was established through the propagation and acceptance of the modern products of the Western civilization rather than through the preservation of its past experience and pursuit of the new at the same time. Accordingly, it is difficult to apply directly to East Asian societies Koselleck's hypothesis; while mapping out his Basic Concept of History, he assumed that, in the so-called 'age of saddle,' semantic struggle over concepts becomes active between the past experience and the horizon of expectation on the future, and concepts undergoes 'temporalization', 'democratization', 'ideologization', 'politicization.'The struggle over the old and new conceptions in Korea was most noticeable in the opposition of the Neo-Confucian scholars of Hwangseongsinmun and the theorists of civilization of Doknipsinmun. The opposition and struggle demanded the change of understanding in every field, but there was difference of opinion over the conception of the past traditional knowledge system. For the theorists of civilization, 'the old(舊)' was not just 'past' and 'old-fashioned' things, but rather an obstacle to the building of new civilization. On the other hand, it contained the possibility of regeneration(新) for the Neo-Confucian scholars; that is, they suggested finding a guide into tomorrow by taking lessons from the past. The traditional knowledge system lost their holy status of learning(聖學) in the process of its change into a 'new learning(新學),' and religion and religious tradition also weakened. The traditional knowledge system could change itself into modern learning by accepting scientific methodology which pursues objectivity and rationality. This transformation of the traditional knowledge system and 'the formation of the new learning from the old learning' was accompanied by the intersection between the old and new conceptions. It is necessary to pay attention to the role played by the concept of Sil(hak)(實學) or Practical Learning in the intersection of the old and new conceptions. Various modern media published before and after the 20th century show clearly the multi-layered development of the old and new conceptions, and it is noticeable that 'Sil(hak)' as conceptual frame of reference contributed to the transformation of the traditional knowledge system into the new learning. Although Silhak often designated, or was even considered equivalent to, the Western learning, Neo-Confucian scholars reinterpreted the concept of 'Silhak' which the theorists of civilization had monopolized until then, and opened the way to change the traditional knowledge system into the new learning. They re-appropriated the concept of Silhak, and enabled it to be invested with values, which were losing their own status due to the overwhelming scientific technology. With Japanese occupation of Korea by force, the attempt to transform the traditional knowledge system independently was obliged to reach its own limit, but its theory of 'making new learning from old one' can be considered to get over both the contradiction of Dondoseogi(東道西器: principle of preserving Eastern philosophy while accepting Western technology) and the de-subjectivity of the theory of civilization. While developing its own logic, the theory of Dongdoseogi was compelled to bring in the contradiction of considering the indivisible(道and 器) as divisible, though it tried to cope with the reality where the principle of morality and that of competition were opposed each other and the ideologies of 'evolution' and 'progress' prevailed. On the other hand, the theory of civilization was not free from the criticism that it brought about a crack in subjectivity due to its internalization of the West, cutting itself off from the traditional knowledge system.