• Journal of KIISE:Computer Systems and Theory
• /
• v.30 no.5_6
• /
• pp.324-329
• /
• 2003

The public-key cryptosystems such as Diffie-Hellman Key Distribution and Elliptical Curve Cryptosystems are built on the basis of the operations defined in GF(2$^{m}$ ):addition, subtraction, multiplication and multiplicative inversion. It is important that these operations should be computed at high speed in order to implement these cryptosystems efficiently. Among those operations, as being the most time-consuming, multiplicative inversion has become the object of lots of investigation Formant's theorem says $\beta$$^{-1}$ =$\beta$$^{2}$sup m/-2/, where $\beta$$^{-1}$ is the multiplicative inverse of $\beta$$\in$GF(2$^{m}$ ). Therefore, to compute the multiplicative inverse of arbitrary elements of GF(2$^{m}$ ), it is most important to reduce the number of times of multiplication by decomposing 2$^{m}$ -2 efficiently. Among many algorithms relevant to the subject, the algorithm proposed by Itoh and Tsujii[2] has reduced the required number of times of multiplication to O(log m) by using normal basis. Furthermore, a few papers have presented algorithms improving the Itoh and Tsujii's. However they have some demerits such as complicated decomposition processes[3,5]. In this paper, in the case of 2$^{m}$ -2, which is mainly used in practical applications, an efficient algorithm is proposed for computing the multiplicative inverse at high speed by using both the factorization formula x$^3$-y$^3$=(x-y)(x$^2$＋xy＋y$^2$) and normal basis. The number of times of multiplication of the algorithm is smaller than that of the algorithm proposed by Itoh and Tsujii. Also the algorithm decomposes 2$^{m}$ -2 more simply than other proposed algorithms.

• The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
• /
• v.24 no.2
• /
• pp.208-225
• /
• 2019

To understand the mean surface circulation and surface currents in the East Sea, trajectories of surface drifters passed through the East Sea from 1991 to 2017 were analyzed. By analyzing the surface drifter trajectory data, the main paths of surface ocean currents were grouped and the variation in each main current path was investigated. The East Korea Warm Current (EKWC) heading northward separates from the coast at $36{\sim}38^{\circ}N$ and flows to the northeast until $131^{\circ}E$. In the middle (from $131^{\circ}E$ to $137^{\circ}E$) of the East Sea, the average latitude of the currents flowing eastward ranges from 36 to $40^{\circ}N$ and the currents meander with large amplitude. When the average latitude of the surface drifter paths was in the north (south) of $37.5^{\circ}N$, the meandering amplitude was about 50 (100) km. The most frequent route of surface drifters in the middle of the East Sea was the path along $37.5-38.5^{\circ}N$. The surface drifters, which were deployed off the coast of Vladivostok in the north of the East Sea, moved to the southwest along the coast and were separated from the coast to flow southeastward along the cyclonic circulation around the Japan Basin. And, then, the drifters moved to the east along $39-40^{\circ}N$. The mean surface current vector and mean speed were calculated in each lattice with $0.25^{\circ}$ grid spacing using the velocity data of surface drifters which passed through each lattice. The current variance ellipses were calculated with $0.5^{\circ}$ grid spacing. Because the path of the EKWC changes every year in the western part of the Ulleung Basin and the current paths in the Yamato Basin keep changing with many eddies, the current variance ellipses are relatively large in these region. We present a schematic map of the East Sea surface current based on the surface drifter data. The significance of this study is that the surface ocean circulation of the East Sea, which has been mainly studied by numerical model simulations and the sea surface height data obtained from satellite altimeters, was analyzed based on in-situ Lagrangian observational current data.

• Journal of the Korean Institute of Landscape Architecture
• /
• v.49 no.6
• /
• pp.80-92
• /
• 2021

Mount Tai, with an elevation of 1,532 meters, has a reputation as 'The Most Revered of the Five Sacred Mountains(五嶽獨尊)', despite not being the highest mountain in China. The literati of the past dynasties created a multitude of works based on the landscape of Mount Tai. Traditional literature is a part of national culture that directly reflects the national characteristics and styles, and is an important part of humanities, which can be linked to landscapes. The purpose of this study is to investigate the landscape elements and characteristics of Mount Tai by analyzing the landscape types and elements and the Kernel Density, Mean Center and Standard Deviational Ellipse of the landscape elements appearing in the representative poems of traditional literature. The research results of this study are summarized as follows. First, Mount Tai is a scenic spot dominated by human activities, different from the natural landscape of prior research related to scenic spots. Second, among the landscape elements of Mount Tai, the importance of "sunrise", "cyan", "towering" and "majestic", "Divine Dragon" is confirmed, symbolizing the hope, brightness, vitality, national stability and prosperity represented by Mount Tai, which can explain the leadership position of Mount Tai. Third, it can be found from the poems about Mount Tai that various landscape elements were embodied in belief (the behavior of gods or emperors) in the Pre-Qin, Sui and Tang dynasties, while in modern times, landscape elements are shown by action (climbing and looking far into distance), so it can be said that the landscape elements have changed from belief landscapes to experience landscapes. Fourth, the spatial distribution of landscape elements in the past dynasties was widely distributed in the Daiding(岱頂). Approaching the modern times, the mean center moved from south outside of Mount Tai to the summit of Mount Tai, and the spatial distribution changed from a widely scattered distribution to narrow linear distribution centered on Mount Tai. The present study is of great significance to provide key factors or spaces for future landscape protection and restoration of Mount Tai.

• Korean Journal of Mineralogy and Petrology
• /
• v.34 no.4
• /
• pp.241-253
• /
• 2021

Manganese nodules have been found in the shallow water depth of the Arctic Ocean as well as in the abyssal plains of the Pacific and Indian Oceans, but detailed study for them were rarely investigated. Manganese nodules, collected from the East Siberian Sea through the Arctic Expedition using Araon ice braking vessel, have a high potential for Mn mineral resources because they have high Mn content with high Mn/Fe ratio. This study investigated the external form, size and weight, internal texture for the non-spherical manganese nodule, which has about 7 % of total nodule from the East Siberian Sea. This study also researched the relative Mn-oxide mineral composition using the peak area ratio of X-ray diffraction pattern and their chemical composition. All data obtained from non-spherical nodules were compared with the spherical ones. Ellipsoidal, platy and irregular types are common among 5 groups of non-spherical manganese nodule based on the external form, and major axis and weight have positive relationship. All non-spherical manganese nodules have core mainly composed of mud sediments. The average Mn oxide mineral contents in nodules are birnessite, buserite and todorokite in descending order. Although mineral composition does not show any correlation with the external form, kind of core or internal structure, todorokite and buserite contents tend to increase and birnessite content decrease from the surface to the core in the nodule. Non-spherical manganese nodules have higher Mn content and Mn/Fe ratio than those from the shallow water depth of the Arctic Sea and even in the deep-sea of the Pacific and Indian Ocean. Although non-spherical nodule is larger and heavier, and has lower Mn content and Mn/Fe ratio than spherical nodule, there are not any differences in mineral composition and internal structure between them. Almost all manganese nodules collected from the East Siberian Sea are attributed to diagenetic process, because they are higher than 5 in Mn/Fe ratio.

• Economic and Environmental Geology
• /
• v.56 no.1
• /
• pp.1-11
• /
• 2023

In this study, we explore the morphological and geochemical characteristics for 440 manganese nodules collected from two different water depths [ARA12B-St52 (150 m, n = 239) and ARA12B-St58i (73 m, n = 201)] on the continental shelf of the East Siberian Sea from the ARA12B expedition in 2021. We also discussed the variations in the characteristics of manganese nodules with varying water depths in the Arctic Sea. The sizes of the nodules are generally greater than 3 cm at both sites. However, there is an obvious difference in the morphology with water depths. For the nodules collected at 150 m, brown-black colored tabular, tube, and ellipsoidal shapes with a rough surface texture are dominant. On the other hand, yellow-brown tabular shapes with a smooth surface texture are common for the nodules collected at 73 m. Furthermore, the slope of trend line between size and weight is significantly different at both sites: particularly, the slopes of nodules at 150 and 73 m are 1.60 and 0.84, respectively. This indicates the difference in the internal structure, porosity, and constituting elements between both nodules. Micro X-ray Flourescence (µ-XRF) results clearly demonstrate that the internal textures and chemical compositions are different with water depths. The nodules at 150 m are composed of a thick Mn-layer and a thin Fe-layer centered on the nucleus, while the nodules at 73 m are alternately grown with thin Mn- and Fe- layers around the nucleus. The average chemical compositions obtained by µ-XRF are 40.6 wt% Mn, 5.2 wt% Fe, and 7.9 Mn/Fe ratio at 150 m, and 10.3 wt% Mn, 19.0 wt% Fe, and 0.6 Mn/Fe ratio at 73 m. The chemical compositions of the nodules at 150 m are similar to those of nodules from the Peru Basin in the Pacific Ocean, while the compositions of the nodules at 73 m are similar to those of nodules from the Cook Islands or the Baltic Sea. The observed morphological and geochemical characteristics of the nodules show a clear difference at the two sites, which indicates that the aqueous conditions and formation processes of the nodules in the Arctic Sea vary with the water depths.

• The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
• /
• v.24 no.2
• /
• pp.267-281
• /
• 2019

Energetic mesoscale eddies in the East Sea (ES) associated with strong mesoscale variability impacting circulation and environments were statistically characterized by analyzing satellite altimeter data collected during 1993-2017 and in-situ data obtained from four cruises conducted between 2015 and 2017. A total of 1,008 mesoscale eddies were detected, tracked, and identified and then classified into 27 groups characterized by mean lifetime (L, day), amplitude (H, m), radius (R, km), intensity per unit area (EI, $cm^2/s^2/km^2$), ellipticity (e), eddy kinetic energy (EKE, TJ), available potential energy (APE, TJ), and direction of movement. The center, boundary, and amplitude of mesoscale eddies identified from satellite altimeter data were compared to those from the in-situ observational data for the four cases, yielding uncertainties in the center position of 2-10 km, boundary position of 10-20 km, and amplitude of 0.6-5.9 cm. The mean L, H, R, EI, e, EKE, and APE of the ES mesoscale eddies during the total period are $95{\pm}104$ days, $3.5{\pm}1.5cm$, $39{\pm}6km$, $0.023{\pm}0.017cm^2/s^2/km^2$, $0.72{\pm}0.07$, $23{\pm}21TJ$, and $588{\pm}250TJ$, respectively. The ES mesoscale eddies tend to move following the mean surface current rather than propagating westward. The southern groups (south of the subpolar front) have a longer L, larger H, R, and higher EKE, APE; and stronger EI than those of the northern groups and tend to move a longer distance following surface currents. There are exceptions to the average characteristics, such as the quasi-stationary groups (the Wonsan Warm, Wonsan Cold, Western Japan Basin Warm, and Northern Subpolar Frontal Cold Eddy groups) and short-lived groups with a relatively larger H, higher EKE, and APE and stronger EI (the Yamato Coastal Warm, Central Yamato Warm, and Eastern Japan Basin Coastal Warm eddy groups). Small eddies in the northern ES hardly resolved using the satellite altimetry data only, were not identified here and discussed with potential over-estimations of the mean L, H, R, EI, EKE, and APE. This study suggests that the ES mesoscale eddies 1) include newly identified groups such as the Hokkaido and the Yamato Rise Warm Eddies in addition to relatively well-known groups (e.g., the Ulleung Warm and the Dok Cold Eddies); 2) have a shorter L; smaller H, R, and lower EKE; and stronger EI and higher APE than those of the global ocean, and move following surface currents rather than propagating westward; and 3) show large spatial inhomogeneity among groups.