• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.101-109
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• 2012

In this paper, we present an algorithm for computing the number of points on the Jacobian varieties of one-dimensional family of genus 3 nonhyperelliptic curves over finite fields. We also provide the explicit formula of the characteristic polynomial of the Frobenius endomorphism of the Jacobian of $C:y^3=x^4+{\alpha}$ over a finite field $\mathbb{F}_p$ with $p{\equiv}1$ (mod 3) and $p{\neq}1$ (mod 4). Moreover, we give some implementation results using Gaudry-Schost method. A 162-bit order is computed in 97 s on a Pentium IV 2.13 GHz computer using our algorithm.

• Journal of Information Processing Systems
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• v.8 no.1
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• pp.145-158
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• 2012

Hyperelliptic Curve Cryptosystem (HECC) is well suited for all kinds of embedded processor architectures, where resources such as storage, time, or power are constrained due to short operand sizes. We can construct genus 3 HECC on 54-bit finite fields in order to achieve the same security level as 160-bit ECC or 1024-bit RSA due to the algebraic structure of Hyperelliptic Curve. This paper explores various possible attacks to the discrete logarithm in the Jacobian of a Hyperelliptic Curve (HEC) and addition and doubling of the divisor using explicit formula to speed up the scalar multiplication. Our aim is to develop a cryptosystem that can sign and authenticate documents and encrypt / decrypt messages efficiently for constrained devices in wireless networks. The performance of our proposed cryptosystem is comparable with that of ECC and the security analysis shows that it can resist the major attacks in wireless networks.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1365-1374
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• 2023

Let F be a periodic singular fiber of genus g with dual fiber F^*, and let T (resp. T^*) be the set of the components of F (resp. F^*) by removing one component with multiplicity one. We give a formula to compute the determinant | det T | of the intersect form of T. As a consequence, we prove that | det T | = | det T^*|. As an application, we compute the Mordell-Weil group of a fibration f : S → ℙ¹ of genus 2 with two singular fibers.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.903-931
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• 1998

Since the modular curves X(N) = $\Gamma$(N)\(equation omitted)＊ (N =1,2,3) have genus 0, we have field isomorphisms K(X(l))(equation omitted)C(J), K(X(2))(equation omitted)(λ) and K(X(3))(equation omitted)( $j_3$) where J, λ are the classical modular functions of level 1 and 2, and $j_3$ can be represented as the quotient of reduced Eisenstein series. When N = 4, we see from the genus formula that the curve X(4) is of genus 0 too. Thus the field K(X(4)) is a rational function field over C. We find such a field generator $j_4$(z) = x(z)/y(z) (x(z) = $\theta$$_3$((equation omitted)), y(z) = $\theta$$_4$((equation omitted)) Jacobi theta functions). We also investigate the structures of the spaces $M_{k}$($\Gamma$(4)), $S_{k}$($\Gamma$(4)), M(equation omitted)((equation omitted)(4)) and S(equation omitted)((equation omitted)(4)) in terms of x(z) and y(z). As its application, we apply the above results to quadratic forms.rms.

• Journal of Species Research
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• v.1 no.1
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• pp.56-67
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• 2012

During a study of harpacticoid copepods from Korea, one species of the family Orthopsyllidae was found by rinsing macroalgae collected from the intertidal and subtidal zones at Hangaechang, Munseum Islet in Jeju Island of Korea. The Orthopsyllus is closely related to Orthopsyllus linearis curvaspinata Mielke, 1993, however it is distinguished from the original description by the combined characters of slightly slender caudal seta V in the female, relatively short and ovoid caudal ramus, the seta formula of P3, and the length of P2 and P4 endopod in the male. Since Orthopsyllus linearis (Claus, 1866) is notorious for its incomplete previous descriptions and therefore its polymorphic status, it is premature to fix the status of present Orthopsyllus species from Korea, without the detailed comparative study among the congeners. However due to the urgent need for the report of the genus in the region, we report this species as Orthopsyllus linearis (Claus, 1866) like but different one within the genus: Orthopsyllus cf. linearis (Claus,1866). This is the first report of the genus Orthopsyllus for the first time in Korea.

• Journal of Species Research
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• v.1 no.2
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• pp.156-174
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• 2012

Monchenkocyclops gen. nov. was erected to accommodate M. changi sp. nov. from South Korea (type species), M. mirabdullayevi sp. nov. from Kazakhstan, M. biarticulatus (Monchenko, 1972) comb. nov. from Uzbekistan, and M. biwensis (Ishida, 2005) comb. nov. from Japan. The latter species was originally described from surface-water habitats of the ancient Lake Biwa in the genus Diacyclops Kiefer, 1927, while two Central Asian species were previously collected from groundwater habitats and assigned to the genus Acanthocyclops Kiefer, 1927. Monchenkocyclops changi is also found in subterranean waters, and described here in detail. It is morphologically most similar to its Uzbek congener (not to the Japanese one), which rises some interesting zoogeographical questions about the disjunct distribution of this genus. Range fragmentation is a more plausible explanation for this distribution pattern than range expansion, and we emphasize four lines of evidence that support this hypothesis. Four species of Monchenkocyclops share not only the same segmentation of the swimming legs, but also the exact same armature formula of all swimming legs, in addition to many other morphological characters, such as the caudal rami shape and armature, absence of exopod on the antenna, similar shape of the seminal receptacle, fifth leg, etc. They can be distinguished mostly by the relative length of different armature elements, such as the innermost terminal caudal setae, and inner setae and apical spines on the third endopodal segment of the fourth leg. A dichotomous key to species is provided.

• Animal cells and systems
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• v.4 no.4
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• pp.319-324
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• 2000

Species boundaries among the Alcyonacean soft coral, the genus Dendronephthya, are often obscured by inter- and intraspecific morphological variations. In the present study, we attempted to infer the genetic relationships of eight dendronephthians based on their molecular characters, the internal transcribed spacer (ITS) regions of ribosomal DNA, and then compared this result together with the random amplified polymorphic DNA (RAPD) data from our previous investigation. Dendronephthya. putteri and D. suensoni formed a divaricate form - VI grade specific clade, whereas D. castanea, D. gigantea, D. aurea and D. spinifera, formed a umbellate and glomerate form - IV and III grade specific clade. Therefore, we confirmed that the main characters the growth form and the anthocodial grade and formula, are important in identification of the species in dendronephthians despite some problems. Also, the relationships of the growth form are clarified as the glomerate form is much closer to the umbellate form than to the divaricate form based on two sets of independent molecular data. However, we cannot determine the molecular markers which limit the species boundaries among this genus with ITS sequences.

• Journal of Plant Biology
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• v.37 no.2
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• pp.245-252
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• 1994

Pollens of 20 species of Sedum were investigated with a scanning electron microscope. The pollen morphology of Sedum was rather variable, within particular species or even within a single inflorescence. Differences occurred in the number and shape of apertures and surface sculpture. Besides 3-colporate, various aperture types including 2-syncolporate, 3-syncolporate, 40stephanocolporate, 5-stephanocolporate, zonate, and irregular types were found in a single specimen. Also, striate-rugulose and psilate sculpture were found in S. viviparum. No correlation was found between the pollen morphology and the floral formula. Pollen characters appeared to be not useful for infrageneric classification of Korean Sedum.

• Herbal Formula Science
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• v.24 no.4
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• pp.323-333
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• 2016

Objectives : The purpose of this study was to investigate musk deer in taxonomic status and genus species. We investigated the characteristic of musk deer for medicinal usages. Methods : To identifications of musk deer on the taxonomic status and genus species, the literary investigation were conducted on the Korean, China, and Japan pharmacopoeia and published herbal books, CITES Species Lists too. Results : Musk deer placement in a separate family status is the Moschidae. M. chrysogaster Hodgson and M. sifanicus Przewalski was the same species. So, Alpine musk deer revised M. chrysogaster Hodgson[=M. sifanicus Przewalski]. Geographic distribution of M. moschiferus L. divided Sibirica group and himalaica group. Group himalaica contains three subspecies: Korean musk deer(M. moschiferus parvipes Hol.), Chinese musk deer(M. chrysogaster Hodgson), and Himalayan musk deer(M. leucogaster Hodgson). The genetic divergence between M. moschiferus L. and other species was clearly distinguished from the others. M. berezovskii Flerove was less than the others. However, the divergence among M. chrysogaster Hodgson, M. fuscus Li, and M. leucogaster Hodgson were quite low. Musk deers are mostly distributed around the high-plateau. Moschus were from Nepal, Bhutan, Russia, China. Forest musk deer(M. berezovskii Flerove) farming was conducted in China from 1950s. In the Korean hebal pharmacopoeia, Moschus include l-muscone($C_{16}H_{30}O$ : 238.40) over 2% for quantitative test. Conclusions : There are three species of musk deer, Siberian musk deer(M. moschiferus L.), forest musk deer(M. berezovskii Flerove), and Alpine musk deer(M. chrysogaster Hodgson) for medicinal usages.

• Korean Journal of Microbiology
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• v.55 no.3
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• pp.268-273
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• 2019

The intestinal microbiomes vary according to the factors such environment, age and diet. The purpose of this study was to compare the gut microbial diversity between Korean infants receiving breast-fed milk and formula-fed milk. We analyzed microbial communities in stool samples collected from 80 Korean infants using next generation sequencing. Phylum level analysis revealed that microbial communities in both breast-fed infants group (BIG) was dominated by Actinobacteria ($74.22{\pm}3.48%$). Interestingly, the phylum Actinobacteria was dominant in formula-fed infants group A (FIG-A) at $73.46{\pm}4.12%$, but the proportions of phylum Actinobacteria were lower in formulafed infants group B and C (FIG-B and FIG-C) at $66.52{\pm}5.80%$ and $68.88{\pm}4.33%$. The most abundant genus in the BIG, FIG-A, FIG-B, and FIG-C was Bifidobacterium, comprising $73.09{\pm}2.31%$, $72.25{\pm}4.93%$, $63.81{\pm}6.05%$, and $67.42{\pm}5.36%$ of the total bacteria. Furthermore, the dominant bifidobacterial species detected in BIG and FIG-A was Bifidobacterium longum at $68.77{\pm}6.07%$ and $66.85{\pm}4.99%$ of the total bacteria. In contrast, the proportions of B. longum of FIG-B and FIG-C were $58.94{\pm}6.20%$ and $61.86{\pm}5.31%$ of the total bacteria. FIG-A showed a community similar to BIG, which may be due to the inclusion of galactooligosaccharide, galactosyllactose, synergy-oligosaccharide, bifidooligo and improvement material of gut microbiota contained in formula-milk. We conclude that 5-Bifidus factor contained in milk powder promotes the growth of Bifidobacterium genus in the intestines.