• Honam Mathematical Journal
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• v.26 no.3
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• pp.247-256
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• 2004

Buchmann and Williams[1] proposed a key exchange system making use of the properties of the maximal order of an imaginary quadratic field. $H{\ddot{u}}hnlein$ et al. [6,7] also introduced a cryptosystem with trapdoor decryption in the class group of the non-maximal imaginary quadratic order with prime conductor q. Their common techniques are based on the properties of the invertible ideals of the maximal or non-maximal orders respectively. Kim and Moon [8], however, proposed a key-exchange system and a public-key encryption scheme, based on the class semigroups of imaginary quadratic non-maximal orders. In Kim and Moon[8]'s cryptosystem, a non-invertible ideal is chosen as a generator of key-exchange ststem and their secret key is some characteristic value of the ideal on the basis of Zanardo et al.[9]'s quantity for ideal equivalence. In this paper we propose the methods for finding the non-invertible ideals corresponding to non-primitive quadratic forms and clarify the structure of the class semigroup of non-maximal order as finitely disjoint union of groups with some quantities correctly. And then we correct the misconceptions of Zanardo et al.[9] and analyze Kim and Moon[8]'s cryptosystem.

• The Journal of the Korea institute of electronic communication sciences
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• v.6 no.1
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• pp.90-96
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• 2011

In this paper, we propose a new discrete logarithm problem(DLP) based on the class semigroups of imaginary quadratic non-maximal orders using the special character of non-invertible ideal and analysis its security. To do this, we first explain the mathematical background explicitly and prove some properties of Cls (O) which relate to constructing the DLP and guaranteeing the security. To test the security of the proposed DLP, we compare the class number of the maximal order with that of the non-maximal order and investigate the unique factorization problems of ideals between class groups of the maximal orders and class semigroups of non-maximal orders to ensure the security of the cryptosystem.

• The Journal of the Korea institute of electronic communication sciences
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• v.4 no.4
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• pp.270-273
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• 2009

In 1988, Buchmann et al. proposed a public key cryptosystem making use of ideals of the maximal orders in quadra tic fields which may pave the way for a public key cryptosystem using imaginary quadratic non-invertible ideals as generators. Next year, H$\ddot{u}$hnlein, Tagaki et al. published the cryptosystem with trapdoor and conductor prime p over non-maximal orders. On the other hand Kim and Moon proposed a public key cryptosystrem and a key distribution cry ptotsystem over class semigroup in 2003. We, in this paper, introduce and analyze the cryptotsystems mentioned above.

• The Korean Journal of Physiology
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• v.1 no.1
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• pp.91-101
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• 1967

The maximal oxygen intake (MOI) was determined in 54 males (23 nonathletes, 10 basketball players, 8 hand ball players, 7 weight lifters and 6 long distance runners) and in 49 females (24 non-athletes, 16 basketball players and 9 volley ball players) by using a treadmill method outlined in Part I of the present investigation and the following results were obtained: (1) The maximal aerobic work capacity varied from the lowest value of 1,008 kg-m/min in female non-athletes to the highest value of approximately 2,000 kg-m/min in male basketball players and long distance runners. Values of other groups varied from 1,400 kg-m/min in male non-athletes and female athletes to 1,800 kg-m/min in male hand ball players. (2) The MOI per unit body weight varied from the lowest value of 41.3 ml/min/kg in female non-athletes to the highest value of 67.6 ml/min/kg in male long distance runners. Values of other groups were in the order of 47 to 55 ml/min/kg. (3) The heart rate during maximal aerobic work performance varied from the lowest value of approximately 180 per min in female basketball players and male long distance runners to the highest value of 190 or above in nonathletes of both sexes. (4) An estimate of oxygen debt as measured during 15 minutes following the maximal work was 3.841 in female non-athletes, 4.681 in female athletes, 5.561 in male non-athletes and 6.321 in male athletes. These results indicate that the MOI per unit body weight as well as the oxygen debt of Korean non-athletes were comparable to, while corresponding values of Korean athletes were considerably lower than, those of other countries such as Japan, the United States of America and Europe.

• Communications of the Korean Mathematical Society
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• v.21 no.3
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• pp.577-586
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• 2006

In this paper we will propose the methods for finding the non-invertible ideals corresponding to non-primitive quadratic forms and clarify the structures of class SEMIGROUPS of imaginary quadratic orders which were given by Zanardo and Zannier [8], and we will give a general algorithm for calculating power of ideals/classes via the Dirichlet composition of quadratic forms which is applicable to cryptography in the class semigroup of imaginary quadratic non-maximal order and revisit the cryptosystem of Kim and Moon [5] using a Zanardo and Zannier [8]'s quantity as their secret key, in order to analyze Jacobson [7]'s revised cryptosystem based on the class semigroup which is an alternative of Kim and Moon [5]'s.

• Honam Mathematical Journal
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• v.28 no.2
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• pp.185-196
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• 2006

A scheme based on the cryptography for enforcing multilevel security in a system where hierarchy is represented by a partially ordered set was first introduced by Akl et al. But the key generation algorithm of Akl et al. is infeasible when there is a large number of users. In 1985, MacKinnon et al. proposed a paper containing a condition which prevents cooperative attacks and optimizes the assignment in order to overcome this shortage. In 2005, Kim et al. proposed key management systems for multilevel security using one-way hash function, RSA algorithm, Poset dimension and Clifford semigroup in the context of modern cryptography. In particular, the key management system using Clifford semigroup of imaginary quadratic non-maximal orders is based on the fact that the computation of a key ideal $K_0$ from an ideal $EK_0$ seems to be difficult unless E is equivalent to O. We, in this paper, show that computing preimages under the bonding homomorphism is not difficult, and that the multilevel cryptosystem based on the Clifford semigroup is insecure and improper to the key management system.

• Applied Science and Convergence Technology
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• v.27 no.5
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• pp.86-89
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• 2018

Observations of neutrino oscillations are very strong evidence for the existence of neutrino masses and mixing. From recent experimental results on neutrino oscillation, we find that neutrino mixing angles are quite consistent with the so-called tri-bi-maximal mixing pattern, but the deviation from observational results is non-negligible. However, the tri-bi-maximal mixing pattern is still useful as a leading order approximation and provides a good guideline to search for the flavor symmetry in the neutrino sector. We introduce the $S_4$ permutation symmetry as a flavor symmetry to the standard model of particle physics with additional particle contents of heavy right-handed neutrinos and scalar fields. Finally, we obtain the tri-bi-maximal mixing pattern as a mixing matrix in the lepton sector within the suggested model. To derive the required unitary mixing matrix for the neutrino sector, the double seesaw mechanism is utilized.

• Communications for Statistical Applications and Methods
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• v.25 no.5
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• pp.453-470
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• 2018

We study how to distinguish the parameters of the sparse autoregressive (AR) process from zero using a non-convex penalized estimation. A class of non-convex penalties are considered that include the smoothly clipped absolute deviation and minimax concave penalties as special examples. We prove that the penalized estimators achieve some standard theoretical properties such as weak and strong oracle properties which have been proved in sparse linear regression framework. The results hold when the maximal order of the AR process increases to infinity and the minimal size of true non-zero parameters decreases toward zero as the sample size increases. Further, we construct a practical method to select tuning parameters using generalized information criterion, of which the minimizer asymptotically recovers the best theoretical non-penalized estimator of the sparse AR process. Simulation studies are given to confirm the theoretical results.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.643-647
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• 2013

Let G be a group and let $p$ be a prime number. If the set $\mathcal{A}(G)$ of all commuting automorphisms of G forms a subgroup of Aut(G), then G is called $\mathcal{A}(G)$-group. In this paper we show that any $p$-group with cyclic maximal subgroup is an $\mathcal{A}(G)$-group. We also find the structure of the group $\mathcal{A}(G)$ and we show that $\mathcal{A}(G)=Aut_c(G)$. Moreover, we prove that for any prime $p$ and all integers $n{\geq}3$, there exists a non-abelian $\mathcal{A}(G)$-group of order $p^n$ in which $\mathcal{A}(G)=Aut_c(G)$. If $p$ > 2, then $\mathcal{A}(G)={\cong}\mathbb{Z}_p{\times}\mathbb{Z}_{p^{n-2}}$ and if $p=2$, then $\mathcal{A}(G)={\cong}\mathbb{Z}_2{\times}\mathbb{Z}_2{\times}\mathbb{Z}_{2^{n-3}}$ or $\mathbb{Z}_2{\times}\mathbb{Z}_2$.

• Fisheries and Aquatic Sciences
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• v.20 no.7
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• pp.13.1-13.7
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• 2017

In order to evaluate the maximal storable period of the raw crab for a non-thermal muscle separation, the quality changes of the leg meat of red snow crab (Chionoecetes japonicus) during freeze storage were investigated. Fresh red snow crabs were stored at $-20^{\circ}C$ for 7 weeks, and the leg muscle was separated by a no heating separation (NHS) method every week. During the storage, considerable loss of the leg muscle did not occur and microbiological risk was very low. In contrast, discoloration appeared at 2-week storage on around carapace and the leg muscle turned yellow at storage 3-week. In physiochemical parameters, protein and free amino acids gradually decreased with storage time, expected that proteolytic enzymes still activated at $-20^{\circ}C$. At 4-week storage, the sensory acceptance dropped down below point 4 as low as inedible and notable inflection points in pH and acidity were observed. The volatile base nitrogen was low, though a little increase was recorded. These results suggested that the maximal storable period at $-20^{\circ}C$ of the raw material was within 2 weeks and it was depended on external factor such as the discoloration. The present study might be referred as basic data for approaches to solve quality loss occurred in non-thermal muscle separation.