• The Journal of Korean Institute of Communications and Information Sciences
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• v.37A no.12
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• pp.1031-1037
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• 2012

We study an algorithm that can efficiently find square roots and cube roots by modifying Tonelli-Shanks algorithm, which has an application in Number Field Sieve (NFS). The Number Field Sieve, the fastest known factoring algorithm, is a powerful tool for factoring very large integer. NFS first chooses two polynomials having common root modulo N, and it consists of the following four major steps; 1. Polynomial Selection 2. Sieving 3. Matrix 4. Square Root. The last step of NFS needs the process of square root computation in Number Field, which can be computed via square root algorithm over finite field.

• East Asian mathematical journal
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• v.35 no.1
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• pp.85-90
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• 2019

In this paper, we are interested in the evaluation of special values of the Dedekind zeta function of a totally real number field. In particular, we revisit Siegel method for values of the zeta function of a totally real number field at negative odd integers and explain how this method is applied to the case of non-normal totally real number field. As one of its applications, we give divisibility property for the values in the special case

• The Journal of the Korea institute of electronic communication sciences
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• v.12 no.6
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• pp.1181-1188
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• 2017

The unit and fundamental units of number fields are important to number field sieves testing primality of more than 400 digits integers and number field seive factoring the number in RSA cryptosystem, and multiplication of ideals and counting class number of the number field in imaginary quadratic cryptosystem. To minimize the time and space in H/W implementation of cryptosystems using fundamental units, in this paper, we introduce the Dirichlet's unit Theorem and propose our process of generating the fundamental units of the number field. And then we present the algorithm generating our fundamental units of the number field to minimize the time and space in H/W implementation and implementation results using the algorithm over the number field.

• Progress in Superconductivity and Cryogenics
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• v.17 no.2
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• pp.31-35
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• 2015

Mapping is a useful tool in the magnetic field analysis and design. In some specific research area, such as the nuclear magnetic resonance (NMR) or the magnetic resonance imaging (MRI), it is important to map the magnetic field in the interesting space with high accuracy. In this paper, an indirect mapping method in the center volume of an air-core solenoid is presented, based on the solution of the Laplace's equation for the field. Through the mathematical analysis on the mapping calculation, we know that the condition number of the matrix, generated by the measurement points, can greatly affect the error of mapping result. Two different arrangement methods of the measurement points in field mapping are described in this paper: helical cylindrical line (HCL) method and parallel cylindrical line (PCL) method. According to the condition number, the HCL method is recommended to measure the field components using one probe. As a simple example, we mapped the magnetic fields in a MRI main magnet system. Comparing the results in the different methods, it is feasible and convenient to apply the condition number to reduce the error in the field mapping calculation. Finally, some guidelines were presented for the magnetic field mapping in the center volume of the air-core solenoid.

• Journal of the Korean Wood Science and Technology
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• v.21 no.4
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• pp.60-63
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• 1993

In the present paper, we discribed distributions patterns of pits on the tracheids of Pinus koraiensis. The number of bordered pits on a tracheid is more numerous than that of cross-field pittings. And they appeared different in the number depending on the shape and size of tracheids. Both pit and cross-field pitting on a tracheid is fewer in number near the pith. The number of bordered pits on the tracheid increased rapidly from pith toward cambial zone but that of cross-field pittings increased gradually. The number of bordered pit and corss-field pitting is more frequent in the first-formed tracheid, and the number of bordered pit decreased rapidly from earlywood to latewood but that of corss-field pittings decreased gradually. Bordered pits on a tracheid are more numerous at the end of tracheids and cross-field pittings occur more frequently in the center part of a tracheid.

• Journal of Ocean Engineering and Technology
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• v.15 no.3
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• pp.28-34
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• 2001

The experimental studies for the artificial reef (AFR) subsidence characteristics in the unsteady flow field and in the unsteady flow-wave field were carried out. The difference of scou $r_sidence characteristics between in the steady flow field and in the unsteady flow field wad discussed and also the long-term subsidence characteristics in the unsteady flow field were investigated. AFR subsidence characteristics was discussed with Keulegan - Carpenter number(KC), Reynolds number (Re),. Shields number (Sn) and dimensionless time (t/Tt). And the difference of subsidence characteristics between in the unsteady flow and in the unsteady flow-wave field was discussed.ed.

• Journal of Ocean Engineering and Technology
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• v.15 no.3
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• pp.29-29
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• 2001

The experimental studies for the artificial reef (AFR) subsidence characteristics in the unsteady flow field and in the unsteady flow-wave field were carried out. The difference of scour/subsidence characteristics between in the steady flow field and in the unsteady flow field wad discussed and also the long-term subsidence characteristics in the unsteady flow field were investigated. AFR subsidence characteristics was discussed with Keulegan - Carpenter number(KC), Reynolds number (Re),. Shields number (Sn) and dimensionless time (t/Tt). And the difference of subsidence characteristics between in the unsteady flow and in the unsteady flow-wave field was discussed.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.375-384
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• 2008

Let $k={\mathbb{F}}_q(T)$ and ${\mathbb{A}}={\mathbb{F}}_q[T]$. Fix a prime divisor ${\ell}$ q-1. In this paper, we consider a ${\ell}$-cyclic real function field $k(\sqrt[{\ell}]P)$ as a subfield of the imaginary bicyclic function field K = $k(\sqrt[{\ell}]P,\;(\sqrt[{\ell}]{-Q})$, which is a composite field of $k(\sqrt[{\ell}]P)$ wit a ${\ell}$-cyclic totally imaginary function field $k(\sqrt[{\ell}]{-Q})$ of class number one. und give various conditions for the class number of $k(\sqrt[{\ell}]{P})$ to be one by using invariants of the relatively cyclic unramified extensions $K/F_i$ over ${\ell}$-cyclic totally imaginary function field $F_i=k(\sqrt[{\ell}]{-P^iQ})$ for $1{\leq}i{\leq}{\ell}-1$.

• Journal of Korean Vacuum Science & Technology
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• v.3 no.1
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• pp.10-15
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• 1999

Using micro-wells on the Mo substrate, we could obtain various tubular-volcano-types of free-standing diamond field emitters by depositing a diamond film detaching the film and turning the film upside down. The field emission characteristics of these structures were investigated as a function of size, shape and the number density of the tubular-volcano-type diamond field emitters. The field emission characteristics, especially the current density, were greatly enhanced with increasing the number density of the tubular-volcano-type diamond field emitters on the Mo substrate. Based on these results, we suggest that the reduction of the well size can give better field emission characteristics by the increase in the number density of the tubular-volcano-type diamond field emitters. Finally, we suggest the feasibility of fabricating a large-area field emission display using our patterned tubular-volcano-type free-standing diamond field emitters.

• Transactions of the Korean Society of Automotive Engineers
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• v.4 no.3
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• pp.1-9
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• 1996

This study investigated torque characteristics for Couette flow experimentally under circumstaces that ferrofluids were between two coaxial spheres. Torque measurement was obtained for the situation where the inner sphere was rotating while the outer sphere was kept stationary. The magnetic field was imposed on the fluid, using a bar magnet which was inserted in the inner sphere. In the laminar flow region the torque increase when the magnetic field is applied and the critical Reynolds number is increased. However, in the transition regime, the effect of the magnetic field on the torque characteristics decrease as Reynolds number increases. The value of torque were the same as those of glycerine solution beyond the cirtical Reynolds number. We also made experimental equation which could obtain coefficient of torque within critical Reynolds number in terms of sphere spacing Reynolds number and magnetic properties of ferrofluid.