• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.591-611
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• 2001

In this paper, we classify elliptic curve by isomorphism classes over some finite fields. We consider finite field as a quotient ring, saying $\mathbb{Z}[i]/{\pi}\mathbb{Z}[i]$ where $\pi$ is a prime element in $\mathbb{Z}[i]$. Here $\mathbb{Z}[i]$ is the ring of Gaussian integers.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.6
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• pp.942-950
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• 1997

Far field acoustic pressure from the evolution and interaction of three-dimensional vortex filament is calculated numerically. A vortex ring is a typical example of the three-dimensional vortex filament. An elliptic vortex ring emits a strong sound signal due to significant distortion and stretching of the vortec filament. The far field acoustic pressure is linearly dependent on the third time derivatives of the vortex positions. A numerical scheme of high resolution is employed to describe in detail the elliptic vortex ring motions which ar highly nonlinear. Descretized vortex filaments are interpolated by using a parametric blending function to remove a possible numerical instability. The distorted vortex filament, owing to the self-induced and the induced velocity from the other vortex segments, is redistributed at each time step. The accuracy and efficiency of the scheme are validated by comparisons with the analytic solution of circular vortex ring interaction.

• ETRI Journal
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• v.33 no.5
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• pp.791-801
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• 2011

Security in wireless sensor networks (WSNs) is an upcoming research field which is quite different from traditional network security mechanisms. Many applications are dependent on the secure operation of a WSN, and have serious effects if the network is disrupted. Therefore, it is necessary to protect communication between sensor nodes. Key management plays an essential role in achieving security in WSNs. To achieve security, various key predistribution schemes have been proposed in the literature. A secure key management technique in WSN is a real challenging task. In this paper, a novel approach to the above problem by making use of elliptic curve cryptography (ECC) is presented. In the proposed scheme, a seed key, which is a distinct point in an elliptic curve, is assigned to each sensor node prior to its deployment. The private key ring for each sensor node is generated using the point doubling mathematical operation over the seed key. When two nodes share a common private key, then a link is established between these two nodes. By suitably choosing the value of the prime field and key ring size, the probability of two nodes sharing the same private key could be increased. The performance is evaluated in terms of connectivity and resilience against node capture. The results show that the performance is better for the proposed scheme with ECC compared to the other basic schemes.

• 한국IT서비스학회:학술대회논문집
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• 2009.05a
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• pp.205-208
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• 2009

이 논문에서는 RFID(Radio Frequency IDentification)에 대한 여러 가지 보안위협에 대하여 간단히 알아보고 그에 대응하는 안전한 암호학적 도구(Primitive)에 대하여 알아보겠다. 공개키 암호시스템(PKC, Public Key Cryptosystem)에 사용되는 타원곡선(EC, Elliptic Curve) 암호, NTRU(N-th degree TRUncated polynomial ring) 암호, Rabin 암호 등은 초경량 하드웨어 구현에 적합한 차세대 암호시스템으로서 안전한 RFID 인증서비스 제공과 프라이버시보호를 가능케 한다. 특히, 본고에서는 초경량 키의 길이, 저전력 소모성, 고속구현 속도를 갖는 타원곡선암호의 안전성에 대한 가이드라인을 제공하겠다.

• 한국ITS학회:학술대회논문집
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• 2004.11a
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• pp.306-310
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• 2004

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.131-146
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• 2018

We generate ring class fields of imaginary quadratic fields in terms of the special values of certain eta-quotients, which are related to the relative norms of Siegel-Ramachandra invariants. These give us minimal polynomials with relatively small coefficients from which we are able to solve certain quadratic Diophantine equations concerning non-convenient numbers.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.11 no.6
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• pp.105-113
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• 2001

Recently, Gallant, Lambert arid Vanstone introduced a method for speeding up the scalar multiplication on a family of elliptic curves over prime fields that have efficiently-computable endomorphisms. It really depends on decomposing an integral scalar in terms of an integer eigenvalue of the characteristic polynomial of such an endomorphism. In this paper, by using an element in the endomorphism ring of such an elliptic curve, we present an alternate method for decomposing a scalar. The proposed algorithm is more efficient than that of Gallant\`s and an upper bound on the lengths of the components is explicitly given.

• Journal of the Korean Institute of Telematics and Electronics
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• v.19 no.3
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• pp.13-18
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• 1982

This Paper is an experimental study on the effective dielectric constant of microstrip line. To quantify the dispersive effects on a microstrip line, the effective dielectric constant, which is the ratio of free space wavelength to guide wavelength, is calculated for teflon substrates. The calculation is based on the Fourier transform of the current distribution on microstrip line. Measurements of effective dielectric constant using a microstrip elliptic resonator and ring resonator are also described. As a result, the computed values of effective dielectric constant agree almost all with measured values, using ring and elliptic resonator, in case of w/h or the ratio of microstrip width to substrate thickness equal unity over frequency range of 8 to 12GHz.

• 한국전산유체공학회:학술대회논문집
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• 2008.03b
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• pp.312-315
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• 2008

The flow structure behind circular and elliptical type rings embedded in a cross-flow was investigated experimentally using two-frame particle image velocimetry (PIV). The experiments were performed in a circulating water channel with a test section of 0.35m height ${\times}$ 0.3m width ${\times}$ 1.1m length. PIV measurements were carried out with varying the Reynolds number in the range of 4.5 ${\times}$ $10^2$ - 4.5 ${\times}$ $10^3$. In the present study, turbulent flow structures in the stream-wise direction and span-wise direction were investigated. The mean velocity field distribution was obtained by statistical-averaging instantaneous velocity fields. The spatial distributions of turbulent statistics such as turbulent intensities and turbulent kinetic energy were also investigated.

• Structural Engineering and Mechanics
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• v.4 no.5
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• pp.469-484
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• 1996

Green's functions are obtained in exact closed-forms for the elastic fields in bi-material elastic solids with slipping interface and differing transversely isotropic properties induced by concentrated point and ring force vectors. For the concentrated point force vector, the Green functions are expressed in terms of elementary harmonic functions. For the concentrated ring force vector, the Green functions are expressed in terms of the complete elliptic integral. Numerical results are presented to illustrate the effect of anisotropic bi-material properties on the transmission of normal contact stress and the discontinuity of lateral displacements at the slipping interface. The closed-form Green's functions are systematically presented in matrix forms which can be easily implemented in numerical schemes such as boundary element methods to solve elastic problems in computational mechanics.