• Journal of applied mathematics & informatics
• /
• 제8권2호
• /
• pp.591-611
• /
• 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.

• 대한기계학회논문집A
• /
• 제21권6호
• /
• pp.942-950
• /
• 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
• /
• 제33권5호
• /
• pp.791-801
• /
• 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
• /
• 한국IT서비스학회 2009년도 춘계학술대회
• /
• pp.205-208
• /
• 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
• /
• 한국ITS학회 2004년도 제3회 정기총회 및 추계학술대회
• /
• pp.306-310
• /
• 2004

• 대한수학회지
• /
• 제55권1호
• /
• pp.131-146
• /
• 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.

• 정보보호학회논문지
• /
• 제11권6호
• /
• pp.105-113
• /
• 2001

최근에 Gallant, Lambert, Vanstone은 소수체 위에 정의된 타원곡선이 효율적으로 계산 가능한 자기준동형을 가질 때 스칼라 곱을 가속화하는 방법을 제안하였다. 이 방법은 실제로 자기준동형의 특성다항식의 고유치를 사용하여 스칼라를 분해하는데 기반을 두고 있다. 본 논문에서는 그러한 타원곡선의 자기준동형 환의 원소를 이용하여 스칼라를 분해하는 개선된 알고리즘을 제안한다. 이 알고리즘은 Gallant 등의 알고리즘보다 속도면에서 효율적이며 분해성분들의 구체적인 상한 값을 줄 수 있다.

• 대한전자공학회논문지
• /
• 제19권3호
• /
• pp.13-18
• /
• 1982

본 논문은 마이크로스트립 선로의 실효 유전률에 관한 실험적인 연구이다. 자유 공간 파장대 관내 파장비의 2승으로 주어지는 실효 유전률을 테프론 유전체판으로 만든 공진기의 공진 현상을 이용하여서 측정하고 이것과 마이로스트립 선로상의 전류 분포를 Fourier 변환하여서 얻은 이론 계산치와를 비교 고찰하여 제작된 원형및 타원형 공진기로 부터 얻어진 실험치와 이론치가 8∼12GHz범위의 X-Band에서 # =1일때 거의 일치하는 결과를 얻을 수 있었다.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2008년도 춘계학술대회논문집
• /
• pp.312-315
• /
• 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
• /
• 제4권5호
• /
• pp.469-484
• /
• 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.