• Proceedings of the Jangjeon Mathematical Society
• /
• 제20권2호
• /
• pp.183-191
• /
• 2017

We get one theorem that there exist solutions for the fourth order semi- linear elliptic Dirichlet boundary value problem with fully nonlinear term. We prove this result by the critical point theory and the variation of linking method.

• Journal of Communications and Networks
• /
• 제4권2호
• /
• pp.81-89
• /
• 2002

In this paper, we design and implement an efficient fair off-line electronic cash system based on Elliptic Curve Discrete Logarithm Problem (ECDLP), in which the anonymity of coins is revocable by a trustee in case of dispute. To achieve this, we employ the Petersen and Poupard s electronic cash system [1] and extend it by using an elliptic curve over the finite field GF($2^n$). This naturally reduces message size by 85% compared with the original scheme and makes a smart card to store coins easily. Furthermore, we use the Baek et al. s provably secure public key encryption scheme [2] to improve the security of electronic cash system. As an extension, we propose a method to add atomicity into new electronic cash system. To the best of our knowledge, this is the first result to implement a fair off-line electronic cash system based on ECDLP with provable security.

• Nonlinear Functional Analysis and Applications
• /
• 제28권3호
• /
• pp.613-622
• /
• 2023

In this paper, finite element method is applied to solve boundary control problem governed by elliptic variational inequality with an infinite number of variables. First, we introduce some important features of the finite element method, boundary control problem governed by elliptic variational inequalities with an infinite number of variables in the case of the control and observation are on the boundary is introduced. We prove the existence of the solution by using the augmented Lagrangian multipliers method. A triangular type finite element method is used.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2001년도 하계학술대회 논문집 D
• /
• pp.2576-2578
• /
• 2001

Elliptic curve cryptosystems based on discrete logarithm problem in the group of points of an elliptic curve defined over a finite field. The discrete logarithm in an elliptic curve group appears to be more difficult than discrete logarithm problem in other groups while using the relatively small key size. An implementation of elliptic curve cryptosystems needs finite field arithmetic computation. Hence finite field arithmetic modules must require less hardware resources to archive high performance computation. In this paper, a new architecture of finite field multiplier using conversion scheme of normal basis representation into polynomial basis representation is discussed. Proposed architecture provides less resources and lower complexity than conventional bit serial multiplier using normal basis representation. This architecture has synthesized using synopsys FPGA express successfully.

• 대한수학회지
• /
• 제36권2호
• /
• pp.355-367
• /
• 1999

We prove the existence of 2N-1 distinct ordered positive solutions of a class of semilinear elliptic Dirichlet boundary value problems on Rn when the forcing term has N distinct positive stable zeros and the coefficient function decaying to the zero at infinity.

• 대한수학회보
• /
• 제38권2호
• /
• pp.237-260
• /
• 2001

The approximation properties for $L^2$-projection, Raviart-Thomas projection, and inverse inequality have been derived in 3 dimensional space. h-p-mixed finite element methods for strongly nonlinear second order elliptic problems are proposed and analyzed in 3D. Solvability and convergence of the linearized problem have been shown through duality argument and fixed point argument. The analysis is carried out in detail using Raviart-Thomas-Nedelec spaces as an example.

• 충청수학회지
• /
• 제27권4호
• /
• pp.707-720
• /
• 2014

We get a theorem which shows the existence of at least three solutions for some elliptic system with Dirichlet boundary condition. We obtain this result by using the finite dimensional reduction method which reduces the infinite dimensional problem to the finite dimensional one. We also use the critical point theory on the reduced finite dimensioal subspace.

• 한국정보통신학회:학술대회논문집
• /
• 한국정보통신학회 2017년도 추계학술대회
• /
• pp.581-583
• /
• 2017

새로운 암호화 알고리즘인 ECC (Elliptic Curve Cyptography)는 elliptic curves을 기반으로 하며, 포인트 연산과 Elliptic Curve Discrete Logarithm Problem (ECDLP)을 포함한다. ECDLP는 쉬운 키 생성과 단방향 암호화, 키의 역생성이 불가능한 특징을 가지고 있다. 이러한 ECDLP의 특징은 개인정보 보호에 매우 강하다. 본 논문에서 제안하는 경량 ECDH 키 생성기 하드웨어는 Elliptic Curve Integrated Encryption Scheme (ECIES) 및 키 공유에 사용할 수 있는 163 비트 공유키를 생성한다. 제안하는 하드웨어 구조에서는 작은 고속 곱셈 알고리즘을 사용하여 확장된 유클리드 알고리즘을 구현했다. 제안하는 하드웨어 구조는 Verilog HDL을 사용하여 설계되었으며, vivado ISE 2016.3과 virtex-7 FPGA 보드를 통해 구현하였다.

• Korean Journal of Mathematics
• /
• 제17권1호
• /
• pp.103-112
• /
• 2009

We show the existence of the solutions for the following nonlinear elliptic problem under the Dirichlet boundary condition. To show the existence of the solutions we use the variational formulation.

• International Journal of Naval Architecture and Ocean Engineering
• /
• 제6권4호
• /
• pp.1197-1208
• /
• 2014

The problem of the oblique water entry of a three dimensional body is considered. Wagner theory is the theoretical framework. Applications are discussed for an elliptic paraboloid entering an initially flat free surface. A dedicated experimental campaign yields a data base for comparisons. In the present analysis, pressure, force and dynamics of the wetted surface expansion are assessed.