• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제7권1호
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• pp.25-31
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• 2003

The concepts of stability of algorithms for solving the symmetric and generalized symmetric-definite eigenproblems are discussed. An algorithm for solving the symmetric eigenproblem $Ax={\lambda}x$ is stable if the computed solution z is the exact solution of some slightly perturbed system $(A+E)z={\lambda}z$. We use both normwise approach and componentwise way of measuring the size of the perturbations in data. If E preserves symmetry we say that an algorithm is strongly stable (in a normwise or componentwise sense, respectively). The relations between the stability and strong stability are investigated for some classes of matrices.

• International Journal of Computer Science & Network Security
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• 제23권1호
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• pp.164-168
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• 2023

As our community has become increasingly dependent on technology, security has become a bigger concern, which makes it more important and challenging than ever. security can be enhanced with encryption as described in this paper by combining RC6 symmetric cryptographic algorithms with RSA asymmetric algorithms, as well as the Vigenère cipher, to help manage weaknesses of RC6 algorithms by utilizing the speed, security, and effectiveness of asymmetric algorithms with the effectiveness of symmetric algorithm items as well as introducing classical algorithms, which add additional confusion to the decryption process. An analysis of the proposed encryption speed and throughput has been conducted in comparison to a variety of well-known algorithms to demonstrate the effectiveness of each algorithm.

• 전자공학회논문지CI
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• 제43권2호
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• pp.1-11
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• 2006

본 연구에서는 대칭 및 비대칭 암호화 알고리즘을 가속화하기 위해, 다수 혹은 긴 워드 연산을 위한 레지스터 파일 확장 구조 (Register File Extension for Multi-words or Long-word Operation: RFEMLO)라는 새로운 레지스터 파일 구조를 제안한다. 암호화 알고리즘은 긴 워드 피연산자에 대한 명령어를 통하여 가속화 할 수 있다는 점에 착안하여, RFEMLO는 하나의 레지스터 명을 통해 여러 개의 레지스터에 접근할 수 있도록 하여 여러 연산자에 대해 동일한 연산을 수행할 수 있도록 하거나, 여러 개의 레지스터를 하나의 데이터로 사용할 수 있게 한다. RFEMLO는 긴 워드 피연산자에 대한 명령어 집합의 추가와 이를 지원하는 기능 유닛을 추가함으로서 범용 프로세서에 적용할 수 있다. 제안된 하드웨어 구조와 명령어 집합의 효율성을 평가하기 위해 Simplescalar/ARM 3.0을 사용하여 대칭 및 비대칭의 다양한 암호화 알고리즘에 적용하였다. 실험 결과, RFEMLO을 적용한 순차적 파이프라인을 가진 프로세서에서 대칭 암호화 알고리즘의 경우 $40%{\sim}160%$의 성능 향상을, 비대칭 암호화 알고리즘의 경우 $150%{\sim}230%$의 높은 성능향상을 얻을 수 있었다. RFEMLO의 적용을 통한 성능 항상은 이슈 폭의 증가를 이용한 슈퍼스칼라 구현에 따른 성능 향상과 비교할 때, 훨씬 적은 하드웨어 비용으로 효과적인 성능 향상을 얻을 수 있음을 확인하였으며 슈퍼스칼라 프로세서에 RFEMLO를 적용하는 경우에도 대칭 암호화 알고리즘에서는 최대 83.6%, 비대칭 암호화 알고리즘에서는 최대 138.6%의 추가적인 성능향상을 얻을 수 있었다.

• International Journal of Computer Science & Network Security
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• 제24권1호
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• pp.196-204
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• 2024

The security of data and information using encryption algorithms is becoming increasingly important in today's world of digital data transmission over unsecured wired and wireless communication channels. Hybrid encryption techniques combine both symmetric and asymmetric encryption methods and provide more security than public or private key encryption models. Currently, there are many techniques on the market that use a combination of cryptographic algorithms and claim to provide higher data security. Many hybrid algorithms have failed to satisfy customers in securing data and cannot prevent all types of security threats. To improve the security of digital data, it is essential to develop novel and resilient security systems as it is inevitable in the digital era. The proposed hybrid algorithm is a combination of the well-known RSA algorithm and a simple symmetric key (SSK) algorithm. The aim of this study is to develop a better encryption method using RSA and a newly proposed symmetric SSK algorithm. We believe that the proposed hybrid cryptographic algorithm provides more security and privacy.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.1-12
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• 2009

Iterative algorithms are proposed for the least-squares symmetric solution of AXB = E with a submatrix constraint. We characterize the linear mappings from their independent element space to the constrained solution sets, study their properties and use these properties to propose two matrix iterative algorithms that can find the minimum and quasi-minimum norm solution based on the classical LSQR algorithm for solving the unconstrained LS problem. Numerical results are provided that show the efficiency of the proposed methods.

• 한국시뮬레이션학회논문지
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• 제2권1호
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• pp.91-106
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• 1993

Load sharing in distributed systems improves systems performance. Research in the field has been focused on steady state performance for load sharing algorithms. However, transient characteristics of such algorithms may be important in a distributed system in which workload for some node is changing. Simulation is the only means to analyze such characteristics. This paper presents a simulation-based analysis of the transient characteristics of four load sharing algorithms ; forward probing, reverse probing, symmetric probing, and multi-threshold symmetric probing algorithms. Discrete event system models for execution of the algorithms in a distributed system has been developed in a SIMSCRIOT II.5 environment. Simulation results indicate that the MSYM algorithm shows the shortest response time in the transient period.

• International Journal of Computer Science & Network Security
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• 제21권4호
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• pp.33-40
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• 2021

The traveling salesman problem (TSP) is one of the well-known and extensively studied NPC problems in combinatorial optimization. To solve it effectively and efficiently, various optimization algorithms have been developed by scientists and researchers. However, most optimization algorithms are designed based on the concept of improving route in the iterative improvement process so that the optimal solution can be finally found. In contrast, there have been relatively few algorithms to find the optimal solution using route construction mechanism. In this paper, we propose a route construction optimization algorithm to solve the symmetric TSP with the help of ratio value. The proposed algorithm starts with a set of sub-routes consisting of three cities, and then each good sub-route is enhanced step by step on both ends until feasible routes are formed. Before each subsequent expansion, a ratio value is adopted such that the good routes are retained. The experiments are conducted on a collection of benchmark symmetric TSP datasets to evaluate the algorithm. The experimental results demonstrate that the proposed algorithm produces the best-known optimal results in some cases, and performs better than some other route construction optimization algorithms in many symmetric TSP datasets.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.641-651
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• 2011

In this paper, with use of the displacement matrix, two special matrices are constructed. By these special matrices the block decompositions of the block symmetric Hankel matrix and the inverse of the Hankel matrix are derived. Hence, the algorithms according to these decompositions are given. Furthermore, the numerical tests show that the algorithms are feasible.

• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.133-150
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• 2007

In a development of efficient primal-dual interior-points algorithms for self-scaled convex programming problems, one of the important properties of such cones is the existence and uniqueness of "scaling points". In this paper through the identification of scaling points with the notion of "(metric) geometric means" on symmetric cones, we extend several well-known matrix inequalities (the classical L$\ddot{o}$wner-Heinz inequality, Ando inequality, Jensen inequality, Furuta inequality) to symmetric cones. We also develop a theory of spectral geometric means on symmetric cones which has recently appeared in matrix theory and in the linear monotone complementarity problem for domains associated to symmetric cones. We derive Nesterov-Todd inequality using the spectral property of spectral geometric means on symmetric cones.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권2호
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• pp.5-16
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• 1999

We introduce a new projector for accelerating convergence of a symmetric eigenvalue problem Ax = x, and devise a power/Lanczos hybrid algorithm. Acceleration can be achieved by removing the hard-to-annihilate nonsolution eigencomponents corresponding to the widespread eigenvalues with modulus close to 1, by estimating them accurately using the Lanczos method. However, the additional Lanczos results can be obtained without expensive matrix-vector multiplications but a very small amount of extra work, by utilizing simple power-Lanczos interconversion algorithms suggested. Numerical experiments are given at the end.