• Journal of the Korea Society of Computer and Information
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• v.19 no.7
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• pp.71-76
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• 2014

There is to be virtually impossible to solve the very large digits of prime number p and q from composite number n=pq using integer factorization in typical public-key cryptosystems, RSA. When the public key e and the composite number n are known but the private key d remains unknown in an asymmetric-key RSA, message decryption is carried out by first obtaining ${\phi}(n)=(p-1)(q-1)=n+1-(p+q)$ and then using a reverse function of $d=e^{-1}(mod{\phi}(n))$. Integer factorization from n to p,q is most widely used to produce ${\phi}(n)$, which has been regarded as mathematically hard. Among various integer factorization methods, the most popularly used is the congruence of squares of $a^2{\equiv}b^2(mod\;n)$, a=(p+q)/2,b=(q-p)/2 which is more commonly used then n/p=q trial division. Despite the availability of a number of congruence of scares methods, however, many of the RSA numbers remain unfactorable. This paper thus proposes an algorithm that directly and immediately obtains ${\phi}(n)$. The proposed algorithm computes $2^k{\beta}_j{\equiv}2^i(mod\;n)$, $0{\leq}i{\leq}{\gamma}-1$, $k=1,2,{\ldots}$ or $2^k{\beta}_j=2{\beta}_j$ for $2^j{\equiv}{\beta}_j(mod\;n)$, $2^{{\gamma}-1}$ < n < $2^{\gamma}$, $j={\gamma}-1,{\gamma},{\gamma}+1$ to obtain the solution. It has been found to be capable of finding an arbitrarily located ${\phi}(n)$ in a range of $n-10{\lfloor}{\sqrt{n}}{\rfloor}$ < ${\phi}(n){\leq}n-2{\lfloor}{\sqrt{n}}{\rfloor}$ much more efficiently than conventional algorithms.

• The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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• v.27 no.3
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• pp.127-143
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• 2022

Recently, many attempts to run numerical ocean models in cloud computing environments have been tried actively. A cloud computing environment can be an effective means to implement numerical ocean models requiring a large-scale resource or quickly preparing modeling environment for global or large-scale grids. Many commercial and private cloud computing systems provide technologies such as virtualization, high-performance CPUs and instances, ether-net based high-performance-networking, and remote direct memory access for High Performance Computing (HPC). These new features facilitate ocean modeling experimentation on commercial cloud computing systems. Many scientists and engineers expect cloud computing to become mainstream in the near future. Analysis of the performance and features of commercial cloud services for numerical modeling is essential in order to select appropriate systems as this can help to minimize execution time and the amount of resources utilized. The effect of cache memory is large in the processing structure of the ocean numerical model, which processes input/output of data in a multidimensional array structure, and the speed of the network is important due to the communication characteristics through which a large amount of data moves. In this study, the performance of the Regional Ocean Modeling System (ROMS), the High Performance Linpack (HPL) benchmarking software package, and STREAM, the memory benchmark were evaluated and compared on commercial cloud systems to provide information for the transition of other ocean models into cloud computing. Through analysis of actual performance data and configuration settings obtained from virtualization-based commercial clouds, we evaluated the efficiency of the computer resources for the various model grid sizes in the virtualization-based cloud systems. We found that cache hierarchy and capacity are crucial in the performance of ROMS using huge memory. The memory latency time is also important in the performance. Increasing the number of cores to reduce the running time for numerical modeling is more effective with large grid sizes than with small grid sizes. Our analysis results will be helpful as a reference for constructing the best computing system in the cloud to minimize time and cost for numerical ocean modeling.