• 한국정보과학회논문지:시스템및이론
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• 제36권6호
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• pp.502-510
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• 2009

Multiprecision Squaring은 공개키 알고리즘을 구성하는 연산 중에서 가장 중요한 연산 중 하나이다. 본 논문에서는 기존의 Multiprecision Squaring 알고리즘을 개선하여 연산 양을 줄임으로 성능을 항상시키는 Squaring 기법들을 제시하고 구현하였다. Scott이[1]에서 제안한 Carry-Catcher Hybrid 곱셈 알고리즘은 Gura가 제안한 Hybrid 곱셈 알고리즘[2]을 계승 발전시킨 것으로 MRACL 라이브러리에 구현되어 있으며, Carry-Catcher Hybrid 방법 사용한 Multiprecision Squaring 알고리즘도 MIRACL에 함께 구현되어 있다. 본 논문에서 이 Carry-Catcher Hybrid Squaring 알고리즘을 발전시켜 보다 효율적인 Squaring 알고리즘인 Lazy Doubling Squaring 알고리즘을 제안하고 구현하였으며, atmega128상에서 성능테스터를 수행하여 Carry-Catcher Hybrid Squaring 알고리즘과 비교하여 더 효율적인 알고리즘임을 보였다. 표준 Squaring 알고리즘이 $S_{ij}\;=\;x_i\;{\ast}\;x_j\;=\;S_{ij}$인 사실을 기반으로 곱셈의 횟수를 절반 가까이 줄인 알고리즘이라면 본 논문에서 제시한 Lazy Doubling Squaring 알고리즘은 $a_0\;{\ast}\;2\;+\;a_1\;{\ast}\;2\;+\;...\;+\;a_{n-1}\;{\ast}\;2\;+\;a_n\;{\ast}\;2\;=\;(a_0\;+\;a_1\;+\;...\;+\;a_{n-1}\;+\;a_n)\;{\ast}\;2$ 라는 사실을 기반으로 하여 doubling 연산 횟수를 획기적으로 줄인 알고리즘으로, MIRACL에 구현되어 있는 Multiprecision Squaring 알고리즘 보다 atmega128상에서 약 25% 정도의 빠른 결과를 얻을 수 있었으며, 저자가 아는 바로는 현재까지 나온 어떤 방법보다 빠르다.

• 제어로봇시스템학회논문지
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• 제10권1호
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• pp.96-102
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• 2004

For sensitivity enhancement, the general assisted-GPS acquisition method adopts not only the coherent accumulation technique but also the non-coherent accumulation technique since the long coherent accumulation period increases the number of frequency search cells. But the non-coherent accumulation technique causes tile squaring loss, which is a dominant factor among the acquisition losses of assisted GPS dealing with weak GPS signals. This paper derives the squaring loss of the previous assisted-GPS acquisition method and proposes an assisted-GPS acquisition method for solving the problem of squaring loss in weak signal environment. In this paper, it is explained that the proposed assisted-GPS acquisition method prevents the squaring loss using a coupled coherent accumulation technique and the number of search cells of the proposed assisted-GPS acquisition method is much smaller than that of the previous assisted-GPS acquisition method. Finally, through the simulation by the GPS simulator, the acquisition success rate of the proposed assisted-GPS acquisition method is compared with that of the previous assisted-GPS acquisition method and the acquisition improvements are shown in weak signal environment.

• 반도체디스플레이기술학회지
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• 제16권3호
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• pp.47-52
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• 2017

Solar cell industry requires high technologies to stabilize apparatuses for the wafer manufacturing. Vibrations of squaring & grinding machines are one of the most critical factors for causing residual stresses of ingots, which are the main reasons of the breakage in the following processes such as wire sawing, cleaning, and modularity. In this study, the structure of a squaring & grinding machine has been analyzed through experiments and computer simulations to figure out the ways to suppress the vibrations effectively, and further to minimize the breakage of wafers. The result shows that simple design changes of applying a few ribs can improve the stability of the machine.

• 한국수학사학회지
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• 제30권4호
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• pp.221-232
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• 2017

In this paper, we discuss how ancient Egyptians find out the area of the circle based on $\ll$Ahmose Papyrus$\gg$. Vogel and Engels studied the quadrature of the circle, one of the basic concepts of ancient Egyptian mathematics. We look closely at the interpretation based on the approximate right triangle of Robins and Shute. As circumstantial evidence for Robbins and Shute's hypothesis, Egyptians prior to the 12th dynasty considered the perception of a right triangle as examples of 'simultaneous equation', 'unit of length', 'unit of slope', 'Egyptian triple', and 'right triangles transfer to Greece'. Finally, we present a method to utilize the squaring the circle by ancient Egyptians interpreted by Robbins and Shute as the dynamic symmetry of Hambidge.

• Journal of Mechanical Science and Technology
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• 제19권11호
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• pp.1975-1987
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• 2005

An input time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via digital computers. In this paper a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed. The mathematical structure of the new discretization method is analyzed. On the basis of this structure the sampled-data representation of nonlinear systems with time-delayed multi-input is presented. The delayed multi-input general equation has been derived. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. Additionally, hybrid discretization schemes that result from a combination of the scaling and squaring technique (SST) with the Taylor series expansion are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method's parameters to meet CPU time and accuracy requirements, are examined as well. A performance of the proposed method is evaluated using a nonlinear system with time delay maneuvering an automobile.

• International Journal of Control, Automation, and Systems
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• 제4권3호
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• pp.293-301
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• 2006

A new discretization method for calculating a sampled-data representation of a nonlinear continuous-time system is proposed. The proposed method is based on the well-known Taylor series expansion and zero-order hold (ZOH) assumption. The mathematical structure of the new discretization method is analyzed. On the basis of this structure, a sampled-data representation of a nonlinear system with a time-delayed input is derived. This method is applied to obtain a sampled-data representation of a non-affine nonlinear system, with a constant input time delay. In particular, the effect of the time discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. 'Hybrid' discretization schemes that result from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method parameters to meet CPU time and accuracy requirements are examined as well. The performance of the proposed method is evaluated using a nonlinear system with a time-delayed non-affine input.

• 전자공학회논문지SC
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• 제39권3호
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• pp.211-219
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• 2002

본 논문에서는 셀룰러 오토마타를 이용하여, GF(2/sup m/)상에서 모듈러 곱셈과 제곱의 연산을 m 클럭 사이클 만에 동시에 처리할 수 있는 연산기를 설계하였다. 이는 Diffie-Hellman key exchange, EIGamal과 같은 대부분의 공개키 암호화 시스템에서의 기본 연산인 유한 필드 상의 모듈러 지수승 연산기 설계에 효율적으로 이용될 수 있다. 또한 셀룰러 오토마타는 간단하고도 규칙적이며, 모듈화 하기 쉽고 계층화 하기 쉬운 구조이므로 VLSI 구현에도 효율적으로 활용될 수 있다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1987년도 전기.전자공학 학술대회 논문집(II)
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• pp.1191-1194
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• 1987

This paper presents a method for computing the powers and inverse of an element in GF($2^m$). This method is based on the squaring algorithm $A^2=\sum\limits_{i=0}^{2m-2}P_i$, where $Pi={\alpha}_{i/2}$ if i is even, Pi=0 otherwise, derived from the multiplication algorithm for two elements in GF($2^m$). The powers and inverses in GF($2^m$) for m=2, 3, 4,5 were obtained using computer program, and used in circuit realization of Galois switching function. The squaring and inverse generating circuits are also shown.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2002년도 ICCAS
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• pp.33.6-33
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• 2002

For RF sensitivity enhancement, the previous assisted GPS acquisition architecture adopts not only the coherent integration technique but also the non-coherent integration technique since the long coherent integration time increases the number of the frequency search cells. But the non-coherent integration technique induces the squaring loss, which is the dominant factor among the acquisition losses of assisted GPS dealing with weak GPS signals. This paper proposes an efficient architecture for weak signal acquisition in assisted GPS. In this paper, it is explained that the proposed architecture reduces the squaring loss using a modified non-coherent integration technique. Furthermore, it is..

• Journal of Mechanical Science and Technology
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• 제20권7호
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• pp.950-960
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• 2006

An output time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via a digital computer. A new method for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed in this paper. This method is applied to the sampled-data representation of a nonlinear system with a constant output time-delay. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. In addition, 'hybrid' discretization schemes resulting from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. A performance of the proposed method is evaluated using two nonlinear systems with time-delay output.