제곱-나눗셈 모듈러 지수연산법

이상운(Sang-Un Lee) 한국컴퓨터정보학회 2013 韓國컴퓨터情報學會論文誌 Vol.18 No.4

암호학의 암호 생성과 해독, 소수판별법의 성능은 대부분 a<SUP>b</SUP> (mod m)의 모듈러 지수연산의 효율적 구현여부로 결정된다. 모듈러 지수연산법에는 제곱-곱셈 방식의 표준 이진법이 최선의 선택으로 알려져 있다. 그러나 큰 자리수의 b에 대해서는 사전처리를 하는 n-ary, (n≥2)이 보다 효율적으로 적용된다. 본 논문에서는 모듈러 지수 나눗셈 방법을 적용한 제곱-나눗셈법과 사전처리 없는 n-ary 제곱-나눗셈법을 제안하였다. 제곱-나눗셈법은 b가 2<SUP>k</SUP>+2<SUP>k-1</SUP>에 근접한 값 또는 2<SUP>k+1</SUP>에 근접한 경우 수행횟수 측면에서 가장 효율적임을 알 수 있었다. 나머지 값들에 대해서는 사전처리 없는 n-ary 제곱-나눗셈법을 적용하는 것이 사전처리를 하는 일반적인 n-ary법에 비해 수행횟수 측면에서 효율적임을 보였다. The performance and practicality of cryptosystem for encryption, decryption, and primality test are primarily determined by the implementation efficiency of the modular exponentiation of a<SUP>b</SUP> (mod m). To compute a<SUP>b</SUP> (mod m), the standard binary squaring (square-and-multiply) still seems to be the best choice. However, in large b bits, the preprocessed n-ary, (n≥2) method could be more efficient than binary squaring method. This paper proposes a square-and-divide and unpreprocessed n-ary square-and-divide modular exponentiation method. Results confirmed that the square-and-divide method is the most efficient of trial number in a case where the value of b is adjacent to 2<SUP>k</SUP>+2<SUP>k-1</SUP> or to 2<SUP>k+1</SUP>. It was also proved that for b out of the beforementioned range, the unpreprocessed n-ary square-and-divide method yields higher efficiency of trial number than the general preprocessed n-ary method.

Unequal Power Dividers Using Uniform Impedance Transmission Lines with Stubs

Young-Chul Yoon,Young Kim 한국전자파학회JEES 2021 Journal of Electromagnetic Engineering and Science Vol.21 No.1

This study proposes an impedance control method in transmission lines using open- or short-circuit stubs for unequal power dividers. The proposed method is based on the conversion of a two-port to a three-port transmission line, which is equivalent to multiplying the impedance at the internal transmission line by a scaling factor and then connecting open- or short-circuit stubs in parallel to each port on the three-port transmission line. To verify the effectiveness of the proposed method, Wilkinson and Gysel power dividers with splitting ratios of 9:1 and 5:1, respectively, using uniform impedance transmission lines with open- or short-circuit stubs at an operating frequency of 2 ㎓ were designed. The experimental measurements of the two power dividers agree well with those of the simulation.

The secant method and the generalized divided differences for solving nonlinear operator equations

B. S. Attili 장전수학회 2006 Advanced Studies in Contemporary Mathematics Vol.13 No.1

We consider solving nonlinear operator equations using the secant method and the generalized divided dierences. We establish some local and semilocal convergence results for the proposed method. Numerical examplesand comparison with the work of others will be presented to demonstrate the efficiency of the method.

Effective Biological Sequence Alignment Method using Divide Approach

Hae-Won Choi(최혜원),Sang-Jin Kim(김상진),Su-Young Pi(피수영) 한국산업정보학회 2012 한국산업정보학회논문지 Vol.17 No.6

This paper presents a new sequence alignment method using the divide approach, which solves the problem by decomposing sequence alignment into several sub-alignments with respect to exact matching subsequences. Exact matching subsequences in the proposed method are bounded on the generalized suffix tree of two sequences, such as protein domain length more than 7 and less than 7. Experiment results show that protein sequence pairs chosen in PFAM database can be aligned using this method. In addition, this method reduces the time about 15% and space of the conventional dynamic programming approach. And the sequences were classified with 94% of accuracy.

Effective Biological Sequence Alignment Method using Divide Approach

최해원,김상진,피수영 한국산업정보학회 2012 한국산업정보학회논문지 Vol.17 No.6

This paper presents a new sequence alignment method using the divide approach, which solves the problem by decomposing sequence alignment into several sub-alignments with respect to exact matching subsequences. Exact matching subsequences in the proposed method are bounded on the generalized suffix tree of two sequences, such as protein domain length more than 7 and less than 7. Experiment results show that protein sequence pairs chosen in PFAM database can be aligned using this method. In addition, this method reduces the time about 15% and space of the conventional dynamic programming approach. And the sequences were classified with 94% of accuracy

중수대명력의 영축 보간법 고찰

김동빈,전준혁 한국과학사학회 2023 한국과학사학회지 Vol.45 No.3

We examined the mathematical method of creating the Yeongchuk-Ipseong 盈縮-立成 (Yeongchuk means “profit and loss” in the movement of the Sun, and Ipseong refers to the table) of the Chongxiu-Daming-li 重修大明曆 using the divided difference principle. Accordingly, we identified the mathematical meaning of the fundamental quantities used in the Yeongchuk interpolation. The method of calculating the daily Yeongchuk-Jonyuk 盈縮-眺朒 (Jonyuk is a temporal quantity corresponding to solar inequality, which is converted via the angular velocity of the Moon) in the Chongxiu-Daming-li is mathematically the same procedure as creating a divided difference table for Yeongchuk-Jonyuk. The interpolation method for Yeongchuk-Jonyuk in the Chongxiu-Daming-li is mathematically identical to modern quadratic interpolation. The limit of the interpolation error is less than ±0.001°, and the difference is similar to the results obtained by the modern second-order polynomial interpolation method. The accuracy of the Yeongchuk interpolation had already reached a high level in the Chongxiu-Daming-li. This suggests that the Shoushi-li 授時曆 did not address the fundamental problem of the Chongxiu-Daming-li in calculating the position of the Sun. The conventional assessment that adopting the third-order interpolation in the Shoushi-li would have improved the accuracy of the solar position should be reconsidered.

A UNIFIED CONVERGENCE ANALYSIS FOR SECANT-TYPE METHODS

Ioannis Konstantinos Argyros,Angel Alberto Magrenan 대한수학회 2014 대한수학회지 Vol.51 No.6

We present a unified local and semilocal convergence analysis for secant-type methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved. Under the same computational cost our semilocal convergence criteria can be weaker; the error bounds more precise and in the local case the convergence balls can be larger and the error bounds tighter than in earlier studies such as [1–3,7–14,16,20,21] at least for the cases of Newton’s method and the secant method. Numerical examples are also presented to illustrate the theoretical results obtained in this study.

A UNIFIED CONVERGENCE ANALYSIS FOR SECANT-TYPE METHODS

Argyros, Ioannis Konstantinos,Magrenan, Angel Alberto Korean Mathematical Society 2014 대한수학회지 Vol.51 No.6

We present a unified local and semilocal convergence analysis for secant-type methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved. Under the same computational cost our semilocal convergence criteria can be weaker; the error bounds more precise and in the local case the convergence balls can be larger and the error bounds tighter than in earlier studies such as [1-3,7-14,16,20,21] at least for the cases of Newton's method and the secant method. Numerical examples are also presented to illustrate the theoretical results obtained in this study.

광역자치단체 분할정부구조와 지방재정지출정향

권경환 대한지방자치학회 2008 한국지방자치연구 Vol.10 No.3

광역자치단체의 분할정부 구조는 지방의회의 다수당과 집행부 수장인 단체장의 당적이 서로 다른 정부구조를 의미한다. 본 연구는 1995년 민선단체장 출범 이후부터 2006년 민선4기 출범 직전 해까지 11년 동안 우리나라 광역자치단체를 분석대상으로 하여 이러한 분할정부 구조가 지방정부 재정지출정향에 미치는 영향을 시계열적·횡단면적 교란요인을 통제한 패널데이타 방법(panel data method)을 활용해 실증적으로 분석하는데 목적이 있다. 이 연구에서는 고정효과모형(fixed effects model)에 기초한 분석결과, 분할정부구조 형태를 띤 광역자치단체에서는 통합정부구조의 광역자치단체에 비해 전반적으로 공공서비스 공급수준이 낮았고, 특히 성장정책을 회피하는 재정지출정향이 나타났다. 그 동안 지방정부의 분할정부구조를 대상으로 한 관련 연구가 일천한 한국적 상황에서 광역자치단체에서 나타난 분할정부구조가 해당 자치단체의 재정지출정향에 미친 영향을 분석한 본 연구는 향후 분할정부구조가 실제로 우리나라 광역 및 기초지자체의 공공서비스 공급수준과 정책선호에 어떤 영향을 미칠 수 있는지를 추론하는데 도움을 줄 수 있을 것이다. The divided government structure of regional or local governments is the kind of power structure in which the majority of the council and chief executive's party affiliation differ from each other. This paper focuses on analyzing the impacts of the divided government structure of Korean regional governments on the spending patterns of regional public expenditures by using panel data of 15 regional governments from 1995 through 2005. In this study, the construct "divided government structure" was operationalized into dummy variable "DIVI2"(divided government type=1, undivided government type=0) through the scale composed of the majority of the council and chief executive's party affiliation. The empirical results indicated that divided-type governments had less expenses related to public service delivery level than undivided-type governments and declined to growth policy. In the meantime, the researches dealing with the divided government structure at the local or regional level were insufficient in Korea. This study will be able to help reason about the impacts of the divided government structure of Korean regional or local governments on the public service delivery level and policy preference in the future.

Extended sufficient semilocal convergence for the Secant method

Cho, Yeol Je,Argyros, Ioannis K.,Hilout, Saï,d Elsevier 2011 COMPUTERS & MATHEMATICS WITH APPLICATIONS - Vol.62 No.2

<P><B>Abstract</B></P><P>We establish new sufficient convergence conditions for the Secant method to a locally unique solution of a nonlinear equation in a Banach space. Using our new concept of recurrent functions, and combining Lipschitz and center-Lipschitz conditions on the divided difference operator, we obtain a new semilocal convergence analysis of the Secant method. Moreover, our sufficient convergence conditions expand the applicability of the Secant method in cases not covered before (Dennis, 1971 <ce:cross-ref refid='br000045'>[9]</ce:cross-ref>, Hernández et al., 2005 <ce:cross-ref refid='br000040'>[8]</ce:cross-ref>, Laasonen, 1969 <ce:cross-ref refid='br000075'>[15]</ce:cross-ref>, Ortega and Rheinboldt, 1970 <ce:cross-ref refid='br000055'>[11]</ce:cross-ref>, Potra, 1982 <ce:cross-ref refid='br000025'>[5]</ce:cross-ref>, Potra, 1985 <ce:cross-ref refid='br000035'>[7]</ce:cross-ref>, Schmidt, 1978 <ce:cross-ref refid='br000090'>[18]</ce:cross-ref>, Yamamoto, 1987 <ce:cross-ref refid='br000060'>[12]</ce:cross-ref>, Wolfe, 1978 <ce:cross-ref refid='br000095'>[19]</ce:cross-ref>). Numerical examples are also provided in this study.</P>