• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.135-143
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• 2011

As a zero set of some multivariate splines, the piecewise algebraic variety is a kind of generalization of the classical algebraic variety. This paper presents an algorithm for isolating real roots of the zero-dimensional piecewise algebraic variety which is based on interval evaluation and the interval zeros of univariate interval polynomials in Bernstein form. An example is provided to show the proposed algorithm is effective.

• International Journal of Control, Automation, and Systems
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• v.5 no.2
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• pp.208-211
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• 2007

In a recently proposed method of model reduction for discrete interval systems, the denominator polynomial of a reduced model is computed by applying interval arithmetic to dominant poles of the original system. However, the denominator polynomial obtained via interval arithmetic usually has poles with larger intervals than desired ones. Hence an unstable polynomial can be derived from the stable polynomial. In this paper a simple technique is presented to partially overcome such a stability problem by accurately preserving desired real dominant poles.

• Journal of Information Technology Services
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• v.19 no.1
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• pp.145-158
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• 2020

With the development and widespread application of online shopping, the number of online consumers has increased. With one click of a mouse, people can buy anything they want without going out and have it sent right to the doors. As consumers benefit from online shopping, people are becoming more concerned about protecting their privacy. In the group buying scenario described in our paper, online shopping was regarded as intra-group communication. To protect the sensitive information of consumers, the polynomial-based encryption key sharing method (Piao et al., 2013; Piao and Kim, 2018) can be applied to online shopping communication. In this paper, we analyze security problems by using a polynomial-based scheme in the following ways : First, in Kamal's attack, they said it does not provide perfect forward and backward secrecy when the members leave or join the group because the secret key can be broken in polynomial time. Second, for simultaneous equations, the leaving node will compute the new secret key if it can be confirmed that the updated new polynomial is recomputed. Third, using Newton's method, attackers can successively find better approximations to the roots of a function. Fourth, the Berlekamp Algorithm can factor polynomials over finite fields and solve the root of the polynomial. Fifth, for a brute-force attack, if the key size is small, brute force can be used to find the root of the polynomial, we need to make a key with appropriately large size to prevent brute force attacks. According to these analyses, we finally recommend the use of a relatively reasonable hash-based mechanism that solves all of the possible security problems and is the most suitable mechanism for our application. The study of adequate and suitable protective methods of consumer security will have academic significance and provide the practical implications.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.449-454
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• 2012

In this paper, we find the minimal polynomial of a primitive root of unity over cyclotomic fields. From this, we factorize cyclotomic polynomials over cyclotomic fields and investigate the coefficients of ${\Phi}_{3n}(x)$ when 3∤$n$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.1-20
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• 2016

The general number field sieve (GNFS) is asymptotically the fastest known factoring algorithm. One of the most important steps of GNFS is to select a good polynomial pair. A standard way of polynomial selection (being used in factoring RSA challenge numbers) is to select a nonlinear polynomial for algebraic sieving and a linear polynomial for rational sieving. There is another method called a nonlinear method which selects two polynomials of the same degree greater than one. In this paper, we generalize Montgomery's method [12] using geometric progression (GP) (mod N) to construct a pair of nonlinear polynomials. We also introduce GP of length d + k with $1{\leq}k{\leq}d-1$ and show that we can construct polynomials of degree d having common root (mod N), where the number of such polynomials and the size of the coefficients can be precisely determined.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.10C
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• pp.614-620
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• 2011

RSA, the most commonly used public-key cryptosystem, is based on the difficulty of factoring very large integers. The fastest known factoring algorithm is the Number Field Sieve(NFS). NFS first chooses two polynomials having common root modulo N and consists of the following four major steps; 1. Polynomial Selection 2. Sieving 3. Matrix 4. Square Root, of which the most time consuming step is the Sieving step. However, in recent years, the importance of the Polynomial Selection step has been studied widely, because one can save a lot of time and memory in sieving and matrix step if one chooses optimal polynomial for NFS. One of the ideal ways of choosing sieving polynomial is to choose two polynomials with same degree. Montgomery proposed the method of selecting two (nonlinear) quadratic sieving polynomials. We proposed two cubic polynomials using 5-term geometric progression.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.213-221
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• 2024

A family of sixth-order multiple-root solver have been developed and the special case of weight function is investigated. The dynamical analysis of selected iterative schemes with uniparametric polynomial weight function are studied using Möbius conjugacy map applied to the form ((z - A)(z - B))^m and the stability surfaces of the strange fixed points for the conjugacy map are displayed. The numerical results are shown through various parameter spaces.

• Proceedings of the Korea Water Resources Association Conference
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• 2020.06a
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• pp.268-268
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• 2020

토양수분량은 수문연구에 있어 중요한 인자 중의 하나이며, 그 필요성이 점차 강조되고 있다. 국내에서도 최근 새로운 관측기기의 도입이나 수자원위성의 개발 등에 관한 연구가 점차 활발하게 이뤄지고 있으나, 토양수분량 자료의 생산, 품질관리 및 배포 시스템에 관한 연구 및 개발이 부족한 실정이다. 반면에 해외에서는 International Soil Moisture Network(ISMN)을 통해 토양수분량 자료의 품질관리 및 배포가 활발하게 이루어지고 있는데, ISMN에서는 토양특성, 강우에 대한 반응, 토양온도, 시계열특성을 이용해 토양수분량 관측 자료를 품질관리 하고 있다. 본 연구에서는 ISMN의 spike 검출 알고리즘에서 그래프 평활화(smoothing)를 위해 이용되는 Savitzky-Golay 필터의 window size와 polynomial order(filter order)를 다양하게 변화시키고, 이를 설마천 관측소에서 측정한 토양수분량 원시자료에 적용하여 window size와 polynomial order별로 편의(bias), 변동(variation), 평균 제곱근 오차(Root Mean Square Error, RMSE)를 산정하였다. 통계산정 결과 원시자료와의 bias는 window size가 3이고 polynomial order가 2인 필터를 적용했을 때 가장 작은 것으로 나타났으며, variance는 window size가 3이고 polynomial order가 2인 필터를 이용했을 때가 원시자료와 가장 유사한 것으로 나타났다. 또한, RMSE는 window size가 5이고 polynomial order가 3일 때 가장 작은 것으로 나타났다. 이는 추후 토양수분량 품질관리를 수행하기 위해 적절한 필터 계수 값을 제시할 수 있는 논문으로 사료된다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.7
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• pp.907-912
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• 1993

In this Paper we have proposed a new method to implement the interpolation of the functions, using a neural network. The architecture of neural network is a three-layer perceptron and the training algorithm is a modified error back propagation algorithm adding neurons to hidden layer. The interpolated functions are sin(7 X), 3rd order polynomial 0.5$\times$3_2$\times$2+X+2.5 and rectangular pulse 0.99 U (X-0.2) -0.99 U(X-0.8) +0.01, where U(X) is the unit step. The root mean squred errors of the interpolated functions are 0.00258, 0.00164 and 0.00116 respectively.

• Journal of the Korea Computer Graphics Society
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• v.6 no.1
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• pp.37-50
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• 2000

Using the complex formulation of plane curves which R. T. Farouki introduced, we can identify any plane polynomial curve with only a polynomial with complex coefficients. In this paper, using the well-known fundamental theorem of algebra, we completely factorize the polynomial over the complex number field C and from the completely factorized form of the polynomial, we find a new necessary and sufficient condition for a plane polynomial curve to be a Pythagorean-hodograph curve, obseving the set of all roots of the complex polynomial corresponding to the plane polynomial curve. Applying this method to space polynomial curves in the three dimensional Minkowski space $R^{2,1}$, we also find the necessary and sufficient condition for a polynomial curve in $R^{2,1}$ to be a PH curve in a new finer form and characterize all possible curves completely.