• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.36 no.10C
• /
• pp.614-620
• /
• 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 the Korea Society of Computer and Information
• /
• v.20 no.4
• /
• pp.111-117
• /
• 2015

The exam scheduling problem has been classified as nondeterministic polynomial time-complete (NP-complete) problem because of the polynomial time algorithm to obtain the exact solution has been unknown yet. Gu${\acute{e}}$ret et al. tries to obtain the solution using linear programming with $O(m^4)$ time complexity for this problem. On the other hand, this paper suggests chromatic number algorithm with O(m) time complexity. The proposed algorithm converts the original data to incompatibility matrix for modules and graph firstly. Then, this algorithm packs the minimum degree vertex (module) and not adjacent vertex to this vertex into the bin $B_i$ with color $C_i$ in order to exam within minimum time period and meet the incompatibility constraints. As a result of experiments, this algorithm reduces the $O(m^4)$ of linear programming to O(m) time complexity for exam scheduling problem, and gets the same solution with linear programming.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.40 no.3
• /
• pp.145-151
• /
• 2003

This study focuses on the hardware implementation of fast and low-complexity multiplier over GF(2$^{m}$ ). Finite field multiplication can be realized in two steps: polynomial multiplication and modular reduction using the irreducible polynomial and we will treat both operation, separately. Polynomial multiplicative operation in this Paper is based on the Permestzi's algorithm, and irreducible polynomial is defined AOP. The realization of the proposed GF(2$^{m}$ ) multipleker-based multiplier scheme is compared to existing multiplier designs in terms of circuit complexity and operation delay time. Proposed multiplier obtained have low circuit complexity and delay time, and the interconnections of the circuit are regular, well-suited for VLSI realization.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2006.11a
• /
• pp.147-157
• /
• 2006

In this paper we consider alternate m machine scheduling problem in which each job having at most two eligible machines should be assigned with the objective of makespan minimization. For this problem, we propose a $O(m2^m)$ time rounding algorithm with performance ratio at most 1.5. For a little general problem where each job can be processed at most three machines, we prove that there cannot exist a polynomial time algorithm with performance ratio less than 1.5.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.21 no.45
• /
• pp.93-100
• /
• 1998

The researches of Linear Programming are Khachiyan Method, which uses Ellipsoid Method, and Karmarkar, Affine, Path-Following and Interior Point Method which have Polynomial-Time complexity. In this study, Karmarkar Method is more quickly solved as 50 times then Simplex Method for optimal solution. but some special problem is not solved by Karmarkar Method. As a result, the algorithm by APL Language is proved time efficiency and optimal solution in the Primal-Dual interior point algorithm. Furthermore Karmarkar Method and Primal-Dual interior point Method is compared in some examples.

• The KIPS Transactions:PartA
• /
• v.18A no.2
• /
• pp.69-74
• /
• 2011

The minimum dominating set problem of a graph G is to find a smallest possible dominating set. The minimum dominating set problem is a well-known NP-complete problem such that it cannot be solved in polynomial time. Heuristic or approximation algorithm, however, will perform well in certain area of application. In this paper, we suggest three different simulated annealing algorithms and experimentally show better efficiency improvement by applying these algorithms to the graph instances developed by DIMACS.

• Proceedings of the KIEE Conference
• /
• 1999.07g
• /
• pp.2809-2811
• /
• 1999

In this paper, we develope an algorithm to calculate field inhomogeneity in MR imaging using a dual fast spin echo pulse sequence. Because phase modulation time can be easily modified with this pulse sequence, high resolution image can be obtained and acquisition time can be reduced compared to gradient echo technique. In the case of phase wrapping in field map, phase corrected using image processing technique. We assume the field pattern to be second order polynomial and apply Pseudo-Inverse equation to calculate second order polynomial coefficients. These coefficients can be used for the shimming of the magnetic field.

• Journal of the Institute of Electronics Engineers of Korea CI
• /
• v.48 no.5
• /
• pp.64-73
• /
• 2011

The problem of Euclidean minimum spanning tree (EMST) is to connect given nodes in a plane with minimum cost. There are many algorithms for the polynomial time problem as EMST. However, for numerous nodes, the algorithms consume an enormous amount of time to find an optimal solution. In this paper, an approximation scheme using a polynomial time approximation scheme (PTAS) algorithm with dividing and parallel processing for the problem is suggested. This scheme enables to construct a large, approximate EMST within a short duration. Although initially devised for the non-polynomial problem, we employ naive PTAS to construct a vast EMST with dynamic programming. In an experiment, the approximate EMST constructed by the proposed scheme with 15,000 input terminal nodes and 16 partition cells shows 89% and 99% saving in execution time for the serial processing and parallel processing methods, respectively. Therefore, our scheme can be applied to obtain an approximate EMST quickly for numerous input terminal nodes.

• 제어로봇시스템학회:학술대회논문집
• /
• 1991.10b
• /
• pp.1930-1933
• /
• 1991

In this paper, the robustness of self turning controller on the continuous time-delay system is investigated. The polynomial identification method using continuous time exponentially weighted least square algorithm is used for estimating the time.-delay system parameters. The pole-zero and pole placement method are adopted for the control algorithm. On considering the control weighting factor and reliability filter the effect of unmodeled dynamics of the plant are examined by the simulation.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.23 no.4
• /
• pp.165-170
• /
• 2023

This paper proposes an algorithm that can obtain a solution with linear time for a set cover problem(SCP) in which there is no polynomial time algorithm as an NP-complete problem so far. Until now, only heuristic greed algorithms are known to select sets that can be covered to the maximum. On the other hand, the proposed algorithm is a competitive algorithm that applies an inclusion-exclusion principle rule to N nodes up to 2nd or 3rd in the maximum number of elements to obtain a set covering all k nodes, and selects the minimum cover set among them. The proposed algorithm compensated for the disadvantage that the greedy algorithm does not obtain the optimal solution. As a result of applying the proposed algorithm to various application cases, an optimal solution was obtained with a polynomial time of O(kn²).