Galois theory of Mathieu groups in characteristic two

이익권 대한수학회 2007 대한수학회지 Vol.44 No.1

Given a eld K and a nite group G, it is a very interest-ing problem, although very dicult, to nd al Galois extens ions over Kwhose Galois group is isomorphic to G. In this paper, we prepare a theo-retical background to study this type of problem when G is the Mathieugroup M 24 and K is a eld of characteristic two.

Mathieu group coverings and Golay codes

이익권 대한수학회 2002 대한수학회지 Vol.39 No.2

We associate binary codes to polynomials over fieldsof characteristic two and show that thebinary Golay codes are associated to the Mathieu group polynomialsin characteristic two. We give two more polynomials whose Galoisgroup is M_{12} but different self-orthogonal binary codes areassociated. Also, we find a family of M_{24}-coverings whichincludes previous ones.

중소기업 스마트팩토리 도입의 중요도 분석

이익권,이광배,이수현,모수원 한국무역보험학회 2023 무역금융보험연구 Vol.24 No.1

Purpose : Synchronization and integration of the business processes and functions through effective and efficient information sharing are vital. Hence, enhancing their competence through the adoption of an appropriate smart factory is crucial to improve their competitiveness in the competitive scenario. Under this backdrop, this paper analyses pertinent factors for adopting an appropriate smart factory. Research design, data, methodology : This research recommends utilizing AHP to investigate the priority in achieving smart factory adoption of SMEs. AHP is amongst the frequently utilized MCDM (multicriteria decision making) techniques and is mostly accepted because it is convenient to use, flexible, and ensures that the comparative questionnaire or matrices are consistent. We establish a research model structure of comprising 4 main criteria and 12 sub-criteria. The main criteria consist of technology, innovation, organization, and environment with sub-criteria of of security, IT infrastructure, reliability, compatibility, innovation receptivity, CEO's commitment to innovation, investment cost, operating cost, human resource retention, competitive pressure, external support, and social impact. Results : This study shows that the most important main variables are technology and innovation for the transportation business and industrial equipment leashing business, respectively. For the transportation business, the most important sub-criteria are CEO's commitment to innovation and security while the least important sub-criteria are social impact and operating cost. Conclusions : This study shows that for the industrial equipment leashing business, the most important sub-criteria are CEO's commitment to innovation and operating cost while the least important sub-criteria are social impact and security.

배후단지 항만물류 기업에 적용 가능한 스마트 팩토리: 광양항 사례연구

이익권(Ig-Kweon Lee),공일종(Il-Jong Kong),이수현(Soo-Hyun Lee),이광배(Kwang-Bae Lee) 조선대학교 지식경영연구원 2021 기업과 혁신연구 Vol.44 No.3

스마트 팩토리는 기획, 생산, 판매와 같은 전 과정에 디지털 자동컨트롤 기능이 결합된 정보통신기술(Information & Communication Technology)을 적용하여 생산과정을 지능화함과 더불어 사물인터넷을 연결하여 생산과정의 모든 상황을 즉각적으로 시시각각 들여다볼 수 있게 함으로써 생산성 향상과 제품의 품질을 충족시킬 수 있는 미래형 공장이라고 정의할 수 있다. 이에 따라 오늘날과 같은 4차 산업혁명 시대에 스마트 팩토리를 제조의 미래 경쟁력으로 인식하고 변화에 적응할 수 있는 다양한 방법을 모색하는 기업은 크게 증가하고 있는 추세이다. 또한 최근 변동하는 환경에 대한 실시간 대응의 중요성이 부각됨에 따라 조직 간 긴밀하고 치밀한 업무협조와 정보 및 지식공유를 통해 가능한 실시간기업(RTE)에 대해서 분석한다. 정부 지원을 받아 스마트 팩토리를 도입한 사유를 670개 기업을 대상으로 실시한 설문조사의 결과를 보면 80%가 스마트 팩토리 도입이 각 기업의 생산성 및 경쟁력 향상에 도움이 될 것으로 봤다. 또 조사대상 기업 중 80%(536개사)는 정부가 생산 이력 자동화를 통한 관리기능 개별운영 및 공정물류 관리로 분류한 기본기준 수준이었다. 광양항 후미단지는 총 54개 업체가 입주해 일반 창고·운수업의 72.1%, 제조업의 25.9%를 차지하고 있으며, 미래에는 스마트 팩토리가 기업의 필수 요소가 될 것으로 예상된다는 점에서 더 늦기 전에 광양항 배후기업을 위한 스마트 팩토리를 적용하여 성공모델을 만들고 주변 기업에 확산시켜 광양항의 경쟁력을 높이는 것이 필요하다고 할 수 있다. Smart factory is a technology initiative by German government in 2010 aiming at establishing a common workshop to innovate in manufacturing techniques. It is the heart of Industry 4.0. To digitize production operations, Internet of Things technologies have to be implemented to gather and inspect process data. Manufacturing companies have to implement heterogeneous cutting-edge technologies to coherently ensure their competitiveness. A massive volume of Internet of Things devices (e.g., sensors and actuators) are leveraged to gather data so as to reinforce safety throughout essential smart cyber-physical system infrastructures. So far, leading manufacturers have begun the journey toward implementing smart factory. However, most firms still lack insight into the challenges and resources for implementing smart factory. As such, this paper identifies the requirements and key challenges, investigates available new technologies, reviews existing studies that have been done for smart factory, and further provides guidance for manufacturers to implementing smart factory in the context of Industry 4.0. According to a survey of 670 companies that introduced Smart Factory with government support, 80% believed that the introduction of Smart Factory would help each company improve productivity and competitiveness. In addition, 80% (536 companies) of the companies surveyed were at the basic level of standards classified by the government as performing individual operations of management functions and managing process logistics through automation of production history. A total of 54 companies are moving into the rear complex of Gwangyang Port, accounting for 72.1% of the general warehouse and transportation industries, and 25.9% of the manufacturing industry. In the future, Smart Factory will be a prerequisite for an enterprise. Before it is too late, it is necessary to introduce a smart factory for the businesses behind Gwangyang Port to create a success model and spread it to neighboring companies to continuously increase the competitiveness of Gwangyang Port through smart factory in the fourth industrial revolution.

정수의 분해를 이용한 ElGamal형 서명기법의 안전성 분석

이익권(Ikkwon Yie),김동렬(Dongryeol Kim) 한국정보보호학회 2004 정보보호학회논문지 Vol.14 No.2

위수가 q인 생성원 g를 사용하는 ElGamal형 서명기법에서는 서명되어질 각 문서마다 message nonce를 구간(0, q - 1 )에서 랜덤하게 선택해야 한다는 것은 잘 알려진 사실이다. H. Kuwakado와 H. Tanaka는 사용된 message nonce가 각각 0 < k₁, k₂≤O(√q)인 서명 두 개가 주어졌을 때, 서명자의 비밀키를 다항식 시간으로 계산해내는 알고리즘을 제안하였다[2]. 최근 R. Gallant, R. Lambert, S. Vanstone등은 정수를 적절히 분해하여 타원곡선암호의 효율성을 개선하는 방법을 제안하였다[3]. 이 논문에서는 타원곡선암호의 고속연산에서 사용되었던 정수의 분해기법을 Kuwakado 등의 알고리즘에 적용하여 message nonce가 ?k₁?,? k₂?≤ O(√q) 인 경우에도 적용할 수 있도록 확장하고, 알고리즘의 효율성 및 공격의 완성도를 개선하였다. For an ElGamal-type signature scheme using a generator g of order q , it has been well-known that the message nonce should be chosen randomly in the interval (0, q - 1 ) for each message to be signed. In [2], H. Kuwakado and H. Tanaka proposed a polynomial time algorithm that gives the private key of the signer if two signatures with message nonces 0 < k₁, k₂≤O(√q) are available. Recently, R. Gallant, R. Lambert, and S. Vanstone suggested a method to improve the efficiency of elliptic curve crytosystem using integer decomposition. In this paper, by applying the integer decomposition method to the algorithm proposed by Kuwakado and Tanaka, we extend the algorithm to work in the case when ?k₁?,? k₂?≤ O(√q) and improve the efficiency and completeness of the algorithm.

A note on N-polynomials over finite fields

김기태,이익권 강원경기수학회 2020 한국수학논문집 Vol.28 No.3

A simple type of Cohen's transformation consists of a polynomial and a linear fractional transformation. We study the effectiveness of Cohen transformation to find N-polynomials over finite fields.

Certain cubic polynomials over finite fields

김형돈,김재문,이익권 대한수학회 2009 대한수학회지 Vol.46 No.1

Motivated by XTR cryptosystem which is based on an irreducible polynomial x^3 -cx^2 +c^px -1 over F_{p^2}, we study polynomials of the form F(c,x)=x^3 -cx^2 +c^qx -1 over F_{q^2}$ with q=p^m. In this paper, we establish a one to one correspondence between the set of such polynomials and a certain set of cubic polynomials over F_q. Our approach is rather theoretical and provides an efficient method to generate irreducible polynomials over F_{q^2}. Motivated by XTR cryptosystem which is based on an irreducible polynomial x^3 -cx^2 +c^px -1 over F_{p^2}, we study polynomials of the form F(c,x)=x^3 -cx^2 +c^qx -1 over F_{q^2}$ with q=p^m. In this paper, we establish a one to one correspondence between the set of such polynomials and a certain set of cubic polynomials over F_q. Our approach is rather theoretical and provides an efficient method to generate irreducible polynomials over F_{q^2}.