• Title/Summary/Keyword: homomorphism

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Secure Data Aggregation Using Enhanced Homomorphism in Smart Grids (스마트 그리드에서 향상된 Homomorphism 을 이용한 안전한 데이터 애그리게이션)

  • Park, Ji-Hae;Choi, Kyung;Doh, In-Shil;Chae, Ki-Joon
    • Proceedings of the Korea Information Processing Society Conference
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    • 2011.04a
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    • pp.993-996
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    • 2011
  • 최근 그린 IT 에 대한 관심이 점차 고조되면서, 이 사업의 일환으로 저탄소, 녹색 성장을 위한 지능형 전력망인 스마트 그리드의 도입이 발 빠르게 진행되고 있다. 스마트 그리드를 통해 전력 공급자와 소비자의 양방향 통신으로 에너지 효율의 최적화가 가능하지만, 동시에 사이버 공격에 의한 개인정보의 노출위험에 대한 우려도 제기되고 있는 상황이다. 데이터의 안전한 전송을 위해 다양한 암호화 방식이 제안되고 있으며, 본 논문에서는 기밀성에만 초점을 맞춘 Homomorphic 암호화의 허점을 보완하기 위하여 additive Homomorphic 방식을 기반으로 하여 데이터 무결성을 보장 할 수 있는 새로운 방식을 제안하였다. 이 메커니즘을 통해 데이터는 최종 목적지까지 안전하게 도달했으며, 위조 및 변조 되지 않았다는 것을 보장받을 수 있다.

SELF-MAPS ON M(ℤq, n + 2) ∨ M(ℤq, n + 1) ∨ M(ℤq, n)

  • Ho Won Choi
    • Journal of the Chungcheong Mathematical Society
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    • v.36 no.4
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    • pp.289-296
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    • 2023
  • When G is an abelian group, we use the notation M(G, n) to denote the Moore space. The space X is the wedge product space of Moore spaces, given by X = M(ℤq, n+ 2) ∨ M(ℤq, n+ 1) ∨ M(ℤq, n). We determine the self-homotopy classes group [X, X] and the self-homotopy equivalence group 𝓔(X). We investigate the subgroups of [Mj , Mk] consisting of homotopy classes of maps that induce the trivial homomorphism up to (n + 2)-homotopy groups for j ≠ k. Using these results, we calculate the subgroup 𝓔dim#(X) of 𝓔(X) in which all elements induce the identity homomorphism up to (n + 2)-homotopy groups of X.

Towards A Dichotomy for the List Switch Homomorphism Problem for Signed Graphs

  • Hyobeen Kim;Mark Siggers
    • Kyungpook Mathematical Journal
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    • v.63 no.3
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    • pp.355-372
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    • 2023
  • We make advances towards a structural characterisation of the signed graphs H for which the list switch H-colouring problem List-S-Hom(H) can be solved in polynomial time. We conjecture two different characterisations, the second refining the first, in the case that the graph H can be switched to a graph in which every negative edge is also positive. Using a recent proof of the first characterisations for reflexive signed graphs, by Bok et. al., we prove the second characterisation for reflexive signed graphs. We also provide several tools for reducing the problem to the bipartite case, and prove a full complexity dichotomy for a related problem.

COHOMOLOGY AND GENERALIZED GOTTLIEB GROUPS

  • Lee, Kee Young
    • Journal of the Chungcheong Mathematical Society
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    • v.18 no.1
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    • pp.23-31
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    • 2005
  • In this paper, we observe the relation between the concept of generalized Gottlieb groups and the Hurewicz homomorphism.

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RELATIVE REGULAR RELATIONS

  • Yu, Jung Ok
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.3
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    • pp.525-534
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    • 2009
  • In this paper the relative regular relations with respect to a homomorphism are defined and it will be given the necessary and sufficient conditions for the relations to be transitive.

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A High-Performance Fault-Tolerant Switching Network and Its Fault Diagnosis (고성능 결함감내 스위칭 망과 결함 진단법)

  • 박재현
    • Journal of KIISE:Information Networking
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    • v.31 no.3
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    • pp.335-346
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    • 2004
  • In this paper, we present a high-performance fault-tolerant switching networks using a deflection self-routing scheme, and present fault-diagnosis method for the network. We use the facts: 1) Each stage of the Banyan network is arrayed as the sequences of a Cyclic group of SEs. 2) There is the homomorphism between adjacent stages from a view of self-routing, so that all of each Cyclic group is the subgroup of the Cyclic group in the next stage, and there are factor groups due to such subgroup and homomorphism. We provide high-performance fault-tolerant switching networks of which the all links including augmented links are used as the alternate links detouring faulty links. We also present the fault diagnosis scheme for the proposed switching network that provide multiple paths for each input-output pair.

INTUITIONISTIC FUZZY SUBGROUPS AND COSETS

  • HUR, KUL;JANG, SU YOUN;KANG, HEE WON
    • Honam Mathematical Journal
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    • v.26 no.1
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    • pp.17-41
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    • 2004
  • In this paper, we obtain the intuitionistic fuzzy subgroups generated by intuitionistic fuzzy sets and some properties preserved by a ring homomorphism. Furthermore, we introduce the concept of intuitionistic fuzzy coset and study some of it's properties.

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STABILITY OF THE CAUCHY FUNCTIONAL EQUATION IN BANACH ALGEBRAS

  • Lee, Jung Rye;Park, Choonkil
    • Korean Journal of Mathematics
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    • v.17 no.1
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    • pp.91-102
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    • 2009
  • Using the fixed point method, we prove the generalized Hyers-Ulam stability of homomorphisms in Banach algebras and of derivations on Banach algebras for the 3-variable Cauchy functional equation.

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THE CONSTRUCTION OF RELATIVE F-REGULAR RELATIONS

  • Song, Hyungsoo
    • Korean Journal of Mathematics
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    • v.9 no.2
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    • pp.123-128
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    • 2001
  • Given a homomorphism ${\Pi}:X{\rightarrow}Y$, with Y minimal, we will introduce the concept of a relative (to ${\Pi}$) F-regular relation which generalize the notions of F-proximality, F-regularity and relative F-proximality, and will study its properties.

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