• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.297-309
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• 2006

In this paper, we consider cooperative games arising from integer domination problem on graphs. We introduce two games, ${\kappa}-domination$ game and its monotonic relaxed game, and focus on their cores. We first give characterizations of the cores and the relationship between them. Furthermore, a common necessary and sufficient condition for the balancedness of both games is obtained by making use of the technique of linear programming and its duality.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.265-275
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• 2006

In this paper, we introduce a fractional domination game arising from fractional domination problems on graphs and focus on its balancedness and concavity. We first characterize the core of the fractional domination game and show that its core is always non-empty taking use of dual theory of linear programming. Furthermore we study concavity of this game.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1275-1281
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• 2011

Many authors studied cooperative games that arise from variants of dominating set games on graphs. In wireless networks, the connected dominating set is used to reduce routing table size and communication cost. In this paper, we introduce a connected dominating set game to model the cost allocation problem arising from a connected dominating set on a given graph and study its core. In addition, we give a polynomial time algorithm for determining the balancedness of the game on a tree, for finding a element of the core.

• Journal of the Korean Data and Information Science Society
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• v.20 no.1
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• pp.49-55
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• 2009

A cooperative game often arises from domination problem on graphs and the core in a cooperative game could be the optimal solution of a linear programming of a given game. In this paper, we define a {k}-fractional domination game which is a specific type of fractional domination games and find the core of a {k}-fractional domination game. Moreover, we may investigate the balancedness of a {k}-fractional domination game using a concept of a linear programming and duality. We also conjecture the concavity for {k}-fractional dominations game which is important problem to find the elements of the core.

• East Asian mathematical journal
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• v.31 no.5
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• pp.717-725
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• 2015

Velzen introduced the rigid and relaxed dominating set games and showed that the rigid game being balanced is equivalent to the relaxed game being balanced in 2004. After then various variants of dominating set games were introduced and it was shown that for each variant, a rigid game being balanced is equivalent to a relaxed game being balanced. It is natural to ask if for any other variant of dominating set game, the balancedness of a rigid game and the balancedness of a relaxed game are equivalent. In this paper, we show that the answer for the question is negative by considering the rigid and relaxed paired-domination games, which is considered as a variant of dominating set games. We characterize the cores of both games and show that the rigid game being balanced is not equivalent to the relaxed game being balanced. In addition, we study the cores of paired-dominations games on paths and cycles.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.269-278
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• 2000

A Boolean function generates a binary sequence which is frequently used in a stream cipher. There are number of critical concepts which a Boolean function, as a key stream generator in a stream cipher, satisfies. These are nonlinearity, correlation immunity, balancedness, SAC(strictly avalanche criterion), PC(propagation criterion) and so on. In this paper, we present the algorithms for generating random nonlinear combining functions satisfying given correlation immune order and nonlinearity. These constructions can be applied for designing the key stream generators. We use Microsoft Visual C++6.0 for our program.

• The Korean Journal of Applied Statistics
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• v.5 no.1
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• pp.19-28
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• 1992

In this paper, minimal balanced $2^t$ fractional factorial designs which permit the estimation of main effects and 2-factor interactions are developed by using a partially balanced array. Such designs are characterized by a minimum number of runs and some balancedness property of the variance-covariance matrix of the estimates. In addition to describing the designs, optimality criteria are discussed and the trace-optimal designs are presented. The proposed designs are especially useful in Taguchi method, where we need to investigate up to 2-factor interactions of the control factors.

• The Pure and Applied Mathematics
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• v.6 no.2
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• pp.79-86
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• 1999

A Boolean function generates a binary sequence which is frequently used in a stream cipher. There are number of critical concepts which a Boolean function, as a key stream generator in a stream cipher, satisfies. These are nonlinearity, correlation immunity, balancedness, SAC (strictly avalanche criterion), PC (propagation criterion) and so on. In this paper we construct an algorithm for finding the correlation immune order of a Boolean function, and check how long to find the correlation immune order of a given Boolean function in our algorithm.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.9 no.1
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• pp.127-134
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• 1999

Boolean functions have an important role for designing block ciphers and hash functions. In this paper, we propose a method for designing optimum correlation immune functions. We also analyze their cryptographic properties - balancedness, nonlinearity, correlation value to the set of linear functions, correlation immunity, propagation characteristic, and algebraic degree. Such functions are special type of Semi-bent functions [2,5]

• Journal of the Korea Institute of Information Security & Cryptology
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• v.8 no.4
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• pp.3-20
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• 1998

해쉬 함수는 임의의 길이를 갖는 메세지를 규정된 길이의 값으로 압축하는 알고리듬으로 메시지 정보의 무결정 , 사용자 인증, 바이러스 침투 예방에 응용될 수 있는 핵심 보안 알고리듬이다. 또한 안전한 해쉬 함수는 일방향성, 충돌회피성, 고속 동작성 등의 특성을 지녀야 한다. 본 노눈에서는 응용에 따라 128, 160, 192, 224, 256 비트 길이로 출력을 생성하고 암호학적으로 강력한 안전성을 지닌 해쉬 알고리듬(HAVES: Hash Algorithm with Variable IEngth Speed)을 제안한다. 이 해쉬 알고리듬은 메시지 블록을 1024비트 단뒤로 처리하고 연산의 효과적인 배열을 통해 비교적 빠른 속도로 동작한다. 제안하는 해쉬 알고리듬은 0-1 균형성(Balancedness), 높은 비선형성(Nonlinearity), 구조적인 선형 비등가성 (Linearly Inequivalent), 상호 출력 무상관성(Mutually Output Uncorrelated), SAC(Strict Avalanche Criterion)를 모두 만족함으로서 효율성과 안전성을 도모한다. 더불어 안전성이 요구되는 실용적인 응용에 맞게 출력 길이를 가변적으로 선택할 수 있도록 했다.