• 한국수학교육학회지시리즈B:순수및응용수학
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• 제6권2호
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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.

• 정보보호학회논문지
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• 제14권4호
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• pp.49-59
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• 2004

공개되지 않은 함수에 대한 입력과 그에 따른 출력을 이용하여 그 함수와 같은 입출력을 가지는 부울함수표현을 찾아내는 것이 부울함수 합성문제이다. 전자공학 및 암호학 분야에서는 이 문제가 수리계획법의 한 부류인 0-1 integer programming 문제로 귀결되며, 본 논문에서는 부울함수 합성문제를 해결하는 하나의 예로 DES 의 비공개 논리인 입력 6비트, 출력 4비트의 S-box에 대한 부울함수표현을 찾는다. 이러한 결과는 임의의 함수에 대한 효율적인 하드웨어 구현과 블록암호 알고리즘의 대수적 구조를 이용한 암호분석기법에 이용될 수 있다.

• 대한수학회보
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• 제60권3호
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• pp.561-574
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• 2023

In this paper, we focus on establishing the MacWilliams-type identities on vectorial Boolean functions with bent component functions. As their applications, we provide a bound for the non-existence of vectorial dual-bent functions with prescribed minimum degree, and several Gleason-type theorems are presented as well.

• 전기학회논문지P
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• 제53권4호
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• pp.210-215
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• 2004

This paper proposes an implicit method for computing the minimum cost feedback vertex set for a graph. For an arbitrary graph, a Boolean function is derived, whose satisfying assignments directly correspond to feedback vertex sets of the graph. Importantly, cycles in the graph are never explicitly enumerated, but rather, are captured implicitly in this Boolean function. This function is then used to determine the minimum cost feedback vertex set. Even though computing the minimum cost satisfying assignment for a Boolean function remains an NP-hard problem, it is possible to exploit the advances made in the area of Boolean function representation in logic synthesis to tackle this problem efficiently in practice for even reasonably large sized graphs. The algorithm has obvious application in flip-flop selection for partial scan. The algorithm proposed in this paper is the first to obtain the MFVS solutions for many benchmark circuits.

• 대한전자공학회논문지
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• 제21권4호
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• pp.43-51
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• 1984

부울함수의 간소화법에서 Quine Mcclustey법은 최소항들의 2진수 표현의 구조를 조사하는 방법을 쓰고 있다. 이 논문에서는 10진수로 표현한 최소항을 가지고 그들간의 큐브관계와 간소화에 따르는 제규칙을 정리로 간추려 표현하고 증명하였으며, 이들을 바탕으로 새로운 알고리즘의 부울함수 간소화법을 제안하였다. 예제를 들어 손작업의 방법을 보였고 아울러 이 과정을 FORTRAN 프로그램으로 작성하였다. 프로그램은 여분항을 포함하여 100개까지의 최소항을 가진 부울함수에 대하여 진성주항을 찾아 인쇄하도록 작성하였는데(배열을 크게 잡으면 그 이상도 가능함), 모든 경우에 손작업과 일치하는 결과를 얻었다.

• 대한수학회보
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• 제58권2호
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• pp.515-526
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• 2021

Denote by ��+ the set of probability measures supported on ℝ+. Suppose V�� is the variance function of the Cauchy-Stieltjes Kernel (CSK) family ��-(��) generated by a non degenerate probability measure �� ∈ ��+. We determine the formula for variance function under boolean multiplicative convolution power. This formula is used to identify the relation between variance functions under the map ${\nu}{\mapsto}{\mathbb{M}}_t({\nu})=({\nu}^{{\boxtimes}(t+1)})^{{\uplus}{\frac{1}{t+1}}}$ from ��+ onto itself.

• 정보보호학회논문지
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• 제11권6호
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• pp.127-134
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• 2001

PKC\`98에서 신 상욱 등은 SHA-1, RIPEMD-160, HAVAL의 장점을 이용한 새로운 해쉬함수를 제안하였다. 제안자들은 해쉬함수에 사용된 부울함수가 SAC(Strict Avalanche Criterion) 특성을 만족한다고 주장하였으나, 실제로는 SAC을 만족하지 않음을 알 수 있다. 본 논문에서는 PKC\`98에 제안된 해쉬함수에 사용된 부울함수가 SAC을 만족하는 경우의 충돌쌍을 찾음으로써, 일반적으로 암호학적으로 안전한 것으로 인식되는 논리를 사용하는 것이 오히려 안전성 저하 요인이 될 수도 있음을 지적한다.

• Kyungpook Mathematical Journal
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• 제48권2호
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• pp.195-206
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• 2008

The purpose of this note is to compare the rings of continuous functions, integer-valued or real-valued, in pointfree topology with those in classical topology. To this end, it first characterizes the Boolean frames (= complete Boolean algebras) whose function rings are isomorphic to a classical one and then employs this to exhibit a large class of frames for which the functions rings are not of this kind. An interesting feature of the considerations involved here is the use made of nonmeasurable cardinals. In addition, the integer-valued function rings for Boolean frames are described in terms of internal lattice-ordered ring properties.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1987년도 전기.전자공학 학술대회 논문집(I)
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• pp.226-229
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• 1987

This paper was aimed to, using a new data structure, develop a set of algorithms to execute the output function of Digital System. These functions were represented as directed, acyclic graphs. by applying many restrictions on vertices on graph, the efficient manipulation of boolean function was accomplished. The results were as follows; 1. A canonical representation of a boolean function was created by the reduction algorithm. 2. The operation of two functions was accomplished using t he apply algorithm, according to the binary operator. 3. The arguments having 1 as the value nf function were enumerated using the satisfy algorithm. 4. Composing TTL 74181 4-bit ALU and 74182 look-ahead carry generator, the ALU having 4-bit and 16-bit as word size was implemented.

• 충청수학회지
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• 제17권1호
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• pp.47-56
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• 2004

The nonlinearity of a Boolean function f on $GF(2)^n$ is the minimum hamming distance between f and all affine functions on $GF(2)^n$ and it measures the ability of a cryptographic system using the functions to resist against being expressed as a set of linear equations. Finding out the exact value of the nonlinearity of given Boolean functions is not an easy problem therefore one wants to estimate the nonlinearity using extra information on given functions, or wants to find a lower bound or an upper bound on the nonlinearity. In this paper we extend the notion of auto-correlations of Boolean functions to vector Boolean functions and obtain upper bounds and a lower bound on the nonlinearity of vector Boolean functions in the context of their auto-correlations. Also we can describe avalanche characteristics of vector Boolean functions by examining the extended notion of auto-correlations.