• Journal of Korea Society of Industrial Information Systems
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• v.11 no.1
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• pp.29-37
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• 2006

Due to the spread of mobile communication with the development of computer network, nowadays various types of multimedia data play an important role in many areas such as entertainments, culture contents, e-commerce or medical science. But for the real application of these data, the security in the course of saving or transferring them through the public network should be assured. In this sense, many encryption algorithm have been developed and utilized. Nonetheless, most of them have focused on the text data. So they may not be suitable to the multimedia application because of their large size and real time constraint. In this paper, a chaotic map has been employed to create a symmetric stream type of encryption scheme which may be applied to the digital images with a large amounts of data. Then an efficient algebraic encryption algorithm based on the elementary operations of the Boolean matrix and image data characteristics.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.337-342
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• 1995

A semiring is a binary system $(S, +, \times)$ such that (S, +) is an Abelian monoid (identity 0), (S,x) is a monoid (identity 1), $\times$ distributes over +, 0 $\times s s \times 0 = 0$ for all s in S, and $1 \neq 0$. Usually S denotes the system and $\times$ is denoted by juxtaposition. If $(S,\times)$ is Abelian, then S is commutative. Thus all rings are semirings. Some examples of semirings which occur in combinatorics are Boolean algebra of subsets of a finite set (with addition being union and multiplication being intersection) and the nonnegative integers (with usual arithmetic). The concepts of matrix theory are defined over a semiring as over a field. Recently a number of authors have studied various problems of semiring matrix theory. In particular, Minc [4] has written an encyclopedic work on nonnegative matrices.

• Biotechnology and Bioprocess Engineering:BBE
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• v.10 no.5
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• pp.400-407
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• 2005

Reverse engineering is defined as the process where the internal structures and dynamics of a given system are inferred and analyzed from external observations and relevant knowledge. The first part of this paper surveys existing techniques for biosystem reverse engineering. Network structure inference techniques such as Correlation Matrix Construction (CMC), Boolean network and Bayesian network-based methods are explained. After the numeric and logical simulation techniques are briefly described, several representative working software tools were introduced. The second part presents our component-based software architecture for biosystem reverse engineering. After three design principles are established, a loosely coupled federation architecture consisting of 11 autonomous components is proposed along with their respective functions.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.849-856
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• 1995

There are some papers on structure theorems for the spaces of matrices over certain semirings. Beasley, Gregory and Pullman [1] obtained characterizations of semiring rank 1 matrices over certain semirings of the nonnegative reals. Beasley and Pullman [2] also obtained the structure theorems of Boolean rank 1 spaces. Since the semiring rank of a matrix differs from the column rank of it in general, we consider a structure theorem for semiring rank in [1] in view of column rank.

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.645-657
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• 1994

If S is a semiring of nonnegative reals, which linear operators T on the space of $m \times n$ matrices over S preserve the column rank of each matrix\ulcorner Evidently if P and Q are invertible matrices whose inverses have entries in S, then $T : X \longrightarrow PXQ$ is a column rank preserving, linear operator. Beasley and Song obtained some characterizations of column rank preserving linear operators on the space of $m \times n$ matrices over $Z_+$, the semiring of nonnegative integers in [1] and over the binary Boolean algebra in [7] and [8]. In [4], Beasley, Gregory and Pullman obtained characterizations of semiring rank-1 matrices and semiring rank preserving operators over certain semirings of the nonnegative reals. We considers over certain semirings of the nonnegative reals. We consider some results in [4] in view of a certain column rank instead of semiring rank.

• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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• pp.9-13
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• 1983

M$_{n}$(F) denotes the set of all n*n matrices over F={0, 1}. For a, b.mem.F, define a+b=max{a, b} and ab=min{a, b}. Under these operations a+b and ab, M$_{n}$(F) forms a multiplicative semigroup (see [1], [4]) and we call it the semigroup of the n*n boolean matrices over F={0, 1}. Since the semigroup M$_{n}$(F) is the matrix representation of the semigroup B$_{n}$ of the binary relations on the set X with n elements, we may identify M$_{n}$(F) with B$_{n}$ for finding all D-classes.l D-classes.

• Proceedings of the KIEE Conference
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• 1987.07b
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• pp.1556-1559
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• 1987

In this paper, a new state assignment method is proposed for the implementation of the area-effective control part. Introducing the, concept of adjacency matrix to control table generated by SDL(Symbolic Description Language) hardware compiler, a state assignment method is proposed with which minimal number of flip flops and effective number of product terms can be obtained to accomplish the area-effective implementation. Also, with substituting the assigned code to state transition table, boolean equations are obtained through 2-level logic minimization. Proposed algorithm is programmed in C-language on VAX-750/UNIX and b efficiency is shown by the practical example.

• Journal of Information Technology Services
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• v.3 no.2
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• pp.99-104
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• 2004

Conventional and public-key cryptography has been widely accepted as a base technology for the design of computer security systems. D-classes have the potential for application to conventional and public-key cryptography. However, there are very few results on D-classes because the computational complexity of D-class computation is NP-complete. This paper discusses the design of algorithms for the efficient computation of D-classes and the Java implementation of them. In addition, the paper implements the same D-class computation algorithms in C and shows the performance of C and Java programming languages for the computation-intensive applications by comparing their execution results.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.47
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• pp.219-232
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• 1998

A lot of difficulties exist in analyzing the structure of a system owing to the complex and organic relations in the systems we face in reality. Focuses have been put on the research of optimal solution in a defined structure, however, on the assumption that the structure of the system has been already defined. With the grasping of the structure as the most prior condition, ISM(Interpretive Structural Modeling) and FSM(Fuzzy Structural Modeling) are suggested as solutions in this paper. ISM uses the systematic application of some elementary notions of graph theory and boolean algebra, FSM uses Fuzzy conception for representing relationship between elements. In FSM, the entries in the relation matrix are taken to value on the interval [0,1] by virtue of a fuzzy binary relation. Numeric examples are used as the actual application as follows.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.35 no.5
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• pp.249-257
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• 2022

This paper presents an improved computational framework for the direct-solution-based finite element tearing and interconnecting (FETI) algorithm. The FETI-local algorithm is further improved herein, and localized Lagrange multipliers are used to define the interface among its subdomains. Selective inverse entry computation, using a property of the Boolean matrix, is employed for the computation of the subdomain interface stiffness and load, in which the original FETI-local algorithm requires a full matrix inverse computation of a high computational cost. In the global interface computation step, the original serial computation is replaced by a parallel multi-frontal method. The performance of the improved FETI-local algorithm was evaluated using a numerical example with 64 million degrees of freedom (DOFs). The computational time was reduced by up to 97.8% compared to that of the original algorithm. In addition, further stable and improved scalability was obtained in terms of a speed-up indicator. Furthermore, a performance comparison was conducted to evaluate the differences between the proposed algorithm and commercial software ANSYS using a large-scale computation with 432 million DOFs. Although ANSYS is superior in terms of computational time, the proposed algorithm has an advantage in terms of the speed-up increase per processor increase.