• KSII Transactions on Internet and Information Systems (TIIS)
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• 제12권12호
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• pp.6161-6176
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• 2018

Pseudorandom numbers are useful in cryptographic operations for using as nonce, initial vector, secret key, etc. Security of the cryptosystem relies on the secret key parameters, so a good pseudorandom number is needed. In this paper, we have proposed a new approach for generation of pseudorandom number. This method uses the three dimensional combinational puzzle Rubik Cube for generation of random numbers. The number of possible combinations of the cube approximates to 43 quintillion. The large possible combination of the cube increases the complexity of brute force attack on the generator. The generator uses cryptographic hash function. Chaotic map is being employed for increasing random behavior. The pseudorandom sequence generated can be used for cryptographic applications. The generated sequences are tested for randomness using NIST Statistical Test Suite and other testing methods. The result of the tests and analysis proves that the generated sequences are random.

• 대한수학회논문집
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• 제12권3호
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• pp.743-754
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• 1997

We introduce a class of finite and infinite moving average (MA) sequences of multivariate random vectors exponential marginals. The theory of dependence is used to show that in various cases the class of MA sequences consists of associated random variables. We utilize positive dependence properties to obtain some probability bounds for the multivariate processes.

• Journal of the Korean Data and Information Science Society
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• 제10권2호
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• pp.415-428
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• 1999

In this paper, we study the saddlepoint approximations for the ratio of two independent sequences of random variables. In Section 2, we review the saddlepoint approximation to the probability density function. In section 3, we derive an saddlepoint approximation formular for the tail probability by following Daniels'(1987) method. In Section 4, we represent a numerical example which shows that the errors are small even for small sample size.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.441-453
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• 2005

In this article we will introduce a real valued random field on a restricted indexed set and construct a classical asymptotic limit theorems on them. We will survey the basic properties of weakly dependent random processes and investigate two major mixing conditions for sequences of random variables. The concepts of weakly dependent sequence of random variables will be generalized to the case of random fields. Finally we will construct a central limit theorem and prove it.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.417-425
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• 2008

For stationary m-dimensional martingale difference sequences we prove the random functional central limit theorems and propose an almost sure consistent estimator for the limiting covariance matrix.

• 정보처리학회논문지C
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• 제12C권2호
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• pp.281-288
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• 2005

최근의 컴퓨터 네트워크에서 teletraffic의 양상은 Poisson 프로세스보다 self-similar 프로세스에 의해서 더 잘 반영된다. 이는 컴퓨터 네트워크의 teletraffic에 관련하여 self-similar한 성질을 고려하지 않는다면, 컴퓨터 네트워크의 성능에 관한 결과는 부정확 할 수밖에 없다는 의미가 된다. 따라서, 통신 네트워크에 관한 시뮬레이션을 수행하기 위한 매우 중요한 요소 중에 하나는 충분히 긴 self-similar한 sequence를 얼마나 잘 생성하느냐의 문제이다. 본 논문에서는 SRA (successive random addition) 방법을 이용한 pseudo-random self-similar sequence 생성기를 구현 및 분석하였다. 본 pseudo-random self-similar sequence 생성기의 성질을 매우 긴 sequence를 생성하는데 요구되는 통계적인 정확도와 생성시간에 대해서 분석하였다. 본 논문에서 제안한 SRA 방법을 이용한 pseudo-random self-similar sequence 생성기의 성능은 Hurst 변수의 상대적인 정확도로 보았을 때, 그리고 sequence의 생성시간을 고려했을 때에 적합함을 보였다. 이 생성기의 이론적 complexity는 n개의 난수를 발생하는데 O(n)이 요구된다.

• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.647-653
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• 2012

In this paper, we consider fuzzy random sets as (measurable) mappings from a probability space into the set of fuzzy sets and prove a uniform strong law of large numbers for sequences of independent and identically distributed fuzzy random sets. Our results generalize those of Bass and Pyke(1984)and Jang and Kwon(1998).

• Journal of Communications and Networks
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• 제7권1호
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• pp.21-28
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• 2005

In this paper, we analyze the performance of code division multiple access (CDMA) systems with orthogonal frequency division multiplexing (OFDM) that employ random spreading sequences in an additive white Gaussian noise (AWGN) channel. We obtain the probability density function (pdf) of the multiple access interference and extend the results to OFDM-CDMA systems to determine the pdf of multiple access and inter-carrier interference in terms of the number of users, the spreading length, the number of sub-carriers, and the frequency offset. We consider the synchronous downlink of cellular multi-carrier CDMA and derive a Gaussian approximation of the multiple access and inter-carrier interference. Overall the effect of frequency offset is shown to vary with the system loading. The analysis in this paper is critical for further development into fading channels and frequency selective multipath channels.

• Communications for Statistical Applications and Methods
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• 제22권6호
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• pp.647-653
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• 2015

Extreme value theory concerns the distributional properties of the maximum of a random sample; subsequently, it has been significantly extended to stationary random sequences satisfying weak dependence restrictions. We focus on distributional mixing condition $D(u_n)$ and the Berman condition based on covariance among weak dependence restrictions. The former is assumed for general stationary sequences and the latter for stationary normal processes; however, both imply the same distributional limit of the maximum of the normal process. In this paper $D(u_n)$ condition is shown weaker than Berman's covariance condition. Examples are given where the Berman condition is satisfied but the distributional mixing is not.

• Communications for Statistical Applications and Methods
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• 제21권3호
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• pp.245-251
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• 2014

Two exponential inequalities are established for a wide class of general weakly dependent sequences of random variables, called ${\psi}$-weakly dependent process which unify weak dependence conditions such as mixing, association, Gaussian sequences and Bernoulli shifts. The ${\psi}$-weakly dependent process includes, for examples, stationary ARMA processes, bilinear processes, and threshold autoregressive processes, and includes essentially all classes of weakly dependent stationary processes of interest in statistics under natural conditions on the process parameters. The two exponential inequalities are established on more general conditions than some existing ones, and are proven in simpler ways.