• The Journal of Korean Institute of Communications and Information Sciences
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• v.38A no.2
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• pp.156-163
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• 2013

The use of an error-correcting code is essential in communication systems where the channel is noisy. When channel coding parameters are unknown at a receiver side, decoding becomes difficult. To perform decoding without the channel coding information, we should estimate the parameters. In this paper, we introduce a method to reconstruct the generator polynomial of BCH(Bose-Chaudhuri-Hocquenghem) codes based on the idea that the generator polynomial is compose of minimal polynomials and BCH code is cyclic code. We present a probability compensation method to improve the reconstruction performance. This is based on the concept that a random data pattern can also be divisible by a minimal polynomial of the generator polynomial. And we confirm the performance improvement through an intensive computer simulation.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 1991.11a
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• pp.40-48
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• 1991

McEliece 공개키 암호체계에 대한 새로운 암호해독적 공격이 제시되어진다. 기존의 암호해독 algorithm이 exponential-time의 complexity를 가지는 반면, 본고에서 제시되어지는 algorithm은 polynomial-time의 complexity를 가진다. 모든 linear codes에는 systematic generator matrix가 존재한다는 사실이 본 연구의 동기가 된다. Public generator matrix로부터, 암호해독에 사용되어질 수 있는 새로운 trapdoor generator matrix가 Gauss-Jordan Elimination의 역할을 하는 일련의 transformation matrix multiplication을 통해 도출되어진다. 제시되어지는 algorithm의 계산상의 complexity는 주로 systematic trapdoor generator matrix를 도출하기 위해 사용되는 binary matrix multiplication에 기인한다. Systematic generator matrix로부터 쉽게 도출되어지는 parity-check matrix를 통해서 인위적 오류의 수정을 위한 Decoding이 이루어진다.

• Journal of information and communication convergence engineering
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• v.8 no.3
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• pp.317-322
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• 2010

This paper presents an algorithm generating inverse element over finite fields GF($3^m$), and constructing method of inverse element generator based on inverse element generating algorithm. An inverse computing method of an element over GF($3^m$) which corresponds to a polynomial over GF($3^m$) with order less than equal to m-1. Here, the computation is based on multiplication, square and cube method derived from the mathematics properties over finite fields.

• The Journal of the Korea institute of electronic communication sciences
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• v.11 no.9
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• pp.885-892
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• 2016

The nonlinear sequence generator called the shrinking generator was designed as nonlinear keystream generator composed by two maximum-length LFSRs. The shrunken sequences generated by the shrinking generator are included in the class of interleaved sequences and can be modelled as one of the output sequences of cellular automata (CA). In this paper, we propose a method for synthesizing a 90/150 CA-based sequence generator to generate a family of sequences with the same characteristic polynomial as the shrunken sequences.

• Journal of Astronomy and Space Sciences
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• v.37 no.3
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• pp.199-208
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• 2020

This paper presents a kinematic ephemeris generator for Korea Pathfinder Lunar Orbiter (KPLO) and its performance test results. The kinematic ephemeris generator consists of a ground ephemeris compressor and an onboard ephemeris calculator. The ground ephemeris compressor has to compress desired orbit propagation data by using an interpolation method in a ground system. The onboard ephemeris calculator can generate spacecraft ephemeris and the Sun/Moon ephemeris in onboard computer of the KPLO. Among many interpolation methods, polynomial interpolation with uniform node, Chebyshev interpolation, Hermite interpolation are tested for their performances. As a result of the test, it is shown that all the methods have some cases that meet requirements but there are some performance differences. It is also confirmed that, the Chebyshev interpolation shows better performance than other methods for spacecraft ephemeris generation, and the polynomial interpolation with uniform nodes yields good performance for the Sun/Moon ephemeris generation. Based on these results, a Kinematic ephemeris generator is developed for the KPLO mission. Then, the developed ephemeris generator can find an approximating function using interpolation method considering the size and accuracy of the data to be transmitted.

• East Asian mathematical journal
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• v.36 no.3
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• pp.359-364
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• 2020

It is known that a 2-generator knot K has a cyclic Alexander module ℤ[t, t^―1]/(Δ(t)) where Δ(t) is the Alexander polynomial of K. In this paper we explicitly show how to reduce 2-generator Alexander modules to cyclic ones by using Chiswell, Glass and Wilsons presentations of 2-generator knot groups $$<\;x,\;y\;{\mid}\;(x^{{\alpha}_1})^{y^{{\gamma}_1}},\;{\cdots}\;,\;(x^{{\alpha}_k})^{y^{{\gamma}_k}}\;>$$ where a^b = bab^-1.

• Journal of the Korea Institute of Military Science and Technology
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• v.4 no.2
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• pp.105-111
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• 2001

The shrinking generator is simple and stateable, and known that has good security properties. The bits of one output( $R_1$) are used to determine whether the corresponding bits of the second output will be used as part of the overall keystream. Two LFSRs consisting the generator generate pseudorandom sequences satisfying Golomb's postulates. We used this property to analyze the stream of LFSR $R_1$ of the generator.

• Proceedings of the IEEK Conference
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• 2004.08c
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• pp.514-518
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• 2004

This paper presents an algorithm generating inverse element over finite fields $GF(3^{m})$, and constructing method of inverse element generator based on inverse element generating algorithm. A method computing inverse of an element over $GF(3^{m})$ which corresponds to a polynomial over $GF(3^{m})$ with order less than equal to m-l. Here, the computation is based on multiplication, square and cube method derived from the mathematics properties over finite fields.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.247-255
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• 2011

Invertible functions with a single cycle property have many cryptographic applications. The main context in which we study them in this paper is pseudo random generation and stream ciphers. In some cryptographic applications we need a generator which generates binary sequences of period long enough. A common way to increase the size of the state and extend the period of a generator is to run in parallel and combine the outputs of several generators with different period. In this paper we will characterize a secure quadratic polynomial on $\mathbb{Z}_{2^n}$, which generates a binary sequence of period long enough and without consecutive elements.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.11 no.1
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• pp.35-42
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• 2001

The primitive polynomial on GF(q) is used in the area of the scrambler, the error correcting code and decode, the random generator and the cipher, etc. The algorithm that generates efficiently the primitive polynomial on GF(q) was proposed by A.D. Porto. The algorithm is a method that generates the sequence of the primitive polynomial by repeating to find another primitive polynomial with a known primitive polynomial. In this paper, we propose the algorithm that is improved in the A.D. Porto algorithm. The running rime of the A.D. Porto a1gorithm is O($\textrm{km}^2$), the running time of the improved algorithm is 0(m(m+k)). Here, k is gcd(k, $q^m$-1). When we find the primitive polynomial with m odor, it is efficient that we use the improved algorithm in the condition k, m>>1.