• 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 the Institute of Electronics Engineers of Korea TC
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• v.47 no.7
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• pp.93-101
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• 2010

In this paper we generate Gold-sequence by using M-sequence which is made by two primitive polynomial of GF(2). Generally M-sequence is generated by linear feedback shift register code generator. Here we show that this matrix of appropriate permutation has Hadamard matrix property. This matrix proves that Gold-sequence through two M-sequence and additive matrix of one column has one of major properties of Hadamard matrix, orthogonal. and this matrix show another property that multiplication with one matrix and transpose matrix of this matrix have the result of unit matrix. Also M-sequence which is made by linear feedback shift register gets Hadamard matrix property mentioned above by adding matrices of one column and one row. And high-speed conversion is possible through L-matrix and the S-matrix.

• Proceedings of the Korea Information Processing Society Conference
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• 2007.05a
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• pp.989-992
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• 2007

In this paper we introduce a new paradigm of physical layer security for wireless network. Existing security protocols like internet's transport layer security protocol has some security flaws that skilled hackers could exploit. Motivated from this point we introduce a new security protocol that works in physical layer which is much less vulnerable to hackers than any other higher layers. In our proposal, we incorporate the proposed security protocol within channel coding as channel coding is an essential part of wireless communication. We utilize the flexibility to choose a generator matrix (or generator polynomial) of a particular code that selects the code words as a core of our protocol. Each pair of wireless node will select a unique generator using their security key before they started to communicate with each other.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1627-1638
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• 2018

In this paper, we study an special type of cyclic codes called skew cyclic codes over the ring ${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p$, where p is a prime number. This set of codes are the result of module (or ring) structure of the skew polynomial ring (${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p$)[$x;{\theta}$] where $v^3=1$ and ${\theta}$ is an ${\mathbb{F}}_p$-automorphism such that ${\theta}(v)=v^2$. We show that when n is even, these codes are either principal or generated by two elements. The generator and parity check matrix are proposed. Some examples of linear codes with optimum Hamming distance are also provided.

• The Journal of the Korea institute of electronic communication sciences
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• v.17 no.2
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• pp.333-342
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• 2022

Cellular Automata (CA) is a discrete and abstract computational model that is being applied in various fields. Applicable as an excellent pseudo-random sequence generator, CA has recently developed into a basic element of cryptographic systems. Several studies on CA-based stream ciphers have been conducted and it has been observed that the encryption strength increases when the radius of a CA's neighbor is increased when appropriate CA rules are used. In this paper, among CAs that can be applied as a one-dimensional pseudo-random number sequence generator (PRNG), one-dimensional 5-neighbor CAs are classified according to the connection state of their neighbors, and the ignition relationship of the characteristic polynomial is obtained. Also this paper propose a synthesis algorithm for an asymmetric 1-D linear 5-neighbor MLCA in which the radius of the neighbor is increased by 2 using the one-dimensional 3-neighbor 90/150 CA state transition matrix.

• The Journal of the Korea institute of electronic communication sciences
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• v.13 no.2
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• pp.383-390
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• 2018

Since cellular automata(CA) is superior to LFSR in randomness, it is applied as an alternative of LFSR in various fields. However, constructing CA corresponding to a given polynomial is more difficult than LFSR. Cattell et al. and Cho et al. showed that irreducible polynomials are CA-polynomials. And Cho et al. and Sabater et al. gave a synthesis method of 90/150 CA corresponding to the power of an irreducible polynomial, which is applicable as a shrinking generator. Swan characterizes the parity of the number of irreducible factors of a trinomial over the finite field GF(2). These polynomials are of practical importance when implementing finite field extensions. In this paper, we show that the trinomial $x^{2^n-1}+X+1$ ($n{\geq}2$) are CA-polynomials. Also the trinomial $x^{2^a(2^n-1)}+x^{2^a}+1$ ($n{\geq}2$, $a{\geq}0$) are CA-polynomials.

• The Journal of the Korea institute of electronic communication sciences
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• v.15 no.6
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• pp.1105-1112
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• 2020

One-dimensional 3-neighborhood Cellular Automata (CA)-based pseudo-random number generators are widely applied in generating test patterns to evaluate system performance and generating key sequence generators in cryptographic systems. In this paper, in order to design a CA-based key sequence generator that can generate more complex and confusing sequences, we study a one-dimensional symmetric 5-neighborhood CA that expands to five neighbors affecting the state transition of each cell. In particular, we propose an n-cell one-dimensional symmetric 5-neighborhood CA synthesis algorithm using the algebraic method that uses the Krylov matrix and the one-dimensional 90/150 CA synthesis algorithm proposed by Cho et al. [6].

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.4
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• pp.379-386
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• 2016

Puncturing is the most common way of increasing the rate of convolutional codes. The puncturing process is done to the original code called the mother code by a specific puncturing pattern. In this article, we investigate into the question whether any convolutional code is obtainable by puncturing some (n, 1) mother codes. We present two sufficient conditions for the mother code and the puncturing pattern to satisfy in order that the punctured code is equivalent to the given (N, K) convolutional code.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.39A no.4
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• pp.165-171
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• 2014

The rate of the channel code can be controlled by various methods. Puncturing is one of the methods of increasing the code rate, and the original code before puncturing is called the mother code. Any (n,k) convolutional code is obtainable by puncturing some mother codes, and the process of finding the mother code is necessary for designing the optimum channel decoder. In this paper, we proved that any (n,n-1) convolutional code has (2,1) mother codes regardless of the puncturing pattern and showed that they must be equivalent.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.42 no.5
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• pp.951-958
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• 2017

In an attack context, the adversary wants to retrieve the message from the intercepted noisy bit stream without any prior knowledge of the channel codes used. The process of finding out the code parameters such as code length, dimension, and generator, for this purpose, is called the blind recognition of channel codes or the reconstruction of channel codes. In this paper, we suggest an improved algorithm of the blind recovery of rate k/n convolutional encoders in a noisy environment. The suggested algorithm improves the existing algorithm by Marazin, et. al. by evaluating the threshold value through the estimation of the channel error probability of the BSC. By applying the soft decision method by Shaojing, et. al., we considerably enhance the success rate of the channel reconstruction.