• Journal of the Korean Institute of Telematics and Electronics B
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• v.28B no.10
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• pp.799-806
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• 1991

Utilizing dual basis, normal basis, and subfield representation, three different finite field multipliers are presented in this paper. First, we propose an extended dual basis multiplier based on Berlekamp's bit-serial multiplication algorithm. Second, a detailed explanation and design of the Massey-Omura multiplier based on a normal basis representation is described. Third, the multiplication algorithm over GF(($2^{n}$) utilizing subfield is proposed. Especially, three different multipliers are designed over the finite field GF(($2^{4}$) and the complexity of each multiplier is compared with that of others. As a result of comparison, we recognize that the extendd dual basis multiplier requires the smallest number of gates, whereas the subfield multiplier, due to its regularity, simplicity, and modularlity, is easier to implement than the others with respect to higher($m{\ge}8$) order and m/2 subfield order.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.14 no.3
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• pp.216-226
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• 1989

In this paper, we explain about an outline of the decoding method for double encoding system using the error correcting capacitance and a simple decoding method. We have been taken formation two-dimension code word of doubly-encoded code using $C_1$(32, 28, 5) and $C_2$(32, 26, 7) Reed-Solomon codes, and had computer simulation of the erroe correcting processes in frequency domain. On these processes, the newly developed digital signal processing technology such as error correction using Berlekamp-Massey algorithm in frequency domain have been proven.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.3C
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• pp.64-68
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• 2005

Reed-Solomon code is one of the most versatile channel codes. The encoder can be implemented with two famous structures: ordinary and bit-serial. The ordinary encoder is generally known to be complex and fast, while the bit-serial encoder is simple and not so fast. However, it may not be true for a longer codeword length at least in VHDL implementation. In this letter, it is shown that, when the encoder is implemented with VHDL, the number of logic gates of the bit-serial encoder might be larger than that of the ordinary encoder if the dual basis conversion table has to be used. It is also shown that the encoding speeds of the two VHDL implemented encoders are exactly same.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.7
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• pp.90-97
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• 1989

In this paper, we have taken the formation of two-dimension codeword named doubly-encoded code using the Reed-Solomon code, C1(32, 28) with minimum distance 5 and C2(32, 26) with minimum distance 7 and we have had computer simulation of these error correcting processes using modeled R-DAT (Rotationary Digital Audio Tape). As the result, the error rate per symbol has been decreased about 0.05 and on these processes, the newly developed digital signal processing technology such as erro correction using Berlekamp-Massey algorithm in frequency domain have been proven.

• Journal of Information Technology Services
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• v.19 no.1
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• pp.145-158
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• 2020

With the development and widespread application of online shopping, the number of online consumers has increased. With one click of a mouse, people can buy anything they want without going out and have it sent right to the doors. As consumers benefit from online shopping, people are becoming more concerned about protecting their privacy. In the group buying scenario described in our paper, online shopping was regarded as intra-group communication. To protect the sensitive information of consumers, the polynomial-based encryption key sharing method (Piao et al., 2013; Piao and Kim, 2018) can be applied to online shopping communication. In this paper, we analyze security problems by using a polynomial-based scheme in the following ways : First, in Kamal's attack, they said it does not provide perfect forward and backward secrecy when the members leave or join the group because the secret key can be broken in polynomial time. Second, for simultaneous equations, the leaving node will compute the new secret key if it can be confirmed that the updated new polynomial is recomputed. Third, using Newton's method, attackers can successively find better approximations to the roots of a function. Fourth, the Berlekamp Algorithm can factor polynomials over finite fields and solve the root of the polynomial. Fifth, for a brute-force attack, if the key size is small, brute force can be used to find the root of the polynomial, we need to make a key with appropriately large size to prevent brute force attacks. According to these analyses, we finally recommend the use of a relatively reasonable hash-based mechanism that solves all of the possible security problems and is the most suitable mechanism for our application. The study of adequate and suitable protective methods of consumer security will have academic significance and provide the practical implications.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.45 no.6
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• pp.96-103
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• 2008

This paper proposes a new low-power and small-area Reed-Solomon decoder. The proposed Reed-Solomon decoder using a novel simplified form of the modified Euclid's algorithm can support low-hardware complexity and low-Power consumption for Reed-Solomon decoding. The simplified modified Euclid's algorithm uses new initial conditions and polynomial computations to reduce hardware complexity, and thus, the implemented architecture consisting of 3r basic cells has the lowest hardware complexity compared with existing modified Euclid's and Berlekamp-Massey architectures. The Reed-Solomon decoder has been synthesized using the $0.18{\mu}m$ Samsung standard cell library and operates at 370MHz and its data rate supports up to 2.9Gbps. For the (255, 239, 8) RS code, the gate counts of the simplified modified Euclid's architecture and the whole decoder excluding FIFO memory are only 20,166 and 40,136, respectively. Therefore, the proposed decoder can reduce the total gate count at least 5% compared with the conventional DCME decoder.

• 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.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.26 no.2
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• pp.301-314
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• 2016

Juels and Sudan's fuzzy vault scheme has been applied to various researches due to its error-tolerance property. However, the fuzzy vault scheme does not consider the difference between people's preferences, even though the authors instantiated movie lover' case in their paper. On the other hand, to make secure and high performance face authentication system, Nyang and Lee introduced a face authentication system, so-called fuzzy face vault, that has a specially designed association structure between face features and ordinary fuzzy vault in order to let each face feature have different weight. However, because of optimizing intra/inter class difference of underlying feature extraction methods, we can easily expect that the face authentication system does not successfully decrease the face authentication failure. In this paper, for ensuring the flexible use of the fuzzy vault scheme, we introduce the bucket structure, which differently implements the weighting idea of Nyang and Lee's face authentication system, and three distribution functions, which formalize the relation between user's weight of preferences and system implementation. In addition, we suggest a matchmaker scheme based on them and confirm its computational performance through the movie database.