• IEMEK Journal of Embedded Systems and Applications
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• v.11 no.4
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• pp.227-233
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• 2016

Efficient finite field arithmetic is essential for fast implementation of error correcting codes and cryptographic applications. Among the arithmetic operations over finite fields, the multiplication is one of the basic arithmetic operations. Therefore an efficient design of a finite field multiplier is required. In this paper, two new bit-parallel systolic multipliers for $GF(2^m)$ fields defined by AOP(all-one polynomial) have proposed. The proposed multipliers have a little bit greater space complexity but save at least 22% area complexity and 13% area-time (AT) complexity as compared to the existing multipliers using AOP. As compared to related works, we have shown that our multipliers have lower area-time complexity, cell delay, and latency. So, we expect that our multipliers are well suited to VLSI implementation.

• Journal of the Korea Society of Computer and Information
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• v.25 no.2
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• pp.41-48
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• 2020

In this paper, we derive a common computational part in an algorithm that can simultaneously perform multiplication and square over finite fields, and propose a low-area bit-parallel systolic array that reduces hardware through sequential processing. The proposed systolic array has less space and area-time (AT) complexity than the existing related arrays. In detail, the proposed systolic array saves about 48% and 44% of Choi-Lee and Kim-Kim's systolic arrays in terms of area complexity, and about 74% and 44% in AT complexity. Therefore, the proposed systolic array is suitable for VLSI implementation and can be applied as a basic component in hardware constrained environment such as IoT.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.18 no.2
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• pp.3-10
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• 2008

The choice of basis for representation of element in $GF(2^m)$ affects the efficiency of a multiplier. Among them, a multiplier using redundant representation efficiently supports trade-off between the area complexity and the time complexity since it can quickly carry out modular reduction. So time of a previous multiplier using redundant representation is faster than time of multiplier using others basis. But, the weakness of one has a upper space complexity compared to multiplier using others basis. In this paper, we propose a new efficient multiplier with consideration that polynomial exponentiation operations are frequently used in cryptographic hardwares. The proposed multiplier is suitable fer left-to-right exponentiation environment and provides efficiency between time and area complexity. And so, it has both time delay of $T_A+({\lceil}{\log}_2m{\rceil})T_x$ and area complexity of (2m-1)(m+s). As a result, the proposed multiplier reduces $2(ms+s^2)$ compared to the previous multiplier using equally-spaced polynomials in area complexity. In addition, it reduces $T_A+({\lceil}{\log}_2m+s{\rceil})T_x$ to $T_A+({\lceil}{\log}_2m{\rceil})T_x$ in the time complexity.($T_A$:Time delay of one AND gate, $T_x$:Time delay of one XOR gate, m:Degree of equally spaced irreducible polynomial, s:spacing factor)

• Proceedings of the IEEK Conference
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• 2002.06b
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• pp.277-280
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• 2002

This paper analyze the characteristics of three multipliers in finite fields GF(2m) from the point of view of processing time and area complexity. First, we analyze structure of three multipliers; 1) LSB-first systolic array, 2) LFSR structure, and 3) CA structure. To make performance analysis, each multiplier was modeled in VHDL and was synthesized for FPGA implementation. The simulation results show that LFSR structure is best from the point of view of area complexity, and LSB systolic array is best from the point of view of processing time per clock.

• Journal of the Institute of Electronics and Information Engineers
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• v.53 no.12
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• pp.42-49
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• 2016

This paper proposes a low-complexity generator which finds the first two minimum values using bit-serial scheme. A low-complexity generator is an important part for low-area LDPC decoders based on the min-sum decoding algorithm because the hardware complexity of generators utilizes a significant portion of LDPC decoders. To reduce hardware complexity, bit-serial LDPC decoders has been studied. The generator of the existing bit-serial LDPC decoders can find only the first minimum value, and thus it leads to a BER performance degradation. The proposed generator using bit-serial scheme finds the first two minimum values. Hence, it can improve the BER performance. In addition, the area-time complexity of the proposed generator is lower than those of the existing generators finding the first two minima.

• Journal of Korea Society of Digital Industry and Information Management
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• v.18 no.1
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• pp.1-9
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• 2022

Galois field arithmetic is important in error correcting codes and public-key cryptography schemes. Hardware realization of these schemes requires an efficient implementation of Galois field arithmetic operations. Multiplication is the main finite field operation and designing efficient multiplier can clearly affect the performance of compute-intensive applications. Diverse algorithms and hardware architectures are presented in the literature for hardware realization of Galois field multiplication to acquire a reduction in time and area. This paper presents a low complexity semi-systolic multiplier to facilitate parallel processing by partitioning Montgomery modular multiplication (MMM) into two independent and identical units and two-level systolic computation scheme. Analytical results indicate that the proposed multiplier achieves lower area-time (AT) complexity compared to related multipliers. Moreover, the proposed method has regularity, concurrency, and modularity, and thus is well suited for VLSI implementation. It can be applied as a core circuit for multiplication and division/exponentiation.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.38 no.6
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• pp.436-445
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• 2001

In this paper, we introduce modulo ( 2$^n$-1) parallel-processing residue multipliers, using Op Amp circuits, and their technological application to designing binary multipliers. The limit of multiplying speed in computational processing is a serious harrier in the advances of VLSI technology. To solve this problem, we implement a class of modulo ( 2$^n$-1) parallel multipliers having superior time complexity to O( log$_2$( log$_2$( log$_2$$^n$))) by applying Op Amp circuits, while investigating their technological application to binary multipliers. Since they have excellent time & area complexity compared with previous parallel multipliers, and are applicable to designing binary multipliers of the same efficiency, such parallel multipliers possess high academic value. Indexing Terms Modular Multipliers. Binary Multipliers. Parallel Processing, Operational Amplifiers, Mersenne Numbers.

• Korean Institute of Interior Design Journal
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• no.41
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• pp.137-145
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• 2003

This research analyzed the space scheme in connection with complexity, one of the new changes in the discount stores, and has a goal of predicting the direction of space scheme in the upcoming complexity era. The research was conducted in the following way. Firstly, this researcher tried to grasp what kinds of changes were required in the overall distribution industry socially and economically. Secondly, the characteristic and situation of discount stores were scrutinized. Thirdly, the domestic stores' complexity status was classified and types of those were elicited. Fourthly, the time-series change and use were analyzed. The result of this analysis reveals that the types of complexity can be divided by location and adjustment to environmental changes. The time-series analysis shows that total operating area, the number of parked cars and the tenant ratio have increased dramatically in 2000 and 2003. And, according to the correlation analysis between factors, the tenant ratio has, a strong correlation with other two factors. Self-complexity takes the basic form of living facilities and complexity with other facilities is combined with other cultural, sales, educational and administrative ones. Mass-complexity is merged with the stadiums, parks or station sites. As you've seen, the concept of complex shopping mall for the realization of one stop shopping and convenience will continue in the days to come. It is desirable that the study on the large-scale shopping spaces will be conducted continually for the preparedness of future life style.

• IEMEK Journal of Embedded Systems and Applications
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• v.7 no.2
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• pp.79-84
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• 2012

Efficient arithmetic design is essential to implement error correcting codes and cryptographic applications over finite fields. This article presents an efficient $AB^2$ multiplier in GF($2^m$) using a polynomial representation. The proposed multiplier produces the result in m clock cycles with a propagation delay of two AND gates and two XOR gates using O($2^m$) area-time complexity. The proposed multiplier is highly modular, and consists of regular blocks of AND and XOR logic gates. Especially, exponentiation, inversion, and division are more efficiently implemented by applying $AB^2$ multiplication repeatedly rather than AB multiplication. As compared to related works, the proposed multiplier has lower area-time complexity, computational delay, and execution time and is well suited to VLSI implementation.

• Journal of the Korea Society of Computer and Information
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• v.28 no.2
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• pp.69-75
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• 2023

Finite field arithmetic operations play an important role in a variety of applications, including modern cryptography and error correction codes. In this paper, we propose an efficient multiplication algorithm over finite fields using the Montgomery multiplication algorithm. Existing multipliers can be implemented using AND and XOR gates, but in order to reduce time and space complexity, we propose an algorithm using NAND and NOR gates. Also, based on the proposed algorithm, an efficient semi-systolic finite field multiplier with low space and low latency is proposed. The proposed multiplier has a lower area-time complexity than the existing multipliers. Compared to existing structures, the proposed multiplier over finite fields reduces space-time complexity by about 71%, 66%, and 33% compared to the multipliers of Chiou et al., Huang et al., and Kim-Jeon. As a result, our multiplier is proper for VLSI and can be successfully implemented as an essential module for various applications.