• Journal of the Institute of Electronics Engineers of Korea SD
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• v.44 no.3 s.357
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• pp.35-42
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• 2007

The finite-field division can be applied to the elliptic curve cryptosystems. However, an efficient algorithm and the hardware design are required since the finite-field division takes much time to compute. In this paper, we propose a radix-4 systolic divider on $GF(2^m)$ with comparative area and performance. The algorithm of the proposed divide, is mathematically developed and new counter structure is proposed to map on low-cost systolic cells, so that the proposed systolic architecture is suitable for YLSI design. Compared to the bit-parallel, bit-serial and digit-serial dividers, the proposed divider has relatively effective high performance and low cost. We design and synthesis $GF(2^{193})$ finite-field divider using Dongbuanam $0.18{\mu}m$ standard cell library and the maximum clock frequency is 400MHz.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.9
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• pp.1115-1124
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• 1988

A two-dimensional systolic array for fast Fourier transform, which has a regular and recursive VLSI architecture is presented. The array is constructed with identical processing elements (PE) in mesh type, and due to its modularity, it can be expanded to an arbitrary size. A processing element consists of two data routing units, a butterfly arithmetic unit and a simple control unit. The array computes FFT through three procedures` I/O pipelining, data shuffling and butterfly arithmetic. By utilizing parallelism, pipelining and local communication geometry during data movement, the two-dimensional systolic array eliminates global and irregular commutation problems, which have been a limiting factor in VLSI implementation of FFT processor. The systolic array executes a half butterfly arithmetic based on a distributed arithmetic that can carry out multiplication with only adders. Also, the systolic array provides 100% PE activity, i.e., none of the PEs are idle at any time. A chip for half butterfly arithmetic, which consists of two BLC adders and registers, has been fabricated using a 3-um single metal P-well CMOS technology. With the half butterfly arithmetic execution time of about 500 ns which has been obtained b critical path delay simulation, totla FFT execution time for 1024 points is estimated about 16.6 us at clock frequency of 20MHz. A one-PE chip expnsible to anly size of array is being fabricated using a 2-um, double metal, P-well CMOS process. The chip was layouted using standard cell library and macrocell of BLC adder with the aid of auto-routing software. It consists of around 6000 transistors and 68 I/O pads on 3.4x2.8mm\ulcornerarea. A built-i self-testing circuit, BILBO (Built-In Logic Block Observation), was employed at the expense of 3% hardware overhead.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.2
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• pp.45-52
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• 2002

In this contributions, we propose a new MSB(most significant bit) algorithm based on AOP(All One Polynomial) and two parallel semi-systolic architectures to computes $AB^2$over finite field $GF(2^m)$. The proposed architectures are based on standard basis and use the property of irreducible AOP(All One Polynomial) which is all coefficients of 1. The proposed parallel semi-systolic architecture(PSM) has the critical path of $D_{AND2^+}D_{XOR2}$ per cell and the latency of m+1. The modified parallel semi-systolic architecture(WPSM) has the critical path of $D_{XOR2}$ per cell and has the same latency with PSM. The proposed two architectures, PSM and MPSM, have a low latency and a small hardware complexity compared to the previous architectures. They can be used as a basic architecture for exponentiation, division, and inversion. Since the proposed architectures have regularity, modularity and concurrency, they are suitable for VLSI implementation. They can be used as a basic architecture for algorithms, such as the Diffie-Hellman key exchange scheme, the Digital Signature Algorithm(DSA), and the ElGamal encryption scheme which are needed exponentiation operation. The application of the algorithms can be used cryptosystem implementation based on elliptic curve.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.1C
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• pp.140-148
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• 2008

Using the self duality of an optimal normal basis(ONB) of type II, we present a bit parallel and bit serial systolic arrays over GF($2^m$) which has a low hardware complexity and a low latency. We show that our multiplier has a latency m+1 and the basic cell of our circuit design needs 5 latches(flip-flops). Comparing with other arrays of the same kinds, we find that our array has significantly reduced latency and hardware complexity.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.361-364
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• 2002

Shortest path problem belongs to the combinatorial optimization problem and plays an important role in the field of computer aided design. It can either be directly applied as in the case of routing or serves as a important subroutine in more complex problems. In this paper, a systolic array for the SSSP(single-source shortest path problem) was derived. The array was modeled and simulated in RTL level using VHDL, then synthesized to a schematic and finally implemented to a layout using the cell library based on 0.35 $\mu\textrm{m}$ CMOS 1-poly 4-metal CMOS technology.

• Journal of Korea Society of Digital Industry and Information Management
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• v.16 no.2
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• pp.1-9
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• 2020

Many cryptographic and error control coding algorithms rely on finite field GF(2m) arithmetic. Hardware implementation of these algorithms needs an efficient realization of finite field arithmetic operations. Finite field multiplication is complicated among the basic operations, and it is employed in field exponentiation and division operations. Various algorithms and architectures are proposed in the literature for hardware implementation of finite field multiplication to achieve a reduction in area and delay. In this paper, a low area and delay efficient semi-systolic multiplier over finite fields GF(2m) using the modified Montgomery modular multiplication (MMM) is presented. The least significant bit (LSB)-first multiplication and two-level parallel computing scheme are considered to improve the cell delay, latency, and area-time (AT) complexity. The proposed method has the features of regularity, modularity, and unidirectional data flow and offers a considerable improvement in AT complexity compared with related multipliers. The proposed multiplier can be used as a kernel circuit for exponentiation/division and multiplication.

• Proceedings of the KIEE Conference
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• 1987.07b
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• pp.1488-1491
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• 1987

This paper describes 16-point FFT processor using systolic array and its implementation into VLSI. Designed FFT processor executes FFT/IFFT arithmetic under mode control and consists of cell array, array controller and input/output buffer memory. For design for testibility, we added built-in self test circuit into designed FFT processor. To verify designed 16-point FFT processor, logic simulation was performed by YSLOG on MICRO-VAXII. From the simulation results, it is estimated that the proposed FFT processor can perform 16-point FFT in about 4400[ns].

• 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 Korean Institute of Telematics and Electronics T
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• v.35T no.1
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• pp.59-66
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• 1998

In this paper, the high-speed decoder for RS(Reed-Solomon) code, one of the most popular error correcting code, is implemented using VHDL. This RS decoder is designed in transform domain instead of most time domain. Because of the simplicity in structure, transform decoder can be easily realized VLSI chip. Additionally the pipeline architecture, which is similar to a systolic array is applied for all design. Therefore, This transform RS decoder is suitable for high-rate data transfer. After synthesis with FPGA technology, the decoding rate is more 43 Mbytes/s and the area is 1853 LCs(Logic Cells). To compare with other product with pipeline architecture, this result is admirable. Error correcting ability and pipeline performance is certified by computer simulation.

• Korean Journal of Clinical Laboratory Science
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• v.45 no.4
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• pp.131-138
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• 2013

Insulin resistance and pancreatic beta cell dysfunction have been established as being related to the diabetes. Lately, what is emphasizing is that those have been shown as something related to the metabolic syndrome and cardiovascular disease. Homeostasis model assessment (HOMA), simple index is calculated on blood levels of fasting glucose and insulin. And HOMA has been widely validated and applied for insulin resistance and pancreatic beta cell dysfunction. We also assessed the factors relative to insulin resistance and ${\beta}$ cell function determined by HOMA. The data from the 2010 Korean National Health and Nutrition Examination Survey were used. Analysis was done for 3,465 nondiabetic subjects (male 1,357, female 2,108). At baseline, anthropometric measurements were done and fasting glucose, insulin, lipid (Total cholesterol, HDL cholesterol, LDL cholesterol and Triglycerides) profiles were measured. HOMA-insulin resistance (HOMA-IR) and beta cell function (HOMA ${\beta}$-cell) were calculated from fasting glucose and insulin levels. In male, the value of HOMA-IR and HOMA ${\beta}$-cell was the highest among 30's and decreased as the age increased. In female, the value of HOMA-IR increased with age, while HOMA ${\beta}$-cell decreased. High HOMA-IR and low HOMA ${\beta}$-cell were associated with the highest value of fasting glucose and systolic blood pressure. Low HOMA-IR and high HOMA ${\beta}$-cell showed the lowest concentration of fasting glucose and the highest concentration of HDL cholesterol. High HOMA-IR and high HOMA ${\beta}$-cell were connected with BMI, Total cholesterol, LDL cholesterol, and Triglycerides. There was a negative correlation between HOMA ${\beta}$-cell and age. The correlation coefficients of HOMA-IR and HOMA ${\beta}$-cell showed the highest value among weight, BMI and WC.