• The Journal of the Korea institute of electronic communication sciences
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• v.7 no.1
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• pp.69-79
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• 2012

In this paper, we restrict the case as m odd, n=mk, and propose and explicitly exhibit the architecture of a new parallel multiplier over the field GF($2^m$) with a type k Gaussian period which is a subfield of the field GF($2^n$) implements multiplication using the parallel multiplier over the extension field GF($2^n$). The complexity of the time and area of our multiplier is the same as that of Reyhani-Masoleh and Hasan's multiplier which is the most efficient among the known multipliers in the case of type IV.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.4C
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• pp.342-349
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• 2008

This paper presents a new digit-serial systolic multiplier over $CF(2^m)$ for cryptographic applications. When input data come in continuously, the proposed array produces multiplication results at a rate of one every ${\lceil}m/D{\rceil}$ clock cycles, where D is the selected digit size. Since the inner structure of the proposed array is tree-type, critical path increases logarithmically proportional to D. Therefore, the computation delay of the proposed architecture is significantly less than previously proposed digit-serial systolic multipliers whose critical path increases proportional to D. Furthermore, since the new architecture has the features of regularity, modularity, and unidirectional data flow, it is well suited to VLSI implementations.

• Proceedings of the KIEE Conference
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• 1993.07a
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• pp.254-257
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• 1993

This paper presents a new method to implement Hebbian learning method on artificial neural network. In hebbian learning algorithm, complexity in terms of multiplications is high. To save the chip area, we consider a new learning circuit. By calculating similarity, or correlation between $X_i$ and $O_i$, large portion of circuits commonly used in conventional neural networks is not necessary for this new hebbian learning circuit named COR. The output signals of COR is applied to weight storage capacitors for direct control the voltages of the capacitors. The weighted sum, ${\Sigma}W_{ij}O_j$, is realized by multipliers, whose output currents are summed up in one line which goes to learning circuit or output circuit. The drain current of the multiplier can produce positive or negative synaptic weights. The pass transistor selects eight learning mode or recall mode. The layout of an learnable six-neuron fully connected Hopfield neural network is designed, and is simulated using PSPICE. The network memorizes, and retrieves the patterns correctly under the existence of minor noises.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2004.05b
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• pp.255-258
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• 2004

Efficient finite field operation in the elliptic curve (EC) public key cryptography algorithm, which attracts much of latest issues in the applications in information security, is very important. Traditional serial finite multipliers root from Mastrovito's serial multiplication architecture. In this paper, we adopt the polynomial basis and propose a new finite field multiplier, inducing numerical expressions which can be applied to exhibit 3 times as much performance as the Mastrovito's. We described the proposed multiplier with HDL to verify and evaluate as a proper hardware IP. HDL-implemented serial GF (Galois field) multiplier showed 3 times as fast speed as the traditional serial multiplier's adding only Partial-sum block in the hardware.

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.7
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• pp.743-751
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• 1999

공개키 암호 시스템에서 모듈러 지수 연산은 주된 연산으로, 이 연산은 내부적으로 모듈러 곱셈을 반복적으로 수행함으로써 계산된다. 본 논문에서는 GF(2m)상에서 수행할 수 있는 Montgomery 알고리즘을 분석하여 right-to-left 방식의 모듈러 지수 연산에서 공통으로 계산 가능한 부분을 이용하여 모듈러 제곱과 모듈러 곱셈을 동시에 수행하는 선형 시스톨릭 어레이를 설계한다. 본 논문에서 설계한 시스톨릭 어레이는 기존의 곱셈기보다 모듈러 지수 연산시 약 0.67배 처리속도 향상을 가진다. 그리고, VLSI 칩과 같은 하드웨어로 구현함으로써 IC 카드에 이용될 수 있다.Abstract One of the main operations for the public key cryptographic system is the modular exponentiation, it is computed by performing the repetitive modular multiplications. In this paper, we analyze Montgomery's algorithm and design a linear systolic array to perform modular multiplication and modular squaring simultaneously. It is done by using common-multiplicand modular multiplication in the right-to-left modular exponentiation over GF(2m). The systolic array presented in this paper improves about 0.67 times than existing multipliers for performing the modular exponentiation. It could be designed on VLSI hardware and used in IC cards.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.16 no.10
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• pp.977-983
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• 2004

An experimental study on saturated flow boiling heat transfer of R113 was peformed in a vertical narrow rectangular channel with offset strip fins. Two-phase pressure gradients and boiling heat transfer coefficients in an electrically heated test section were measured in the range of quality $0{\sim}0.6$, mass flux $17{\sim}43kg/m^{2}s$, and heat flux of $500{\sim}3,000W/m^2$ Two-phase friction multipliers were determined as a function of Lockhart-Martinelli parameter. Local boiling heat transfer coefficients were analysed in terms of mass flux, heat flux and local vapor quality. Correlation for boiling heat transfer coefficients was proposed, which was in good agreement with experimental data.

• Korean Journal of Optics and Photonics
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• v.12 no.2
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• pp.109-114
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• 2001

Optical system has some optical and mechanical constraints. The constraints should be preserved in optimization of optical system. For the purpose, the constraints are combined with the merit function by using Lagrange's undetermined multipliers. We propose an active optimization control by using the fact that the errors of constraints are corrected with higher priority than the other errors of the merit function. In this control, the errors which have large contribution to the merit function are converted into constraints. At that time, if the errors are corrected at once, the optimization will be unstable because of their non-linearity. Hence we introduce a target rate which represents a fraction of error to be corrected, and the errors are corrected progressively. An optimization program was developed on the bases of the proposed active control, and applied to design a photographic lens system. By using the active control, we could get better results compared with conventional damped least squares method. ethod.

• Journal of Semiconductor Engineering
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• v.2 no.3
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• pp.136-141
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• 2021

This paper analyzes the tree expansion for multiple-input multiple-output (MIMO) detection in the viewpoint of hardware implementation. The tree expansion is to calculate path metrics of child nodes performed in every visit to a node while traversing the detection tree. Accordingly, the tree-expansion unit (TEU), which is responsible for such a task, has been an essential component in a MIMO detector. Despite the paramount importance, the analyses on the TEUs in the literature are not thorough enough. Accordingly, we further investigate the hardware complexity of the TEUs to suggest a guideline for selection. In this paper, we focus on a pair of major ways to implement the TEU: 1) a full parallel realization; 2) a transformation of the formulae followed by common subexpression elimination (CSE). For a logical comparison, the numbers of multipliers and adders are first enumerated. To evaluate them in a more practical manner, the TEUs are implemented in a 65-nm CMOS process, and their propagation delays, gate counts, and power consumptions were measured explicitly. Considering the target specification of a MIMO system and the implementation results comprehensively, one can choose which architecture to adopt in realizing a detector.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.18 no.3
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• pp.45-50
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• 2008

The choice of an irreducible polynomial and the representation of elements have influence on the efficiency of operators for finite fields. This paper suggests two serial multiplier for the extention field GF$(p^n)$ where p is odd prime. A serial multiplier using an irreducible binomial consists of (2n+5) resisters, 2 MUXs, 2 multipliers of GF(p), and 1 adder of GF(p). It obtains the mulitplication result after $n^2+n$ clock cycles. A serial multiplier using an AOP consists of (2n+5) resisters, 1 MUX, 1 multiplier of CF(p), and 1 adder of GF(p). It obtains the mulitplication result after $n^2$+3n+2 clock cycles.

• Journal of IKEEE
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• v.25 no.4
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• pp.697-702
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• 2021

Fast Fourier Transform (FFT) is a major signal processing block being widely used. For long-point FFT processing, usually more than 1024 points, its low-complexity implementation becomes very important while retaining high SQNR (Signal-to-Quantization Noise Ratio). In this paper, we present a low-complexity FFT algorithm with a simple dynamic scaling scheme. For the 2048-point pipelined FFT processing, we can reduce the number of general multipliers by half compared to the well-known radix-2 algorithm. Also, the table size for twiddle factors is reduced to 35% and 53% compared to the radix-2 and radix-2² algorithms respectively, while achieving SQNR of more than 55dB without increasing the internal wordlength progressively.