• ETRI Journal
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• v.13 no.2
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• pp.9-14
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• 1991

직병렬 승산기는 피승수와 승수중 어느 하나가 병렬로 입력되고 또다른 수는 직렬로 입력되는 구조를 가지며, 디지틀 신호처리, 온라인 응용, 특수 목적용 계산 시스팀 등에서 많이 이용되고 있다. 본 논문에서는 2 의 보수를 위한 직병렬 승산기의 논리구조를 제안한다. 제안한 2의 보수 직병렬 승산기는 효과적인 2의 보수 직병렬 승산 알고리즘에 의해서 모든 데이터 신호가 국부적 연결만으로 구성되며, 간단하고 모듈화된 하드웨어의 구성으로 쉽게 설계할 수 있다. 이 승산기는 무부호 승산과 마찬가지로 2n+1 사이클만을 필요로 하고, 각 사이클 시간은 무부호 직병렬 승산에 비해서 2의 보수 승산을 위한 XOR 게이트의 지연시간이 추가된 것뿐이다. 또한, 제안한 2의 보수 직병렬 승산기는 VLSI 구현에 매우 적합한 구조를 지닌다.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.4
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• pp.36-42
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• 2002

In this paper, we proposed a multiplicative algorithm for two polynomials with all non-zero coefficients over finite field GF($P^m$). Using the proposed multiplicative algorithm, we constructed the multiplier of modular architecture with parallel in-output. The proposed multiplier is composed of $(m+1)^2$ identical cells, each cell consists of one mod(p) additional gate and one mod(p) multiplicative gate. Proposed multiplier need one mod(p) multiplicative gate delay time and m mod(p) additional gate delay time not clock. Also, our architecture is regular and possesses the property of modularity, therefore well-suited for VLSI implementation.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.14 no.3
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• pp.628-636
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• 2010

In this paper, we present a new type high speed parallel multiplier for performing the multiplication of two polynomials using standard basis in the finite fields GF($2^m$). Prior to construct the multiplier circuits, we design the basic cell of vector code generator(VCG) to perform the parallel multiplication of a multiplicand polynomial with a irreducible polynomial and design the partial product result cell(PPC) to generate the result of bit-parallel multiplication with one coefficient of a multiplicative polynomial with VCG circuits. The presented multiplier performs high speed parallel multiplication to connect PPC with VCG. The basic cell of VCG and PPC consists of one AND gate and one XOR gate respectively. Extending this process, we show the design of the generalized circuits for degree m and a simple example of constructing the multiplier circuit over finite fields GF($2^4$). Also, the presented multiplier is simulated by PSpice. The multiplier presented in this paper uses the VCGs and PPCS repeatedly, and is easy to extend the multiplication of two polynomials in the finite fields with very large degree m, and is suitable to VLSL.

• The KIPS Transactions:PartA
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• v.11A no.1
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• pp.1-10
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• 2004

A cellular array parallel multiplier with parallel-inputs and parallel-outputs for performing the multiplication of two polynomials in the finite fields GF$(2^m)$ is presented in this paper. The presented cellular way parallel multiplier consists of three operation parts: the multiplicative operation part (MULOP), the irreducible polynomial operation part (IPOP), and the modular operation part (MODOP). The MULOP and the MODOP are composed if the basic cells which are designed with AND Bates and XOR Bates. The IPOP is constructed by XOR gates and D flip-flops. This multiplier is simulated by clock period l${\mu}\textrm{s}$ using PSpice. The proposed multiplier is designed by 24 AND gates, 32 XOR gates and 4 D flip-flops when degree m is 4. In case of using AOP irreducible polynomial, this multiplier requires 24 AND gates and XOR fates respectively. and not use D flip-flop. The operating time of MULOP in the presented multiplier requires one unit time(clock time), and the operating time of MODOP using IPOP requires m unit times(clock times). Therefore total operating time is m+1 unit times(clock times). The cellular array parallel multiplier is simple and regular for the wire routing and have the properties of concurrency and modularity. Also, it is expansible for the multiplication of two polynomials in the finite fields with very large m.

• 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.

• The Transactions of the Korea Information Processing Society
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• v.2 no.6
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• pp.969-973
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• 1995

In this paper, a new parallel Multiplier array is proposed to reduce the multiplication time by modifying CAS(carry select adder) cell structure used in the conventional parallel multiplier array. It is named MCSA(modified CSA) that assignes the addend and augend to the inputs of CSA faster than Ci(carry input). Also the designed DCSA (doubled inverted input CSA) is appended after the last product term for the carry propagation adder. The proposed scheme is designed with MCSA and DCSA, and simulated. It is verified that the circuit size is increased about 13% compared with the conventional multiplier array with CSA cell but the operation time is reduced about 52%.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.43 no.5 s.311
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• pp.36-43
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• 2006

In this paper we present a new high-speed parallel multiplier for Performing the bit-parallel multiplication of two polynomials in the finite fields $GF(2^m)$. Prior to construct the multiplier circuits, we consist of the MOD operation part to generate the result of bit-parallel multiplication with one coefficient of a multiplicative polynomial after performing the parallel multiplication of a multiplicand polynomial with a irreducible polynomial. The basic cells of MOD operation part have two AND gates and two XOR gates. Using these MOD operation parts, we can obtain the multiplication results performing the bit-parallel multiplication of two polynomials. Extending this process, we show the design of the generalized circuits for degree m and a simple example of constructing the multiplier circuit over finite fields $GF(2^4)$. Also, the presented multiplier is simulated by PSpice. The multiplier presented in this paper use the MOD operation parts with the basic cells repeatedly, and is easy to extend the multiplication of two polynomials in the finite fields with very large degree m, and is suitable to VLSI. Also, since this circuit has a low propagation delay time generated by the gates during operating process because of not use the memory elements in the inside of multiplier circuit, this multiplier circuit realizes a high-speed operation.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.3
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• pp.510-520
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• 2011

In this paper, we propose a new multiplication algorithm for primitive polynomial with all 1 of coefficient in case that m is odd and even on finite fields $GF(3^m)$, and compose the multiplier with parallel input-output module structure using the presented multiplication algorithm. The proposed multiplier is designed $(m+1)^2$ same basic cells that have a mod(3) addition gate and a mod(3) multiplication gate. Since the basic cells have no a latch circuit, the multiplicative circuit is very simple and is short the delay time $T_A+T_X$ per cell unit. The proposed multiplier is easy to extend the circuit with large m having regularity and modularity by cell array, and is suitable to the implementation of VLSI circuit.

• Journal of the Korea Society of Computer and Information
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• v.18 no.2
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• pp.9-17
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• 2013

In this paper, we propose a new multiplication algorithm for two polynomials using primitive polynomial with all 1 of coefficient on finite fields GF($2^m$), and design the multiplier with high-speed parallel input-output module structure using the presented multiplication algorithm. The proposed multiplier is designed $m^2$ same basic cells that have a 2-input XOR gate and a 2-input AND gate. Since the basic cell have no a latch circuit, the multiplicative circuit is very simple and is short the delay time $D_A+D_X$ per cell unit. The proposed multiplier is easy to extend the circuit with large m having regularity and modularity by cell array, and is suitable to the implementation of VLSI circuit.

• Journal of IKEEE
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• v.8 no.2 s.15
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• pp.172-180
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• 2004

In this paper, a parallel Input/Output modulo multiplier, which is applied to AOTP(All One or Two Polynomials) multiplicative algorithm over $GF(3^m)$, has been proposed using neuron-MOS Down-literal circuit on voltage mode. The three-valued input of the proposed multiplier is modulated by using neuron-MOS Down-literal circuit and the multiplication and Addition gates are implemented by the selecting of the three-valued input signals transformed by the module. The proposed circuits are simulated with the electrical parameter of a standard $0.35{\mu}m$CMOS N-well doubly-poly four-metal technology and a single +3V supply voltage. In the simulation result, the multiplier shows 4 uW power consumption and 3 MHzsampling rate and maintains output voltage level in ${\pm}0.1V$.