• The Transactions of the Korean Institute of Electrical Engineers
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• v.45 no.3
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• pp.444-450
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• 1996

A digital hardware architecture for artificial neural network with learning capability is described in this paper. It is a modified hardware architecture known as HANNIBAL(Hardware Architecture for Neural Networks Implementing Back propagation Algorithm Learning). For implementing an efficient neural network hardware, we analyzed various type of multiplier which is major function block of neuro-processor cell. With this result, we design a efficient digital neural network hardware using serial/parallel multiplier, and test the operation. We also analyze the hardware efficiency with logic level simulation. (author). refs., figs., tabs.

• 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 Security & Cryptology
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• v.13 no.3
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• pp.27-34
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• 2003

Recently, an efficient hardware development for a cryptosystem is concerned. The efficiency of a multiplier for GF($2^n$)is directly related to the efficiency of some cryptosystem. This paper, considering the trade-off between time complexity andsize complexity, proposes a new multiplier architecture having n[n/2] AND gates and n([n/2]+1)- $$\Delta$_n$ = XOR gates, where $$\Delta$_n$=1 if n is even, $$\Delta$_n$=0 otherwise. This size complexity is less than that of existing ${multipliers}^{[5][12]}$which are $n^2$ AND gates and $n^2$-1 XOR gates. While a new multiplier is a serial-parallel multiplier to output a result of multiplication of two elements of GF($2^n$) after 2 clock cycles, the suggested multiplier is more suitable for some cryptographic device having space limitations.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.19 no.6
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• pp.3-15
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• 2009

Recently, Wu proposed a three small classes of finite fields $F_{2^n}$ for low-complexity bit-parallel multipliers. The proposed multipliers have low-complexities compared with those based on the irreducible pentanomials. In this paper, we propose a new Repeated Polynomial(RP) for low-complexity bit-parallel multipliers over $F_{2^n}$. Also, three classes of Irreducible Repeated polynomials are considered which are denoted, respectively, by case 1, case 2 and case3. The proposed RP bit-parallel multiplier has lower complexities than ones based on pentanomials. If we consider finite fields that have neither a ESP nor a trinomial as an irreducible polynomial when $n\leq1,000$. Then, in Wu''s result, only 11 finite fields exist for three types of irreducible polynomials when $n\leq1,000$. However, in our result, there are 181, 232, and 443 finite fields of case 1, 2 and 3, respectively.

• 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)

• Journal of the Korea Institute of Information Security & Cryptology
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• v.16 no.4
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• pp.83-89
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• 2006

In H/W implementation for the finite field, the use of normal basis has several advantages, especially, the optimal normal basis is the most efficient to H/W implementation in GF($2^m$). In this paper, we propose a new, simpler, parallel multiplier over GF($2^m$) having a type II optimal normal basis, which performs multiplication over GF($2^m$) in the extension field GF($2^{2m}$). The time and area complexity of the proposed multiplier is same as the best of known type II optimal normal basis parallel multiplier.

• Proceedings of the IEEK Conference
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• 2000.11b
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• pp.140-143
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• 2000

소형화와 안전성에서 보다 더 진보된 ECC( Elliptic Curve Cryptography) 암호화 알고리즘의 하드웨어적 구현을 제안한다. Basis는 VLSI 구현에 적합한 standard basis이며 m=193 ECC 승산기 회로를 설계하였다. Bit-Parallel 구조를 바탕으로 Digit-Serial/Bit-Parallel 방법으로 구현하였다. 제안된 구조는 VHDL 및 SYNOPSYS로 검증되었다.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.46 no.7
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• pp.29-38
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• 2009

In this paper, a high performance pipelined computing design of parallel multiplier-temporal buffer-parallel accumulator is present for the convolution-based non-cascaded architecture aiming at the real time Discrete Wavelet Transform(DWT) processing. The convolved multiplication of DWT would be reduced upto 1/4 by utilizing the filter coefficients symmetry and the up/down sampling; and it could be dealt with 3-5 times faster computation by LUT-based DA multiplication of multiple filter coefficients parallelized for product terms with an image data. Further, the reutilization of computed product terms could be achieved by storing in the temporal buffer, which yields the saving of computation as well as dynamic power by 50%. The convolved product terms of image data and filter coefficients are realigned and stored in the temporal buffer for the accumulated addition. Then, the buffer management of parallel aligned storage is carried out for the high speed sequential retrieval of parallel accumulations. The convolved computation is pipelined with parallel multiplier-temporal buffer-parallel accumulation in which the parallelization of temporal buffer and accumulator is optimize, with respect to the performance of parallel DA multiplier, to improve the pipelining performance. The proposed architecture is back-end designed with 0.18um library, which verifies the 30fps throughput of SVGA(800$\times$600) images at 90MHz.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.41 no.5
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• pp.29-36
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• 2004

This study focuses on the arithmetical methodology and hardware implementation of low-system-complexity multiplier over GF(2$^{m}$ ) using the trinomial of degree a The proposed parallel-in parallel-out operator is composed of MR, PP, and MS modules, each can be established using the regular array structure of AND and XOR gates. The proposed multiplier is composed of $m^2$ 2-input AND gates and $m^2$-1 2-input XOR gates, and the propagation delay is $T_{A}$+(1+[lo $g_2$$^{m}$ ]) $T_{x}$ . Comparison result of the related multipliers of GF(2$^{m}$ ) are shown by table, it reveals that our operator involve more regular and generalized then the others, and therefore well-suited for VLSI implementation. Moreover, our multiplier is more suitable for any other GF(2$^{m}$ ) operational applications.s.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.6A
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• pp.555-561
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• 2002

In this paper, a new designed circuit of highly parallel multiplier using standard basis over $GF(2^m)$ is presented. Prior to construct the multiplier circuit, we provide the Vector Code Generate Module(VCGM) that generate each vector codes for multiplication. Using these VCGMs, we can get all vector codes necessary for operation and modular sum up each independent corresponding basis, respectively. Following the equations in this paper, we can design generalized multiplier to m. For the proposed circuit in this parer, we show the example in $GF(2^4)$ using VCGMs. In this paper, we build a multiplier with VCGMs, AND blocks, and EX-OR blocks. Therefore the proposed circuit is easy to generalize for m and advantageous for VLSI. Also, it need no memory element and the latency not less fewer then other circuit. We verify the proposed circuit by functional simulation and show its result. Finally, we compare the circuit composition with other works and show its result with a table.