• 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 Institute of Electronics and Information Engineers
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• v.53 no.2
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• pp.70-75
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• 2016

This paper proposes the constructing method of effective multiplier based on the finite fields in case of P=2. The proposed multiplier is constructed by polynomial arithmetic part, mod F(${\alpha}$) part and modular arithmetic part. Also, each arithmetic parts can extend according to m because of it have modular structure, and it is adopted VLSI because of use AND gate and XOR gate only. The proposed multiplier is more compact, regularity, normalization and extensibility compare with earlier multiplier. Also, it is able to apply several fields in recent hot issue IoT configuration.

• Journal of IKEEE
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• v.22 no.4
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• pp.1158-1162
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• 2018

A fast-lock multiplying delay-locked loop (MDLL)-based digital clock frequency multiplier with an anti-harmonic lock capability is presented. The proposed digital frequency multiplier utilizes a new most-significant bit (MSB)-interval search algorithm to achieve fast-locking time without harmonic lock problems. The proposed digital MDLL frequency multiplier is designed in a 65nm CMOS process, and the operating output frequency range is from 1 GHz to 3 GHz. The digital MDLL provides a programmable fractional-ratio frequency multiplication ratios of N/M, where N = 1, 4, 5, 8, 10 and M = 1, 2, 3, respectively. The proposed MDLL consumes 3.52 mW at 1GHz and achieves a peak-to-peak (p-p) output clock jitter of 14.07 ps.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.771-774
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• 1998

In this paper proposes a new bit-parallel structure for a multiplier over GF((Pn)m), with k-nm. Mastrovito Multiplier, Karatsuba-ofman algorithm are applied to the multiplication of polynomials over GF(2n). This operation has a complexity of order O(k log p3) under certain constrains regardig k. A complete set of primitive field polynomials for composite fields is provided which perform modulo reduction with low complexity. As a result, multiplier for fields GF(Pk) with low gate counts and low delays are constructed. The architectures are highly modular and thus well suited for VLSI implementation.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.303-306
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• 2004

There are 49 non-metacyclic p-groups of order less than 1000 with trivial Schur multiplier. In this paper we give a list of deficiency zero presentations for these groups.

• Journal of IKEEE
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• v.8 no.1 s.14
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• pp.54-62
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• 2004

In this paper, we discuss on the design of a current mode CMOS multiplier circuit over $GF(3^m)$. Using the standard basis, we show the variation of vector representation of multiplicand by multiplying primitive element α, which completes the multiplicative process. For the $GF(3^m)$ multiplicative circuit design, we design GF(3) adder and multiplier circuit using current mode CMOS technology and get the simulation results. Using the basic gates - GF(3) adder and multiplier, we build the $GF(3^m)$ multiplier circuit and show the examples for the case m=3. We also propose the assembly of the operation blocks for a complete $GF(3^m)$ multiplier. Therefore, the proposed circuit is easily extensible to other p and m values over $GF(p^m)$ and has advantages for VLSI implementation. We verify the validity of the proposed circuit by functional simulations and the results are provided.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.1C
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• pp.131-139
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• 2008

This paper presents a scalable dual-field Montgomery multiplier based on a new multi-precision carry save adder(MP-CSA), which operates in both types of finite fields GF(p) and GF($2^m$). The new MP-CSA consists of two carry save adders(CSA). Each CSA is composed of n = [w/b] carry propagation adders(CPA) for a modular multiplication with w-bit words, where b is the number of dual field adders(DFA) in a CPA. The proposed Montgomery multiplier has roughly the same timing complexity compared with the previous result, however, it has the advantage of reduced chip area requirements. In addition, the proposed circuit produces the exact modular multiplication result at the end of operation unlike the previous architecture. Furthermore, the proposed Montgomery multiplier has a high scalability in terms of w and m. Therefore, it can be used to multiplier over GF(p) and GF($2^m$) for cryptographic applications.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1535-1548
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• 2008

The analogues of Marcinkiewicz multiplier theorem and Littlewood-Paley theorem are proved for p-Faber series in weighted Smirnov spaces defined on bounded and unbounded components of a rectifiable Jordan curve.

• The Journal of the Acoustical Society of Korea
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• v.19 no.1
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• pp.84-88
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• 2000

In this paper, a low voltage CMOS analog four-quadrant multiplier is presented. The proposed multiplier is composed of two fully differential transconductors and lowers supply voltage down to VT+2VDS,sat+VDS,triode. The designed analog four-quadrant multiplier has simulated by HSPICE using 0.25㎛ n-well CMOS process with a 1.2V supply voltage. Simulation results show that the THD can be 1.28% at maximum differential input of 0.7VP-P.

• Journal of the Institute of Convergence Signal Processing
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• v.2 no.3
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• pp.102-109
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• 2001

In this paper, a new multiplication algorithm which describes the methods of constructing a multiplierover GF(p$^{m}$ ) was presented. For the multiplication of two elements in the finite field, the multiplication formula was derived. Multiplier structures which can be constructed by this formula were considered as well. For example, both GF(3) multiplication module and GF(3) addition module were realized by current-mode CMOS technology. By using these operation modules the basic cell used in GF(3$^{m}$ ) multiplier was realized and verified by SPICE simulation tool. Proposed multipliers consisted of regular interconnection of simple cells use regular cellular arrays. So they are simply expansible for the multiplication of two elements in the finite field increasing the degree m.