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

• Proceedings of the Korean Institute of Communication Sciences Conference
• /
• 2004.07a
• /
• pp.109-109
• /
• 2004

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.13 no.5
• /
• pp.179-187
• /
• 2003

Recently efficient implementation of finite field operation has received a lot of attention. Among the GF($2^m$) arithmetic operations, multiplication process is the most basic and a critical operation that determines speed-up hardware. We propose a hardware architecture using Mastrovito method to reduce processing time. Existing Mastrovito multipliers using the special generating trinomial p($\chi$)=$x^m$+$x^n$+1 require $m^2$-1 XOR gates and $m^2$ AND gates. The proposed multiplier needs $m^2$ AND gates and $m^2$＋($n^2$-3n)/2 XOR gates that depend on the intermediate term xn. Time complexity of existing multipliers is $T_A$+( (m-2)/(m-n) +1+ log$_2$(m) ) $T_X$ and that of proposed method is $T_X$＋(1＋ log$_2$(m-1)＋ n/2 ) )$T_X$. The proposed architecture is efficient for the extension degree m suggested as standards: SEC2, ANSI X9.63. In average, XOR space complexity is increased to 1.18% but time complexity is reduced 9.036%.

• Journal of the Korean Institute of Telematics and Electronics A
• /
• v.31A no.5
• /
• pp.58-67
• /
• 1994

In this paper, It was designed the 2.8GHz local oscillator which convert 14.5 14.8GHz uplink frequency to 11.7 12.0GHz downlink frequency by the receiving mixer on the communication satellite transponder according to the rating of domestic satellite. Mukunghwa 1. To prevent the variation of the communication channel bandwidth, it needs a high stability and low phase noise characteristics. So we designed to get the target frequencey by multipling the output signal from the crystal oscillator. We got the simplicity of the circuit by manufacturing the X4 multiplier with transistor which is ordinarily used as a device of a below X3 multiplier for the efficiency.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.44 no.9
• /
• pp.1-9
• /
• 2007

For an efficient implementation of cryptosystems based on arithmetic in a finite field $GF(2^n)$, their hardware implementation is an important research topic. To construct a multiplier with low area complexity, the divide-and-conquer technique such as the original Karatsuba-Ofman method and multi-segment Karatsuba methods is a useful method. Leone proposed an efficient parallel multiplier with low area complexity, and Ernst at al. proposed a multiplier of a multi-segment Karatsuba method. In [1], the authors proposed new $MSK_5$ and $MSK_7$ methods with low area complexity to improve Ernst's method. In [3], the authors proposed a method which combines $MSK_2$ and $MSK_3$. In this paper we propose an efficient multiplication method by combining $MSK_2,\;MSK_3\;and\;MSK_5$ together. The proposed method reduces $116{\cdot}3^l$ gates and $2T_X$ time delay compared with Gather's method at the degree $25{\cdot}2^l-2^l with l>0.

• Communications of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.527-533
• /
• 2018

Let $\mathcal{X}$ be a countably generated Hilbert module over a locally $C^*$-algebra $\mathcal{A}$ in multiplier module M($\mathcal{X}$) of $\mathcal{X}$. We propose the necessary and sufficient condition such that a sequence $\{h_n:n{{\in}}\mathbb{N}\}$ in M($\mathcal{X}$) is a standard frame of multipliers in $\mathcal{X}$. We also show that if T in $b(L_{\mathcal{A}}(\mathcal{X}))$, the space of bounded maps in set of all adjointable maps on $\mathcal{X}$, is surjective and $\{h_n:n{{\in}}\mathbb{N}\}$ is a standard frame of multipliers in $\mathcal{X}$, then $\{T{\circ}h_n:n{\in}\mathbb{N}}$ is a standard frame of multipliers in $\mathcal{X}$, too.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.44 no.8
• /
• pp.30-37
• /
• 2007

An exponentiation in $GF(2^m)$ is a basic operation for several algorithms used in cryptography, digital signal processing, error-correction code and so on. Existing hardware implementations for the exponentiation operation organize by Right-to-Left method since a merit of parallel circuit. Our paper proposes a polynomial exponentiation structure with a trinomial that is organized by Left-to-Right method and that utilizes a weakly dual basis. The basic idea of our method is to decrease time delay using precomputation tables because one of two inputs in the Left-to-Right method is fixed. Since $T_{sqr}$ (squarer time delay) + $T_{mul}$(multiplier time delay) of ow method is smaller than $T_{mul}$ of existing methods, our method reduces time delays of existing Left-to-Right and Right-to-Left methods by each 17%, 10% for $x^m+x+1$ (irreducible polynomial), by each 21%, 9% $x^m+x^k+1(1, by each 15%, 1% for $x^m+x^{m/2}+1$.

• Proceedings of the Korean Information Science Society Conference
• /
• 2001.10c
• /
• pp.46-48
• /
• 2001

본 논문에서는 Baugh-Wooley 승산 알고리즘을 '8x8-bit 15 stage 파이프라인 배열 숭산기', '8x8-bit 2 stage 파이프라인 배열 숭산기', '순수 조합 논리 배열 승산기'의 방식으로 FPGA상에서 구현하였으며, 각 구현방식의 성능을 비교 분석하였다.

• Journal of the Korean Society of Combustion
• /
• v.4 no.1
• /
• pp.27-38
• /
• 1999

We constructed a wire-cylinder type pulsed corona discharge system for $NO_x$ removal, which was operated in room temperature. A emission spectrometer was built with a boxcar averager and monochrometer equipped with photo-multiplier tube detector. The sensitivity of the emission spectrometer was greatly improved by synchronizing the emission spectrometer with pulsed corona discharge system using a triggered spark-gap switch. $N_2$ spectrum($c^3{\Pi}_u{\rightarrow}X^1{\Sigma}_g{^+}$) was measured in the range of 300 - 450 nm and oxidizing OH radical emission($A^2{\Sigma}^+{\rightarrow}X^2{\Pi}$) was measured in case $N_2$ was supplied with water bubbling. As wet gas composition of inlet $N_2$ supplied in the discharge system increased, the intensity of OH emission was increased and saturated at wet gas composition 50%. We also investigated additive effect of $C_2H_4,\;H_2O,\;H_2O_2$ on the intensity of OR emission and $NO/NO_2/NO_x$ reduction and analysed the related reaction mechanism in corona discharge process. $H_2O_2$ additive increased the intensity of OH emission and $NO/NO_x$ reduction.

• Journal of Biomedical Engineering Research
• /
• v.24 no.2
• /
• pp.83-89
• /
• 2003

The gas electron multiplier placed in the drift volume of conventional gas detectors, is a conceptually simple device for producing a large gas gain by concentrating the drift electric field over a very short distance to the point that electron avalanching occurs(〉 10$^4$ V/cm), greatly increasing the number of drifting electrons. This device consists of a thin insulating foil of several tens of urn in thickness. covered on each side with a thin metal layer(Cu), with tiny holes, usually 100 ${\mu}{\textrm}{m}$ or less in diameter. and with a spacing of 100-200 ${\mu}{\textrm}{m}$ through the entire foil. perforated by using chemical etching or high-powered laser beam technique In this study, we have investigated its operating properties with various experimental conditions, and demonstrated the possibility of using this device as a digital X-ray imaging sensor, by acquiring X-ray images based on the scintillation properties of the gas electron multiplier with standard CCD camera.