• 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 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.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.13 no.5
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• pp.179-187
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• 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 Advanced Navigation Technology
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• v.18 no.2
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• pp.178-184
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• 2014

CMOS technology based on PCA is very efficient at an implementation of memory or ALU. However, there has been a growing interest in quantum-dot cellular automata (QCA) because of the limitation of CMOS scaling. In this paper, we propose a design of PCA architecture based on QCA. In the proposed PCA design, we utilize D flip-flop and XOR logic gate without wire crossing technique, and design a input and rule control switches. In experiment, we perform the simulation of the proposed PCA architecture by QCADesigner. As the result, we confirm the efficiency the proposed architecture.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.18 no.6A
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• pp.17-25
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• 2008

The differential power attack (DPA)[8] is a very powerful side-channel attack tool against various cryptosystems and the masking method[10] is known to be one of its algorithmic countermeasures. But it is non-trivial to apply the masking method to non-linear functions, especially, to arithmetic adders. This paper proposes simple and efficient masking methods applicable to arithmetic adders. For this purpose, we use the fact that every combinational logic circuit (including the adders) can be decomposed into basic logic gates (AND, OR, NAND, NOR, XOR, XNOR, NOT) and try to devise efficient masking circuits for these basic gates. The resulting circuits are then applied to the arithmetic adders to get their masking algorithm. As applications, we applied the proposed masking methods to SEED and SHA-1 in hardware.

• The KIPS Transactions:PartC
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• v.14C no.5
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• pp.431-438
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• 2007

RFID system is core technology that construct ubiquitous environment for replacement of barcode technology. Use ratio of RFID system rapidly increase because the technology has many good points such as identification speed, storage space, convenience etc. But low-cost tag operates easily by query of reader, so the system happened user privacy violent problem by tag information exposure. The system studied many ways for security application, but operation capability of low-cost tag is about $5K{\sim}10K$ gates, but only $250{\sim}3K$ gates allocated security part. So it is difficult to apply security to the system. Therefore, this scheme uses dividing 64 bits and reduces arithmetic, so proposed scheme provide mutual authentication that can apply to low-cost RFID system. Existing methods divide by 4 and used 96 bits. However, that reduces 32 bits length for lightweight and reduced from communication number of times of 7 times to 5 times. Also, because offer security by random number than existing scheme that generate two random numbers, that is more efficient. However, uses hash function for integrity that was not offered by XOR arithmetic and added extension of proposed scheme. Extended scheme is not offered efficiency than methods that use XOR arithmetic, but identification distance is mode that is proposed secure so that can use in for RFID system.

• 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.

• Journal of the Korea Society of Computer and Information
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• v.19 no.12
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• pp.369-384
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• 2014

Since the start of gifted education in 2002, educational support system has now been established, and sufficient growth in quantitative aspects has been achieved in Korea. On the other hand, they report that there are insufficient points in terms of education quality. In other words, most of the gifted education simply expands knowledge by prior-learning. In order to improve the quality of gifted education, they should enhance critical-thinking and creativity able to apply interdisciplinary principles or phenomena for solving problems. In this study, we designed and developed a convergent teaching-learning materials based on the concept of integrated education, which explore the process that basic logic operations such as AND, OR, XOR do the role of computer cells. A survey result showed that student satisfaction(usefulness, understanding, interest) of the materials is significantly higher than that of other traditional learning topics, and the design intent was met.

• Journal of the Korea Society of Computer and Information
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• v.17 no.3
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• pp.1-10
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• 2012

A low-complexity Multiplication over GF(2m) and multiplier circuit has been proposed by using cyclic-shift coefficients and the irreducible trinomial. The proposed circuit has the parallel input/output architecture and shows the lower-complexity than others with the characteristics of the cyclic-shift coefficients and the irreducible trinomial modular computation. The proposed multiplier is composed of $2m^2$ 2-input AND gates and m (m+2) 2-input XOR gates without the memories and switches. And the minimum propagation delay is $T_A+(2+{\lceil}log_2m{\rceil})T_X$. The Proposed circuit architecture is well suited to VLSI implementation because it is simple, regular and modular.

• 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.