• Journal of the Korean Institute of Telematics and Electronics C
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• v.35C no.2
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• pp.29-35
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• 1998

This paper describes architectures and design of a SIMD type parallel image processing chip called SliM-II. The chiphas a linear array of 64 processing elements (PEs), operates at 30 MHz in the worst case simulation and gives at least 1.92 GIPS. In contrast to existing array processors, such as IMAP, MGAP-2, VIP, etc., each PE has a multiplier that is quite effective for convolution, template matching, etc. The instruction set can execute an ALU operation, data I/O, and inter-PE communication simulataneously in a single instruction cycle. In addition, during the ALU/multiplier operation, SliM-II provides parallel move between the register file and on-chip memory as in DSP chips, SliM-II can greatly reduce the inter-PE communication overhead, due to the idea a sliding, which is a technique of overlapping inter-PE communication with computation. Moreover, the bandwidth of data I/O and inter-PE communication increases due to bit-parallel data paths. We used the COMPASS$^{TM}$ 3.3 V 0.6.$\mu$m standrd cell library (v8r4.10). The total number of transistors is about 1.5 muillions, the core size is 13.2 * 13.0 mm$^{2}$ and the package type is 208 pin PQ2 (Power Quad 2). The performance evaluation shows that, compared to a existing array processors, a proposed architeture gives a significant improvement for algorithms requiring multiplications.s.

• 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.

• Proceedings of the KIEE Conference
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• 2006.10c
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• pp.142-144
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• 2006

In this paper, the Ternary adder and multiplier are implemented by current-mode CMOS. First, we implement the ternary T-gate using current-mode CMOS which have an effective availability of integrated circuit design. Second, we implement the circuits to be realized 2-variable ternary addition table and multiplication table over finite fields GF(3) with the ternary T-gates. Finally, these operation circuits are simulated by Spice under $1.5{\mu}m$ CMOS standard technology, $1.5{\mu}m$ unit current, and 3.3V VDD voltage. The simulation results have shown the satisfying current characteristics. The ternary adder and multiplier implemented by current-mode CMOS are simple and regular for wire routing and possess the property of modularity with cell array.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.5
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• pp.2680-2700
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• 2017

Finite field arithmetic over GF($2^m$) is used in a variety of applications such as cryptography, coding theory, computer algebra. It is mainly used in various cryptographic algorithms such as the Elliptic Curve Cryptography (ECC), Advanced Encryption Standard (AES), Twofish etc. The multiplication in a finite field is considered as highly complex and resource consuming operation in such applications. Many algorithms and architectures are proposed in the literature to obtain efficient multiplication operation in both hardware and software. In this paper, a modified serial multiplication algorithm with interleaved modular reduction is proposed, which allows for an efficient realization of a sequential polynomial basis multiplier. The proposed sequential multiplier supports multiplication of any two arbitrary finite field elements over GF($2^m$) for generic irreducible polynomials, therefore made versatile. Estimation of area and time complexities of the proposed sequential multiplier is performed and comparison with existing sequential multipliers is presented. The proposed sequential multiplier achieves 50% reduction in area-delay product over the best of existing sequential multipliers for m = 163, indicating an efficient design in terms of both area and delay. The Application Specific Integrated Circuit (ASIC) and the Field Programmable Gate Array (FPGA) implementation results indicate a significantly less power-delay and area-delay products of the proposed sequential multiplier over existing multipliers.

• International Journal of Computer Science & Network Security
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• v.22 no.9
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• pp.414-426
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• 2022

Elliptic Curve Cryptography (ECC) is one of the finest cryptographic technique of recent time due to its lower key length and satisfactory performance with different hardware structures. In this paper, a High Throughput Multiplier architecture is introduced for Elliptic Cryptographic applications based on concurrent computations. With the aid of the concurrent computing approach, the High Throughput Concurrent Computation (HTCC) technology that was just presented improves the processing speed as well as the overall efficiency of the point-multiplier architecture. Here, first and second distinct group operation of point multiplier are combined together and synthesised concurrently. The synthesis of proposed HTCC technique is performed in Xilinx Virtex - 5 and Xilinx Virtex - 7 of Field-programmable gate array (FPGA) family. In terms of slices, flip flops, time delay, maximum frequency, and efficiency, the advantages of the proposed HTCC point multiplier architecture are outlined, and a comparison of these advantages with those of existing state-of-the-art point multiplier approaches is provided over GF(2¹⁶³), GF(2²³³) and GF(2²⁸³). The efficiency using proposed HTCC technique is enhanced by 30.22% and 75.31% for Xilinx Virtex-5 and by 25.13% and 47.75% for Xilinx Virtex-7 in comparison according to the LC design as well as the LL design, in their respective fashions. The experimental results for Virtex - 5 and Virtex - 7 over GF(2²³³) and GF(2²⁸³)are also very satisfactory.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.1025-1028
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• 1998

Hardware to implement the parallelized Floating-point rounding algorithm is described. For parallelized additions, we propose an addition module which has carry selection logic to generate two results accoring to the input valuse. A multiplication module for parallelized multiplications is also proposed to generate Sum and Carry bits as intermediate results. Since these modules process data in IEEE standard Floatingpoint double precision format, they are designed for 53-bit significands including hidden bits. Multiplication module is designed with a Booth multiplier and an array multiplier.

• IEMEK Journal of Embedded Systems and Applications
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• v.14 no.6
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• pp.313-319
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• 2019

Finite field operations have played an important role in error correcting codes and cryptosystems. Recently, the necessity of efficient computation processing is increasing for security in cyber physics systems. Therefore, efficient implementation of finite field arithmetics is more urgently needed. These operations include addition, multiplication, division and inversion. Addition is very simple and can be implemented with XOR operation. The others are somewhat more complicated than addition. Among these operations, multiplication is the most important, since time-consuming operations, such as exponentiation, division, and computing multiplicative inverse, can be performed through iterative multiplications. In this paper, we propose a multiplexer based parallel computation algorithm that performs Montgomery multiplication over finite field using redundant basis. Then we propose an efficient multiplexer based semi-systolic multiplier over finite field using redundant basis. The proposed multiplier has less area-time (AT) complexity than related multipliers. In detail, the AT complexity of the proposed multiplier is improved by approximately 19% and 65% compared to the multipliers of Kim-Han and Choi-Lee, respectively. Therefore, our multiplier is suitable for VLSI implementation and can be easily applied as the basic building block for various applications.

• IEMEK Journal of Embedded Systems and Applications
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• v.12 no.1
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• pp.11-18
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• 2017

Finite field arithmetic has been extensively used in error correcting codes and cryptography. Low-complexity and high-speed designs for finite field arithmetic are needed to meet the demands of wider bandwidth, better security and higher portability for personal communication device. In particular, cryptosystems in GF($2^m$) usually require computing exponentiation, division, and multiplicative inverse, which are very costly operations. These operations can be performed by computing modular AB multiplications or modular $AB^2$ multiplications. To compute these time-consuming operations, using $AB^2$ multiplications is more efficient than AB multiplications. Thus, there are needs for an efficient $AB^2$ multiplier architecture. In this paper, we propose a low latency Montgomery $AB^2$ multiplier using redundant representation over GF($2^m$). The proposed $AB^2$ multiplier has less space and time complexities compared to related multipliers. As compared to the corresponding existing structures, the proposed $AB^2$ multiplier saves at least 18% area, 50% time, and 59% area-time (AT) complexity. Accordingly, it is well suited for VLSI implementation and can be easily applied as a basic component for computing complex operations over finite field, such as exponentiation, division, and multiplicative inverse.

• Journal of the Korea Society of Computer and Information
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• v.20 no.2
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• pp.1-10
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• 2015

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 design the multiplier with parallel input-output module structure using the presented multiplication algorithm. The proposed multiplier is designed $(m+1)^2$ same basic cells. 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.

• The KIPS Transactions:PartA
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• v.15A no.3
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• pp.161-166
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• 2008

In this paper, an efficient digit-serial systolic array is proposed for multiplication in finite field GF($2^m$) using the polynomial basis representation. The proposed systolic array is based on the most significant digit first (MSD-first) multiplication algorithm and produces multiplication results at a rate of one every "m/D" clock cycles, where D is the selected digit size. Since the inner structure of the proposed multiplier is tree-type, critical path increases logarithmically proportional to D. Therefore, the computation delay of the proposed architecture is significantly less than previously proposed digit-serial systolic multipliers whose critical path increases proportional to D. Furthermore, since the new architecture has the features of a high regularity, modularity, and unidirectional data flow, it is well suited to VLSI implementation.