• 융합신호처리학회 학술대회논문집
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• 한국신호처리시스템학회 2000년도 하계종합학술대회논문집
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• pp.353-356
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• 2000

This paper proposes a 16-bit $\times$ 16-bit multiplier for 2 twos-complement binary numbers with complex structure and implements it on a FPGA.

• JSTS:Journal of Semiconductor Technology and Science
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• 제17권1호
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• pp.101-109
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• 2017

This paper presents a high-throughput low-complexity 512-point eight-parallel mixed-radix multipath delay feedback (MDF) fast Fourier transform (FFT) processor architecture for orthogonal frequency division multiplexing (OFDM) applications. To decrease the number of twiddle factor (TF) multiplications, a mixed-radix $2^4/2^3$ FFT algorithm is adopted. Moreover, a dual-path shared canonical signed digit (CSD) complex constant multiplier using a multi-layer scheme is proposed for reducing the hardware complexity of the TF multiplication. The proposed FFT processor is implemented using TSMC 90-nm CMOS technology. The synthesis results demonstrate that the proposed FFT processor can lead to a 16% reduction in hardware complexity and higher throughput compared to conventional architectures.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권5호
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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.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2005년도 춘계종합학술대회
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• pp.925-927
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• 2005

The study is about a finite field multiplying unit, which performs a calculation t-times as fast as the Mastrovito's multiplier architecture, suggesting and using the 2-times faster multiplier architecture. Former studies on finite field multiplication architecture includes the serial multiplication architecture, the array multiplication architecture, and the hybrid finite field multiplication architecture. Mastrovito's serial multiplication architecture has been regarded as the basic architecture for the finite field multiplication, and in order to exploit parallelism, as much resources were expensed to get as much speed in the finite field array multipliers. The array multiplication architecture has weakness in terms of area/performance ratio. In 1999, Parr has proposed the hybrid multipcliation architecture adopting benefits from both architectures. In the hybrid multiplication architecture, the main hardware frame is based on the Mastrovito's serial multiplication architecture with smaller 2-dimensional array multipliers as processing elements, so that its calculation speed is fairly fast costing intermediate resources. However, as the order of the finite field, complex integers instead of prime integers should be used, which means it cannot be used in the high-security applications. In this paper, we propose a different approach to devise a finite field multiplication architecture using Mastrovito's concepts.

• 대한임베디드공학회논문지
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• 제12권1호
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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.

• 대한전자공학회논문지SP
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• 제42권2호
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• pp.143-150
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• 2005

본 논문에서는 OFDM 시스템에 적용하기 위한 새로운 Radix-24 FFT 알고리즘을 제안하고 이 알고리즘을 기반으로 하는 효율적인 파이프라인 FFT 프로세서 구조를 제안한다. Radix-24 알고리즘 기반의 파이프라인 FFT 구조는 Radix-긴 알고리즘 구조와 같은 개수의 곱셈기를 가지고 있으나, 전체 프로그래머블 복소 곱셈기의 절반에 해당하는 곱셈기를 본 논문에서 제안한 CSD(Canonic Signed Digit) 상수 복소 곱셈기로 대체하여 곱셈기의 복잡도를 $30\%$이상 줄이는 효과가 있다. 0.35um CMOS 삼성공정의 합성 시뮬레이션을 통해 제안한 CSD 상수 복소 곱셈기는 기존의 프로그래머블 복소 곱셈기에 비교하여 $60\%$이상 면적효율을 갖는 것으로 분석되었다. 이러한 FFT 구조는 면적과 전력 면에서 높은 효율을 필요로 하는 무선 OFDM 응용분야에 핵심 블록인 큰 포인트 크기를 갖는 FFT 프로세서 설계에 효과적으로 적용될 것이다.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2001년도 춘계종합학술대회
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• pp.307-310
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• 2001

디지털 통신 시스템의 기저대역 신호처리 회로의 핵심 연산블록으로 사용될 수 있는 파라미터화 된 복소수 승산기 IP (Intellectual Property)를 설계하였다. 사용자의 필요에 따라 승수와 피승수의 비트 수를 8-b∼24-b 범위에서 2-b 단위로 선택할 수 있도록 파라미터화 하였으며, GUI 환경의 코어 생성기 (PCMUL_GEN)에 의해 지정된 비트 치기의 복소수 승산기의 VHDL 코드를 생성한다. 설계된 복소수 승산기 IP 코어는 redundant binary (RB) 수치계와 본 논문에서 제안하는 새로운 방식의 radix-4 Booth 인코딩/디코딩 회로를 적용함으로써, 내력 구조 및 배선이 단순화되어 고집적/고속/저전력의 장점을 갖는다. 설계된 IP는 Xilinx FPGA 보드로 구현하여 기능을 검증하였다.

• 전자공학회논문지C
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• 제34C권2호
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• pp.29-37
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• 1997

A new algorithm and parallel architecture for high-speed complex number multiplication is presented, and a prototype chip based on the proposed approach is designed. By employing redundant binary (RB) arithmetic, an N-bit complex number multiplication is simplified to two RB multiplications (i.e., an addition of N RB partial products), which are responsible for real and imaginary parts, respectively. Also, and efficient RB encoding scheme proposed in this paper enables to generate RB partial products without additional hardware and delay overheads compared with binary partial product generation. The proposed approach leads to a highly parallel architecture with regularity and modularity. As a results, it results in much simpler realization and higher performance than the classical method based on real multipliers and adders. As a test vehicle, a prototype 8-b complex number multiplier core has been fabricated using $0.8\mu\textrm{m}$ CMOS technology. It contains 11,500 transistors on the area of about $1.05 \times 1.34 textrm{mm}^2$. The functional and speed test results show that it can safely operate with 200 MHz clock at $V_{DD}=2.5 V$, and consumes about 90mW.

• 전자공학회논문지
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• 제51권10호
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• pp.64-71
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• 2014

곱셈기는 멀티미디어 통신 시스템과 같이 다양한 신호처리 알고리즘을 갖는 복잡한 연산을 수행한다. 곱셈기는 상대적으로 큰 전달 지연시간, 높은 전력 소모, 큰 면적을 갖는다. 이 논문은 멤리스터-CMOS 기반의 재구성 가능한 곱셈기를 제안하여 곱셈기 회로의 면적을 줄이고 다양한 응용프로그램에 최적화 된 비트폭을 제공한다. 멤리스터-CMOS 기반의 재구성 가능한 곱셈기의 성능은 1.8 V 공급전압에서 멤리스터 SPICE 모델과 180 nm CMOS 공정으로 검증했다. 검증 결과 제안한 멤리스터-CMOS 기반의 재구성 가능한 곱셈기는 종래의 것과 비교시 면적, 지연시간, 전력소모가 각각 61%, 38%, 28% 개선되었고, twin-precision 곱셈기와 면적 비교에서도 22% 개선되었다.

• 한국정보전자통신기술학회논문지
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• 제11권5호
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• pp.475-480
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• 2018

In OFDM-based systems, FFT is a critical component since it occupies large area and consumes more power. In this paper, we present a low hardware-cost and low power 512-point pipelined FFT design method for OFDM applications. To reduce the number of twiddle factors and to choose simple design architecture, the radix-$2^4-2^3$ algorithm are exploited. For twiddle factor multiplication, we propose a new canonical signed digit (CSD) complex multiplier design method to minimize the hardware-cost. In hardware implementation with Intel FPGA, the proposed FFT design achieves more than about 28% reduction in gate count and 18% reduction in power consumption compared to the previous approaches.