• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.11C
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• pp.892-897
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• 2008

In this paper, a new architecture for digit-parallel/bit-serial GF$(2^m)$ multiplier with low latency is proposed. The proposed multiplier operates in polynomial basis of GF$(2^m)$ and produces multiplication results at a rate of one per D clock cycles, where D is the selected digit size. The digit-parallel/bit-serial multiplier is faster than bit-serial ones but with lower area complexity than bit-parallel ones. The most significant feature of the proposed architecture is that a trade-off between hardware complexity and delay time can be achieved.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.38 no.3
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• pp.51-51
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• 2001

본 논문에서는 CMOS 로직과 pass-transistor logic(PTL)의 장점만을 가진 새로운 복합모드로직(Compound Mode Logic)을 제안하였다. 제안된 로직은 VLSI설계에서 중요하게 부각되고 있는 저전력, 고속 동작이 가능하며 실제로 전가산기를 설계하여 측정 한 결과 복합모드 로직의 power-delay 곱은 일반적인 CMOS로직에 비해 약 22% 개선되었다 제안한 복합모드 로직을 이용하여 고성능 32×32-bit 곱셈기를 설계 제작하였다. 본 논문의 곱셈기는 개선된 사인선택(Sign Select) Booth 인코더, 4-2 및 9-2 압축기로 구성된 데이터 압축 블록, 그리고 carry 생성 블록을 분리한 64-bit 조건 합 가산기로 구성되어 있다. 0.6um 1-poly 3-metal CMOS 공정을 이용하여 제작된 32×32-bit 곱셈기는 28,732개의 트랜지스터와 1.59×l.68 ㎜2의 면적을 가졌다. 측정 결과 32×32-bit 곱셈기의 곱셈시간은 9.8㎱ 이었으며, 3.3V 전원 전압에서 186㎽의 전력 소모를 하였다.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.19 no.2
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• pp.49-61
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• 2009

Finite Field multiplication operation is one of the most important operations in the finite field arithmetic. Recently, Fan and Dai introduced a Shifted Polynomial Basis(SPB) and construct a non-pipeline bit-parallel multiplier for $F_{2^n}$. In this paper, we propose a new bit-parallel shifted polynomial basis type I and type II multipliers for $F_{2^n}$ defined by an irreducible trinomial $x^{n}+x^{k}+1$. The proposed type I multiplier has more efficient the space and time complexity than the previous ones. And, proposed type II multiplier have a smaller space complexity than all previously SPB multiplier(include our type I multiplier). However, the time complexity of proposed type II is increased by 1 XOR time-delay in the worst case.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.10
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• pp.64-71
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• 2014

Multiplier performs a complex arithmetic operation in various signal processing algorithms such as multimedia and communication system. The multiplier also suffers from its relatively large signal propagation delay, high power dissipation, and large area requirement. This paper presents memristor-CMOS based reconfigurable multiplier reducing area occupation of the multiplier circuitry and increasing compatibility using optimized bit-width for various applications. The performance of the memristor-CMOS based reconfigurable multiplier are estimated with memristor SPICE model and 180 nm CMOS process under 1.8 V supply voltage. The circuit shows performance improvement of 61% for area, 38% for delay and 28% for power consumption respectively compared with the conventional reconfigurable multipliers. It also has an advantage for area reduction of 22% against a twin-precision multiplier.

• Journal of Korea Society of Industrial Information Systems
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• v.10 no.3
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• pp.57-63
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• 2005

Kim and Fenn et al. proposed two modular AB multipliers based on LFSR(Linear Feedback Shift Register) architecture. These multipliers use AOP, which has all coefficients with '1', as an irreducible polynomial. Thereby, they have good hardware complexity compared to the previous architectures. This paper proposes a modular $AB^2$ multiplier based on LFSR architecture and a modular exponentiation architecture to improve the hardware complexity of the Kim's. Our multiplier also use the AOP as an irreducible polynomial as the Kim architecture. Simulation result shows that our multiplier reduces the hardware complexity about $50\%$ in the perspective of XOR and AND gates compared to the Kim's. The architecture could be used as a basic block to implement public-key cryptosystems.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.40 no.12
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• pp.80-86
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• 2003

Elliptic curve cryptosystem(ECC) offers the highest security per bit among the known publick key system. The benefit of smaller key size makes ECC particularly attractive for embedded applications since its implementation requires less memory and processing power. In this paper, we propose a new multiplier structure with configurable output sizes and operation cycles. The number of output bits can be freely chosen in the new architecture with the performance-area trade-off depending on the application. Using the architecture, a 193-bit normal basis multiplier and inversion unit are designed in GF(2$^{m}$ ). It is implemented using HDL and 0.35${\mu}{\textrm}{m}$ CMOS technology and the operation is verified by simulation.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.18 no.3
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• pp.45-50
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• 2008

The choice of an irreducible polynomial and the representation of elements have influence on the efficiency of operators for finite fields. This paper suggests two serial multiplier for the extention field GF$(p^n)$ where p is odd prime. A serial multiplier using an irreducible binomial consists of (2n+5) resisters, 2 MUXs, 2 multipliers of GF(p), and 1 adder of GF(p). It obtains the mulitplication result after $n^2+n$ clock cycles. A serial multiplier using an AOP consists of (2n+5) resisters, 1 MUX, 1 multiplier of CF(p), and 1 adder of GF(p). It obtains the mulitplication result after $n^2$+3n+2 clock cycles.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2001.11a
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• pp.411-414
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• 2001

본 논문에서는 유한체 연산을 바탕으로 하는 공개키 암호화 프로세서를 위한 효율적인 곱셈기 구조를 제안한다. 제안된 곱셈기는 다항식으로 항이 모두 1인, AOP, 기약 다항식을 사용하였다. 제안된 구조는 LFSR 구조에 기반한 곱셈기 구조이다. VHDL 코드 시뮬레이션 결과 제안된 구조가 기존의 구조에 비해서 보다 효율적인 구조 복잡도를 가짐을 알 수 있었다.

• Journal of Korea Society of Industrial Information Systems
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• v.18 no.5
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• pp.67-72
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• 2013

A low-power bypassing Booth multiplier for mobile multimedia applications is proposed. The bypassing structure directly transfers input values to outputs without switching the internal nodes of a multiplier, enabling low-power design. The proposed Booth multiplier adopts the bypassing structure while the bypassing is usually adopted in the Braun multipliers. Simulation results show the proposed Booth multiplier achieves an 11% reduction in terms of the proposed FoM compared to prior works.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.10a
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• pp.740-743
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• 2008

RSA crypto-processors equipped with more than 1024 bits of key space handle the entire key stream in units of blocks. The RSA processor which will be the target design in this paper defines the length of the basic word as 128 bits, and uses an 256-bits register as the accumulator. For efficient execution of 128-bit multiplication, $32b^*32b$ multiplier was designed and adopted and the results are stored in 8 separate 128-bit registers according to the stalks flag. In this paper, a fast 32bit nodular multiplier which is required to execute 128-bit MAC (multiplication and accumulation) operation is proposed. The proposed architecture prototype of the multiplier unit was automatically synthesized, and successfully operated at the frequency in the target RSA processor.