IEMEK Journal of Embedded Systems and Applications (대한임베디드공학회논문지)

Institute of Embedded Engineering of Korea (대한임베디드공학회)
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Low-latency Montgomery AB2 Multiplier Using Redundant Representation Over GF(2m))

GF(2m) 상의 여분 표현을 이용한 낮은 지연시간의 몽고메리 AB2 곱셈기

  • Received : 2016.11.14
  • Accepted : 2016.12.27
  • Published : 2017.02.28
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Abstract

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.

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