The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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Design of Systolic Multipliers in GF(2$^{m}$ ) Using an Irreducible All One Polynomial

기약 All One Polynomial을 이용한 유한체 GF(2$^{m}$ )상의 시스톨릭 곱셈기 설계

  • 권순학 (성균관대학교 수학과) ;
  • 김창훈 (대구대학교 컴퓨터정보공학) ;
  • 홍춘표 (대구대학교 컴퓨터정보공학과)
  • Published : 2004.08.01
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Abstract

In this paper, we present two systolic arrays for computing multiplications in CF(2$\^$m/) generated by an irreducible all one polynomial (AOP). The proposed two systolic mays have parallel-in parallel-out structure. The first systolic multiplier has area complexity of O(㎡) and time complexity of O(1). In other words, the multiplier consists of m(m+1)/2 identical cells and produces multiplication results at a rate of one every 1 clock cycle, after an initial delay of m/2+1 cycles. Compared with the previously proposed related multiplier using AOP, our design has 12 percent reduced hardware complexity and 50 percent reduced computation delay time. The other systolic multiplier, designed for cryptographic applications, has area complexity of O(m) and time complexity of O(m), i.e., it is composed of m+1 identical cells and produces multiplication results at a rate of one every m/2+1 clock cycles. Compared with other linear systolic multipliers, we find that our design has at least 43 percent reduced hardware complexity, 83 percent reduced computation delay time, and has twice higher throughput rate Furthermore, since the proposed two architectures have a high regularity and modularity, they are well suited to VLSI implementations. Therefore, when the proposed architectures are used for GF(2$\^$m/) applications, one can achieve maximum throughput performance with least hardware requirements.

본 논문에서는 AOP(All One Polynomial)에 의해 결정되는 유한체 GF(2$^{m}$ )상의 곱셈을 위한 두 가지 종류의 시스톨릭 어레이를 제안한다. 제안된 두 시스톨릭 어레이 모두 패러럴 입출력 구조를 가진다. 첫 번째 제안된 곱셈기는 O($m^2$)의 면적 복잡도와 O(1)의 시간 복잡도를 가진다. 다시 말하면, 이 곱셈기는 m(m+1)/2 개의 동일한 셀들로 이루어지며 초기 m/2+1 사이클 지연 후, 1 사이클마다 곱셈의 결과를 출력한다. 첫 번째 제안된 곱셈기를 기존의 AOP를 사용하는 병렬형 시스톨릭 곱셈기와 비교 분석한 결과 하드웨어 및 계산지연 시간에 있어 각각 12% 및 50%의 성능 개선을 보인다. 두 번째 제안된 시스톨릭 곱셈기는 암호응용을 위해 선형 어레이로 설계되었으며, O(m)의 면적 복잡도와 O(m)의 시간 복잡도를 가진다. 즉, m+1 개의 동일한 셀들로 이루어지며 m/2+1 사이클마다 곱셈의 결과를 출력한다. 두 번째 곱셈기를 기존의 선형 시스톨릭 곱셈기들과 비교 분석한 결과, 하드웨어, 계산지연 시간, 그리고 처리율에 있어 각각 43%, 83%, 그리고 50%의 성능 개선을 보인다. 또한 제안된 곱셈기들은 높은 규칙성과 모듈성을 가지기 때문에 VLSI 구현에 매우 적합하다. 따라서 GF(2$^{m}$ ) 응용을 위해, 본 연구에서 제안된 곱셈기들을 사용하면 최소의 하드웨어 사용으로 최대의 성능을 얻을 수 있다.

Keywords

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