Journal of the Institute of Electronics Engineers of Korea SC (전자공학회논문지SC)

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A Design of Multiplier Over $GF(2^m)$ using the Irreducible Trinomial

$GF(2^m)$의 기약 3 항식을 이용한 승산기 설계

  • 황종학 (인하대학교 전자공학과) ;
  • 심재환 (인하대학교 전자공학과) ;
  • 최재석 (인덕대학 메카트로닉스과) ;
  • 김흥수 (인하대학교 전자공학과)
  • Published : 2001.02.28
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Abstract

The multiplication algorithm using the primitive irreducible trinomial $x^m+x+1$ over $GF(2^m)$ was proposed by Mastrovito. The multiplier proposed in this paper consisted of the multiplicative operation unit, the primitive irreducible operation unit and mod operation unit. Among three units mentioned above, the Primitive irreducible operation was modified to primitive irreducible trinomial $x^m+x+1$ that satisfies the range of 1$x^m,{\cdots},x^{2m-2}\;to\;x^{m-1},{\cdots},x^0$ is reduced. In this paper, the primitive irreducible polynomial was reduced to the primitive irreducible trinomial proposed. As a result of this reduction, the primitive irreducible trinomial reduced the size of circuit. In addition, the proposed design of multiplier was suitable for VLSI implementation because the circuit became regular and modular in structure, and required simple control signal.

[ $GF(2^m)$ ]의 기약 3항식인 $x^m+x+1$을 이용한 승산기 알고리즘은 Mastrovito에 의해 제안되었다. 본 논문에서는 기약 3항식 $x^m+x+1$에서 1$GF(2^m)$상의 원시 기약 3 항식을 전개하여 회로를 간략화 하였으며, 제안된 승산기 설계는 규칙적이며 모듈러 구조, 그리고 간단한 제어신호를 요하기 때문에 VLSI 실현이 용이하다고 사료된다.

Keywords

References

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