정보처리학회논문지A (The KIPS Transactions:PartA)

한국정보처리학회 (Korea Information Processing Society)
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유한체 GF(2m)상의 셀 배열 병렬 승산기의 설계

A Design of Cellular Array Parallel Multiplier on Finite Fields GF(2m)

  • 성현경 (상지대학교 컴퓨터·정보공학부)
  • 발행 : 2004.02.01
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초록

본 논문에서는 유한체 GF$(2^m)$상에서 두 다항식의 승산을 실현하는 병렬-입력 및 병렬-출력을 갖는 셀 배열 병렬 승산기를 제시한다 이 승산기는 승산연산부, 기약다항식연산부. MOD연산부로 구성한다. 승산연산부는 AND 게이트와 XOR 게이트로 설계한 기본 셀의 배열로 이루어지며, 기약다항식연산부는 XOR 게이트와 D 플림플롭회로를 사용하여 구성하며, MOD연산부는 AND 게이트와 XOR 게이트에 의한 기본 셀을 배열하여 구성하였다. 제시한 승산기는 PSpice 시뮬레이션을 통하여 동작특성을 보였으며, 클럭신호의 주기를 l${\mu}\textrm{s}$로 하였다. 제시한 셀 배열 병렬 승산기는 m=4인 경우에 AND 게이트의 수가 24개, XOR 게이트의 수가 32개 필요하며, D 플립플롭회로가 4개 필요하다. 또한, AOP 기약 다항식을 사용하면 AND 게이트와 XOR 게이트의 수가 24개 필요하며 D 플립플롭은 사용되지 않는다. 셀 배열 병렬 승산기의 승산연산부의 동작시간은 1 단위시간(클럭시간)이 소비되고, 기약다항식연산부에 의한 MOD연산부의 동작시간은 m 단위시간(클럭시간)이 소비되어 전체 동작시간은 m+1 단위시간(클럭시간)이 소비된다. 본 논문에서 제시한 셀 병렬 승산기는 회선경로 선택의 규칙성, 간단성, 배열의 모듈성과 병렬동작의 특징을 가지며, 특히 차수 m이 매우 큰 유한체강의 두 다항식의 승산에서 확장성을 갖는다.

A cellular array parallel multiplier with parallel-inputs and parallel-outputs for performing the multiplication of two polynomials in the finite fields GF$(2^m)$ is presented in this paper. The presented cellular way parallel multiplier consists of three operation parts: the multiplicative operation part (MULOP), the irreducible polynomial operation part (IPOP), and the modular operation part (MODOP). The MULOP and the MODOP are composed if the basic cells which are designed with AND Bates and XOR Bates. The IPOP is constructed by XOR gates and D flip-flops. This multiplier is simulated by clock period l${\mu}\textrm{s}$ using PSpice. The proposed multiplier is designed by 24 AND gates, 32 XOR gates and 4 D flip-flops when degree m is 4. In case of using AOP irreducible polynomial, this multiplier requires 24 AND gates and XOR fates respectively. and not use D flip-flop. The operating time of MULOP in the presented multiplier requires one unit time(clock time), and the operating time of MODOP using IPOP requires m unit times(clock times). Therefore total operating time is m+1 unit times(clock times). The cellular array parallel multiplier is simple and regular for the wire routing and have the properties of concurrency and modularity. Also, it is expansible for the multiplication of two polynomials in the finite fields with very large m.

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참고문헌

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