Journal of the Institute of Electronics Engineers of Korea SD (대한전자공학회논문지SD)

The Institute of Electronics and Information Engineers (대한전자공학회)
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Digit-Serial Finite Field Multipliers for GF($3^m$)

GF($3^m$)의 Digit-Serial 유한체 곱셈기

  • Chang, Nam-Su (Graduate School of Information Management and Security, Korea University) ;
  • Kim, Tae-Hyun (Graduate School of Information Management and Security, Korea University) ;
  • Kim, Chang-Han (School of Information & Communication systems, Semyung University) ;
  • Han, Dong-Guk (Electronics and Telecommunications Research Institute) ;
  • Kim, Ho-Won (Dept. of Computer Science & Engineering, Pusan University)
  • 장남수 (고려대학교 정보경영공학전문대학원) ;
  • 김태현 (고려대학교 정보경영공학전문대학원) ;
  • 김창한 (세명대학교 정보통신학부) ;
  • 한동국 (한국전자통신연구원) ;
  • 김호원 (부산대학교 정보컴퓨터공학부)
  • Published : 2008.10.25
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Abstract

Recently, a considerable number of studies have been conducted on pairing based cryptosystems. The efficiency of pairing based cryptosystems depends on finite fields, similar to existing public key cryptosystems. In general, pairing based ctyptosystems are defined over finite fields of chracteristic three, GF($3^m$), based on trinomials. A multiplication in GF($3^m$) is the most dominant operation. This paper proposes a new most significant digit(MSD)-first digit- serial multiplier. The proposed MSD-first digit-serial multiplier has the same area complexity compared to previous multipliers, since the modular reduction step is performed in parallel. And the critical path delay is reduced from 1MUL+(log ${\lceil}n{\rceil}$+1)ADD to 1MUL+(log ${\lceil}n+1{\rceil}$)ADD. Therefore, when the digit size is not $2^k$, the time delay is reduced by one addition.

최근 페어링 기반의 암호시스템에 대한 연구가 활발히 진행되고 있으며, 암호시스템의 효율성은 기존의 공개키 암호시스템과 같이 유한체에 의존한다. 페어링 기반의 암호시스템의 경우 주로 GF($3^m$)에서 고려되며 유한체 연산에서 곱셈 연산이 효율성에 가장 큰 영향을 미친다. 본 논문에서는 삼항 기약다항식 기반의 새로운 GF($3^m$) MSD-first Digit-Serial 곱셈기를 제안한다. 제안하는 MSD-first Digit-Serial 곱셈기는 모듈러 감산 연산부를 병렬화하여 공간복잡도는 기존의 결과와 거의 같으나 Critical Path Delay가 기존의 1MUL+(log ${\lceil}n{\rceil}$+1)ADD에서 1MUL+(log ${\lceil}n+1{\rceil}$)ADD으로 감소한다. 따라서 Digit이 $2^k$가 아닌 경우 1번의 덧셈에 대한 시간 지연이 감소한다.

Keywords

References

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