한국정보과학회논문지:시스템및이론 (Journal of KIISE:Computer Systems and Theory)

한국정보과학회 (Korean Institute of Information Scientists and Engineers)
권호 표지

All-One Polynomial에 의해 정의된 유한체 $GF(2^m) $ 상의 새로운 Low-Complexity Bit-Parallel 정규기저 곱셈기

A New Low-complexity Bit-parallel Normal Basis Multiplier for$GF(2^m) $ Fields Defined by All-one Polynomials

  • 장용희 (한국항공대학교 정보통신공학과) ;
  • 권용진 (한국항공대학교 전자.정보통신.컴퓨터공학부)
  • 발행 : 2004.02.01
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⟨ 이전 논문 다음 논문 ⟩

초록

대부분의 공개키 기반 암호시스템은 유한체 $GF(2^m)$ 상의 산술 연산들을 기반으로 구축된다. 이들 연산 중 덧셈을 제외한 다른 연산들은 곱셈 연산을 반복하여 계산되므로, 곱셈 연산의 효율적인 구현은 공개키 기반 암호시스템에서 매우 중요하다. 본 논문에서는 All-One Polynomial에 의해 정의된 $GF(2^m)$ 상의 효율적인 Bit-Parallel 정규기저 곱셈기를 제안한다. 게이트 및 시간적인 면에서 본 곱셈기의 복잡도(complexity)는 이전에 제안된 같은 종류의 곱셈기 보다 낮거나 동일하다. 또한, 본 논문의 곱셈기는 아키텍처가 규칙적(regular)이어서 VLSI 구현에 적합하다.

Most of pubic-key cryptosystems are built on the basis of arithmetic operations defined over the finite field GF$GF(2^m)$ .The other operations of finite fields except addition can be computed by repeated multiplications. Therefore, it is very important to implement the multiplication operation efficiently in public-key cryptosystems. We propose an efficient bit-parallel normal basis multiplier for$GF(2^m)$ fields defined by All-One Polynomials. The gate count and time complexities of our proposed multiplier are lower than or equal to those of the previously proposed multipliers of the same class. Also, since the architecture of our multiplier is regular, it is suitable for VLSI implementation.

키워드

참고문헌

  1. A. Reyhani-Masoleh and M.A. Hasan, 'A New Construction of Massey-Omura Parallel Multiplier over GF($2^m$),' IEEE Trans. Computers, vol. 51, no. 5, pp. 511-520, May 2002 https://doi.org/10.1109/TC.2002.1004590
  2. C.K. Koc and B. Sunar, 'Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finites Fields,' IEEE Trans. Computers, vol. 47, no. 3, pp. 353-356, Mar. 1998 https://doi.org/10.1109/12.660172
  3. C.Y. Lee, E.H. Lu, and J.Y. Lee, 'Bit-Parallel Systolic Multipliers for GF($2^m$) Fields Defined by All-One and Equally Spaced Polynomials,' IEEE Trans. Computers, vol. 50, no. 5, pp. 385-393, May 2001 https://doi.org/10.1109/12.926154
  4. T. Itoh and S. Tsujii, 'Structure of Parallel Multiplier for a Class of Fields GF($2^m$),' Information and Computation, vol. 83, pp. 21-40, 1989 https://doi.org/10.1016/0890-5401(89)90045-X
  5. M.A. Hasan, M.Z. Wang, and V.K. Bhargava, 'Modular Construction of Low Complexity Parallel Multipliers for a Class of Finite Fields GF($2^m$),' IEEE Trans. Computers, vol. 41, no. 8, pp. 962-971, Aug. 1992 https://doi.org/10.1109/12.156539
  6. M.A. Hasan, M.Z. Wang, and V.K. Bhargava, 'A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields,' IEEE Trans. Computers, vol. 42, no. 10, pp. 1278-1280, Oct. 1993 https://doi.org/10.1109/12.257715
  7. C.C. Wang, T.K. Truong, H.M. Shar, L.J. Deutsch, J.K. Omura, and I.S. Reed, 'VLSI Architecture for Computing Multiplications and Inverses in GF($2^m$),' IEEE Trans. Computers, vol. 34, no. 8, pp. 709-716, Aug. 1985 https://doi.org/10.1109/TC.1985.1676616
  8. H. Wu and M.A. Hasan, 'Low Complexity Bit-Parallel Multipliers for a Class of Finite Fields,' IEEE Trans. Computers, vol. 47, no. 8, pp. 883-887, Aug. 1998 https://doi.org/10.1109/12.707588
  9. R.C. Muffin, I.M. Onyszchuk, S. A. Vanstone, and R.M. Wilson, 'Optimal Normal Bases in GF($p^n$),' Discrete Applied Mathematics, vol. 22, pp. 149-161, 1988/89 https://doi.org/10.1016/0166-218X(88)90090-X