Browse > Article
http://dx.doi.org/10.13067/JKIECS.2012.7.1.069

An Architecture of the Fast Parallel Multiplier over Finite Fields using AOP  

Kim, Yong-Tae (광주교육대학교 수학교육과)
Publication Information
The Journal of the Korea institute of electronic communication sciences / v.7, no.1, 2012 , pp. 69-79 More about this Journal
Abstract
In this paper, we restrict the case as m odd, n=mk, and propose and explicitly exhibit the architecture of a new parallel multiplier over the field GF($2^m$) with a type k Gaussian period which is a subfield of the field GF($2^n$) implements multiplication using the parallel multiplier over the extension field GF($2^n$). The complexity of the time and area of our multiplier is the same as that of Reyhani-Masoleh and Hasan's multiplier which is the most efficient among the known multipliers in the case of type IV.
Keywords
AOP(All One Polynomial); finite field; parallel multiplier;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 H. Wu and M.A. Hasan, "Low Complexity bit-parallel multipliers for a class of finite fields", IEEE Trans. Vol.47, No.8, pp. 883-887, Aug. 1998,
2 C.C Wang, T.K. Truong, H.M. Shao, L.J. Deutsch, J.K. Omura, and I.S. Reed,"VLSI architectures for computing multiplications and inverses in GF($2^m$)", IEEE Trans. Vol.34, No.8, pp. 709-716, Aug., 1985,
3 A.J. Menezes, I.F. Blake, X. Gao, R.C. Mullin, S.A. Vanstone, and T. Yaghoobian, "Applications of finite fields", Kluwer Academic, 1993.
4 김용태, "유한체의 합성체위에서의 고속 연산기", 한국전자통신학회논문지, 제6권, 3호, pp. 389-395, 2011.
5 S. Gao Jr. and H.W. Lenstra, "Optimal normal bases", Designs, Codes and Cryptography, Vol. 2, pp. 315-323, 1992.   DOI
6 김용태, "복소 이차체위에서의 공개키 암호계에 관한 소고", 한국전자통신학회논문지, 4권, 4호, pp. 270-273, 2009.
7 A. Reyhani-Masolleh and M.H. Hasan, "A new multiplier over $GF(2^m)$", IEEE Trans. Vol.51, No.5, pp. 512-520, May, 2002,
8 A. Reyhani-Masolleh and M.H. Hasan, "Efficient multiplication beyond optimal normal bases", IEEE Trans. Vol. 52, No. 4, pp. 428-439, April, 2003,
9 M.A. Hasan, M.Z. Wang, and V.K. Bhargava, "A modified Massey-Omura parallel multiplier for a class of finite fields", IEEE Trans. Vol. 42, No. 10, pp. 1278-1280, Oct., 1993,
10 IEEE P1363, "Standard specifications for public key cryptography", Draft 13, 1999.
11 Y. Kim, "Efficient Serial Gaussian Normal Basis Multipliers over Binary Extension Fields", 한국전자통신학회논문지, 4권, 3호, pp. 197-203, 2009.