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http://dx.doi.org/10.13089/JKIISC.2006.16.4.83

A New Parallel Multiplier for Type II Optimal Normal Basis  

Kim Chang-Han (Information & Communication Systems, Semyung University)
Jang Sang-Woon (National Security Research Institute)
Lim Jong-In (Graduate School of Information Security(GSIS), Korea University)
Ji Sung-Yeon (Graduate School of Information Security(GSIS), Korea University)
Abstract
In H/W implementation for the finite field, the use of normal basis has several advantages, especially, the optimal normal basis is the most efficient to H/W implementation in GF($2^m$). In this paper, we propose a new, simpler, parallel multiplier over GF($2^m$) having a type II optimal normal basis, which performs multiplication over GF($2^m$) in the extension field GF($2^{2m}$). The time and area complexity of the proposed multiplier is same as the best of known type II optimal normal basis parallel multiplier.
Keywords
유한체 연산;병렬곱셈 연산기;타입 II 최적 정규기저;
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1 B. Sunar and C.K. Koc,'An efficient optimal normal basis type II multiplier', IEEE Trans. vol.50, no.1, pp. 83-88, Jan., 2001   DOI   ScienceOn
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   DOI   ScienceOn
3 M. Elia and M. Leone, 'On the In herent Space Complexity of Fast Parallel Multipliers for GF$2^{m}$', IEEE Trans. Computers, Vol. 51, no. 3, pp.346-351, Mar. 2002   DOI   ScienceOn
4 A.J. Menezes, I.F. Blake, X. Gao, R.C. Mullin, S.A. Vanstone, and T. Yaghoobian, Applications of finitr fields, Kluwer Academic, 1993
5 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   DOI   ScienceOn
6 ANSI X 9.63, Public key cryptography for the financial services industry : Elliptic curve key agreement and transport protocols, draft, 1998
7 IEEE P1363, Standard specifications for public key cryptography, Draft 13, 1999
8 C.H. Kim, S. Oh, and J. Lim,'A new hardware architecture for operations in GF($2^{n}$)', IEEE Trans. vol.51, no.1, pp. 90-92, Jan, 2002   DOI   ScienceOn
9 Nat'l Inst. of Standard and Technology, Digital Signature Standard, FIPS 186-2, Jan. 2000
10 S. Gao Jr. and H.W. Lenstra, 'Optimal normal bases', Designs, Codes and Cryptography, vol. 2, pp.315-323, 1992   DOI
11 C.K. Koc and B. Sunar, 'Low-complexity bit-parallel canonical and normal basis multipliers for a class of finite fields', IEEE Trans. vol.47, no.3, pp. 353-356, Mar, 1998   DOI   ScienceOn
12 A. Reyhani-Masolleh and M.H. Hasan, 'A new construction of Massey-Omura parallel multiplier over GF($2^{m}$)', IEEE Trans. vol.51, no.5, pp. 512-520, May, 2002
13 R. Lidl and H. Niederreiter, Introduction to finite fields and its applications, Cambridge Univ. Press, 1994