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A New Multiplication Algorithm and VLSI Architecture Over $GF(2^m)$ Using Gaussian Normal Basis  

Kwon, Soon-Hak (성균관대학교 수학과)
Kim, Hie-Cheol (대구대학교 정보통신공학과)
Hong, Chun-Pyo (대구대학교 정보통신공학과)
Kim, Chang-Hoon (대구대학교 정보통신공학과)
Publication Information
The Journal of Korean Institute of Communications and Information Sciences / v.31, no.12C, 2006 , pp. 1297-1308 More about this Journal
Abstract
Multiplications in finite fields are one of the most important arithmetic operations for implementations of elliptic curve cryptographic systems. In this paper, we propose a new multiplication algorithm and VLSI architecture over $GF(2^m)$ using Gaussian normal basis. The proposed algorithm is designed by using a symmetric property of normal elements multiplication and transforming coefficients of normal elements. The proposed multiplication algorithm is applicable to all the five recommended fields $GF(2^m)$ for elliptic curve cryptosystems by NIST and IEEE 1363, where $m\in${163, 233, 283, 409, 571}. A new VLSI architecture based on the proposed multiplication algorithm is faster or requires less hardware resources compared with previously proposed normal basis multipliers over $GF(2^m)$. In addition, we gives an easy method finding a basic multiplication matrix of normal elements.
Keywords
GNB; Finite Field; Elliptic Curve Cryptosystem; Multiplication; VLSI;
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