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Erschienen in:
2005 | OriginalPaper | Buchkapitel
A Fast Inversion Algorithm and Low-Complexity Architecture over GF(2 m )
verfasst von : Sosun Kim, Nam Su Chang, Chang Han Kim, Young-Ho Park, Jongin Lim
Erschienen in: Computational Intelligence and Security
Verlag: Springer Berlin Heidelberg
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The performance of public-key cryptosystems is mainly appointed by the underlying finite field arithmetic. Among the basic arithmetic operations over finite field, the multiplicative inversion is the most time consuming operation. In this paper, a fast inversion algorithm over
GF
(2
m
) with the polynomial basis representation is proposed. The proposed algorithm executes in about 27.5% or 45.6% less iterations than the extended binary gcd algorithm (EBGA) or the montgomery inverse algorithm (MIA) over
GF
(2
163
), respectively. In addition, we propose a new hardware architecture to apply for low-complexity systems. The proposed architecture takes approximately 48.3% or 24.9% less the number of reduction operations than [4] or [8] over
GF
(2
239
), respectively. Furthermore, it executes in about 21.8% less the number of addition operations than [8] over
GF
(2
163
).