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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Efficient Exponentiation in GF(p m ) Using the Frobenius Map
verfasst von : Mun-Kyu Lee, Howon Kim, Dowon Hong, Kyoil Chung
Erschienen in: Computational Science and Its Applications - ICCSA 2006
Verlag: Springer Berlin Heidelberg
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The problem of exponentiation over a finite field is to compute
A
e
for a field element
A
and a positive integer
e
. This problem has many useful applications in cryptography and information security. In this paper, we present an efficient exponentiation algorithm in optimal extension field (OEF)
GF
(
p
m
), which uses the fact that the Frobenius map, i.e., the
p
-th powering operation is very efficient in OEFs. Our analysis shows that the new algorithm is twice as fast as the conventional square-and-multiply exponentiation. One of the important applications of our new algorithm is random generation of a base point for elliptic curve cryptography, which is an attractive public-key mechanism for resource-constrained devices. We present a further optimized exponentiation algorithm for this application. Our experimental results show that the new technique accelerates the generation process by factors of 1.62–6.55 over various practical elliptic curves.