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Published in:
2009 | OriginalPaper | Chapter
Finite Field Multiplication Combining AMNS and DFT Approach for Pairing Cryptography
Authors : Nadia El Mrabet, Christophe Negre
Published in: Information Security and Privacy
Publisher: Springer Berlin Heidelberg
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Pairings over elliptic curves use fields
$\mathbb{F}_{p^k}$
with
p
≥ 2
160
and 6 <
k
≤ 32. In this paper we propose to represent elements in
$\mathbb{F}_p$
with AMNS sytem of [1]. For well chosen AMNS we get roots of unity with sparse representation. The multiplication by these roots are thus really efficient in
$\mathbb{F}_p$
. The DFT/FFT approach for multiplication in extension field
$F_{p^k}$
is thus optimized. The resulting complexity of a multiplication in
$\mathbb{F}_{p^k}$
combining AMNS and DFT is about 50% less than the previously recommended approach [2].