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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Faster Squaring in the Cyclotomic Subgroup of Sixth Degree Extensions
verfasst von : Robert Granger, Michael Scott
Erschienen in: Public Key Cryptography – PKC 2010
Verlag: Springer Berlin Heidelberg
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This paper describes an extremely efficient squaring operation in the so-called ‘cyclotomic subgroup’ of
$\mathbb{F}_{q^6}^{\times}$
, for
$q \equiv 1 \bmod{6}$
. Our result arises from considering the Weil restriction of scalars of this group from
$\mathbb{F}_{q^6}$
to
$\mathbb{F}_{q^2}$
, and provides efficiency improvements for both pairing-based and torus-based cryptographic protocols. In particular we argue that such fields are ideally suited for the latter when the field characteristic satisfies
$p \equiv 1 \pmod{6}$
, and since torus-based techniques can be applied to the former, we present a compelling argument for the adoption of a single approach to efficient field arithmetic for pairing-based cryptography.