2009 | OriginalPaper | Buchkapitel
Fast Hashing to G 2 on Pairing-Friendly Curves
verfasst von : Michael Scott, Naomi Benger, Manuel Charlemagne, Luis J. Dominguez Perez, Ezekiel J. Kachisa
Erschienen in: Pairing-Based Cryptography – Pairing 2009
Verlag: Springer Berlin Heidelberg
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Pairings on elliptic curves usually take as input a point in a subgroup
G
1
of an elliptic curve group
$E({\mathbb{F}}_p)$
and a point in a subgroup
G
2
of
$E'({\mathbb{F}}_{p^d})$
for some twist
E
′ of
E
. In this paper we consider the problem of hashing to
G
2
when the group
G
2
has prime order. The naive approach requires multiplication in the group
$E'({\mathbb{F}}_{p^d})$
by a large cofactor. Our main result is to describe a fast method to compute this cofactor multiplication; our method exploits an efficiently computable homomorphism.