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Title:
Fast hashing to G2 on pairing friendly curves
Authors: Michael Scott, Naomi Benger, Manuel Charlemagne, Luis J. Dominguez Perez, Ezekiel J. Kachisa
Abstract:When using pairing-friendly ordinary elliptic curves over prime fields to implement identity-based protocols, there is often a need to hash identities to points on one or both of the two elliptic curve groups of prime order r involved in the pairing. Of these G_1 is a group of points on the base field E(\F_p) and G_2 is instantiated as a group of points with coordinates on some extension field, over a twisted curve E'(\F_{p^d}), where d divides the embedding degree k. While hashing to G_1 is relatively easy, hashing to G_2 has been less considered, and is regarded as likely to be more expensive as it appears to require a multiplication by a large cofactor. In this paper we introduce a fast method for this cofactor multiplication on G_2 which exploits an efficiently computable homomorphism.
ePrint: https://eprint.iacr.org/2008/530
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