## CryptoDB

### Paper: Fast hashing to G2 on pairing friendly curves

Authors: Michael Scott Naomi Benger Manuel Charlemagne Luis J. Dominguez Perez Ezekiel J. Kachisa URL: http://eprint.iacr.org/2008/530 Search ePrint Search Google 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.
##### BibTeX
@misc{eprint-2008-18094,
title={Fast hashing to G2 on pairing friendly curves},
booktitle={IACR Eprint archive},
keywords={implementation / Tate Pairing, Addition Chains},
url={http://eprint.iacr.org/2008/530},
note={ mike@computing.dcu.ie 14231 received 18 Dec 2008},
author={Michael Scott and Naomi Benger and Manuel Charlemagne and Luis J. Dominguez Perez and Ezekiel J. Kachisa},
year=2008
}