International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Naomi Benger

Publications

Year
Venue
Title
2014
EPRINT
2014
EPRINT
2014
CHES
2008
EPRINT
Fast hashing to G2 on pairing friendly curves
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.