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 G1 is a group of points on the base field E(Fp) and G2 is instantiated as a group of points with coordinates on some extension field, over a twisted curve E (Fpd ), where d divides the embedding degree k. While hashing to G1 is relatively easy, hashing to G2 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 G2 which exploits an efficiently computable homomorphism.

• Type: Conference
• Year: 2009
• Where: PAIRING
• Authors: Michael Scott, Naomi Benger, Manuel Charlemagne, Luis J. Dominguez Perez, Ezekiel J. Kachisa
• Keywords: Cryptography, Elliptic Curve, Elliptic Curve Groups, Ordinary Elliptic Curves, PAIRING 2009