Paper 2008/530

Fast hashing to G2 on pairing friendly curves

Michael Scott, Naomi Benger, Manuel Charlemagne, Luis J. Dominguez Perez, and Ezekiel J. Kachisa


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.

Available format(s)
Publication info
Published elsewhere. Unknown where it was published
Tate PairingAddition Chains
Contact author(s)
mike @ computing dcu ie
2008-12-19: received
Short URL
Creative Commons Attribution


      author = {Michael Scott and Naomi Benger and Manuel Charlemagne and Luis J.  Dominguez Perez and Ezekiel J.  Kachisa},
      title = {Fast hashing to G2 on pairing friendly curves},
      howpublished = {Cryptology ePrint Archive, Paper 2008/530},
      year = {2008},
      note = {\url{}},
      url = {}
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