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Fast Hashing to G2 on Pairing-Friendly Curves

  • Michael Scott
  • Naomi Benger
  • Manuel Charlemagne
  • Luis J. Dominguez Perez
  • Ezekiel J. Kachisa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5671)

Abstract

Pairings on elliptic curves usually take as input a point in a subgroup G 1 of an elliptic curve group \(E({\mathbb{F}}_p)\) and a point in a subgroup G 2 of \(E'({\mathbb{F}}_{p^d})\) for some twist E′ of E. In this paper we consider the problem of hashing to G 2 when the group G 2 has prime order. The naive approach requires multiplication in the group \(E'({\mathbb{F}}_{p^d})\) by a large cofactor. Our main result is to describe a fast method to compute this cofactor multiplication; our method exploits an efficiently computable homomorphism.

Keywords

Tate pairing addition chains 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Michael Scott
    • 1
  • Naomi Benger
    • 1
  • Manuel Charlemagne
    • 1
  • Luis J. Dominguez Perez
    • 1
  • Ezekiel J. Kachisa
    • 1
  1. 1.School of ComputingDublin City University, BallymunDublin 9Ireland

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