Paper 2012/072

Particularly Friendly Members of Family Trees

Craig Costello


The last decade has witnessed many clever constructions of parameterized families of pairing-friendly elliptic curves that now enable implementors targeting a particular security level to gather suitable curves in bulk. However, choosing the best curves from a (usually very large) set of candidates belonging to any particular family involves juggling a number of efficiency issues, such as the nature of binomials used to construct extension fields, the hamming-weight of key pairing parameters and the existence of compact generators in the pairing groups. In light of these issues, two recent works considered the best families for k=12 and k=24 respectively, and detailed subfamilies that offer very efficient pairing instantiations. In this paper we closely investigate the other eight attractive families with 8 \leq k <50, and systematically sub-divide each family into its family tree, branching off until concrete subfamilies are highlighted that simultaneously provide highly-efficient solutions to all of the above computational issues.

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Publication info
Published elsewhere. Unknown where it was published
pairing-friendly curvessubfamiliespairing implementation
Contact author(s)
craig costello @ qut edu au
2012-02-23: received
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      author = {Craig Costello},
      title = {Particularly Friendly Members of Family Trees},
      howpublished = {Cryptology ePrint Archive, Paper 2012/072},
      year = {2012},
      note = {\url{}},
      url = {}
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