Paper 2006/471

Multiplication and Squaring on Pairing-Friendly Fields

Augusto Jun Devegili, Colm Ó~hÉigeartaigh, Michael Scott, and Ricardo Dahab


Pairing-friendly fields are finite fields that are suitable for the implementation of cryptographic bilinear pairings. In this paper we review multiplication and squaring methods for pairing-friendly fields $\fpk$ with $k \in \{2,3,4,6\}$. For composite $k$, we consider every possible towering construction. We compare the methods to determine which is most efficient based on the number of basic $\fp$ operations, as well as the best constructions for these finite extension fields. We also present experimental results for every method.

Note: Correction of a typo in the formula for squaring in cubic extensions and reordering of the author list.

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Published elsewhere. Unknown where it was published
finite fieldspairingsefficient implementation
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augusto @ ic unicamp br
2007-02-20: revised
2006-12-14: received
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      author = {Augusto Jun Devegili and Colm Ó~hÉigeartaigh and Michael Scott and Ricardo Dahab},
      title = {Multiplication and Squaring on Pairing-Friendly Fields},
      howpublished = {Cryptology ePrint Archive, Paper 2006/471},
      year = {2006},
      note = {\url{}},
      url = {}
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