Multiplication and Squaring on Pairing-Friendly Fields

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 ∈ {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.

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