[Resource Topic] 2008/096: Optimal Pairings

Welcome to the resource topic for 2008/096

Optimal Pairings

Authors: F. Vercauteren


In this paper we introduce the concept of an \emph{optimal pairing}, which by definition can be computed using only \log_2 r/ \varphi(k) basic Miller iterations, with r the order of the groups involved and k the embedding degree. We describe an algorithm to construct optimal ate pairings on all parametrized families of pairing friendly elliptic curves. Finally, we conjecture that any non-degenerate pairing on an elliptic curve without efficiently computable endomorphisms different from powers of Frobenius requires at least \log_2 r/ \varphi(k) basic Miller iterations.

ePrint: https://eprint.iacr.org/2008/096

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