CryptoDB
Optimal Pairings
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Abstract: | 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. |
BibTeX
@misc{eprint-2008-17773, title={Optimal Pairings}, booktitle={IACR Eprint archive}, keywords={public-key cryptography / Tate pairing, ate pairing, elliptic curves, finite fields}, url={http://eprint.iacr.org/2008/096}, note={ frederik.vercauteren@esat.kuleuven.be 13945 received 2 Mar 2008, last revised 7 Mar 2008}, author={F. Vercauteren}, year=2008 }