NIST FIPS.186-4 has standardized 5 ECC curves on field 𝔽𝑝 (P-192, P-224, P-256, P-384, P-521) and 10 elliptic curves on binary fields. None of them seem to have pairings. Are there any standard curves which support pairings? Are there any libraries which support those curves?
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Are there any standard curves which support pairings?
No, there are currently no pairing-friendly NIST curves; NIST has not announced any plans to approve of either a pairing-friendly curve, or any cryptographical operation that involves a pairing operation.
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$\begingroup$ Why is it so? Pairings are used in many schemes right. NIST is now conducting competitions for lattice-based crypto. I'm surprised why it is not caring for more practical pairing-based crypto. $\endgroup$– satyaMay 5, 2019 at 13:46
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$\begingroup$ IRTF via the CFRG group is working on some pairing friendly curves. They have several drafts involving curves and protocols using them $\endgroup$– NatanaelMay 5, 2019 at 23:22