NIST FIPS.186-4 has standardized 5 ECC curves on field $\mathbb{F}_p$ (P-192, P-224, P-256, P-384, P-521) and 10 elliptic curves on binary fields. I need to use ECC curves without pairings for my scheme.

I am not sure which of these curves have pairings, and which of them don't.

  • $\begingroup$ these curves are intentionally standardized to make the use of pairings impractical. $\endgroup$ – Youssef El Housni Dec 13 '18 at 10:51
  • $\begingroup$ So, doesn't NIST have any standards for curves with pairings? What curves are used for pairing-based cryptography then? $\endgroup$ – satya Dec 13 '18 at 11:44
  • $\begingroup$ No there are no standards just yet. You can read this paper about pairings-friendly elliptic curves: eprint.iacr.org/2006/372.pdf $\endgroup$ – Youssef El Housni Dec 14 '18 at 14:07

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