# Elliptic Curves for Pairings

how can is possible to know if an elliptic curve is suitable for protocols that adopt pairing?

For example, in Certificateless Cryptography with pairing, is it possible to know if all elliptic curves (e.g. $$secp160k1/r1$$, $$secp192r1/k1$$ and so on) are suitable?

Is there a list that facilitate me to see if a curve can be adopt for Certificateless or not?

## 1 Answer

The usual curves we use in ECC are often not suitable for pairing-based cryptography (e.g. you may not find an efficient bilinear mapping), while pairing-friendly curves may not be suitable for normal ECC (e.g. in gap Diffie–Hellman groups, DDH is not hard).

There is an IETF draft on Pairing-Friendly Curves, summarizing the popular curves used in pairing-based cryptography