[Back] Elliptic curves are used fairly extensively in public key encryption (such as in Bitcoin and Tor). A BN-curve (Barreto-Naehrig curve) [paper] defines an elliptic curve which can be used for pairings that allow for a high security and efficiency level. This page uses pairings over a 256-bit BN curve and derives a signature for a message.
Elliptic Curve key pairing is also used with zk-SNARKs and zero-knowledge proofs. It can be used for "encrypted multiplication".