//Elliptic curve cryptography (ECC) is an approach to public-key cryptography 
based on the algebraic structure of elliptic curves over finite fields.
One of the main benefits in comparison with non-ECC cryptography [..]  
is the same level of security provided by keys of smaller size.//
from its [[https://en.wikipedia.org/wiki/Elliptic_curve_cryptography|Wikipedia entry]] 2015-11-05


http://arstechnica.com/security/2013/10/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/1/

GnuPG 2.1 supports ECC.

|= Function |= Protocol |= Curve         |= Spec.   |= Library dependency   |=Token  |
| Signature  | ECDSA     |NIST P-256      | RFC6637 |           |Gnuk 1.2|
| Signature  | ECDSA     |NIST P-384      | RFC6637 |           |        |
| Signature  | ECDSA     |NIST P-521      | RFC6637 |           |        |
| Signature  | ECDSA     |brainpoolP256r1 |         |           |        |
| Signature  | ECDSA     |brainpoolP384r1 |         |           |        |
| Signature  | ECDSA     |brainpoolP512r1 |         |           |        |
| Signature  | ECDSA     |secp256k1       |         |libgcrypt 1.7|Gnuk 1.2|
| Signature  | EDDSA     |Ed25519         | draft RFC4880bis        |           |Gnuk 1.2|
| Encryption | ECDH    	 |NIST P-256      | RFC6637 |           |Gnuk 1.2|
| Encryption | ECDH    	 |NIST P-384      | RFC6637 |           |        |
| Encryption | ECDH    	 |NIST P-521      | RFC6637 |           |        |
| Encryption | ECDH    	 |brainpoolP256r1 |         |           |        |
| Encryption | ECDH    	 |brainpoolP384r1 |         |           |        |
| Encryption | ECDH    	 |brainpoolP512r1 |         |           |        |
| Encryption | ECDH    	 |secp256k1       |         |libgcrypt 1.7|Gnuk 1.2|
| Encryption | ECDH    	 |Curve25519      |         |libgcrypt 1.7|Gnuk 1.2|

https://datatracker.ietf.org/doc/draft-koch-openpgp-rfc4880bis/