//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 | [[https://tools.ietf.org/html/rfc6637|RFC6637]] |           |Gnuk 1.2|
| Signature | ECDSA | NIST P-384 | [[https://tools.ietf.org/html/rfc6637|RFC6637]] |           |        |
| Signature | ECDSA | NIST P-521 | [[https://tools.ietf.org/html/rfc6637|RFC6637]] |           |        |
| Signature | ECDSA | brainpoolP256r1 |         |           |        |
| Signature | ECDSA | brainpoolP384r1 |         |           |        |
| Signature | ECDSA | brainpoolP512r1 |         |           |        |
| Signature | ECDSA | secp256k1 |         |libgcrypt 1.7|Gnuk 1.2|
| Signature | EDDSA | Ed25519   | [[https://tools.ietf.org/html/draft-koch-openpgp-rfc4880bis|RFC4880bis draft]] |           |Gnuk 1.2|
| Encryption | ECDH | NIST P-256 | [[https://tools.ietf.org/html/rfc6637|RFC6637]] |           |Gnuk 1.2|
| Encryption | ECDH | NIST P-384 | [[https://tools.ietf.org/html/rfc6637|RFC6637]] |           |        |
| Encryption | ECDH | NIST P-521 | [[https://tools.ietf.org/html/rfc6637|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|