//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 | [[https://beta.csrc.nist.gov/Projects/Elliptic-Curve-Cryptography|NIST ECC]]: [[http://csrc.nist.gov/groups/ST/toolkit/documents/dss/NISTReCur.pdf|P-256]] | [[https://tools.ietf.org/html/rfc6637|RFC6637]] |           |Gnuk 1.2|
| Signature | ECDSA | [[https://beta.csrc.nist.gov/Projects/Elliptic-Curve-Cryptography|NIST ECC]]: [[http://csrc.nist.gov/groups/ST/toolkit/documents/dss/NISTReCur.pdf|P-384]] | [[https://tools.ietf.org/html/rfc6637|RFC6637]] |           |        |
| Signature | ECDSA | [[https://beta.csrc.nist.gov/Projects/Elliptic-Curve-Cryptography|NIST ECC]]: [[http://csrc.nist.gov/groups/ST/toolkit/documents/dss/NISTReCur.pdf|P-521]] | [[https://tools.ietf.org/html/rfc6637|RFC6637]] |           |        |
| Signature | ECDSA | [[http://www.ecc-brainpool.org/download.htm|ECC Brainpool]]: [[https://tools.ietf.org/html/rfc5639|brainpoolP256r1]] |   |            |        |
| Signature | ECDSA | [[http://www.ecc-brainpool.org/download.htm|ECC Brainpool]]: [[https://tools.ietf.org/html/rfc5639|brainpoolP384r1]] |   |         |        |
| Signature | ECDSA | [[http://www.ecc-brainpool.org/download.htm|ECC Brainpool]]: [[https://tools.ietf.org/html/rfc5639|brainpoolP512r1]] |   |        |        |
| Signature | ECDSA | [[http://www.secg.org/|SECG]]: [[http://www.secg.org/sec2-v2.pdf|secp256k1]] |         |libgcrypt 1.7|Gnuk 1.2|
| Signature | EdDSA | [[https://tools.ietf.org/html/rfc8032|RFC8032: Ed25519]] | [[https://tools.ietf.org/html/draft-koch-openpgp-rfc4880bis|RFC4880bis draft]] |           |Gnuk 1.2|
| Encryption | ECDH | [[https://beta.csrc.nist.gov/Projects/Elliptic-Curve-Cryptography|NIST ECC]]: [[http://csrc.nist.gov/groups/ST/toolkit/documents/dss/NISTReCur.pdf|P-256]] | [[https://tools.ietf.org/html/rfc6637|RFC6637]] |           |Gnuk 1.2|
| Encryption | ECDH | [[https://beta.csrc.nist.gov/Projects/Elliptic-Curve-Cryptography|NIST ECC]]: [[http://csrc.nist.gov/groups/ST/toolkit/documents/dss/NISTReCur.pdf|P-384]] | [[https://tools.ietf.org/html/rfc6637|RFC6637]] |           |        |
| Encryption | ECDH | [[https://beta.csrc.nist.gov/Projects/Elliptic-Curve-Cryptography|NIST ECC]]: [[http://csrc.nist.gov/groups/ST/toolkit/documents/dss/NISTReCur.pdf|P-521]] | [[https://tools.ietf.org/html/rfc6637|RFC6637]] |           |        |
| Encryption | ECDH | [[http://www.ecc-brainpool.org/download.htm|ECC Brainpool]]: [[https://tools.ietf.org/html/rfc5639|brainpoolP256r1]] |    |         |        |
| Encryption | ECDH | [[http://www.ecc-brainpool.org/download.htm|ECC Brainpool]]: [[https://tools.ietf.org/html/rfc5639|brainpoolP384r1]] |    |         |        |
| Encryption | ECDH | [[http://www.ecc-brainpool.org/download.htm|ECC Brainpool]]: [[https://tools.ietf.org/html/rfc5639|brainpoolP512r1]] |    |         |        |
| Encryption | ECDH | [[http://www.secg.org/|SECG]]: [[http://www.secg.org/sec2-v2.pdf|secp256k1]] |         |libgcrypt 1.7|Gnuk 1.2|
| Encryption | ECDH | [[https://tools.ietf.org/html/rfc7748|RFC7748: Curve25519]] |         |libgcrypt 1.7|Gnuk 1.2|