ECDSA backend
diff --git a/docs/hazmat/primitives/asymmetric/ec.rst b/docs/hazmat/primitives/asymmetric/ec.rst
index f88b965..798fbab 100644
--- a/docs/hazmat/primitives/asymmetric/ec.rst
+++ b/docs/hazmat/primitives/asymmetric/ec.rst
@@ -1,11 +1,30 @@
.. hazmat::
-Elliptic Curve
-==============
+Elliptic Curve Cryptography
+===========================
.. currentmodule:: cryptography.hazmat.primitives.asymmetric.ec
+,, method:: generate_private_key(curve, backend):
+
+ .. versionadded:: 0.5
+
+ Generate a new private key on ``curve`` for use with ``backend``.
+
+ :param backend: A
+ :class:`~cryptography.hazmat.primtives.interfaces.EllipticCurve`
+ provider.
+
+ :param backend: A
+ :class:`~cryptography.hazmat.backends.interfaces.EllipticCurveBackend`
+ provider.
+
+ :returns: A new instance of a
+ :class:`~cryptography.hazmat.primtivies.interfaces.EllipticCurvePrivateKey`
+ provider.
+
+
.. class:: EllipticCurvePrivateNumbers(private_value, public_numbers)
.. versionadded:: 0.5
@@ -25,6 +44,19 @@
The private value.
+ .. method:: private_key(backend)
+
+ Convert a collection of numbers into a private key suitable for doing
+ actual cryptographic operations.
+
+ :param backend: A
+ :class:`~cryptography.hazmat.backends.interfaces.EllipticCurveBackend`
+ provider.
+
+ :returns: A new instance of a
+ :class:`~cryptography.hazmat.primtivies.interfaces.EllipticCurvePrivateKey`
+ provider.
+
.. class:: EllipticCurvePublicNumbers(x, y, curve)
@@ -49,3 +81,149 @@
:type: int
The affine y component of the public point used for verifying.
+
+ .. method:: public_key(backend)
+
+ Convert a collection of numbers into a public key suitable for doing
+ actual cryptographic operations.
+
+ :param backend: A
+ :class:`~cryptography.hazmat.backends.interfaces.EllipticCurveBackend`
+ provider.
+
+ :returns: A new instance of a
+ :class:`~cryptography.hazmat.primtivies.interfaces.EllipticCurvePublicKey`
+ provider.
+
+
+Elliptic Curve Signature Algorithms
+-----------------------------------
+
+.. class:: ECDSA(algorithm)
+ .. versionadded:: 0.5
+
+ The ECDSA signature algorithm first standardized in NIST publication
+ `FIPS 186-3`_, and later in `FIPS 186-4`_.
+
+ :param algorithm: An instance of a
+ :class:`~cryptography.hazmat.primitives.interfaces.HashAlgorithm`
+ provider.
+
+ .. code-block:: pycon
+
+ >>> from cryptography.hazmat.backends import default_backend
+ >>> from cryptography.hazmat.primitives import hashes
+ >>> from cryptography.hazmat.primitives.asymmetric import ec
+ >>> private_key = ec.generate_private_key(
+ ... ec.SECT283K1(), default_backend()
+ ... )
+ >>> signer = private_key.signer(ec.ECDSA(hashes.SHA256()))
+ >>> signer.update(b"this is some data I'd like")
+ >>> signer.update(b" to sign")
+ >>> signature = signer.finalize()
+
+Elliptic Curves
+---------------
+
+All named curves are providers of
+:class:`~cryptography.hazmat.primtives.interfaces.EllipticCurve`.
+
+There is `some concern`_ that the non-Koblitz NIST curves (identified by names
+that start with "B" or "P") may have been intentionally weakened by their
+generation process.
+
+
+.. class:: SECT571K1
+ .. versionadded:: 0.5
+
+ SECG curve ``sect571k1``. Also called NIST K-571.
+
+
+.. class:: SECT409K1
+ .. versionadded:: 0.5
+
+ SECG curve ``sect409k1``. Also called NIST K-409.
+
+
+.. class:: SECT283K1
+ .. versionadded:: 0.5
+
+ SECG curve ``sect283k1``. Also called NIST K-283.
+
+
+.. class:: SECT233K1
+ .. versionadded:: 0.5
+
+ SECG curve ``sect233k1``. Also called NIST K-233.
+
+
+.. class:: SECT163K1
+ .. versionadded:: 0.5
+
+ SECG curve ``sect163k1``. Also called NIST K-163.
+
+
+.. class:: SECT571R1
+ .. versionadded:: 0.5
+
+ SECG curve ``sect571r1``. Also called NIST B-571.
+
+
+.. class:: SECT409R1
+ .. versionadded:: 0.5
+
+ SECG curve ``sect409r1``. Also called NIST B-409.
+
+
+.. class:: SECT283R1
+ .. versionadded:: 0.5
+
+ SECG curve ``sect283r1``. Also called NIST B-283.
+
+
+.. class:: SECT233R1
+ .. versionadded:: 0.5
+
+ SECG curve ``sect233r1``. Also called NIST B-233.
+
+
+.. class:: SECT163R2
+ .. versionadded:: 0.5
+
+ SECG curve ``sect163r2``. Also called NIST B-163.
+
+
+.. class:: SECP521R1
+ .. versionadded:: 0.5
+
+ SECG curve ``secp521r1``. Also called NIST P-521.
+
+
+.. class:: SECP384R1
+ .. versionadded:: 0.5
+
+ SECG curve ``secp384r1``. Also called NIST P-384.
+
+
+.. class:: SECP256R1
+ .. versionadded:: 0.5
+
+ SECG curve ``secp256r1``. Also called NIST P-256.
+
+
+.. class:: SECT224R1
+ .. versionadded:: 0.5
+
+ SECG curve ``secp224r1``. Also called NIST P-224.
+
+
+.. class:: SECP192R1
+ .. versionadded:: 0.5
+
+ SECG curve ``secp192r1``. Also called NIST P-192.
+
+
+
+.. _`FIPS 186-3`: http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
+.. _`FIPS 186-4`: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf
+.. _`some concern`: https://crypto.stackexchange.com/questions/10263/should-we-trust-the-nist-recommended-ecc-parameters
diff --git a/docs/hazmat/primitives/interfaces.rst b/docs/hazmat/primitives/interfaces.rst
index 34e4e93..d5ca59a 100644
--- a/docs/hazmat/primitives/interfaces.rst
+++ b/docs/hazmat/primitives/interfaces.rst
@@ -411,7 +411,6 @@
`EdDSA`_.
.. classmethod:: signer(signature_algorithm)
-
Sign data which can be verified later by others using the public key.
:param signature_algorithm: An instance of a
@@ -421,7 +420,6 @@
:returns:
:class:`~cryptography.hazmat.primitives.interfaces.AsymmetricSignatureContext`
- .. attribute:: curve
:type: :class:`~cryptography.hazmat.primitives.interfaces.EllipticCurve`
@@ -440,8 +438,7 @@
An elliptic curve public key.
- .. classmethod:: verifier(signer, signature_algorithm)
-
+ .. classmethod:: verifier(signature, signature_algorithm)
Verify data was signed by the private key associated with this public
key.