.. hazmat::
.. module:: cryptography.hazmat.primitives.asymmetric.ec
.. function:: generate_private_key(curve)
.. versionadded:: 0.5
Generate a new private key on ``curve``.
:param curve: An instance of :class:`EllipticCurve`.
:returns: A new instance of :class:`EllipticCurvePrivateKey`.
.. function:: derive_private_key(private_value, curve)
.. versionadded:: 1.6
Derive a private key from ``private_value`` on ``curve``.
:param int private_value: The secret scalar value.
:param curve: An instance of :class:`EllipticCurve`.
:returns: A new instance of :class:`EllipticCurvePrivateKey`.
.. versionadded:: 0.5
The ECDSA signature algorithm first standardized in NIST publication FIPS 186-3, and later in FIPS 186-4.
Note that while elliptic curve keys can be used for both signing and key exchange, this is bad cryptographic practice. Instead, users should generate separate signing and ECDH keys.
| param algorithm: | An instance of :class:`~cryptography.hazmat.primitives.hashes.HashAlgorithm`. |
|---|
>>> from cryptography.hazmat.primitives import hashes
>>> from cryptography.hazmat.primitives.asymmetric import ec
>>> private_key = ec.generate_private_key(
... ec.SECP384R1()
... )
>>> data = b"this is some data I'd like to sign"
>>> signature = private_key.sign(
... data,
... ec.ECDSA(hashes.SHA256())
... )The signature is a bytes object, whose contents are DER encoded as
described in RFC 3279. This can be decoded using
:func:`~cryptography.hazmat.primitives.asymmetric.utils.decode_dss_signature`.
If your data is too large to be passed in a single call, you can hash it separately and pass that value using :class:`~cryptography.hazmat.primitives.asymmetric.utils.Prehashed`.
>>> from cryptography.hazmat.primitives.asymmetric import utils
>>> chosen_hash = hashes.SHA256()
>>> hasher = hashes.Hash(chosen_hash)
>>> hasher.update(b"data & ")
>>> hasher.update(b"more data")
>>> digest = hasher.finalize()
>>> sig = private_key.sign(
... digest,
... ec.ECDSA(utils.Prehashed(chosen_hash))
... )Verification requires the public key, the DER-encoded signature itself, the signed data, and knowledge of the hashing algorithm that was used when producing the signature:
>>> public_key = private_key.public_key()
>>> public_key.verify(signature, data, ec.ECDSA(hashes.SHA256()))As above, the signature is a bytes object whose contents are DER
encoded as described in RFC 3279. It can be created from a raw (r,s)
pair by using
:func:`~cryptography.hazmat.primitives.asymmetric.utils.encode_dss_signature`.
If the signature is not valid, an :class:`~cryptography.exceptions.InvalidSignature` exception will be raised.
If your data is too large to be passed in a single call, you can hash it separately and pass that value using :class:`~cryptography.hazmat.primitives.asymmetric.utils.Prehashed`.
>>> chosen_hash = hashes.SHA256()
>>> hasher = hashes.Hash(chosen_hash)
>>> hasher.update(b"data & ")
>>> hasher.update(b"more data")
>>> digest = hasher.finalize()
>>> public_key.verify(
... sig,
... digest,
... ec.ECDSA(utils.Prehashed(chosen_hash))
... )Note
Although in this case the public key was derived from the private one, in a typical setting you will not possess the private key. The Key loading section explains how to load the public key from other sources.
.. versionadded:: 0.5
The collection of integers that make up an EC private key.
.. attribute:: public_numbers
:type: :class:`~cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers`
The :class:`EllipticCurvePublicNumbers` which makes up the EC public
key associated with this EC private key.
.. attribute:: private_value
:type: int
The private value.
.. method:: private_key()
Convert a collection of numbers into a private key suitable for doing
actual cryptographic operations.
:returns: A new instance of :class:`EllipticCurvePrivateKey`.
Warning
The point represented by this object is not validated in any way until
:meth:`EllipticCurvePublicNumbers.public_key` is called and may not
represent a valid point on the curve. You should not attempt to perform
any computations using the values from this class until you have either
validated it yourself or called public_key() successfully.
.. versionadded:: 0.5
The collection of integers that make up an EC public key.
.. attribute:: curve :type: :class:`EllipticCurve` The elliptic curve for this key.
.. attribute:: x
:type: int
The affine x component of the public point used for verifying.
.. attribute:: y
:type: int
The affine y component of the public point used for verifying.
.. method:: public_key()
Convert a collection of numbers into a public key suitable for doing
actual cryptographic operations.
:raises ValueError: Raised if the point is invalid for the curve.
:returns: A new instance of :class:`EllipticCurvePublicKey`.
.. classmethod:: from_encoded_point(curve, data)
.. versionadded:: 1.1
.. note::
This has been deprecated in favor of
:meth:`~cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey.from_encoded_point`
Decodes a byte string as described in `SEC 1 v2.0`_ section 2.3.3 and
returns an :class:`EllipticCurvePublicNumbers`. This method only
supports uncompressed points.
:param curve: An
:class:`~cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve`
instance.
:param bytes data: The serialized point byte string.
:returns: An :class:`EllipticCurvePublicNumbers` instance.
:raises ValueError: Raised on invalid point type or data length.
:raises TypeError: Raised when curve is not an
:class:`~cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve`.
.. versionadded:: 1.1
The Elliptic Curve Diffie-Hellman Key Exchange algorithm standardized in NIST publication 800-56A.
For most applications the shared_key should be passed to a key
derivation function. This allows mixing of additional information into the
key, derivation of multiple keys, and destroys any structure that may be
present.
Note that while elliptic curve keys can be used for both signing and key exchange, this is bad cryptographic practice. Instead, users should generate separate signing and ECDH keys.
Warning
This example does not give forward secrecy and is only provided as a demonstration of the basic Diffie-Hellman construction. For real world applications always use the ephemeral form described after this example.
>>> from cryptography.hazmat.primitives import hashes
>>> from cryptography.hazmat.primitives.asymmetric import ec
>>> from cryptography.hazmat.primitives.kdf.hkdf import HKDF
>>> # Generate a private key for use in the exchange.
>>> server_private_key = ec.generate_private_key(
... ec.SECP384R1()
... )
>>> # In a real handshake the peer is a remote client. For this
>>> # example we'll generate another local private key though.
>>> peer_private_key = ec.generate_private_key(
... ec.SECP384R1()
... )
>>> shared_key = server_private_key.exchange(
... ec.ECDH(), peer_private_key.public_key())
>>> # Perform key derivation.
>>> derived_key = HKDF(
... algorithm=hashes.SHA256(),
... length=32,
... salt=None,
... info=b'handshake data',
... ).derive(shared_key)
>>> # And now we can demonstrate that the handshake performed in the
>>> # opposite direction gives the same final value
>>> same_shared_key = peer_private_key.exchange(
... ec.ECDH(), server_private_key.public_key())
>>> # Perform key derivation.
>>> same_derived_key = HKDF(
... algorithm=hashes.SHA256(),
... length=32,
... salt=None,
... info=b'handshake data',
... ).derive(same_shared_key)
>>> derived_key == same_derived_key
TrueECDHE (or EECDH), the ephemeral form of this exchange, is strongly preferred over simple ECDH and provides forward secrecy when used. You must generate a new private key using :func:`generate_private_key` for each :meth:`~EllipticCurvePrivateKey.exchange` when performing an ECDHE key exchange. An example of the ephemeral form:
>>> from cryptography.hazmat.primitives import hashes
>>> from cryptography.hazmat.primitives.asymmetric import ec
>>> from cryptography.hazmat.primitives.kdf.hkdf import HKDF
>>> # Generate a private key for use in the exchange.
>>> private_key = ec.generate_private_key(
... ec.SECP384R1()
... )
>>> # In a real handshake the peer_public_key will be received from the
>>> # other party. For this example we'll generate another private key
>>> # and get a public key from that.
>>> peer_public_key = ec.generate_private_key(
... ec.SECP384R1()
... ).public_key()
>>> shared_key = private_key.exchange(ec.ECDH(), peer_public_key)
>>> # Perform key derivation.
>>> derived_key = HKDF(
... algorithm=hashes.SHA256(),
... length=32,
... salt=None,
... info=b'handshake data',
... ).derive(shared_key)
>>> # For the next handshake we MUST generate another private key.
>>> private_key_2 = ec.generate_private_key(
... ec.SECP384R1()
... )
>>> peer_public_key_2 = ec.generate_private_key(
... ec.SECP384R1()
... ).public_key()
>>> shared_key_2 = private_key_2.exchange(ec.ECDH(), peer_public_key_2)
>>> derived_key_2 = HKDF(
... algorithm=hashes.SHA256(),
... length=32,
... salt=None,
... info=b'handshake data',
... ).derive(shared_key_2)Elliptic curves provide equivalent security at much smaller key sizes than other asymmetric cryptography systems such as RSA or DSA. For many operations elliptic curves are also significantly faster; elliptic curve diffie-hellman is faster than diffie-hellman.
Note
Curves with a size of less than 224 bits should not be used. You should strongly consider using curves of at least 224 :term:`bits`.
Generally the NIST prime field ("P") curves are significantly faster than the other types suggested by NIST at both signing and verifying with ECDSA.
Prime fields also minimize the number of security concerns for elliptic-curve cryptography. However, there is some concern that both the prime field and binary field ("B") NIST curves may have been weakened during their generation.
Currently cryptography only supports NIST curves, none of which are considered "safe" by the SafeCurves project run by Daniel J. Bernstein and Tanja Lange.
All named curves are instances of :class:`EllipticCurve`.
.. versionadded:: 0.5
SECG curve secp256r1. Also called NIST P-256.
.. versionadded:: 0.5
SECG curve secp384r1. Also called NIST P-384.
.. versionadded:: 0.5
SECG curve secp521r1. Also called NIST P-521.
.. versionadded:: 0.5
SECG curve secp224r1. Also called NIST P-224.
.. versionadded:: 0.5
SECG curve secp192r1. Also called NIST P-192.
.. versionadded:: 0.9
SECG curve secp256k1.
.. versionadded:: 2.2
Brainpool curve specified in RFC 5639. These curves are discouraged for new systems.
.. versionadded:: 2.2
Brainpool curve specified in RFC 5639. These curves are discouraged for new systems.
.. versionadded:: 2.2
Brainpool curve specified in RFC 5639. These curves are discouraged for new systems.
.. versionadded:: 0.5
SECG curve sect571k1. Also called NIST K-571. These binary curves are
discouraged for new systems.
.. versionadded:: 0.5
SECG curve sect409k1. Also called NIST K-409. These binary curves are
discouraged for new systems.
.. versionadded:: 0.5
SECG curve sect283k1. Also called NIST K-283. These binary curves are
discouraged for new systems.
.. versionadded:: 0.5
SECG curve sect233k1. Also called NIST K-233. These binary curves are
discouraged for new systems.
.. versionadded:: 0.5
SECG curve sect163k1. Also called NIST K-163. These binary curves are
discouraged for new systems.
.. versionadded:: 0.5
SECG curve sect571r1. Also called NIST B-571. These binary curves are
discouraged for new systems.
.. versionadded:: 0.5
SECG curve sect409r1. Also called NIST B-409. These binary curves are
discouraged for new systems.
.. versionadded:: 0.5
SECG curve sect283r1. Also called NIST B-283. These binary curves are
discouraged for new systems.
.. versionadded:: 0.5
SECG curve sect233r1. Also called NIST B-233. These binary curves are
discouraged for new systems.
.. versionadded:: 0.5
SECG curve sect163r2. Also called NIST B-163. These binary curves are
discouraged for new systems.
.. versionadded:: 0.5
A named elliptic curve.
.. attribute:: name
:type: str
The name of the curve. Usually the name used for the ASN.1 OID such as
``secp256k1``.
.. attribute:: key_size
:type: int
Size (in :term:`bits`) of a secret scalar for the curve (as generated
by :func:`generate_private_key`).
.. versionadded:: 0.5
.. versionchanged:: 1.6
:class:`~cryptography.hazmat.primitives.asymmetric.utils.Prehashed`
can now be used as an ``algorithm``.
A signature algorithm for use with elliptic curve keys.
.. attribute:: algorithm
:type: :class:`~cryptography.hazmat.primitives.hashes.HashAlgorithm` or
:class:`~cryptography.hazmat.primitives.asymmetric.utils.Prehashed`
The digest algorithm to be used with the signature scheme.
.. versionadded:: 0.5
An elliptic curve private key for use with an algorithm such as ECDSA.
.. method:: exchange(algorithm, peer_public_key)
.. versionadded:: 1.1
Performs a key exchange operation using the provided algorithm with
the peer's public key.
For most applications the ``shared_key`` should be passed to a key
derivation function. This allows mixing of additional information into the
key, derivation of multiple keys, and destroys any structure that may be
present.
:param algorithm: The key exchange algorithm, currently only
:class:`~cryptography.hazmat.primitives.asymmetric.ec.ECDH` is
supported.
:param EllipticCurvePublicKey peer_public_key: The public key for the
peer.
:returns bytes: A shared key.
.. method:: public_key()
:return: :class:`EllipticCurvePublicKey`
The EllipticCurvePublicKey object for this private key.
.. method:: sign(data, signature_algorithm)
.. versionadded:: 1.5
Sign one block of data which can be verified later by others using the
public key.
:param data: The message string to sign.
:type data: :term:`bytes-like`
:param signature_algorithm: An instance of
:class:`EllipticCurveSignatureAlgorithm`, such as :class:`ECDSA`.
:return bytes: The signature as a ``bytes`` object, whose contents are
DER encoded as described in :rfc:`3279`. This can be decoded using
:func:`~cryptography.hazmat.primitives.asymmetric.utils.decode_dss_signature`,
which returns the decoded tuple ``(r, s)``.
.. attribute:: curve
:type: :class:`EllipticCurve`
The EllipticCurve that this key is on.
.. attribute:: key_size
.. versionadded:: 1.9
:type: int
Size (in :term:`bits`) of a secret scalar for the curve (as generated
by :func:`generate_private_key`).
.. method:: private_numbers()
Create a :class:`EllipticCurvePrivateNumbers` object.
:returns: An :class:`EllipticCurvePrivateNumbers` instance.
.. method:: private_bytes(encoding, format, encryption_algorithm)
Allows serialization of the key to bytes. Encoding (
:attr:`~cryptography.hazmat.primitives.serialization.Encoding.PEM` or
:attr:`~cryptography.hazmat.primitives.serialization.Encoding.DER`),
format (
:attr:`~cryptography.hazmat.primitives.serialization.PrivateFormat.TraditionalOpenSSL`,
:attr:`~cryptography.hazmat.primitives.serialization.PrivateFormat.OpenSSH`
or
:attr:`~cryptography.hazmat.primitives.serialization.PrivateFormat.PKCS8`)
and encryption algorithm (such as
:class:`~cryptography.hazmat.primitives.serialization.BestAvailableEncryption`
or :class:`~cryptography.hazmat.primitives.serialization.NoEncryption`)
are chosen to define the exact serialization.
:param encoding: A value from the
:class:`~cryptography.hazmat.primitives.serialization.Encoding` enum.
:param format: A value from the
:class:`~cryptography.hazmat.primitives.serialization.PrivateFormat` enum.
:param encryption_algorithm: An instance of an object conforming to the
:class:`~cryptography.hazmat.primitives.serialization.KeySerializationEncryption`
interface.
:return bytes: Serialized key.
.. versionadded:: 0.5
An elliptic curve public key.
.. attribute:: curve :type: :class:`EllipticCurve` The elliptic curve for this key.
.. method:: public_numbers()
Create a :class:`EllipticCurvePublicNumbers` object.
:returns: An :class:`EllipticCurvePublicNumbers` instance.
.. method:: public_bytes(encoding, format)
Allows serialization of the key data to bytes. When encoding the public
key the encodings (
:attr:`~cryptography.hazmat.primitives.serialization.Encoding.PEM`,
:attr:`~cryptography.hazmat.primitives.serialization.Encoding.DER`) and
format (
:attr:`~cryptography.hazmat.primitives.serialization.PublicFormat.SubjectPublicKeyInfo`)
are chosen to define the exact serialization. When encoding the point
the encoding
:attr:`~cryptography.hazmat.primitives.serialization.Encoding.X962`
should be used with the formats (
:attr:`~cryptography.hazmat.primitives.serialization.PublicFormat.UncompressedPoint`
or
:attr:`~cryptography.hazmat.primitives.serialization.PublicFormat.CompressedPoint`
).
:param encoding: A value from the
:class:`~cryptography.hazmat.primitives.serialization.Encoding` enum.
:param format: A value from the
:class:`~cryptography.hazmat.primitives.serialization.PublicFormat` enum.
:return bytes: Serialized data.
.. method:: verify(signature, data, signature_algorithm)
.. versionadded:: 1.5
Verify one block of data was signed by the private key associated
with this public key.
:param signature: The DER-encoded signature to verify.
A raw signature may be DER-encoded by splitting it into the ``r``
and ``s`` components and passing them into
:func:`~cryptography.hazmat.primitives.asymmetric.utils.encode_dss_signature`.
:type signature: :term:`bytes-like`
:param data: The message string that was signed.
:type data: :term:`bytes-like`
:param signature_algorithm: An instance of
:class:`EllipticCurveSignatureAlgorithm`.
:returns: None
:raises cryptography.exceptions.InvalidSignature: If the signature does
not validate.
.. attribute:: key_size
.. versionadded:: 1.9
:type: int
Size (in :term:`bits`) of a secret scalar for the curve (as generated
by :func:`generate_private_key`).
.. classmethod:: from_encoded_point(curve, data)
.. versionadded:: 2.5
Decodes a byte string as described in `SEC 1 v2.0`_ section 2.3.3 and
returns an :class:`EllipticCurvePublicKey`. This class method supports
compressed points.
:param curve: An
:class:`~cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve`
instance.
:param bytes data: The serialized point byte string.
:returns: An :class:`EllipticCurvePublicKey` instance.
:raises ValueError: Raised when an invalid point is supplied.
:raises TypeError: Raised when curve is not an
:class:`~cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve`.
This sample demonstrates how to generate a private key and serialize it.
>>> from cryptography.hazmat.primitives import serialization
>>> from cryptography.hazmat.primitives.asymmetric import ec
>>> private_key = ec.generate_private_key(ec.SECP384R1())
>>> serialized_private = private_key.private_bytes(
... encoding=serialization.Encoding.PEM,
... format=serialization.PrivateFormat.PKCS8,
... encryption_algorithm=serialization.BestAvailableEncryption(b'testpassword')
... )
>>> serialized_private.splitlines()[0]
b'-----BEGIN ENCRYPTED PRIVATE KEY-----'You can also serialize the key without a password, by relying on :class:`~cryptography.hazmat.primitives.serialization.NoEncryption`.
The public key is serialized as follows:
>>> public_key = private_key.public_key()
>>> serialized_public = public_key.public_bytes(
... encoding=serialization.Encoding.PEM,
... format=serialization.PublicFormat.SubjectPublicKeyInfo
... )
>>> serialized_public.splitlines()[0]
b'-----BEGIN PUBLIC KEY-----'This is the part that you would normally share with the rest of the world.
This extends the sample in the previous section, assuming that the variables
serialized_private and serialized_public contain the respective keys
in PEM format.
>>> loaded_public_key = serialization.load_pem_public_key(
... serialized_public,
... )
>>> loaded_private_key = serialization.load_pem_private_key(
... serialized_private,
... # or password=None, if in plain text
... password=b'testpassword',
... ).. versionadded:: 2.4
.. attribute:: SECP192R1
Corresponds to the dotted string ``"1.2.840.10045.3.1.1"``.
.. attribute:: SECP224R1
Corresponds to the dotted string ``"1.3.132.0.33"``.
.. attribute:: SECP256K1
Corresponds to the dotted string ``"1.3.132.0.10"``.
.. attribute:: SECP256R1
Corresponds to the dotted string ``"1.2.840.10045.3.1.7"``.
.. attribute:: SECP384R1
Corresponds to the dotted string ``"1.3.132.0.34"``.
.. attribute:: SECP521R1
Corresponds to the dotted string ``"1.3.132.0.35"``.
.. attribute:: BRAINPOOLP256R1
.. versionadded:: 2.5
Corresponds to the dotted string ``"1.3.36.3.3.2.8.1.1.7"``.
.. attribute:: BRAINPOOLP384R1
.. versionadded:: 2.5
Corresponds to the dotted string ``"1.3.36.3.3.2.8.1.1.11"``.
.. attribute:: BRAINPOOLP512R1
.. versionadded:: 2.5
Corresponds to the dotted string ``"1.3.36.3.3.2.8.1.1.13"``.
.. attribute:: SECT163K1
.. versionadded:: 2.5
Corresponds to the dotted string ``"1.3.132.0.1"``.
.. attribute:: SECT163R2
.. versionadded:: 2.5
Corresponds to the dotted string ``"1.3.132.0.15"``.
.. attribute:: SECT233K1
.. versionadded:: 2.5
Corresponds to the dotted string ``"1.3.132.0.26"``.
.. attribute:: SECT233R1
.. versionadded:: 2.5
Corresponds to the dotted string ``"1.3.132.0.27"``.
.. attribute:: SECT283K1
.. versionadded:: 2.5
Corresponds to the dotted string ``"1.3.132.0.16"``.
.. attribute:: SECT283R1
.. versionadded:: 2.5
Corresponds to the dotted string ``"1.3.132.0.17"``.
.. attribute:: SECT409K1
.. versionadded:: 2.5
Corresponds to the dotted string ``"1.3.132.0.36"``.
.. attribute:: SECT409R1
.. versionadded:: 2.5
Corresponds to the dotted string ``"1.3.132.0.37"``.
.. attribute:: SECT571K1
.. versionadded:: 2.5
Corresponds to the dotted string ``"1.3.132.0.38"``.
.. attribute:: SECT571R1
.. versionadded:: 2.5
Corresponds to the dotted string ``"1.3.132.0.39"``.
.. function:: get_curve_for_oid(oid)
.. versionadded:: 2.6
A function that takes an :class:`~cryptography.x509.ObjectIdentifier`
and returns the associated elliptic curve class.
:param oid: An instance of
:class:`~cryptography.x509.ObjectIdentifier`.
:returns: The matching elliptic curve class. The returned class conforms
to the :class:`EllipticCurve` interface.
:raises LookupError: Raised if no elliptic curve is found that matches
the provided object identifier.