.. hazmat:: Elliptic curve cryptography =========================== .. module:: cryptography.hazmat.primitives.asymmetric.ec .. function:: generate_private_key(curve, backend) .. versionadded:: 0.5 Generate a new private key on ``curve`` for use with ``backend``. :param backend: A :class:`EllipticCurve` provider. :param backend: A :class:`~cryptography.hazmat.backends.interfaces.EllipticCurveBackend` provider. :returns: A new instance of a :class:`EllipticCurvePrivateKey` 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.hashes.HashAlgorithm` provider. .. doctest:: >>> 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.SECP384R1(), 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() The ``signature`` is a ``bytes`` object, whose contents is DER encoded as described in :rfc:`6979`. This can be decoded using :func:`~cryptography.hazmat.primitives.asymmetric.utils.decode_rfc6979_signature`. .. class:: EllipticCurvePrivateNumbers(private_value, public_numbers) .. 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(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:`EllipticCurvePrivateKey` provider. .. class:: EllipticCurvePublicNumbers(x, y, curve) .. 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(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:`EllipticCurvePublicKey` provider. Elliptic Curves --------------- Elliptic curves provide equivalent security at much smaller key sizes than asymmetric cryptography systems such as RSA or DSA. For some operations they can also provide higher performance at every security level. According to NIST they can have as much as a `64x lower computational cost than DH`_. .. note:: Curves with a size of `less than 224 bits`_ should not be used. You should strongly consider using curves of at least 224 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 providers of :class:`EllipticCurve`. .. 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. .. class:: SECP256K1 .. versionadded:: 0.9 SECG curve ``secp256k1``. Key Interfaces ~~~~~~~~~~~~~~ .. class:: EllipticCurve .. versionadded:: 0.5 A named elliptic curve. .. attribute:: name :type: string The name of the curve. Usually the name used for the ASN.1 OID such as ``secp256k1``. .. attribute:: key_size :type: int The bit length of the curve's base point. .. class:: EllipticCurveSignatureAlgorithm .. versionadded:: 0.5 A signature algorithm for use with elliptic curve keys. .. attribute:: algorithm :type: :class:`~cryptography.hazmat.primitives.hashes.HashAlgorithm` The digest algorithm to be used with the signature scheme. .. class:: EllipticCurvePrivateKey .. versionadded:: 0.5 An elliptic curve private key for use with an algorithm such as `ECDSA`_ or `EdDSA`_. .. method:: signer(signature_algorithm) Sign data which can be verified later by others using the public key. The signature is formatted as DER-encoded bytes, as specified in :rfc:`6979`. :param signature_algorithm: An instance of a :class:`EllipticCurveSignatureAlgorithm` provider. :returns: :class:`~cryptography.hazmat.primitives.asymmetric.AsymmetricSignatureContext` .. method:: public_key() :return: :class:`EllipticCurvePublicKey` The EllipticCurvePublicKey object for this private key. .. class:: EllipticCurvePrivateKeyWithNumbers .. versionadded:: 0.6 Extends :class:`EllipticCurvePrivateKey`. .. method:: private_numbers() Create a :class:`EllipticCurvePrivateNumbers` object. :returns: An :class:`EllipticCurvePrivateNumbers` instance. .. class:: EllipticCurvePrivateKeyWithSerialization .. versionadded:: 0.8 Extends :class:`EllipticCurvePrivateKey`. .. 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` 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. .. class:: EllipticCurvePublicKey .. versionadded:: 0.5 An elliptic curve public key. .. method:: verifier(signature, signature_algorithm) Verify data was signed by the private key associated with this public key. :param bytes signature: The signature to verify. DER encoded as specified in :rfc:`6979`. :param signature_algorithm: An instance of a :class:`EllipticCurveSignatureAlgorithm` provider. :returns: :class:`~cryptography.hazmat.primitives.asymmetric.AsymmetricVerificationContext` .. attribute:: curve :type: :class:`EllipticCurve` The elliptic curve for this key. .. class:: EllipticCurvePublicKeyWithNumbers .. versionadded:: 0.6 Extends :class:`EllipticCurvePublicKey`. .. method:: public_numbers() Create a :class:`EllipticCurvePublicNumbers` object. :returns: An :class:`EllipticCurvePublicNumbers` instance. .. class:: EllipticCurvePublicKeyWithSerialization .. versionadded:: 0.6 Extends :class:`EllipticCurvePublicKey`. .. method:: public_numbers() Create a :class:`EllipticCurvePublicNumbers` object. :returns: An :class:`EllipticCurvePublicNumbers` instance. .. method:: public_bytes(encoding, format) Allows serialization of the key to bytes. Encoding ( :attr:`~cryptography.hazmat.primitives.serialization.Encoding.PEM` or :attr:`~cryptography.hazmat.primitives.serialization.Encoding.DER`) and format ( :attr:`~cryptography.hazmat.primitives.serialization.PublicFormat.SubjectPublicKeyInfo`) 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.PublicFormat` enum. :return bytes: Serialized key. .. _`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 .. _`less than 224 bits`: http://www.ecrypt.eu.org/ecrypt2/documents/D.SPA.20.pdf .. _`64x lower computational cost than DH`: https://www.nsa.gov/business/programs/elliptic_curve.shtml .. _`minimize the number of security concerns for elliptic-curve cryptography`: http://cr.yp.to/ecdh/curve25519-20060209.pdf .. _`SafeCurves`: http://safecurves.cr.yp.to/ .. _`ECDSA`: https://en.wikipedia.org/wiki/ECDSA .. _`EdDSA`: https://en.wikipedia.org/wiki/EdDSA