aboutsummaryrefslogtreecommitdiffstats
path: root/libmproxy/contrib
diff options
context:
space:
mode:
Diffstat (limited to 'libmproxy/contrib')
0 files changed, 0 insertions, 0 deletions
generated by cgit v1.2.3 (git 2.25.1) at 2025-09-10 22:51:21 +0000
50'>50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 
.. 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 curve: An instance of :class:`EllipticCurve`.

    :param backend: An instance of
        :class:`~cryptography.hazmat.backends.interfaces.EllipticCurveBackend`.

    :returns: A new instance of :class:`EllipticCurvePrivateKey`.


.. function:: derive_private_key(private_value, curve, backend)

    .. versionadded:: 1.6

    Derive a private key from ``private_value`` on ``curve`` for use with
    ``backend``.

    :param int private_value: The secret scalar value.

    :param curve: An instance of :class:`EllipticCurve`.

    :param backend: An instance of
        :class:`~cryptography.hazmat.backends.interfaces.EllipticCurveBackend`.

    :returns: A new instance of :class:`EllipticCurvePrivateKey`.


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
        :class:`~cryptography.hazmat.primitives.hashes.HashAlgorithm`.

    .. 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()
        ... )
        >>> 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 is 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`.

    .. doctest::

        >>> from cryptography.hazmat.primitives.asymmetric import utils
        >>> chosen_hash = hashes.SHA256()
        >>> hasher = hashes.Hash(chosen_hash, default_backend())
        >>> 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 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()))

    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`.

    .. doctest::

        >>> chosen_hash = hashes.SHA256()
        >>> hasher = hashes.Hash(chosen_hash, default_backend())
        >>> 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.


.. 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: An instance of
            :class:`~cryptography.hazmat.backends.interfaces.EllipticCurveBackend`.

        :returns: A new instance of :class:`EllipticCurvePrivateKey`.


.. class:: EllipticCurvePublicNumbers(x, y, curve)

    .. 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(backend)

        Convert a collection of numbers into a public key suitable for doing
        actual cryptographic operations.

        :param backend: An instance of
            :class:`~cryptography.hazmat.backends.interfaces.EllipticCurveBackend`.

        :raises ValueError: Raised if the point is invalid for the curve.
        :returns: A new instance of :class:`EllipticCurvePublicKey`.

    .. method:: encode_point()

        .. versionadded:: 1.1

        Encodes an elliptic curve point to a byte string as described in
        `SEC 1 v2.0`_ section 2.3.3. This method only supports uncompressed
        points.

        :return bytes: The encoded point.

    .. classmethod:: from_encoded_point(curve, data)

        .. versionadded:: 1.1

        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`.

Elliptic Curve Key Exchange algorithm
-------------------------------------

.. class:: ECDH()

    .. versionadded:: 1.1

    The Elliptic Curve Diffie-Hellman Key Exchange algorithm first standardized
    in NIST publication `800-56A`_, and later in `800-56Ar2`_.

    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.

    .. 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.

    .. doctest::

        >>> from cryptography.hazmat.backends import default_backend
        >>> 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(), default_backend()
        ... )
        >>> # 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(), default_backend()
        ... )
        >>> 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',
        ...     backend=default_backend()
        ... ).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',
        ...     backend=default_backend()
        ... ).derive(same_shared_key)
        >>> derived_key == same_derived_key
        True

    ECDHE (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:

    .. doctest::

        >>> from cryptography.hazmat.backends import default_backend
        >>> 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(), default_backend()
        ... )
        >>> # 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(), default_backend()
        ... ).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',
        ...     backend=default_backend()
        ... ).derive(shared_key)
        >>> # For the next handshake we MUST generate another private key.
        >>> private_key_2 = ec.generate_private_key(
        ...     ec.SECP384R1(), default_backend()
        ... )
        >>> peer_public_key_2 = ec.generate_private_key(
        ...     ec.SECP384R1(), default_backend()
        ... ).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',
        ...     backend=default_backend()
        ... ).derive(shared_key_2)

Elliptic Curves
---------------

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`.

.. class:: SECP256R1

    .. versionadded:: 0.5

    SECG curve ``secp256r1``. Also called NIST P-256.


.. class:: SECP384R1

    .. versionadded:: 0.5

    SECG curve ``secp384r1``. Also called NIST P-384.


.. class:: SECP521R1

    .. versionadded:: 0.5

    SECG curve ``secp521r1``. Also called NIST P-521.


.. class:: SECP224R1

    .. 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``.


.. class:: BrainpoolP256R1

    .. versionadded:: 2.2

    Brainpool curve specified in :rfc:`5639`. These curves are discouraged
    for new systems.

.. class:: BrainpoolP384R1

    .. versionadded:: 2.2

    Brainpool curve specified in :rfc:`5639`. These curves are discouraged
    for new systems.

.. class:: BrainpoolP512R1

    .. versionadded:: 2.2

    Brainpool curve specified in :rfc:`5639`. These curves are discouraged
    for new systems.

.. class:: SECT571K1

    .. versionadded:: 0.5

    SECG curve ``sect571k1``. Also called NIST K-571. These binary curves are
    discouraged for new systems.


.. class:: SECT409K1

    .. versionadded:: 0.5

    SECG curve ``sect409k1``. Also called NIST K-409. These binary curves are
    discouraged for new systems.


.. class:: SECT283K1

    .. versionadded:: 0.5

    SECG curve ``sect283k1``. Also called NIST K-283. These binary curves are
    discouraged for new systems.


.. class:: SECT233K1

    .. versionadded:: 0.5

    SECG curve ``sect233k1``. Also called NIST K-233. These binary curves are
    discouraged for new systems.


.. class:: SECT163K1

    .. versionadded:: 0.5

    SECG curve ``sect163k1``. Also called NIST K-163. These binary curves are
    discouraged for new systems.


.. class:: SECT571R1

    .. versionadded:: 0.5

    SECG curve ``sect571r1``. Also called NIST B-571. These binary curves are
    discouraged for new systems.


.. class:: SECT409R1

    .. versionadded:: 0.5

    SECG curve ``sect409r1``. Also called NIST B-409. These binary curves are
    discouraged for new systems.


.. class:: SECT283R1

    .. versionadded:: 0.5

    SECG curve ``sect283r1``. Also called NIST B-283. These binary curves are
    discouraged for new systems.


.. class:: SECT233R1

    .. versionadded:: 0.5

    SECG curve ``sect233r1``. Also called NIST B-233. These binary curves are
    discouraged for new systems.


.. class:: SECT163R2

    .. versionadded:: 0.5

    SECG curve ``sect163r2``. Also called NIST B-163. These binary curves are
    discouraged for new systems.




Key Interfaces
~~~~~~~~~~~~~~

.. class:: EllipticCurve

    .. 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`).


.. class:: EllipticCurveSignatureAlgorithm

    .. 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.


.. class:: EllipticCurvePrivateKey

    .. versionadded:: 0.5

    An elliptic curve private key for use with an algorithm such as `ECDSA`_ or
    `EdDSA`_. An elliptic curve private key that is not an
    :term:`opaque key` also implements
    :class:`EllipticCurvePrivateKeyWithSerialization` to provide serialization
    methods.

    .. 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 bytes data: The message string to sign.

        :param signature_algorithm: An instance of
            :class:`EllipticCurveSignatureAlgorithm`, such as :class:`ECDSA`.

        :return bytes: Signature.

    .. 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`).


.. class:: EllipticCurvePrivateKeyWithSerialization

    .. versionadded:: 0.8

    This interface contains additional methods relating to serialization.
    Any object with this interface also has all the methods from
    :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.

     .. 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 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.

    .. 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 bytes signature: The signature to verify.

        :param bytes data: The message string that was signed.

        :param signature_algorithm: An instance of
            :class:`EllipticCurveSignatureAlgorithm`.

        :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`.


.. class:: EllipticCurvePublicKeyWithSerialization

    .. versionadded:: 0.6

    Alias for :class:`EllipticCurvePublicKey`.



Serialization
~~~~~~~~~~~~~

This sample demonstrates how to generate a private key and serialize it.


.. doctest::

    >>> from cryptography.hazmat.backends import default_backend
    >>> from cryptography.hazmat.primitives import hashes
    >>> from cryptography.hazmat.primitives.asymmetric import ec
    >>> from cryptography.hazmat.primitives import serialization

    >>> private_key = ec.generate_private_key(ec.SECP384R1(), default_backend())

    >>> 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:


.. doctest::

    >>> 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.


Key loading
~~~~~~~~~~~

This extends the sample in the previous section, assuming that the variables
``serialized_private`` and ``serialized_public`` contain the respective keys
in PEM format.

.. doctest::

    >>> loaded_public_key = serialization.load_pem_public_key(
    ...     serialized_public,
    ...     backend=default_backend()
    ... )

    >>> loaded_private_key = serialization.load_pem_private_key(
    ...     serialized_private,
    ...     # or password=None, if in plain text
    ...     password=b'testpassword',
    ...     backend=default_backend()
    ... )


Elliptic Curve Object Identifiers
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. class:: EllipticCurveOID

    .. 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"``.


.. _`FIPS 186-3`: https://csrc.nist.gov/csrc/media/publications/fips/186/3/archive/2009-06-25/documents/fips_186-3.pdf
.. _`FIPS 186-4`: https://csrc.nist.gov/publications/detail/fips/186/4/final
.. _`800-56A`: https://csrc.nist.gov/publications/detail/sp/800-56a/revised/archive/2007-03-14
.. _`800-56Ar2`: https://csrc.nist.gov/publications/detail/sp/800-56a/rev-2/final
.. _`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
.. _`elliptic curve diffie-hellman is faster than diffie-hellman`: https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1100&context=cseconfwork
.. _`minimize the number of security concerns for elliptic-curve cryptography`: https://cr.yp.to/ecdh/curve25519-20060209.pdf
.. _`SafeCurves`: https://safecurves.cr.yp.to/
.. _`ECDSA`: https://en.wikipedia.org/wiki/ECDSA
.. _`EdDSA`: https://en.wikipedia.org/wiki/EdDSA
.. _`forward secrecy`: https://en.wikipedia.org/wiki/Forward_secrecy
.. _`SEC 1 v2.0`: http://www.secg.org/sec1-v2.pdf