.. py:module:: ethereum.crypto.elliptic_curve

Elliptic Curves
^^^^^^^^^^^^^^^


.. only:: stage1

Module Contents
---------------

Classes
~~~~~~~

.. autoapisummary::

   ethereum.crypto.elliptic_curve.EllipticCurve



Functions
~~~~~~~~~

.. autoapisummary::
   :nosignatures:

   ethereum.crypto.elliptic_curve.secp256k1_recover



Attributes
~~~~~~~~~~

.. autoapisummary::

   ethereum.crypto.elliptic_curve.SECP256K1N
   ethereum.crypto.elliptic_curve.F
   ethereum.crypto.elliptic_curve.T


Module Details
---------------

SECP256K1N
~~~~~~~~~~



.. py:data:: SECP256K1N
   
   

.. undocinclude:: /../src/ethereum/crypto/elliptic_curve.py
   :language: python
   :lines: 14-14


F
~



.. py:data:: F
   
   

.. undocinclude:: /../src/ethereum/crypto/elliptic_curve.py
   :language: python
   :lines: 16-16


T
~



.. py:data:: T
   
   

.. undocinclude:: /../src/ethereum/crypto/elliptic_curve.py
   :language: python
   :lines: 17-17


secp256k1_recover
~~~~~~~~~~~~~~~~~


.. function:: secp256k1_recover(r: ethereum.base_types.U256, s: ethereum.base_types.U256, v: ethereum.base_types.U256, msg_hash: ethereum.crypto.hash.Hash32) -> ethereum.base_types.Bytes
   :noindexentry:

   Recovers the public key from a given signature.

   :param r: TODO
   :param s: TODO
   :param v: TODO
   :param msg_hash: Hash of the message being recovered.

   :returns: **public_key** -- Recovered public key.
   :rtype: `ethereum.base_types.Bytes`




.. undocinclude:: /../src/ethereum/crypto/elliptic_curve.py
   :language: python
   :pyobject: secp256k1_recover

EllipticCurve
~~~~~~~~~~~~~


Superclass for integers modulo a prime. Not intended to be used
directly, but rather to be subclassed.


.. class:: EllipticCurve(x: F, y: F)


   Bases: :py:obj:`Generic`\ [\ :py:obj:`F`\ ]

   

   .. py:attribute:: __slots__
         :annotation: = ['x', 'y']

      

   

   .. py:attribute:: FIELD
         :annotation: :Type[F]

      

   

   .. py:attribute:: A
         :annotation: :F

      

   

   .. py:attribute:: B
         :annotation: :F

      

   

   .. py:attribute:: x
         :annotation: :F

      

   

   .. py:attribute:: y
         :annotation: :F

      

   .. py:method:: __eq__(other: object) -> bool

      Test two points for equality.


   .. py:method:: __str__() -> str

      Stringify a point as its coordinates.


   .. py:method:: point_at_infinity() -> T
      :classmethod:

      Return the point at infinity. This is the identity element of the group
      operation.

      The point at infinity doesn't actually have coordinates so we use
      `(0, 0)` (which isn't on the curve) to represent it.


   .. py:method:: double() -> T

      Add a point to itself.


   .. py:method:: __add__(other: T) -> T

      Add two points together.


   .. py:method:: mul_by(n: int) -> T

      Multiply `self` by `n` using the double and add algorithm.