@@ -47,10 +47,16 @@ code:
4747 .. tip ::
4848
4949 You can also use :py:class: `~ecdsa.curves.Curve ` to get the curve
50- parameters from a PEM or DER file. Or use the
50+ parameters from a PEM or DER file. You can also use
51+ :py:func: `~ecdsa.curves.curve_by_name ` to get a curve by specifying its
52+ name.
53+ Or use the
5154 :py:func: `~ecdsa.curves.find_curve ` to get a curve by specifying its
5255 ASN.1 object identifier (OID).
5356
57+ Affine coordinates
58+ ------------------
59+
5460After taking hold of curve parameters you can create a point on the
5561curve. The :py:class: `~ecdsa.ellipticcurve.Point ` uses affine coordinates,
5662i.e. the :math: `x` and :math: `y` from the curve equation directly.
@@ -82,6 +88,8 @@ methods of the object:
8288
8389 print (" x: {0} , y: {1} " .format(point_c.x(), point_c.y()))
8490
91+ Projective coordinates
92+ ----------------------
8593
8694When using the Jacobi coordinates, the point is defined by 3 integers,
8795which are related to the :math: `x` and :math: `y` in the following way:
@@ -123,3 +131,7 @@ the regular implementation:
123131
124132 point_c = point_a + point_b
125133 print (" x: {0} , y: {1} " .format(point_c.x(), point_c.y()))
134+
135+ All the other operations, like scalar multiplication or point addition work
136+ on projective points the same as with affine representation, but they
137+ are much more effective computationally.
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