Add Elliptic Curve and docs

examples/elliptic/point_at_infinity.py

@@ -0,0 +1,43 @@
+#!/usr/bin/env python3
+
+from Cryptotools.Groups.point import Point
+from Cryptotools.Groups.curve import Curve
+import numpy as np
+import matplotlib.pyplot as plt
+from math import sqrt
+
+
+a = 3
+b = 8
+
+curve = Curve(a, b, Curve.WEIERSTRASS)
+x = curve.x
+curve.generatePoints()
+y = curve.y
+yn = curve.yn
+points = curve.getPoints()
+pointsReverse = curve.getPointsSym()
+
+P = points[10]
+Q = curve.find_reverse(P)
+
+# We made the addition
+# The result is the point at infinity
+R = curve.add(P, Q)
+print(f"{R.x} {R.y}")
+
+
+plt.figure(figsize=(10, 6))
+plt.plot(x, y, color='b', label=f'$y^2 = x^3 + {a}x + {b}$')
+plt.plot(x, yn, color='b', )
+plt.plot(P.x, P.y, marker='o', color="red")
+plt.annotate('P', (P.x, P.y + 0.5))
+
+plt.plot(Q.x, Q.y, marker='o', color="red")
+plt.text(-1 , 11, f"R = infinity")
+plt.annotate('Q', (Q.x, Q.y + 0.5))
+
+
+plt.axline([P.x, P.y], [Q.x, Q.y], color="red")
+plt.legend()
+plt.show()