Add Elliptic Curve and docs

examples/elliptic/curve_scalar.py

@@ -0,0 +1,44 @@
+#!/usr/bin/env python3
+
+import matplotlib.pyplot as plt
+from Cryptotools.Groups.curve import Curve
+from Cryptotools.Groups.point import Point
+
+
+a = 3
+b = 8
+
+curve = Curve(a, b, Curve.WEIERSTRASS)
+x = curve.x
+curve.generatePoints()
+y = curve.y
+yn = curve.yn
+points = curve.getPoints()
+
+P = points[10]
+nP = curve.scalar(P, 5)
+print(f"{nP.x} {nP.y}")
+
+# For testing, we may add n times with the addition operation for the Scalar Multiplication
+tmp = Point(0, 0)
+for i in range(5):
+    tmp = curve.add(P, tmp)
+
+# Unfortunately, the result is approximatively the same
+# the multiplication need to be more accurate
+# if tmp == nP:
+#   print(True)
+
+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(nP.x, nP.y, marker='o', color="red")
+plt.annotate('nP', (nP.x, nP.y + 0.5))
+
+
+
+plt.legend()
+plt.show()