Add Elliptic Curve Cryptography

examples/elliptic/ecc_generator.py

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+#!/usr/bin/env python3
+
+import matplotlib.pyplot as plt
+from Cryptotools.Groups.elliptic import Elliptic
+from Cryptotools.Groups.point import Point
+
+# https://course.ece.cmu.edu/~ece733/lectures/21-intro-ecc.pdf
+
+
+a = 3
+b = 7 
+n = 53 # Must be prime number
+
+E = Elliptic(n, a, b)
+E.quadraticResidues()
+Ep = E.pointsE()
+#print(E.getQuadraticResidues())
+
+# Now, we can make the Addition Table
+#for p in Ep:
+#    for q in Ep:
+#        nP = E.add(p, q)
+#        print(f"({p.x}, {p.y}), ({q.x}, {q.y}) {nP.x, nP.y}")
+#    print()
+#
+#print()
+
+# In cryptography, where is the public key and where is the private key on the elliptic curve ???
+# For the graphic
+MAX=n
+
+fig, ax = plt.subplots()
+ax.legend(fontsize=14)
+ax.grid()
+
+# We generate x for the graphic
+x = list()
+x = [i for i in range(0, MAX)]
+
+# Drawing the point.
+for p in Ep:
+    ax.plot(p.x, p.y, 'bo')
+
+# Find the order of the Curve
+order = E.findOrder()
+cofactor = E.cofactor
+print(f"Order: {order}")
+print(f"Cofactor: {cofactor}")
+
+# Lets make an example, here, G is the first element of all points (except the point at infinity)
+G = Ep[1]
+
+for i in range(1, 15):
+    P = E.scalar(G, i)
+
+    plt.plot(P.x, P.y, marker='o', color="red")
+    plt.annotate(f'P{i}', (P.x, P.y + 0.5))
+    
+    # Check if the point exist in the curve
+    if E.pointExist(P):
+        print(f"The point P ({P.x}, {P.y}) lies on the Curve")
+    else:
+        print(f"The point P ({P.x}, {P.y}) doesn't lies on the Curve")
+
+plt.show()