First commit

examples/cyclic.py

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+#!/usr/bin/env python3
+
+from Cryptotools.Groups.cyclic import Cyclic
+from Cryptotools.Numbers.primeNumber import isPrimeNumber
+from random import choice
+
+
+def operation(a, b, n):
+    return (a ** b) % n
+
+n = 19
+g = list()
+for i in range(1, n):
+    g.append(i)
+   
+print(f"n = {n}")
+print(f"G = {g}")
+
+cyclic = Cyclic(g, n, operation)
+order = len(g) # Length of the group
+print(f"len: {order}")
+print(f"prime: {isPrimeNumber(order)}")
+    
+cyclic.generator()
+  
+print(f"All generators: {cyclic.getGenerators()}")
+print(f"Is cyclic: {cyclic.isCyclic()}")
+
+# Check if the abelian group is respected
+print(f"It is an abelian group: {cyclic.closure()}\n")
+
+
+e = choice(cyclic.getGenerators())
+z = list()
+for a in range(1, n):
+    res = operation(e, a, n)
+    z.append(res)
+
+print(z)
+if z == g:
+    print(f"The group generated with the generator {e} works")