First commit

examples/cyclic_test.py

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+#!/usr/bin/env python3
+
+from Cryptotools.Groups.cyclic import Cyclic
+from Cryptotools.Utils.utils import gcd
+from Cryptotools.Numbers.primeNumber import isPrimeNumber
+from random import choice
+
+
+def operation(a, b, n):
+    return (a ** b) % n
+
+def test1(n):
+    """
+        We test with n is not prime but the order of the group is a prime number
+    """
+    g = list()
+    g2 = list()
+    for i in range(1, n):
+        #if gcd(i, n) == 1:
+        g.append(i)
+    
+    print(f"n = {n}")
+    print(f"G = {g}")
+    Gsorted = sorted(g)
+
+    cyclic = Cyclic(g, n, operation)
+    order = len(g) # https://en.wikipedia.org/wiki/Order_(group_theory)
+    print(f"len: {order}")
+    print(f"prime: {isPrimeNumber(order)}")
+    g2 = list()
+    for i in range(1, order):
+        if gcd(i, order) == 1:
+            g2.append(i)
+            pass
+    
+    print(g2)
+    # Pick a number in the previous list and check if we can generate all number with it
+    item = choice(g2)
+    print()
+ 
+    # if the order is prime, the group is cyclic ?
+
+    # Check if we have all items
+    g3 = list()
+    for i in range(1, n):
+        res = operation(i, item, n)
+        if gcd(res, item) == 1:
+            g3.append(res)
+            #print(res)
+            pass
+
+    G2sorted = sorted(g2)
+    G3sorted = sorted(g3)
+    print()
+    # print(f"{g} = {cyclic.generator(g)}")
+    gen = cyclic.generator()
+    
+    print(f"All generators: {cyclic.getGenerators()}")
+    print(f"Is cyclic: {cyclic.isCyclic()}")
+
+    print()
+    print(G2sorted)
+    print(G3sorted)
+    if G3sorted == Gsorted:
+        print(f"Matching with item {item}") # Always match with item 1
+
+    # Check if the abelian group is respected
+    print(f"It is an abelian group: {cyclic.closure()}\n")
+
+
+
+test1(19)
+test1(12)