First commit

examples/cyclic_subgroup.py

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+#!/usr/bin/env python3
+from Cryptotools.Groups.cyclic import Cyclic
+from Cryptotools.Numbers.primeNumber import getPrimeNumber
+from random import randint, choice
+from math import log, log10
+
+"""
+    Here, we will try to understand why we need to have a generator when we encrypt data for Diffie-Hellman
+    https://crypto.stackexchange.com/questions/25489/why-does-diffie-hellman-need-be-a-cyclic-group
+"""
+def operation(a, b, n):
+    return (a ** b) % n
+
+def getGenerator(gr, p):
+    cyclic = Cyclic(gr, p, operation)
+    generators = cyclic.getGenerators()
+    print(f"All generators: {generators}")
+    cyclic.identity()
+    print(f"Identity: {cyclic.getIdentity()}")
+    
+    return generators
+
+
+gr = list()
+# Public value
+p = 13
+g = 0
+for i in range(1, p):
+    gr.append(i)
+
+print(f"p = {p}")
+print(f"G = {gr}")
+# We try with a generator which is not in list
+generators = getGenerator(gr, p)
+
+g = 3 # In the group
+#g =  # Not in the group
+#print(f"g = {g}")
+
+
+
+# Try to compute the cyclic subgroup
+for G in range(p + 1):
+    res = 0
+    for a in range(G):
+        r = operation(G, a, p)
+        res = res + r
+    if res == p:
+        print(f"G = {G}; res = {res}")