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examples/cyclic_dlp.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, log2
+
+"""
+    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):
+    index = 1
+    for g in range(2, p):
+        z = list()
+        for entry in range(1, p):
+            res = operation(g, index, p)
+            #if res not in z:
+            z.append(res)
+            index = index + 1
+        print(f"{g}: {sorted(z)}")
+
+def generateGroupByG(gr, p, g):
+    index = 1
+    z = list()
+    for entry in range(1, p):
+        res = operation(g, index, p)
+        #if res not in z:
+        z.append(res)
+        index = index + 1
+    return z
+
+def computePublicKey(key, p, g):
+    return (g ** key) % p
+
+
+gr = list()
+# Public value
+p = 5
+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
+cyclic = Cyclic(gr, p, operation)
+generators = cyclic.getGenerators()
+print(f"All generators: {generators}")
+
+# Generate group with g = 2
+grWithG = generateGroupByG(gr, p, 2)
+print(f"Group generated with g = 2: {grWithG}")
+
+for a in grWithG:
+    # print(f"log2({a}) = {log(a, 2)}") # Same as below
+    print(f"log2({a}) = {log2(a)}")
+
+print()
+
+for a in range(1, len(grWithG) + 1):
+    print(f"log2({a}) = {log2(a)}")