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examples/dh_no_generator.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):
+    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 getGenerator2(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
+
+def computeEphemeralKey(public, secret, p):
+    return (public ** secret) % p
+
+gr = list()
+# Public value
+p = 43
+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}")
+
+g = 3 # In the group
+print(f"g = {g}")
+
+# We can compute with the secret key
+secretKeyA = 5
+secretKeyB = 10
+publicKeyA = computePublicKey(secretKeyA, p, g)
+publicKeyB = computePublicKey(secretKeyB, p, g)
+print(f"Public key A: {publicKeyA}")
+print(f"Public key B: {publicKeyB}\n")
+
+# Here, g is in the generator, we need to compute all values until that match with publicKeyA
+for a in range(1, p):
+    res = operation(g, a, p)
+    if res == publicKeyA:
+        print(f"Brute forced secret key of A: {a}")
+
+for a in range(1, p):
+    res = operation(g, a, p)
+    if res == publicKeyB:
+        print(f"Brute forced secret key of B: {a}")
+
+print()
+
+#for a in generators:
+#    print(a)
+#
+#print()
+
+# Here, we generate all key withthe same generator
+keys = list()
+for a in range(1, p):
+    keys.append(operation(g, a, p))
+
+print((keys))
+print(sorted(keys))
+
+print()
+
+print(f"Keys with g = 4: {sorted(getGenerator2(gr, p, 4))}")
+
+# Do the same, but g is not a generator
+g = 4 # Not in the generator group
+publicKeyA = computePublicKey(secretKeyA, p, g)
+publicKeyB = computePublicKey(secretKeyB, p, g)
+print(f"Public key A: {publicKeyA}")
+print(f"Public key B: {publicKeyB}")
+
+keys = list()
+for a in range(1, p):
+    keys.append(operation(g, a, p))
+print(keys)
+
+# Eve sniff the traffic and knows p, g and publicKeyA and B
+# Eve, knows p and g, because it's public
+# Eve need to guess the secretKey of A.
+# For doing that, we iterate all posibility until that match with the publicKeyA
+
+#for a in range(1, 4):
+#    res = operation(g, a, p)
+#    print(res)