From 49a976280259622a4955aa3e3a3e43a2442de72e Mon Sep 17 00:00:00 2001
From: Sam Hadow <sam.hadow@inbox.lv>
Date: Wed, 24 Apr 2024 09:55:49 +0200
Subject: [PATCH] documenting 2 keys outputing the same first 6 bytes

---
 main.py | 78 ++++++++++++++++++++++++++++++++++++++++++++++++++-------
 1 file changed, 69 insertions(+), 9 deletions(-)

diff --git a/main.py b/main.py
index 4d0d0cd..ea31a7f 100755
--- a/main.py
+++ b/main.py
@@ -87,7 +87,7 @@ def css_encrypt(text, key):
 
 def test_encrypt():
     print("test encryption: text 0xffffffffff, key 0x0 ∈ {0, 1}^40")
-    cipher = int.from_bytes(css_encrypt(0xffffffffff, [0]*40), byteorder='big')
+    cipher = int.from_bytes(css_encrypt(0xffffffffff, [0]*40))
     print(f'cipher: {hex(cipher)}')
     clear = int.from_bytes(css_encrypt(cipher, [0]*40))
     print(f'decrypted: {hex(clear)}')
@@ -167,29 +167,89 @@ def attack(Bytes=gen_6_bytes()):
     for process in processes:
         process.join()
 
-    while not result_queue.empty():
-        key = result_queue.get()
-        print(f'key found: \t{key}')
-        return [int(bit) for bit in key]
+    key = result_queue.get()
+    print(f'key found: \t{key}')
+    return [int(bit) for bit in key]
 
 def test_attack(n=1):
     success = 0
     print(f'testing attack in 2^16 against CSS {n} times (keys randomly generated each time)\n')
     for _ in range(n):
         key = [randint(0, 1) for _ in range(40)]
-        # key = [1]*40
         key_string = ''.join(str(bit) for bit in key)
         print(f'key generated: \t{key_string}')
         Bytes = gen_6_bytes(key)
         found_key = attack(Bytes)
+        failed = []
         if found_key == key:
             success += 1
+        else:
+            failed.append(key)
         print()
     print(f'{success}/{n} success')
+    if len(failed)>0:
+        print("fails:")
+        for key in failed:
+            print("".join(str(bit) for bit in key))
+
+def test_fail():
+    taps17 = [0, 14]
+    taps25 = [0, 3, 4, 12]
+    key = [1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1]
+    key2 = [1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0]
+    print(f'both of these keys seem to output the same first 6 bytes, it only differs starting from byte 7:\n{"".join(str(bit) for bit in key)}\n{"".join(str(bit) for bit in key2)}\n')
+    lfsr17 = lfsr(key[:16]+[1], taps17)
+    lfsr172 = lfsr(key2[:16]+[1], taps17)
+    lfsr25 = lfsr(key[16:]+[1], taps25)
+    lfsr252 = lfsr(key2[16:]+[1], taps25)
+    x = []
+    y = []
+    x2 = []
+    y2=[]
+    for _ in range(7):
+        x_bin = ""
+        y_bin = ""
+        x_bin2 = ""
+        y_bin2 = ""
+        for _ in range(8):
+            x_bin += str(lfsr17.shift())
+            y_bin += str(lfsr25.shift())
+            x_bin2 += str(lfsr172.shift())
+            y_bin2 += str(lfsr252.shift())
+        x.append(int(x_bin[::-1], 2))
+        y.append(int(y_bin[::-1], 2))
+        x2.append(int(x_bin2[::-1], 2))
+        y2.append(int(y_bin2[::-1], 2))
+    print(f'LFSR outputs with 1st key: lfsr17: {x}  lfsr25: {y}')
+    print(f'LFSR outputs with 2nd key: lfsr17: {x2}  lfsr25: {y2}\n')
+    c = 0
+    c2 = 0
+    for i in range(7):
+        s = x[i]+y[i]+c
+        if s>255:
+            c=1
+        else:
+            c=0
+        s2 = x2[i]+y2[i]+c2
+        if s2>255:
+            c2=1
+        else:
+            c2=0
+        print(f'8bits addition at step {i} equal for both keys: {s%256}={s2%256} : {s%256==s2%256}')
+
+    text = 0xffffffffffff
+    cipher = int.from_bytes(css_encrypt(text, key))
+    cipher2 = int.from_bytes(css_encrypt(text, key))
+    print(f'\nencrypting 0xffffffffffff (6 bytes)\nwith 1st key: {hex(cipher)}\nwith 2nd key: {hex(cipher2)}\nboth outputs are equal: {cipher==cipher2}\n')
 
 
 test_lfsr17()
-print()
+print("\n")
 test_encrypt()
-print()
-test_attack(5)
+print("\n")
+# time to test attack with 100 keys
+# CPU: 6 cores at 3.8GHz
+# ~65 seconds
+test_attack(10)
+print("\n")
+test_fail()