1. Enigma? Several Images from Wikipedia (an online encyclopedia)

2. Single rotor with 8 letters ABCDEFGHABCDEFGH ABCDEFGHABCDEFGH first position ABCDEFGHABCDEFGH ABCDEFGHABCDEFGH one rotation ABCDEFGHABCDEFGH ABCDEFGHABCDEFGH two rotations

4. Rotors and Reflector Key pressed Lights

5. Rotors

6. Second rotor advances after 26 rotations of first, third after 26 rotations of second How many different ciphers before repetition? 17,576 characters before repeat

7. Rotor settings 26 possible start settings each –indicated by a letter for each 26x26x26 total settings for three rotors –17,576 possible settings Rotors can be interchanged –How many possible orders? Total settings? 3x2x1 = 6 possible orders Overall total 6 x 17,576 = 105,456 total possibilities

8. Reflector With no reflector, would need to use the machine “in reverse” to decipher – quite difficult Reflector cannot take a letter to itself – no circuit Consequences of reflector: –No letter encrypted to itself –Self-inverse: if L1 goes to L2, then L2 goes to L1 –Latter means machine with same setting can be used to decipher!

9. Keyboard – Lights wiring A key pressed Plugboard A-A S-D Rotors and reflector A in and S out S switched to D by plugboard D lights

10. Plugboard Plugboard added at Keyboard/Light side of rotors Each wire switches two letters (from key to rotors and from rotors to lights) Initially 6 wires interchanged 12 letters –Yields about 10 11 = 100,000,000,000 possiblities

11. Total Possibilities 10 11 x 105,456 = 10 16 –Checking one per minute would take more than 5 x 10 12 days. –Brute force was not an option!

12. Later additions Select 3 rotors from a set of 5 –60 possible arrangements of rotors instead of 6 –Later 8 rotors used by German navy (336) Number of exchanges in plugboard went from 6 to 10, increasing the number of possibilities by a factor of 1500 Navy added a non-rotating fourth “rotor”

13. Enigma Procedures Sender and receiver both need machine on same settings Settings for each day distributed in codebooks Day key specified settings for –Rotor order (6, 60, or 336 choices) –Rotor setting (17,576 choices) –Plugboard setting (10 11 choices, later 10 14 )

14. Enigma Procedures If same setting used for many messages (e.g. all messages in one day) then code could easily be broken How can this be avoided? Use a different key for every message How to distribute message keys? Encode message key using day key

15. Enigma Procedures Use a different key for each message Send message key encoded using day key, then send message using the message key Day key is used on “random” characters so cannot be compromised

16. Early German Army procedure Send message key twice, so as to be sure it is received correctly (if no match, then resend) This weakness was exploited by the Polish cryptanalysts

17. Later Developments Message key sent only once Set back British decoders for a few months Turing adopted a known plaintext attack (cribs) Used German errors –Cillies: patterns to message key girlfriend initials, neighboring keys on keyboard –Common message patterns (cribs)