Enigma?

Several Images from Wikipedia

(an online encyclopedia)

Single rotor with 8 letters

A

B

C

D

E

F

G

H

A

B

C

D

E

F

G

H

first position

A

B

C

D

E

F

G

H

A

B

C

D

E

F

G

H

one rotation

A

B

C

D

E

F

G

H

A

B

C

D

E

F

G

H

two rotations

Rotors and Reflector

Key pressed

Lights

Rotors

Rotors

• 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

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 ordersOverall total 6 x 17,576 = 105,456 total possibilities

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!

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

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 1011 = 100,000,000,000 possiblities

Total Possibilities

• 1011 x 105,456 = 1016

– Checking one per minute would take more than 5 x 1012 days.

– Brute force was not an option!

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”

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 (1011 choices, later 1014)

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

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

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

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)