Lecture 8: Cracking the Codes based on Tony Sale s Codes & Ciphers Web Page Today s Topics Cipher Systems Substitution Ciphers Cracking Caesar s Cipher Polyalphabetic Substitution The Enigma Machine Rotors, Reflectors, Plugboard Weakness in Disguise The Military Enigma Sending & Receiving The complexity of Enigma Slide 1 Cipher Systems The objective of a cipher system is to make it very difficult and time-consuming, for an interceptor to decrypt the message. Decryption need not be impossible just impractical. This is achieved by arranging for there to be a vast number of different possible message keys, i.e. different ways in which the system could have been configured when the message was enciphered. Otherwise the interceptor can simply try them all out! Slide 2 Substitution Ciphers Substitution ciphers (of which the Enigma was a sophisticated development) involve substituting one letter for another according to some rule. The simplest substitution is Caesar's cipher: ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFG...ABCDEFGHIJKLMNOPQRSTUVWXYZ To encipher, the letter on the bottom row is written down as the substitution for the text letter on the top row. To decipher, the received cipher is looked up in the bottom row and the text letter read off from the top row above it. Slide 3 1
Cracking Caesar s Cipher ABCDEFGHIJKLMNOPQRSTUVWXYZ YZABCDEFGHIJKLMNOPQRSTUVWX In this case the message key, which the recipient needs to know, is just the displacement between the two alphabets (3). This is a simple example of a cipher system which shows an immediate flaw: there are only 26 possible message keys and so anyone can just try them out. (Example: crack EMRGR) "Vercingetorix Throws Down His Arms At the Feet of Caesar" L. Royer, 1888. By kind permission of Forum Romanum. Slide 4 Caesar Improved A more sophisticated system uses a random series of characters for the lower alphabet. ABCDEFGHIJKLMNOPQRSTUVWXYZ IPHBOSFCQZJNTWGLMYRXDKEUVA Now the recipient has to know the substitution alphabet, and this sequence of letters is in effect the message key. There are a huge numbers of possible substitutions 403,291,461,126,605,635,584,000,000 Slide 5 How Secure? ABCDEFGHIJKLMNOPQRSTUVWXYZ IPHBOSFCQZJNTWGLMYRXDKEUVA Cipher systems of this kind are still easily broken by using common-sense facts such as that E is the most common letter, THE the most common word, and so forth. NB Having a large number of possible keys does not in itself provide security. (This is really the same principle as allows you to solve crossword anagrams. There are vast numbers of possible permutations of the letters, but most of them can be eliminated because they lead to impossible words.) Slide 6 2
Polyalphabetic Substitution In the 19th century various schemes for polyalphabetic systems were invented. In these, there is more than one substitution alphabet and they are used in rotation, or by some other rule. System of encoding of Heinrich Cornelius Agrippa von Nettelsheim ( occulted philosophia, Cologne, 1533, Li 3, CH. 30) reproduced in the treaty of numerology of Blaise de Vigenere, Traicté of the figures, or secretes manners ofescrire (Paris, 1586, F 275 v). This is what led to the Enigma. If the rule is simple then statistical methods can still easily break the cipher. By the 20th century it became possible to carry out substitutions by using electrical connections to mechanise the dreary and difficult work of looking up tables in a handbook. Slide 7 The Enigma Machine The basic Enigma was invented in 1918 by Arthur Scherbius in Berlin. It enciphers a message by performing a number of substitutions one after the other. Scherbius' idea was to achieve these substitutions by electrical connections. Slide 8 and so on ad infinitum It is not much more difficult to compose substitutions which are to be performed one after the other. The bottom row of terminals can simply be connected to the entry terminals of another set of wires Slide 9 3
Two steps forward. Now this as it stands is no advance at all, since we might as well have combined the two substitutions into one. but suppose the second set of wirings is displaced by 2 letters Each displacement on the bottom row now gives rise to a completely different substitution alphabet. Slide 10 The Reason for Rotors An effective way to achieve this displacement is to implement the substitutions in a wheel, rather than in the strips we have shown. Then the shifts are achieved by rotations of one wheels against another. This was the basis of the Enigma machine. Adding a third wheel gives rise to 26x26=676 different substitution alphabets. However the Enigma machine was given another element of complexity by the inventor Willi Korn, who added a reflector. Slide 11 The reflector Instead of using the output from the third wheel as the cipher of the input letter, this output is fed into a fixed reflector plate which is simply a swapping of letters in pairs. The output from this is in turn passed back through the rotors in the reverse direction, arriving back at the entry disc. Thus in total seven substitutions are performed in succession by the basic Enigma: by the three wheels, then by the reflector swapping, then by the three wheels in the reverse direction. One effect of this extra complexity is that there are now 26x26x26=17,576 different substitution alphabets arising from different positions of the wheels moving with respect to the fixed reflector. Slide 12 4
Weakness in disguise The addition of the reflector made the Enigma a simpler system. The reflector made the Enigma machine reciprocal. If A is enciphered to Q, then Q will be enciphered to A. This knowledge is of considerable use to the interceptor who is trying to break the system. Also no letter can ever encipher to itself. This severe cryptographic weakness was much exploited first by the Poles and then by Bletchley Park. Slide 13 Enigma Rotors (or wheels) (1)The finger notches used to turn the rotors to a start position. (2)The alphabet RING round the circumference of the rotor (3)The shaft upon which the rotors turn. (4)The catch which locks the alphabet ring to the core (5)The CORE containing the cross-wiring between contacts and discs. (6)The spring loaded contacts to make contact with the next rotor. (7)The discs embedded into the core to make contact with the spring-loaded contacts in the next rotor. (8)The CARRY notch attached to the alphabet ring Slide 14 Enigma Rotors (or wheels) These rotors were manufactured with their wirings buried inside and they could not be modified in use. In the 1930s, the Enigma had only three different kinds of rotor, I II and III. These rotors could be assembled on the shaft in any order giving 6 (i.e. 3x2x1) possible configurations. In 1938 the Germans added rotors IV and V to the repertoire, thus giving 60 (i.e. 5x4x3) configurations by choosing a set of three rotors from the five. Some further wheels were brought into use during the course of the war but basically the rotors remained unchanged throughout. Slide 15 1
Wheels Set 16-14-12 Slide 16 The Rotor Wheels (in situ) Slide 17 Changing Rotors Slide 18 2
Points of Contact Slide 19 Rotors (Side View) Slide 20 Rotor Contacts Slide 21 3
The Military Enigma Machines Slide 22 Under the bonnet. Slide 23 The Plugboard or Stecker The plugboard or 'Stecker', visible on the front of the machine, was the most important addition made to the basic Enigma when turning it into a machine for military use. Unlike the rotors, it could be rewired by the operator. However it was not a rotor it did not rotate. It could effect a 'swapping' of letters, like the reflector. The operator simply inserted plugs so as to connect pairs of letters (generally 10 pairs, in wartime use) and this had the effect of hard-wiring such a swapping. Slide 24 4
The Steckerboard Slide 25 A Stecker Connection Slide 26 The Plugboard Because the plugboard affected both the incoming current from the keyboard and the outgoing current to the lamps. it left unchanged the reciprocal property of the Enigma. It also meant that the military Enigma still had the property that no letter could ever be enciphered to itself. This was a very grave mistake in the design. Slide 27 5
The Ring Setting The enigma allowed each rotor to be set by the operator in any one of 26 possible settings. The ring-setting determined the relationship between the window letters and the actual scramblings The carry mechanism was also affected by the ring setting. The carry notch was arranged to be in a different position for each of the rotors I, II, III, IV, V. This turned out to be a bad cryptographic mistake; it helped analysts at Bletchley Park to identify the right hand rotor in use. Slide 28 The Message Key In order to begin, the message key, (the complete and exact configuration of the machine in its starting position), had to be conveyed to the intended recipient of the message. The Germans, following Scherbius's original suggestions, decided to specify exactly everything except the rotor start position for each 24-hour period. This was achieved by pre-printing setting sheets a month's settings on one sheet, which was distributed by courier. Slide 29 Sending a message 1. Set the Enigma machine into the base configuration for the day as given in the setting sheet for the month. 2. Select a three letter start position, (the indicator), from which to encipher the selected three letter message key. 3. Turn the rotors to the indicator position, key in the message key, twice, and note down the lamps that light. 4. Turn the rotors to the message key letters and key in the message to be sent, noting down the lamps as they light. 5. Give the enciphered message plus its preamble to the radio operator to transmit by Morse code. Slide 30 1
Receiving a message 1. Set the Enigma machine into the same base configuration for the day from the setting sheet. 2. Turn the rotors to the indicator letters received in the preamble to the message. 3. Key in the next six letters to reveal the repeated message key as the lamps light. 4. Turn the rotors to the message key letters. Key in and decrypt the cipher text. Slide 31 The Complexity of The Enigma The 3-rotor Enigma has 26x26x26 = 17,576 possible rotor states for each of 6 wheel orders giving 6x17,576 = 105,456 machine states. For each of these the plugboard (with ten pairs of letters connected) can be in 150,738,274,937,250 possible states. The total number of combinations is thus (even for the simplest military Enigma) of the order of 15,000,000,000,000,000,000 and then there is the ring-setting complication on top of this. Slide 32 2