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Enigma - The German Mystery - Cryptography in WWII pt. 2

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Hi everyone. I'm doing a series of posts on cryptography in WW2. In this post I will be discussing the first of the four main cryptographic machines I'll be focusing on and perhaps the most well know, the infamous Enigma. I'll be talking about what made Enigma special, what made it effective, and then I will be diving into the problems that plagued Enigma and which eventually led to the cracking of the machine, first by the Polish, then the British bombes, and finally the American bombe systems. 

I am assuming everyone reading this knows something about cryptographic theory and the electromechanical rotors of the time. If you don't feel free to read Part 1 which will bring you up to speed. The original post was placed in off topic section of the forums, it feels at home here which is where the rest will go.

Part 1 - A Primer

Part 2 - Enigma - The German Mystery

Part 3 - SIGABA - The American Big Machine

Part 4 - TypeX - A British Response

Enigma

In world war 1 the powers that be used manual code and cypher systems to secure their information. But with the advent of the machine age these methods suddenly became extremely vulnerable to mathematical and mechanical code breaking machines. A better solution was critically needed. 

Enigma was created as a solution for army level and below cryptography, and the naval equivalent. Although it was not the only device, with D-day approaching other machines like the various SZ-42 and T-52 machines assumed greater importance at higher levels of command. In 1925 the German army purchased several examples of the ENIGMA commercially built cypher. 

The Enigma machine used by the German army utilized three rotors arranged one after the other in what is a textbook example of a regular rotor machine. As was discussed in the primer every rotor had an input side and output. A letter on the input would be swapped for another. Such as a 'A' becoming an 'F'. This was done by wiring the input contact 'A' to the output contact 'F'. Each rotor did this for the entire alphabet, swapping one letter for the other. This nest of wires was called a 'maze'.

Related image

The wire maze is shown above. You can see the input contacts on the far right with the output contacts on the far left. 

Image result for enigma assembling the rotor set

You can see three rotors assembled together above. The cleverness of this setup was that on a daily basis they would swap the orders of the rotors and their starting positions. Changing the cryptographic settings of the machine each time. 

One of the first innovations of Enigma, and perhaps its first Achilles heel, is that the Germans created a reflector at the end. Basically a signal would go through the three rotors, swapping letters each time, until it hit the reflector whereupon it would pull a U-turn and re-enter the final rotor at another entry contact and go back through the rotors again. Making two passes.

Image result for enigma assembling the rotor set

Above is a paper illustration. Input is on the right side, then the first rotor, then the second rotor, then the third rotor, and at the end on the left is the reflector. See how an output of F is set to a D and then shot back through again?

The Achilles heel in this is that any letter entering the rotor system cannot be enciphered back as itself. So if you pressed 'f' it would be impossible to get an 'f' back out. This is crucial, it means that if you are trying to crack Enigma with a 1000 word document. If any letters coming out of your attempted solution matches the enciphered message then you did it wrong. This meant that a lot less time is being wasted on false readings.

It would not be a rotor machine if the rotors did not rotate. The Enigma rotors rotated in the following way:

Rotor 1 - Advanced one step for every key press

Rotor 2 - Advanced one step for every 26 advancements of rotor 1

Rotor 3 - Advanced one step for every 26 advancements of rotor 2

This meant that there were 17,576 possible rotor positions before you repeated the original.

This system of advancement was the second Achilles heel of Enigma, TypeX, and just about every rotor system out there except SIGABA (which made SIGABA so great). Every key press changed the cypher. Which meant that no two consecutive letters can share the same position of the rotors. By knowing that the cypher keeps changing every letter you failed to create even a pseudo-random pattern.

Image result for enigma plugboard

The next revolutionary step of Enigma was the plugboard. On the front of Enigma is a board with holes for every letter. An operator can manually tie two letters together. If A-O are connected then after coming through the rotor maze a signal reading "O" becomes "A" and visa versa. This massively increased the security of the machine. I cannot understate how much more secure this made Enigma. Before the plugboard the original Enigma in use was cracked by the Polish in 1932, only seven years old and LONG before WW2. It was the addition of the plugboard that resecured the machine. 

The third major Achilles heel of Enigma, and in my mind the crucial. Was pretty poor operational discipline. To understand why you need to understand the fact that despite all these operational features even the Germans knew that it only takes a determined enemy so much time to break through the cypher. That's why it is so customizable, by the end of the war Army systems had 8 different rotors they could use (and they could flip them backwards), the plugboard could handle anywhere from 1 to 13 different cables (in use they usually stuck with 10). Every day the Germans would change which rotors were in the machine, their starting positions, and the plugboards. These settings were held in the famous code books. In the navy they were written in water soluble ink so they could be destroyed by a simple dunking. Entire buildings in the US and Britain were dedicated to SOLELY figuring out the day's plugboard and rotor settings. Once you have those decryption is easy. 

Operator error was so predictable that the British figured that they could count on one time a day some operator somewhere would screw up. One example is that after the U-boats were getting slaughtered the navy resecured Enigma by adding a fourth rotor. This threw the allies for a loop, although they were anticipating the switch because the planning for the replacement had been discussed over the previously broken 3 rotor system. 

 

One submarine radio man sent a four-rotor encrypted message but messed up his settings. So he reset the machine back to the 3 rotor configuration and resent it. He probably didn't see anything wrong, but he had just handed the British a message encoded with the new system and the correct solution for it. That one screw-up brought the end of the 4 rotor system months earlier then it should have been cracked.

Image result for enigma navy

Enigma Naval variant, notice the fourth rotor up top.

I also have to give the Polish a lot of credit, they cracked Enigma long before anyone else did and built the first cryptographic bombe's dedicated to cracking it. It was only the addition of the plugboard that ended their efforts, they didnt have the resources to cracking that riddle. In 1939 they turned over all of their work to the French and the British which provided an incredible head start to the allies.

1024px-RebuiltBombeFrontView.jpg

Shown above is the working rebuilt British cryptographic bombe, created to attack Enigma coded traffic. Each drum represents the action of an enigma rotor. 

Next time I will be discussing the American SIGABA machine, the opponent of Enigma and PURPLE and ally of TypeX.

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