Sunday Science: The Lorenz Machine

A Lorenz SZ40 on display at Bletchley Park.

The Enigma machine is instantly synonymous with the codebreaking work done around the Second World War. But you may not have heard of the Lorenz machine - which was a much tougher encryption nut to crack and was responsible for passing the most important messages between German high command.

Enigma only had three to four wheels, which were used to scramble messages being passed between the German forces. Lorenz had 12 wheels. 

To put this into context, there were 159 million million million possible settings to choose from when you're setting up an Enigma machine.

​For Lorenz, there were more than 1,000 million million million million million million million million million million million million million million million million million million million million million million million million million million million million total number of combinations.

Or 10^170.

How did the Lorenz machine work?

​For an encrypted message to be successfully passed between two Lorenz machines, they both had to have the same wheel settings. 

Lorenz was attached to a teleprinter and the message  to be encrypted or decrypted came in ​as a long stream of paper imprinted with Baudot teleprinter code.

The Baudot code is a character code where each letter is represented by five bits: either a + or a -.

So, the letter A could be "+----" and the letter Z "+---+", for example.

What the Lorenz machine would do is add on a random letter to the one being passed in the message.

For example, let's say we want to pass the letter A as the message between two Lorenz machines. The Lorenz may generate the letter Z as the key.
Lorenz code = message + key.
So, to encrypt the message, you just have to add each bit (the + or -) of the letter 'A' with each bit of its key 'Z'. The resulting letter will be encrypted.
If two symbols are the same, then we generate a "+" bit in the encrypted code. If they are different then we get a "-".
In other words: + + + = + or - + - = +
And: + + - = - or - + + = -.
So, if we go back to our example where we are encrypting a letter A with a key of Z:
Message A: + - - - -
Key           Z: + - - - +
Code        D: + + + + -
So, using these rules the letter 'A' is encrypted as a letter 'D' using the key 'Z'.
Here's the clever part. If you receive the letter 'D' and know the key is the letter 'Z' - you can add the bits together again to get the letter A out. In other words, the system works both ways so you can encrypt and decrypt your message - if you know the key.
The key was produced using the combination of the two sets of five wheels on the Lorenz machine, whose movement were controlled using two motor wheels.
So, using these rules the letter 'A' is encrypted as a letter 'D' using the key "Z'.

Here's the clever part. If you receive the letter 'D' and know the key is the letter 'Z' - you can add the bits together again to get the letter A out. In other words, the system works both ways so you can encrypt and decrypt your message - if you know the key.

The key was produced using the combination of the two sets of five wheels on the Lorenz machine, whose movement were controlled using two motor wheels.

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How was Lorenz broken?

The real breakthrough for Lorenz came due to operator error. The same Lorenz-encoded message was sent twice - but the operator was so annoyed that they had to retype the 4,000 character message, they put in some abbreviations.

This meant that the codebreakers at Bletchley had two copies of the same message, with a few alterations and using the same key.

So, if you add the code together, then two messages can be inferred and the code can be broken.

You can get the all-important key.

Mathematician Bill Tutte was given the key to see if he could find any patterns to identify the length of the key. This involved him writing out the key in long rows.

When we wrote the key out in rows of 41, a pattern started to appear. This meant the first wheel in the Lorenz machine had a period of 41.

The pattern wasn't perfect and this left Bill to deduce that there was another wheel that sometimes moved. He was right - he'd worked out that Lorenz relied on two sets of wheels.

Using this approach, Bill and other codebreakers could deduce the layout of the Lorenz machine - without ever seeing the machine itself.

Bill Tutte also came up with a procedure to work out the initial settings on the Lorenz machine. Although this procedure worked in principle, it would have taken too long to carry out and decipher messages by hand.

So, the process was automated and the world's first computer Colossus came into being. 

More on Colossus next week.

Extra reading and watching

For a more in-depth explanation of the Lorenz Cipher and how it was broken, click here. If you want to play with a replica of the Lorenz cipher system - check out this amazing Virtual Lorenz machine from the UK's National Museum of Computing (TNMC).​

And here's a quick video covering the "unbreakable" Lorenz code:

What is Sunday Science?

Hello. I’m the freelance writer who gets tech. I have two degrees in Physics and, during my studies, I became increasingly frustrated with the complicated language used to describe some outstanding scientific principles. Language should aid our understanding — in science, it often feels like a barrier.
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So, I want to simplify these science sayings and this blog series “Sunday Science” gives a quick, no-nonsense definition of the complex-sounding scientific terms you often hear, but may not completely understand. 

If there’s a scientific term or topic you’d like me to tackle in my next post, fire an email to [email protected] or leave a comment below. If you want to sign up to our weekly newsletter, click here.