Paper Lorenz

Using Paper Lorenz

1. Turn the Psi, Chi and Mu wheels to a random starting position or use the Ablesetafel on the other sheet to get your QEP code.
2. Using the Teleprinter Addition Square, add together the first letter of your message with the letter shown on the Psi wheel.
3. Add that letter to the one shown on the Chi wheel
4. Write down the new letter, this is your cipher text
5. If Mu wheel is currently showing x, step the Psi wheel one letter clockwise otherwise continue.
6. Turn the Mu wheel one letter clockwise.
7. Turn the Chi wheel one letter clockwise.
8. Repeat from step 2 for each letter of your message.
9. To decrypt, repeat as above but using the cipher text instead of the plaintext message

Example: encrypting a message

In this example, we will encrypt the message "SECRET" using the start positions Psi 1, Mu 1, Chi 1

• Turn all three wheels so that the black arrows are pointing to number 1 (as on the picture above)
  This is our starting position for this message, a different starting position will give a different result.
• The first letter of our message is the letter S and we are going to "add" this to the two key letters generated by the Lorenz (the Psi and Chi).
  Adding the letters normally involves converting them to their ITA2 5 bit codes then adding those together using modulo-2 (or XOR) to give another letter. If you want more detail on how this was done for real, follow this link: The Lorenz Machine.
• Look at the Psi wheel, the current letter the wheel is encoding is P
• Find the sheet showing the Teleprinter Addition Square - this is a table which gives the resulting letter when adding together any two letters.
• To add together S + P find the letter S on one axis and the letter P on the other axis and check which letter is shown where the two meet.
  Hint: Use a ruler or straight edge of a paper to line up on row S first then read down from P.
  It doesn't matter which way around you choose, adding S + P is the same as adding P + S!
• The answer should be the letter W
• Now, using the same method, we want to add the W we just got to the Chi wheel key letter shown N.
• The final answer, and our first cipher letter, should be the character 8 - write this down!
• The real Lorenz, after enciphering a letter, would move the wheels in a set pattern so our second letter will be enciphered using a different two key letters. This means that even if our second letter in our message was the same as the first, the cipher message will be two different letters.
  Follow these rules to change the three cipher wheels.
  1. Look at the current value of the Mu (or motor) wheel, it will either be a cross or a dot.
     If it is a cross, turn the Psi wheel one position clockwise.
     If the Mu wheel is pointing to a dot, continue to the next step without moving the Psi wheel.
     In our example, Mu is in position 1 and showing a dot - don't change anything and just move to step 2.
  2. Always move the Mu wheel one position clockwise.
     It should now be set to position 2, another dot.
  3. Always move the Chi wheel one position clockwise.
     It should now be set to position 2, character 4.
• Now we repeat the above from the second instruction for our next plain text letter E. We want to add E + P + 4 which should give the answer Y.
  Note: the key letter for the Chi wheel has changed for our second letter, while the Psi wheel has remained at the same one.
• Move the wheels on as per the rules above.
  Mu is a dot, no change to Psi. Move Mu and Chi one position clockwise.
• The third letter of our message is C, so the next sum should be adding C + P + L which equals R
• Again move the wheels as per the rules above.
  Mu is a cross this time, move the Psi wheel on one position to the number 2, character N and also move the Mu and Chi wheels.
• Fourth letter is R and this time, both Psi and Chi are different key letters. R + N + N = R
• Fifth letter E + N + F = /
• Sixth letter T + T + U = U
• Therefore, our final cipher text is 8YRR/U

Note that in the table above, the Chi wheels change letter for each letter of the message, while the Psi wheels often stay the same. This "stagger" was meant to create a larger pattern of key string which would not repeat very often, but actually was one of the main flaws that allowed the codebreakers at Bletchley Park to break this cipher. See First Break for more detail on how this was done and how the world's first computer was invented!

Deciphering a message is exactly the same - just set the start positions of all three wheels to the same as you enciphered the message then add the first letter of the cipher text to the Psi and Chi rather than the plain text. 8 + P + N = S. Repeat the same steps as listed above to retrieve your message.

To enciper our message "SECRET" on Virtual Lorenz to see if we get the same result, we first need to set Virtual Lorenz to be a model SZ40 (the basic model) and to set the pins to the Bream message settings.

Select the Prefs menu then select Settings

Make sure the top Lorenz Model switch is set to SZ40

Check that the KT-Schalter (Plaintext Switch) is set to Aus (off).

Select the BREAM pattern button to set the pins on the wheels

Now click Close (at the bottom of the settings menu).

Our start wheel setting is where all of the wheels are set to position 01. If you have moved any wheels, just rotate them all back to 01.

Make sure the Lorenz is switch on - the red switch in the bottom center of the machine should be set to Ein.

To encipher our message, use the keyboard on screen or just type our message SECRET

If all is set correctly, you should find the lower Send/Recv tape shows 8YRR/U - exactly as we generated using Paper Lorenz!

Note: The Lorenz wheels actually turn backwards with respect to the numbers on the wheels - the last Chi wheel (12) goes from position 1 to 23..22.21 etc rather than counting upwards so the letters generated for Paper Lorenz do not match with the positions on the actual wheels but they do run in order!

For example, if you wanted to start Paper Lorenz with a start position of Psi=1, Mu=2, Chi=3 and then wanted to set Virtual Lorenz to start on the same position we can do the following.

The Psi wheels are already set to position 1 so leave the first five wheels all set to 01

Both of the Mu wheels need to move one position on. These are the two wheels marked 6 and 7 on Lorenz. Turn them one position down each (6 should show 37, 7 should show 61).

All of the Chi wheels need to move on two positions. Press the down arrow on all of the last five wheels (8-12) twice. Final settings (40,30,28,25,22).

This should now be set to the same settings as Paper Lorenz.

Important Note: Once any of the wheels on Paper Lorenz get past their highest setting (23 for Chi, 13 for Mu or 19 for Psi), our limited wheels on paper will no longer match up with the real Lorenz, so if you are brave enough to try adding more than a few characters or so and want it to be deciphered on Virtual Lorenz, make sure you start with a low starting position on the wheels.