The Rebuild of Heath Robinson

The Lorenz problem.




The German Lorenz machine was used to encipher teleprinter traffic between command centres of the German Army. The cipher used the Additive method invented in 1918 by Gilbert Vernam in America. This method involved adding together the teleprinter code bit patterns, bit by bit, of the input text character and an obscuring character generated by the Lorenz machine, giving the transmitted cipher character. When this addition was performed binary modulo two (XOR), at the receiving end the same obscuring character regenerated by the receiving Lorenz machine, added to the received cipher character cancelled out the original obscuring character and revealed the original text character. In fact the Lorenz machine generated and added successively two obscuring characters from two sets of five wheels known as Chi and Psi in Bletchley Park. The Chi wheels incremented regularly every time a text character was entered, the Psi wheels incremented erratically, but as a group of five, depending on two other wheels known in the Park as Motor or Mu wheels. This had all been deduced by John Tiltman, Bill Tutte and others by early 1942. There were two parts to the solution of Lorenz. Firstly to work out the patterns around the periphery of each wheel and secondly to determine the wheel pattern start position for each wheel.


Chi wheel patterns starting at position 1 on the Chi wheels

Chi1 ..xxxx.xx....xxx..x.x...x.xxxx.x.xxx...x.|
Chi2 ..xx.xx..x..xx..xxxx.x...xxx..x|
Chi3 .xx.xx..xx...xx...xxx.x..xx..|
Chi4 ..x....xxx.xx..xxxx..x..xx|
Chi5 ..x.x..x.xxxx....xx..xx|

Chi wheels turned to 32,2,2,16,2

Chi1 x .xxx...x.|..xxxx.xx....xxx..x.x...x.xxxx."
Chi2 . xx.xx..x..xx..xxxx.x...xxx..x|."
Chi3 x x.xx..xx...xx...xxx.x..xx..|."
Chi4 x xxx..x..xx|..x....xxx.xx.."
Chi5 . x.x..x.xxxx....xx..xx|."
.....F VJXU4O9QO

The Chi stream obscuring characters generated as the wheels turned for each text character typed in.

The same wheel patterns were found to be set over various periods and over many messages but the wheel pattern start positions were changed for every message and just for the Chi wheels this gave a 22,000,000 combination.

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