There were at least two major things that gave Britain’s codebreakers at Bletchley Park a headstart in breaking the German Enigma code machine.
* A German spy defected before the war and gave the French a working military Enigma machine and a starter codebook. The French shared this to the British and the Polish
* the Poles could decrypt three-cylinder enigma codes. The Germans added a plugboard
Initial plugboards were broken with perforated sheets.
* the Poles created a Bomba machine that could handle the three cylinder codes
Germans increased to three wheels out of five then added a more complex plugboard and they invaded Poland. Three out of five wheels means they would have needed 60 Bomba machines.
The full later war Enigma’s with the full number of wheels and the full plugboard had 158,962,555,217,826,360,000 combinations.
The British took over and Turing made superior Bombe machines.
The British knew about finding the known plain-text from things like weather reports.
The British air force (RAF) would bomb specific targets in the hope of generating a coded message from the German which contained specific coordinates they could then decrypt. This was called gardening. This would generate more known words to decrypt.
Alan Turing came up with Conditional Sequential Bayesian Probabilities. This was used to help guess what the first two-rotor wheel setting were. The frequency of letters in German would still be recognizable in encrypted text. Knowing the first two rotors would simplify the problem by 676 times.
They used sheets again but over a lightbox. They would slide the sheets over the texts to help see non-random patterns. The person who was best was Hugh Alexander, a master chess player.
They built more and more Bombe’s to handle the permutations. There were 40-50 Bombe’s in the UK at the end of the war. The US built about 200 Bombe’s.
The conditional sequential Bayesian probability, Banburismus, was classified until 2010.
They were sending settings and text for decryption over copper undersea cable to the US for assistance in decoding more messages.
Colossus first special electronic vacuum tube computer to decrypt WW2 high command codes
The Lorenz code machine was used to encode Hitler and high command messages.
The Lorenz high command machine had 2501 wheel settings or 6.5*10150.
Total settings 10170
The Germans made a key mistake. A German resent a long 4000 character message. The resent message were almost the same but the repeated message used abbreviations and shorter words. The British code breakers were able to determine the cryptographic key.
They then used other techniques to determine the structure of the machine and then the changing settings.