How did Turing break enigma?
In: Technology
Enigma was broken more than once. Turing had nothing to do with the earliest breakthroughs. Those were done by the Polish (it’s common now to think of the Poles as inept idiots in WW2, charging panzers with cavalry, etc., but the fact is that a couple of brilliant Polish mathematicians made the key breakthroughs before the war. I think they even had a hard time convincing the Brits how important the work was.
As I recall, the earliest breakthroughs (by the Poles) were in realizing that the fundamental design of Enigma caused certain patterns in the output. Like, it’s not possible for the letter “A” to be encrypted back into the letter “A”. And that the german operators would always start a message by sending a 3-letter group twice, and that group would be the “new” setting for the rest of the message. i.e.
* All german units on this day set their machine to “todays” starting settings
* The operator then picks 3 random letters (maybe “FUK”)
* He sends the 3 random letters twice (FUKFUK)
* He then changes the machine to the setting FUK
* He then sends the rest of the message
The Poles figured out that there’s a pattern caused by the basic design of the machine, that if you have the first 6 letters of a thousand messages from the same day, you can figure out the starting settings, because the 1st and 4th letters are the same, 2nd and 5th, and 3rd and 6th. FUKFUK becomes AGVBKY. DIKDIK becomes LTQWQX, etc. It also helps knowing that the most common choices are FUK, DIK, 123, ABC, etc.
Unfortunately, the German’s changed their procedures to stop sending the repeats.
Then, the Allies (Brits? Poles? not sure) figured out stuff like “It’s really common for this one german guy to send a message every morning at 6:03AM. We don’t know who or where he is, but his telegraph speed, spacing, etc are really unique We call him Dickhead. Maybe he’s sending a daily weather report? German army daily weather reports are supposed to be in the format “DDMMYYHHMM WETTER BEIM <location> “. Maybe some guys don’t stick to the format, but the guy sending every day at exactly 6:03AM seems anal retentive. Lets assume the first 22 letters of his message decode to this exact phrase. What combination of settings yields the encoded message we got?
I believe they called these kinds of giveaways “cilly”s. (don’t know why.) One cilly was “Heil Hitler”. Like, if you *know* that half the messages sent today have “Heil_Hitler” as the last 11 letters, that sure helps break the code.
Of course, the Germans got better, and they changed their behaviors, etc.
I believe Turing’s key contribution was finding a cycle pattern that must exist due to the mechanical design, that was more fundamental than what the Poles found, i.e. didn’t rely on operator mistakes, just was a basic failure in the concept.
It was that there are cycles in the patterns that would be a clue to how the enigma was set up that day. Like if you examine thousands of messages without even knowing what they are, and you find that a pattern with five letters (maybe “GYXMVR”) and also four letters (maybe “RLKZ” and five letters (maybe “ZUXQG”) that “connect” (G-R, R-Z, Z-G) can occur, then the machine can’t have been set up with cylinder #2 in the first slot. (Note: I think this isn’t exactly right, but it’s close to the solution).
Figuring this out took processing a huge amount of messages looking for these cycles. Hundreds of humans working feverishly on thousands of pages of printed out messages. The movies suggest this was a “did we solve it today” problem, but in reality, they’d work on a particular day worth of data for a week or a month before figuring it out, sometimes. That’s worth it because decoding the ten thousand messages the German army sent last Tuesday still tells you a lot.
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