How did they get over the catch-22 that if they used the information that Nazis could guess it came from breaking the code but if they didn’t use the information there was no point in having it.
EDIT. I tagged this as mathematics because the movie suggests the use of mathematics, but does not explain how you use mathematics to do it (it’s a movie!). I am wondering for example if they made a slight tweak to random search patterns so that they still looked random but “coincidentally” found what we already knew was there. It would be extremely hard to detect the difference between a genuinely random pattern and then almost genuinely random pattern.
In: Mathematics
There’s a good book called [Bodyguard of Lies ](https://en.wikipedia.org/wiki/Bodyguard_of_Lies)that covers WW2 from an intelligence perspective. To summarize, they knew very well that if the fascists figured out Engima was comprised that they’d change to a different system.
So, they would engineer situations to create plausble alternative explanations. For example, if the Allies had intercepted a transmission that a very valuable cargo ship was to leave port on to-morrow at 8 AM, they’d arrange for a fly by of an on obsever aircraft that morning, and so forth.
Unfortunately, they could not do it all of the time. At one point, the British knew the Luftwaffe was going to bomb Coventry and realized that if they evactuated the city, it’d give the game away. [They did what they could but had to allow the city to be hit.](https://winstonchurchill.org/resources/myths/coventry-what-really-happened/)
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