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
They avoided using too much of the information, carefully restricted who could access it, and created various ruses to make it appear that they had alternative sources of intelligence. None of this was new or unique to the Second World War: it’s standard spycraft stuff.
A similar issue comes up in counterintelligence: if you have convinced an enemy spy to turn traitor, how do you stop your enemy from realising that they have suddenly stopped getting useful information from them? Well, you continue to allow them to send some information, but remove some of the detail or ensure it arrives a bit too late to be useful. Then you can mix in some fake information that will actively hurt the enemy (e.g. by suggesting that you are about to launch an attack in one location, when you are actually planning an attack somewhere completely different).
Of course, your enemy will be aware of all these possibilities and will be careful to obscure their own knowledge, so you will never be completely certain whether they suspect something is up.
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