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
You do use the information, but you have to be very clever about when you are using it. For example, you might decide to use it non-optimally in some cases where it can be confused for a plausible coincidence. Imagine you have decoded that there is going to be a bombing of CITY on DATE. For some reason, high command has decided that this needs to be defended against. Military planners now need to come up with a plausible excuse for why CITY *just happened to have* some form of air defense that it would not otherwise have. But you also can’t make it too obvious. So maybe you divert a fraction of one of your armies in the region to temporarily be stationed there during DATE. You can’t divert the entire army without being obvious about it, but surely they can spare some anti-air capable machinery.
Depending on how secure(/paranoid) you want to be about the ruse, you can feed some fake documents/orders about the diverted forces complete with fake reasons to operatives that you are *pretty sure* are Nazi spies (top tip; don’t automatically arrest someone if you know they are a spy). Figuring this stuff out is essentially the day job of military intelligence.
You cannot use your decoded information *constantly* though. High command and military intelligence will need to coordinate/plan/decide what information is important enough to act on, what is irrelevant enough not to act on (irrelevant in the terms of the greater war), and what information is important enough to act on with such force it is obvious you have a decoder.
edit; there are far more fun things you can do. You can simply lie about having some form of new radar tech. Or you pretend that eating carrots has improved your pilot’s eyesight to justify your better intelligence. One of the ‘fun’ things about war is that there is chaos on all sides. Your excuses don’t have to be perfect because your opponent does not have the time and resources to verify everything anyway. Everyone on all sides is working with incomplete and often unverified and/or vague data. Your excuses only need to be *plausible*.
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