One of my favorites is in Imitation Game when Alan Turing and his team finally crack Enigma's encryption. A truly remarkable feat for its time. One of the cryptographers is eager to rush and tell the commander but Alan has to stop him because if the British Royal Navy intercepts a Nazi U-boat, then the Nazi command will know that Enigma's encryption has been compromised.

In order to prevent the Nazis from knowing that Enigma has been defeated, Turing's team has to pretend that they haven't cracked the code. Which means they have to find a way to leak false information to British high command which is then leaked to the public so they can slowly bring the war to an end using systematic mathematic analysis. They have to make the least number of moves to prevent the Nazis from getting wise but the most to end the war as soon as possible.

It shows how we reverse counter intelligence used back then as well as the birth of GCHQ and large-scale government intelligence agencies.