Note that even though Hitler's conclusion was correct, this is still really just Hitler's paranoia showing though.
It is likely that the Allies had become used to never being grossly surprised, leading to a degree of over confidence that cost lives in December 1944. Hitler's paranoia had finally advanced to such state in 1944 that he was convinced the Allies were eavesdropping on his intelligence so he insisted that all plans drawn up for that attack NOT use the cracked cypher. The most obvious single battle that was influenced by ENIGMA may, ironically, be the (early stages of the) Battle of the Bulge.
