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I was watching a WW2 documentary yesterday and learned Nazi Germany’s encryption had already been (mostly) cracked by the time they entered the war, which (don’t quote me) significantly influenced the outcome of the war.The Poles had broken Enigma before the outbreak of war (1945-09-01) with the help of intelligence from France. Bletchley Park used computers to speed up the process of going through the messages.[0]
It has been remarked that 'cracking Enigma shortened the war by X years',[1] so for some people this could be considered "significantly influenced".
However, after reading Engineers of Victory by Paul Kennedy:
> Kennedy recounts the inside stories of the invention of the cavity magnetron, a miniature radar “as small as a soup plate,” and the Hedgehog, a multi-headed grenade launcher that allowed the Allies to overcome the threat to their convoys crossing the Atlantic; the critical decision by engineers to install a super-charged Rolls-Royce engine in the P-51 Mustang, creating a fighter plane more powerful than the Luftwaffe’s; and the innovative use of pontoon bridges (made from rafts strung together) to help Russian troops cross rivers and elude the Nazi blitzkrieg. He takes readers behind the scenes, unveiling exactly how thousands of individual Allied planes and fighting ships were choreographed to collectively pull off the invasion of Normandy, and illuminating how crew chiefs perfected the high-flying and inaccessible B-29 Superfortress that would drop the atomic bombs on Japan.
* https://www.penguinrandomhouse.com/books/91616/engineers-of-...
I think there were more important developments than cracking Enigma, as influential as that could have been.
If we're talking about codes, then I think the Americans breaking the Japanese ones was more important: the US would have won regardless just because of industrial output, but the intercepts allowed things like being able to predict Midway and being able to take out Yamamoto had more meaningful operational results than what was gained out of Ultra, IMHO.
In the European theatre, I think the Merlin engine was much more critical to the outcome of the war (especially in the Battle of Britain), and the cavity magnetron was more important in the Battle of the Atlantic (along with re-learning to use convoys, like was done in WW1).
[0] Bletchley Park broke other codes, like Lorenz; see William "Bill" Tutte.
[1] https://old.reddit.com/r/AskHistorians/comments/2pq5fa/