You know, Enigma itself isn't broken "as such" -- it is simply that the Germans (yes, I am one of them) used the Enigma incorrectly.

They repeated the message key (i.e. they encoded it twice) so Turing was able to host something similar to a plain-text attack. Considering the key-space was not that huge, and he had all the resources he needed, it got easy.

When the German Navy stopped encoding the message key twice, they resorted to stealing a code-book (one of the books with the master keys, you know, like a keyring these days).