Which cipher machine's naval version had four rotors?

Enigma. The German navy added a fourth rotor in February 1942, and the effect at Bletchley Park was immediate and total - the U-boat traffic went dark for most of a year, and shipping losses in the Atlantic rose accordingly.

What broke it was not cleverness but capture. Codebooks and a short-signal weather cipher were recovered from U-559 in October 1942 by three men who swam to the sinking submarine; two of them went down with it. The documents gave the way in, and the traffic reopened that December. The other standing weakness was procedural: Enigma could never encipher a letter as itself, and German operators sent predictable phrases at predictable times, which gave the cribs the machinery ran on.

The secret held for thirty years. Everyone involved was bound to silence, captured machines were sold on to other governments who went on using them in good faith, and the story only became public in 1974 - which means much of the standard history of the war was written by people who did not know the most important thing about it. Turing, who designed the bombe and the statistical method behind the naval attack, was prosecuted for homosexuality in 1952 and died two years later.