The conventional wisdom is that the successful US cryptanalytic efforts
against Japanese naval codes was a closely-held secret. I've just
stumbled on a source that disputes that. In "The Unknown Battle of
Midway: The Destruction of the American Torpedo Squadrons" (Alvin Kernan,
Yale University Press, 2005), the author states:
Rumors began to circulate that the Japanese were planning to invade
little Midway Atoll and draw our ships out to fight the great sea
battle their strategy had long anticipated. Our information, we
heard, at the scuttlebutt, came from code breakers...
Unbelievably, the Japanese never tumbled throughout the entire war
to the fact that their codes had been broken, and the U.S. Navy,
equally blindly, continued to believe that its ability to read one
after another of the Japanese codes remained a deep, dark secret
from its own sailors. But when the American carriers sailed from
Pearl Harbor to the Battle of Midway everyone aboard knew what was
in the wind and how we knew it.
The source for this statement isn't clear. The author himself was an
enlisted sailor on one of the American carriers (he was an ordnanceman for
a torpedo squadron), so it may be first person knowledge. Later in the
second paragraph, there's a footnote to Prange et al's "Miracle at
Midway", but I don't have that reference.
--Steven M. Bellovin, http://www.cs.columbia.edu/~smb
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