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The Wikipedia page on Joseph Rochefort states:

One of the Station HYPO staff, Jasper Holmes, had the idea of faking a failure of the water supply on Midway Island. He suggested using an unencrypted emergency warning in the hope of provoking a Japanese response, thus establishing whether Midway was a target. Rochefort took the idea to Layton, who put it to Nimitz. Nimitz approved, and the garrison commander was told by submarine cable to immediately radio in [1.] "plain-language" an emergency request for water as an explosion in the water desalination system meant that they had only enough water for two weeks. [2.] An apparently "follow-up" report was to be made in one of the strip-cipher code systems that the Japanese were known to have captured on Wake. As the plan was to convince Washington, Rochefort tactfully let Fleet Radio Unit, Melbourne (FRUMEL) notify the main objects of the deception (Washington) of the Japanese message by reporting a message from the AF Air Unit saying that they had only enough water for two weeks: "This will confirm identity of AF". Rochefort then sent a reminder on Friday. [15]

The Japanese took the bait. Within hours they broadcast instructions to load additional water desalination equipment, confirming Rochefort's analysis.[16][page needed] Layton notes the instructions also "produced an unexpected bonus". They revealed the assault was to come before mid-June.

I don't understand how the Japanese believed the US so foolishly?

  1. Why would they reckon that the US would broadcast a true emergency request on water unecrypted? It doesn't make sense for them to broadcast a weakness unencrypted. In a true emergency, wouldn't the US summon for help encryptedly, even to non-US allies like Australia and New Zealand?

  2. Why'd they fall for the "follow-up"? The US knew that the Japanese captured this "strip-cipher code systems" on Wake. Thus why would the Japanese reckon that the US would use it unquestionably in good faith?

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    Regarding the use of a "compromised cipher"... Did the Japanese know that the USA knew that the cipher had been compromised (SOP would have been to destroy the ciphers before capture)? And even if the USA knew the cipher had been compromised they would hace needed some time to issue and safely distribute a new one, so it would have not been too much out of the ordinary for some not so important messages to use the old cipher.
    – SJuan76
    Apr 19, 2019 at 11:34
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    A point not raised (so far) in the two answers is that the salinization story was concocted and used precisely because it was of the class of messages that the U.S.N. routinely sent unencrypted. That was what made the ruse believable: a station completely unaware that it was the the target of an upcoming Japanese assault, thousands of miles from any Japanese forces, simply reported urgent need for water and replacement salinization equipment.
    – Pieter Geerkens
    Feb 15, 2020 at 20:39

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Japanese didn't realize their code was partially broken, and their beliefs were less important

First thing you need to understand is that Japanese naval code JN-25 was already partially compromised before the events with fake water supply problem. In fact, Americans already knew there soon would've been operation at objective "AF". Rochefort suspected it was Midway, but he had to prove it. But as you can see, US had significant advantage.

Second, Japanese had no idea JN-25 was partially broken. This was their biggest weakness in whole affair. Had they known they would not have used it, especially for important messages concerning strategic operations.

Final piece of the puzzle, fake message about desalinization plant, is just icing on the cake. Japanese listening stations had to report intercepted US radio traffic...after all it was their job. Analyzing authenticity of the message was not. Those who did analyze the message, its authenticity and the source, decided to play safe and transmit message about additional desalinization equipment for objective AF.

Even if the Japanese did not re-transmit message about desalinization plant, identity of objective AF would likely be discovered trough usual traffic like weather reports (trick all sides used in WW2). For example, if Japanese transmitted that weather over objective AF is such and such, US could simply deduce possible locations by comparing their own weather reports over strategic locations and finding most likely. Granted, this may not be enough to win Midway battle, but at some point of time breaking of JN-25 code would eventually pay off for US.

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Firstly, there is nothing 'foolish' about it. Military planning is about contingencies. The Japanese listening stations had received a report, they forwarded that report using a code they believed to be secure, and the planners modified their plans for the attack on Midway to deal with the contingency that it may have been true.

The Japanese believed their main naval code, the Navy General Operational Code (dubbed JN-25 by the US codebreakers) was secure. So their listening posts simply reported what the Midway garrison was saying, using that secure code.

Of course, with the benefit of 20/20 hindsight, we know that JN-25 wasn't secure, and that Station Hypo in Hawaii was able to decrypt enough of the intercepted traffic to piece together much of the Japanese attack plan at Midway. The Japanese commanders didn't have that luxury.

There is an interesting Fact Sheet about JN-25 by Geoffrey Sinclair which provides a lot of background information about the code itself which you may find helpful if you wish to research further into this subject.

Having received the report, the Japanese commanders then sensibly modified their planning just in case. That's how contingency planning works. If there is a known contingency that you may have to deal with, you modify your plans accordingly.

In this case, if the report that the water desalination facilities at Midway were seriously damaged was true, they'd certainly need the extra desalination equipment; if it turned out that the report wasn't true, the extra equipment would do no harm and might still be useful anyway.

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