Actually even after shooting down Adm. Yamamato’s aircraft I think Japan still didn’t know that their codes. The various efforts that the allies took to keep the axis from figuring it out that the codes had been broken was quite extensive.
The one time pad can be proven to be unbreakable as long as you can figure out how to distribute the keys to the people who need them. The problem is you need 1 bit of key for each bit of data you wish to encrypt.