So the Germans used the Enigma machine to encrypt their communications during WWII, and the deciphering of the Enigma code was one of the factors that gave the Allies a decisive advantage during the war. But what did the Allies use to encrypt their communications and how did the Germans deal with deciphering them?
I've posted about Allied codes before, in this thread, and about German attempts to break them in this thread.
TL/DR:
The British had a cipher machine called Typex, which was very similar to Enigma. The RN used book codes for the early part of the war. These were also used by the British and American merchant marines. The Americans had a more complex cipher machine called SIGABA, which was far more secure than Typex or Enigma. A Combined Cipher Machine was produced in 1943, to allow messages encrypted on a Typex machine to be decrypted on a SIGABA machine and vice versa. At a tactical level, some US units, mainly the USMC and the Army's 4th Infantry Division, employed Native American code talkers, speaking the Navajo and Comanche languages. The Germans were able to break the book codes used for merchant ships and by the RN, but had little success with those enciphered on one of the machines. They also broke a code used by the US State Department, and were able to obtain secret reports about the British forces in North Africa.
The allies also had Navajo code talkers. These men spoke in codes that were based in the Navajo language, which has a very complex grammar so is difficult to figure out. The Axis powers had no Navajo speakers amongst them, nor did they know that the code was based on the Navajo language, not English, meaning they could never break the code.