ENIGMA was a cipher machine used by the German armed forces to encrypt messages sent by radio. ENIGMA was believed to be so secure that even the capture of a machine by the Allies was not considered serious, since the cipher key was changed once or twice a day. In fact, ENIGMA was a patented commercial product. Between the wars, the inventor of ENIGMA tried with limited success to sell his machine to large corporations for the purpose of encrypting telegrams sent to their international business concerns. Around that time the German armed forces began to realize that only communication by radio offered the speed and flexibility necessary to maintain contact with distant ships, Uboats and rapidly moving land forces. Knowing that their signals would be monitored by the enemy, a reliable and secure means of encrypting radio traffic was essential. ENIGMA, which offered more than 712 million possible key combinations, seemed unbreakable.
ULTRA was the name given by the Allies to decrypted ENIGMA intercepts. There are a number of excellent books detailing how ENIGMA was broken and exploited (see Recommended Reading below). The center of the British codebreaking effort was based at Bletchley Park. Several machines called "Turing bombes" were constructed to test and reduce the number of possible keys for each message before decryption. Great care was taken both to disguise the real source of ULTRA and, when the information was distributed to Allied field commanders, to exploit the information in such a manner that the Germans would not suspect that ENIGMA was not secure. Various types of ENIGMA machines were used by the Italians and Japanese as well (the Japanese machine cipher was called PURPLE by the Americans - it's decrypts were called MAGIC).