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The mechanization of cryptography was in full force when World War II broke out. To the dismay of the allies, top level messages by the Germans and Japanese were enciphered with complex machines that produced 'unbreakable' ciphertext using a complex series of rotors. Yet by the end of the war, messages encrypted with these machines were being deciphered with ease. How did it happen?
The first step in answering the question 'How did it happen?' is to first ask: How did it begin?
A German named Arthur Scherbius developed the Enigma rotor machine in the early 1920's. Scherbius had obtained the rights to a patent for a rotor cryptography machine from Alexander Koch who filed the patent in 1919 but never produced a machine. Scherbius's first machine, the Model A, was a large unwieldy device the size of a cash register. His next model shrunk to just larger than a typewriter, and a model c was a portable version that could not print. All of these devices failed commercially, though. Scherbius's company, Chiffriermashinen Aktiengesellschaft ("Cipher Machines Corporation"), tried to promote the Enigmas at various conventions and conferences. And despite the company's excellent slogan, "one secret, well protected, may pay the whole cost of the machine", the machines were a disaster.
The company disbanded in 1934 failing to ever produce a dividend in its ten-year existence. The company's assets were transferred to another cipher company start up created by two of the members of the board of directors on the old company. The commercial success of the new company was never fully tested as Hitler began rearming Germany for the Second World War and pounced on the Enigma as a secure communications system. The portable Enigma Model C became the de facto standard for top Army, Navy and Air Force messages, and the new company was probably kept busy (whether it received monetary compensation or was taken over by the military forces is unknown).
NOTE: For a full mechanical description, you should read our lesson about rotor systems in the crypto vault. For our purposes, we'll only give a cursory overview of the system.
The Enigma utilized several 'rotors'. On each of these disks there were 26 contacts (representing letters). Each contact was connected through wiring to another contact, so that applying electricity to one contact would output electricity at another contact on the same rotor (a basic monoalphabetic substitution). To complicate the machine, the rotor turns each time a key is pressed which changes the wiring. This would produce a polyalphabetic ciphertext with 26 alphabets (an 'a' would not produce the same letter until it was pressed for the 27th time). Polyalphabetc ciphers were nothing amazing, though. To make it revolutionary, the Enigma added more rotors. After the first rotor made one complete revolution, the second rotor moved one spot so that now instead of just 26 alphabets, there were 676 (26*26). More rotors added more security. And despite the security of so many alphabets, the Germans also added several modifications to their Enigma that raised the possibilities up to 10 quadrillion alphabets. With numbers like this, the Germans felt they had a right to be confident, and joined long line of cryptographers to believe falsely in large numbers.