Cracking Enigma:

Click here to go directly to the bombe simulator.

The math involved in the Enigma is straightforward, and the system is very strong when used correctly and securely. However, because of their overconfidence, users of the Enigma unnecessarily gave away the ability to read their messages.

The first advances in cracking the Enigma were made by the Polish in the 1930s. At that point, the machine only used three rotors in six possible combinations (3 nPr 3). Although breaking the Enigma in the 1930s was a major accomplishment, the Polish were unable to crack the Enigma after the German military took over its development in World War II. The Germans increased the number of rotor combinations to 60 by adding an additional two rotors to the pool (though the machine still only used 3).

The British then continued working on deciphering the Enigma, starting where the Poles left off. A man by the name of Alan Turing, then a young mathematician, built a machine to crack the Enigma while working for the British government. This man's work on building the Turing Bombe, as it is called, gave the foundation for modern computing. The NSA said that were it not for this man's work, computers would not have developed until some time later than they did.

Image Courtesty of the National Cryptologic Museum.

In any case, the Bombe could chug along and eventually crack an Enigma code in about 15 hours. A modern computer can do the same task in several minutes. Although the math behind it is best left to a textbook, we have included a small simulator of the Bombe.

The Bombe was able to break codes because of weaknesses in the way the Germans used Enigma. Although the Enigma was quite secure when used correctly, the Germans were guilty of some oversights:

• The wiring of the rotors was changed seldom, if ever, during the war. The Allies were able to exploit this when they got their hands on Enigma, and thus the rotor wiring. Knowing that information reduces the number of possible code settings to several million, a number easily tackled by the Bombe. (Rotor wiring is what determines which letter is substituted for which when a message goes through the encryption system.)

• The beginning of a message was often predictable. Usually, the German equivalent of "TO GENERAL SMITH" invariably started a message. Knowing what some of a message reads is usually extremely helpful in cracking a code.

If the German government had the foresight, they might have made several modifications to the Enigma to drastically increase the number of possible settings. By making these changes, it would have been virtually impossible for the allies to break the Enigma. Even with the help of the modern computer, it would be difficult (but not impossible).

• Using more rotors. The Germans had only 3 rotors in most enigmas. With every additional rotor, millions of new permutations must be checked by the cracker.
• Tightening security of the Enigmas themselves. If the allies had been unable to get even one enigma, it would have been harder to predict how it operated, and find its weaknesses.
• Having the rotors not move in a speedometer style fashion. By adding more places in the alphabet where the second and third rotor move, it would have become exceedingly difficult for the Bombe to operate.
• Changing the wiring of the rotors frequently. Although this would have been a major undertaking, the secrecy of rotor wiring supplies the greatest security to the machine. By making them unpredictable, it would have been nearly impossible to crack the Enigma.
• Keeping tabs on enigma operators to check for protocol breaches. It only takes one foul-up to compromise all encrypted traffic.

We have provided a simulator of the Bombe. Just like the original, it isn't consistent, often gets it wrong, and is pretty hard to use. However, sometimes it does work. If you are interested, though, it is a fascinating piece of hardware (or software, in this case).