Enigmatic Cryptography of World War 2

World War II saw many mathematical advances that enabled the proliferation of mechanical cryptography, or codes. Nearly every nation had its own code or cipher that other combatants would attempt to break in order to access military communication. Cryptography is sometimes called the forerunner of computer science because of the related fields that it encompasses.

Before World War II, most codes were primitive. Egyptian, Roman, and Greek rulers used codes to send messages; a famous early method was the Caesar shift cipher, where all the letters in a message would be shifted up or down the alphabet by an agreed upon number, then shifted back by the receiver.

As early as at the beginning of the war, Polish agents broke Germany's first Enigma code, which was created by a machine.

The British were early to understand the potency of codebreaking and set up the ULTRA program, which had help from the knowledge that Poland's crytographers had gleaned from the first Enigma engine. By recruiting young mathematicians, the Ultra program cracked a few German codes, once crucially in April 1940 before D-day. However, the Ultra program was still limited, and many times, like at the Battle of the Bulge in the Ardennes forest, could only perform guesswork of military movements based on the allocation of resources. The Allies also learned that, even when Germany's intentions could be deciphered, often there was not enough military strength to stop the Wehrmacht.

In North Africa, codebreakers were more successful, finding out the number of Rommel's tanks, among other things. Additionally, captured German ships, like the submarine U-110, sometimes carried complete Enigma machines that allowed the Allies to completely crack German codes, giving them the edge in the Battle of the Atlantic. However, this was just one in a pattern; German commanders would frequently change codes while Ultra tried to keep up.

In the Pacific theater, the Japanese military used a system called "Purple", which was a machine that had two typewriters, capable of 70 trillion different combinations. Eventually, American intelligence agents noticed the pattern of three divisions per month where the key, which changed every day, was repeated, allowing them to break the codes.

In the end, most codes were partially or completely broken, sometimes without the targeted government realizing. One code, however, remained unbroken; the Navajo language, which was broadcast between soldiers of the Navajo Native American tribe, proved too complex to break.

Sources:
Weilin Tan, Joohyung Ha, Young Soo Kim, Martina Canevari, "WWII cryptography and its relationship to the discipline “computer science” ," UC Berkeley, http://courses.ischool.berkeley.edu/i103/su09/slides/projects/WWII-cryptography.pdf
Tony M. Damico, 2009, "A Brief History of Cryptography," Student Pulse, http://www.studentpulse.com/articles/41/a-brief-history-of-cryptography
History Net: Where History Comes Alive - World & US History Online, 6-12-2006, "World War II: Ultra," http://www.historynet.com/world-war-ii-ultra-the-misunderstood-allied-secret-weapon.htm
Alberto-Perez, 3-22-2013, "How the U.S. Cracked Japan's 'Purple Encryption Machine' at the Dawn of World War II," io9, http://io9.gizmodo.com/how-the-u-s-cracked-japans-purple-encryption-machine-458385664