Imagine yourself in a particular position to stop the Nazies from from taking the lives of hundreds of thousands of innocent people. What would be your best course of action? For a guy named Bill Tutte, his solution was none of those. His solution? Numbers
Humble Beginnings
William Thomas Tutte was from Newmarket, Suffolk. His parents were workers at Fitzroy House stables, where he was born. His dad was an estate gardener, and his mom was a housekeeper. When he was 10, Tutte became a scholar at the Cambridge and County High School for Boys, where he enrolled in 1928. He got another scholarship in 1935, this time to study natural sciences at Trinity College, Cambridge, where he took chemistry and finished with flying colors. In 1940, he took Mathematics, a decision that would make a historical shift in the first World War.
He and his three friends, Leonard Brooks, Cedric Smith, and Arthur Stone, were among the first to solve the problem of squaring the square, a mathematical problem of tiling an integral square using other integral squares with certain conditions set, thought to be impossible. The four went under the pseudonym Blanche Descartes and published their work in an academic journal.
The Lorenz Code
The interception was standard during World War II, with both sides wanting to know each other’s moves, plans, and strategies. As a result, they aimed to create the most undecipherable codes as means of communicating confidential information.
On the Nazi side, The German Army High Command summoned Lorenz company and asked them to develop a high-security teleprinter cipher machine that would allow them to communicate covertly via a radio. The result was the cipher machine designed according to the additive method of Gilbert Vernam for enciphering teleprinter messages that he invented in 1918.
Teleprinters use Baudot code, a 32-symbol alphabet with several variations that adapt depending on the users and languages before it was standardized under International Telegraph Alphabet No. 2. Its output comprises five channels, each with a stream of bits that can be represented as hole or no- hole, dot, or cross.
A substitution technique called Vernam Cipher is then used to encipher the text message per character to create a set of almost undecipherable characters before the letter woudl be finally transmitted to whomever was supposed to receive it. Once received, the enciphered characters would then be decrypted so the reader could read the original message.
To ensure that there would not be a recognizable pattern, Vernam suggested that the characters should be completely random and pre-punched on a paper tape. Such a purely accidental one-time pad system would make the code unbreakable. Lorenz’s company created a machine to generate the obscuring character sequence more easily. Unfortunately, the device could not generate a completely random sequence of characters and had instead produced what was known as pseudo-random sequences that would soon bring their downfall. When the cipher system was created, the Germans had high trust in it that it was used by the Nazi High Command and Hitler himself.
Breaking the Code
Tutte joined the codebreaking operation at Bletchley Park in 1941, where other mathematicians like Alan Turing, known to have solved the Enigma code used by the German Navy. He was assigned to work on the Lorenz cipher that the British were clueless on how to break.
What Tutte did first was to analyze the intercepted code and find repeated characters that helped him identify the size of the wheel in the machine. It was grueling work, and he needed an automated approach to attacking the code, which led to the construction of the Colossus machines. They successfully break into the encoded messages, and at times, they could decode the notes simultaneously as the German recipients were reading them.
Breaking the Lorenz cipher gave them an advantage that proved valuable, especially during the preparations for the Normandy Invasion. Bill Tutte’s work on the Lorenz cipher was undoubtedly one of the most outstanding intellectual achievements during World War II, showing how numbers helped overthrow the Nazi regime.
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