The Art of Codebreaking

Codebreaking is a fascinating area of mathematics. It focuses on deciphering encrypted messages without the secret key.


The famous example is the German Enigma code machine used during WWII. British mathematicians at Bletchley Park broke the code and read the messages, which helped shorten the war by two years.

Try this substitution cipher resource for kids to get them into the code breaking mood. It uses shapes광주흥신소 for numbers and requires some problem solving.


As the codebreakers huddled around Friedman’s machine, they listened for a signal that might reveal the first sign of a pattern. A sequence of repeated symbols indicating a cipher key was being used to scramble a message.

The cryptanalysts had just cracked the first of Germany’s complex electromechanical cipher machines: the Enigma. These machines scrambled letters into encrypted form with rotors and plugboards. The Germans confidently believed their Enigma messages were uncrackable, but the mathematical prowess of Britain’s Bletchley Park code breakers proved them wrong.

Although the work was incredibly intense, the codebreakers had a jovial camaraderie with each other. They drank beer in mock-Tudor pubs, played chess with each other, and even participated in amateur theatrical productions. But they did not flaunt their success. The bowler-hatted city commuters who stopped at Eastcote’s pubs on their way home had no idea that their comrades were engaging in crucial secret work for the survival of civilization.광주흥신소

Even senior Bletchley figures, like Hugh Alexander, who led the team at GCHQ in Cheltenham after World War II, understood that peace would be an illusion for many parts of the world. Conflicts bred by competing ideologies or the disintegration of empires would always be a threat. And even if the world could manage to avoid a nuclear holocaust, the manoeuvres of Soviet leaders might provoke another bout of bloodshed.


When you think of spies and secret agents, you might think of nifty gadgets, foreign travel and being shaken but not stirred. But the truth is that cryptanalysts (the name for code breakers) use tons of maths – from simple addition and subtraction, to data handling and logical thinking. It’s these skills that helped cryptanalysts uncover plots, identify traitors and win battles.

One of the most common ways to decipher a message is through a technique called frequency analysis. This is based on the idea that certain letters are used more often in a language than others. For example, the letter ‘e’ appears more frequently in English than ‘k’ or ‘q’. This means that, if you’re trying to decipher a substitution cipher (a method that replaces letters with other ones), you can begin with the most common letters and work your way up.

Another way to decipher a message is by using timing, power and electromagnetic radiation. This is what the code breakers of Bletchley Park used when they tackled the Nazi’s Enigma code, helping to shorten the war and saving 14 million lives in the process. And recently, computational neuroscientist Eva Dyer, of the University of Pennsylvania and Georgia Institute of Technology, used cryptographic techniques similar to those applied to the Enigma cypher to predict, from brain activity alone, which direction a person will move their arm.


A codebreaker has to be prepared to work for months and even years, staring at strings of nonsensical letters searching for some sort of pattern. In addition, there are a lot of little things that can go wrong, which makes it even harder. For example, it is quite possible to count the number of bits in a message incorrectly and to miss the correct length of a buffer (a piece of memory used to hold information between operations). There are tens, possibly hundreds of obscure little mistakes that can be made, and they add up to huge computational costs.

It took a team of Swedish researchers several weeks and powerful computers to crack stage 10 of the Cipher Challenge, but that would not be practical for a thief who wanted to decipher a credit card number. A real cipher needs to be more complex than this.

Despite all this, the GCHQ staff were delighted to see so many people around the world take part in the Challenge and get excited about codebreaking and cryptography. Whether or not you were able to crack all ten messages, we hope this book will inspire you to learn more about these fascinating subjects. You will also be able to find links to some of the material published during the Challenge, including an excellent essay by Jim Gillogly and John Palagyi, who were runners-up in the Challenge, and a highly readable report by the Swedish team that cracked stage 10. All GCHQ proceeds from this book will go to Heads Together, the campaign launched by The Duke and Duchess of Cambridge and Prince Harry to tackle stigma and provide support for mental health challenges.


While it is well-known that the British at Bletchley Park were ultimately successful in reading German naval messages, many people may not realize just how much of a difference that work made. Without the Allied ability to read German military communications, the war could have been far bloodier.

The first hints of success with the Purple machine came in early 1941, when a British team intercepted a message from a U-boat commander asking for advice on a navigation problem. This was followed soon after by the capture of a German trawler carrying cipher machines, cryptanalytical equipment and a complete library of ciphers, signal books and navigation charts. The Bletchley team was able to decipher the entire captured message within hours.

It was the first of many successes that would eventually give the Allied forces a constant pulse on enemy activity. This ability allowed them to track enemy convoys, sink Japanese supply ships and gun down Isoroku Yamamoto, the architect of Pearl Harbor.

While these codebreaking successes were impressive, they still took a significant toll on the lives of the personnel involved. Especially in the later years of the war, as the demand for intelligence rose, military leaders began turning to a group of recruits that had been overlooked for a variety of reasons: women. Sworn to secrecy and armed with the tools of their trade, these women left behind their homes and families for work that was, in many ways, a sexy job for women back then.