The History and Mathematics of Codes and Code Breaking

Tag: WWII (Page 1 of 2)

The Allies Work Better Under Pressure

It is no secret that Allied code breakers bested German code makers during World War II which contributed enormously to an Allied victory in the war. Germany's overconfidence in the strength of its Enigma cipher definitely contributed to the Allies' code breaking success, but another main contribution was the pressure that Germany forced against the Allies. The Allies were on their heels trying to defend against Germany, which led countries to band together and individual cryptographers to band together to fight a common enemy. The necessity for the Allies to break Enigma in order to thwart the Axis' attacks brought Poland, England, France, and America together which gave them the resources to crack Enigma and Purple (Japan's encryption method).

Without the pressure the Axis powers were putting the Allies under, they would not have felt the urgency to break Enigma and Purple. The Allies won this war on intelligence because they were on the defense and needed to break Enigma and Purple in order to turn the tables against the Axis, while the Axis got complacent and confident about their machines because they were able to advance through Europe and the Pacific without their code being decrypted. Since the Allies were under such pressure, they had to find a way to gain the advantage. Therefore, countries such as Poland and England teamed up and individuals such as the mathematicians at Bletchley Park teamed up to crack the Enigma and Purple ciphers. Without the pressure that the Axis' exerted on the Allies, the Allies would not have been so desperate to find any way possible to crack Germany and Japan's seemingly unbreakable ciphers.

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Divided and Conquered

The Allied cryptanalysts were victorious over the German cryptographers due to a variety of reasons; however, one rather simple reason is often overlooked: the allies had a much larger and much more unified base of cryptologists than the Germans.

Germany had a total of around 30,000 people working in the intercepting, decoding, and coding of messages. The European Axis powers had a grand total of 36,000 people working in those endeavors. The Allied powers had a number closer to 60,000 people doing the same jobs, nearly twice that of the Axis powers. Just think about the implications of this: more people leads to more intercepted messages, which leads to more cipher text to work with (a historically beneficial resource in terms of breaking codes), and more people leads to more brain power trying more techniques to break the same code.

In addition to this, Germany did not have a central cryptology base like the Allies did at Bletchley Park. The Germans were spread out among 6 different bases, and would often overlap in each other's efforts, duplicating each other's work and thus wasting time and resources. There was some collaboration but not nearly to the degree of the Allies. In Andrew's blog post, he discusses the importance of collaboration in the field of cryptology so I will not expand upon this as much.

Finally, the Germans never created a bombe-like machine that could decipher messages which can very easily be attributed to the division and smaller size of the German forces. Without this key technology, Germans had to do a lot of the leg work manually which is much much more time-consuming and much less reliable. The bombe and other machines like it (Colossus and Tunny) exponentially increased the cryptographic progress of the Allies, catapulting them far ahead of the Axis powers.


Click here to see my primary source.

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German Cryptography is still Human Cryptography

During WWII, Germans sent out thousands of messages encrypted using the supposedly unbreakable Enigma machine. It was discovered after the war that German intelligence knew that these messages could be captured by the Allies, but they could not think anyone would have the time or resources to possibly decipher them. This strongly held idea that Enigma was unbreakable was perhaps the greatest mistake of Germany.

Another factor, besides German overconfidence, that allowed the Allies to decipher German messages were the patterns discovered when Enigma was used. These patterns were precisely the result of non-randomness that describes human nature. Some keys were easily guessed because the letters on the Enigma keyboard were next to each other. Other keys may have been similarly predictable because they resembled German names, or they were used repeatedly. These were called "cillies." Ironically, an effort to consciously combat human un-randomness was also a mistake on Germany's part. By avoiding "obvious" plugboard settings and arranging rotors to avoid repeated positions, the amount of possible settings were drastically reduced.

Human nature in and of itself is never truly random; this is a basic fact we learn in our statistics classes. If you asked a population to randomly choose a number between 1 and 4, would a fourth of the people choose each of the numbers? Polls have shown that, instead, a clear majority would choose the number 3. In the same manner, cipher keys are not always a random garble of letters. They are often derived from meaningful words or phrases that may be pertinent to the message or the receiver/sender of the message.

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Rejewski and Turing

One of the main reasons for the success of the Allied cryptanalysts at Bletchley Park over German cryptographers is the acquisition of the previous work of the Polish on the German Enigma. Polish cryptanalyst, Marian Rejewski, led the polish to first break Enigma in 1932, and kept up with breaking any new security the Germans implemented to strengthen Enigma, until in 1939, when the Germans increased the number of plugboard connections from 5 to 8 to 7 to 10, which made cryptanalysis extremely more difficult. This spurred the Polish to disclose all their work on Enigma to the Allies, especially as the likelihood for another war was growing. Thus, when war broke out and the need to break Enigma became of utmost importance, the Allies had a head start on breaking the codes, as they already had acquired intelligence on Enigma.

Another curious and more indirect reason why the Allies were ultimately successful was because Britain never found out that Alan Turing was a homosexual. Turing was the one of the most important men in the war in that he led the cryptanalyst team at Bletchley Park to victory in breaking Enigma. At the time, homosexuality in Britain was illegal and it was very fortunate that the state never found out about Alan Turing’s case during the war, otherwise Turing probably would never had made it to Bletchley.  Needless to say, if Turing had not been working for the Allies during the war, Enigma may never have been broken and the Germans may have won.

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Allies versus Germans: they won because they were Allies

It is my opinion that one of the prominent and yet overlooked reasons that the Allied cryptanalysts were able to end up winning against German cryptographers was that they were indeed Allies. Although there were times when they kept information from each other, they were able to share their breakthroughs in a way that Germany could not share with its allies. Every time an advancement in breaking the code was made it was possible for them to share that advancement with each other, and this allowed them to break more codes faster. Germany, on the other hand could not share breakthroughs with codewriting and codebreaking with its allies. This is for a pretty obvious reason.

The Allies were only intent on defeating Germany and its allies, to keep the world balance as it was. Germany and its allies were intent on conquering as much territory as possible. This meant that Germany was afraid to share information with its allies, because there was always the chance that once they defeated the Allies, they would turn on each other. An interesting parallel of this would be that of supervillains. The issue with them joining together to defeat superheroes was and is always that they can't work together for very long before turning on each other.

The Allies could communicate with each other. Germany could not do so. This, as simple as it is, is one of the key reasons that the cryptanalysts worked so efficiently. The Allies were allies.


Ethical, Unethical, or Both?

I am of the opinion that there are two ways that the question can be looked at. Personal ethics, I think, are different than the ethics of a nation. This is something that must be taken into account when questioning the ethics of decisions surrounding national security; it most certainly must be taken into account when considering the Zimmerman telegram.

From a personal standpoint, this decision is unquestionably unethical. Letting America know the contents of the Zimmerman telegram would have saved American lives, and potentially shortened the length of the war. Although it could be argued that more lives might have been lost if Germany knew that the code had been broken, I vastly disagree. Creating a new and equally strong code for their messages would have taken Germany a long period of time, because creating codes that function and are very strong is not an entirely simple process. Even if Germany became aware that their code had been broken, with the advantage given to both America and Britain, the war may have been won before the new code was invented. It is completely unethical for someone to break a code with the intention of shortening the war, and then not use the broken code to save as many lives as possible.

At the other end of this issue is the standpoint of national ethicality.  It is my opinion that a nations ethics are typically focused first and foremost selfishly, on the survival of that specific nation. It is quite possible that Admiral Hall believed that telling the Americans about the contents of the Zimmerman telegram would jeopardize the very survival of his nation, in which case he simply obeyed his national ethics, which told him that survival came first. In following this duty to his country he also follows another part of national ethicality, that the homeland must come first.

With these two sides to keep in mind, it is impossible for me to conclude that one is more correct than the other. Personally, it is unethical. Nationally, it seems it may have been quite ethical. In the end, this is a murky issue. However, in the tumultuous and interconnected times we live in today, this will be an issue I think we will revisit very soon.

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Strategical rather than unethical

After the Zimmermann telegram was deciphered, Admiral Hall chose to withhold the important information regarding the unrestricted submarine warfare and put many Americans’ lives on the line.

The decision itself at that moment seemed unethical because it resulted in the death of many innocent Americans. However, thinking in a larger scale, Hall’s action was justifiable. Firstly, given this war context, the ethical considerations probably weren’t be the top priority for people who dedicated themselves for the future of their country. Instead of thinking about whether their decisions might be ethical, they would probably spending more time weighing up the consequences of their actions, which, in Hall’s case, was the potential long-term consequences of disclosing their advanced cryptographic progression to the world. Hall realized that it might eventually make the British lose the advantage of using their advanced cryptographic techniques to gather the information that would be extremely valuable to them in the war.

Another text written by Sun-Tze in the Art of War says that “if you know your enemies and know yourself, you will not be imperiled in a hundred battles.” Sun-Tze’s words implies that in order to win the battle, not only should us try to gather as much information as we can about the enemies, but also try to avoid exposing any of our own progression to the enemies. That was exactly what Hall did. His action enabled the British to see through German’s plot while keeping the Germany in the dark, hence gaining significant advantages in the long run. In this sense, I believe that Hall’s decision shouldn’t be considered unethical, but simply strategical.



The Morality of Admiral Hall's Actions

Upon learning the intended plans of the Germans from deciphering the Zimmerman telegram, it was ethical of Admiral Hall to withhold such information from the President.


One may argue that Admiral Hall should morally concede the information to the President so that Britain may be subsequently informed, and lives could be potentially saved during the outbreak of unrestricted submarine warfare. Yet, if America was to intervene before German acted out their plan, they would’ve “concluded that their method of encryption had been broken,” leading them to “develop a new and stronger encryption system” (Singh 113). This grants the possibility of the German’s using an extremely more complicated encryption system, one that the cryptanalysts in Britain’s Room 40 may never solve in their lifetime, to act out their unrestricted submarine warfare unopposed. This, in turn, could’ve led to a higher number of wartime casualties, especially among passenger ships. Thus, through decrypting future German telegrams without their knowledge that their encryption system had already been broken, Admiral Hall’s actions could potentially save many more lives than he would’ve had he passed on the information.


Furthermore, as history proved, by not informing the President, Admiral Hall ensured that the Germans did not realize the Americans had broken their encryption system, granting the Americans an advantage in decrypting any future German messages encrypted by the same system. Eventually the Mexican version of the Zimmermann telegram led America to retaliate, granting the same outcome had the Admiral actually passed on the information, but without the Germans discovering their blunder.


A Boost of Motivation

The mindset for the Allies had changed between the First World War and the Second World War. After their success in cracking Germany’s ciphers in the First World War, the Allies felt like that could crack anything Germany tries to encipher. However, once the Germans started using the Enigma machines, the Allies were stumped. This change in attitude might be attributed to the fact that they were not in direct threat at that time so they didn’t have the motivation to try to decipher the messages. That along with the hopelessness that might come with failed attempts would make them lose motivation. Poland, however, was threatened so they had to do everything they could to decipher those messages. Therefore, with the help of Schmidt and Rejewski, they reached a breakthrough in cracking the enigma. If it wasn’t for their breakthroughs, the Allies may not have been able to crack it. Gaining that knowledge may have been the motivation they needed to fully uncover how the Enigma machine works. The Allies were also able to pick up on some keys that Germany’s operators would send. The operators would sometimes pick three consecutive letters from the keyboard which the Allies started picking up on.

Photo credit: "Enigma Machine (Bletchley Park)" by Tim Gage via Flickr CC

Photo credit: "Enigma Machine (Bletchley Park)" by Tim Gage via Flickr CC

Sometimes they would repeat the same keys and therefore the cryptanalysts would be able to predict them. Overall, cracking the Enigma took the efforts and collaboration of many individuals working as a team.

On the Shoulders of Giants

In the beginning of World War II, Great Britain was under less threat from the ever-expanding German forces on the European continent. Poland, on the other hand, was sandwiched between the Soviet Union to the east and rapidly encroaching Nazi armies to the west. Under the pressure of otherwise being forced under Nazi rule, the Polish cipher bureau made incredible headway in analysis of early German Enigma intercepts.

Bletchley Park Bombe

"Bletchley Park Bombe"
Photo by Antoine Taveneaux- Licensed under Public Domain by Wikipedia Commons

When Great Britain’s ships were attacked by German subs, a greater need to decipher Enigma arose. What was perhaps the most important contribution to British cryptanalysts’ efforts was the fact that they were able to build upon the Polish cryptanalysts’ work. Without those insights, the analysts at Bletchley Park might never have developed a full image of how the Enigma machine worked. Or rather, they might not have fully understood the weaknesses of the cipher (as well as its operators). For example, the Polish cipher bureau supplied copies of the military models of the Enigma machines to the British and French, and also provided the operator procedures that were in use at the time. This allowed groups like Bletchley Park’s Hut 6 to focus on finding a way to crack Enigma without the use of fragments such as the six-letter message key repeats at the beginning of every message. Additionally, the cryptological bombe that Alan Turing developed was based on a model designed by Polish cryptoanalyst Marian Rejewski, mechanizing the process of working out daily message keys.

Through collaboration and the ability to build upon the work of earlier cryptanalysts, the British were able to break the Enigma cipher. Not only did this save Allied lives and make victory much easier, but also the decryption shortened World War II in Europe and saved the lives of many in the Axis states who would have otherwise been killed in the longer fighting.

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