The History and Mathematics of Codes and Code Breaking

Tag: Singh (Page 1 of 3)

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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Contextual Ethics

Ethics in times of war must be thought of differently from ethics in times of peace, however much we may want it to be otherwise. The focus of ethics during wartimes turns to utilitarianism. Utilitarianism is sacrificing the wellbeing of a few for the good of the many. It is “big-picture” thinking, striving to benefit as many people as possible, even if that means a few people must get hurt along the way.

When thought of in that context, Britain’s Admiral Hall’s decision not to tell American President Woodrow Wilson about the Zimmerman telegram makes perfect sense. If he had told President Wilson the contents of the telegram, the Germans would have been alerted to the fact that the British were able to read their messages, and would have changed their codes and created additional obstacles for Britain’s cryptanalysts, potentially costing Allied lives. The danger posed to America by Germany’s U-boat warfare, by comparison, put far less lives at risk, especially because it seemed likely that the United States would enter the war after the beginning of the U-boat attacks.

The reason Admiral Hall’s decision would seem unethical in the context of today is that the major powers of the world have not been involved in a worldwide or home-turf war in some 70 years, since the end of the Second World War. The focus of ethics has shifted from utilitarianism to a more deontological ethical viewpoint. Deontology, contrary to utilitarianism, concentrates on how ethical an action is without consideration for the consequences of the action. In this situation, it would seem Admiral Hall had a moral obligation to inform President Wilson of the Zimmerman telegram, simply because it would be “the right thing to do.” However, when thought of in the context of the First World War, Admiral Hall’s decision to bring the United States into the war in a more roundabout way seems the more logical and ethical choice.

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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.


Changing perspectives on cryptography

It is not surprising that using frequency analysis to solve substitution required a sophisticated level of scholarship in the 9th century. It might take decades of textual study, statistics knowledge and mathematical insights for the Arabian cryptanalysts to successfully find this method. In The Code Book, Singh also suggests that the Muslim civilization provided an ideal cradle because “every Muslim is obliged to pursue knowledge in all its forms” and the scholars “had the time, money and materials required to fulfill their duty.” (Singh 16)

Today’s amateur cryptanalysts seem to still fulfill these “requirements”. Nowadays people with only a few years of education would already have certain level of knowledge in such fields. The resources are so accessible now that they no longer need to be“scholars” but indeed anyone with any intention or interest about cryptography. Undoubtedly only a small amount of people will be trained as professional cryptanalysts, but it’s incredibly easy for anyone to search about cryptography, share thoughts with others about the ciphers they write, or take an online cryptography course.

Today’s generation is a group of people that are taught to solve puzzles when little and raised with films or literature talking about cryptography often in one form or another. With the emerging technologies in hand and a broad access to the subject, people nowadays have entirely new perspective on cryptography. On the other hand, people back in time were strictly limited by the resources they had and the little exposure to the knowledge. Politics might also come into play since a large proportion of citizens interested in inventing or breaking codes might not be the best interest of a monarchical government at that time.

Easier to Learn, or Easier to Access?

I believe that, while a high level of scholarship was required to develop the frequency analysis approach, it is not critical to the use of this approach. When the world was new to this subject--when it had just discovered ciphers and keys and cryptanalysis--all of the knowledge was completely new. It was the cutting edge, so not many people understood it yet. It was essential to attain a high level of education to comprehend the mysteries of cryptology. However, with the modern education system, and modern technology, people have the information necessary more readily available. People can access the "mathematics, statistics, and linguistics" necessary to equip themselves for code making and codebreaking. Also, the easy access means that the information surrounds the human population. We have billions of pieces of data sitting at our fingertips, just waiting in that ever-present "cloud." Because of this access, and as a result of the heightened academic expectations, "amateur" cryptanalysts can use previously lengthy and difficult methods of analysis with much more ease. The civilization has reached a "sufficiently sophisticated level of scholarship in several disciplines," and therefore the people of that civilization may achieve the same accomplishments which the Islamic civilization discovered. However, as a result of the constant inundation of information prevalent in our society, and the resultant size of the body of common knowledge, amateur cryptanalysts can now use approaches such as frequency analysis, which was so arduously sought out, without any formal training.

Ancient Influences On A Modern World

In a world enveloped by constant communication and endless data transfer, the necessity for privacy remains a top priority. With the aid of cryptography, society hopes to maintain secrecy in various interests, ranging from personal matters to governmental espionage. Yet how secure can we ever truly become?

As human civilizations advanced, the intricacies of cryptography drastically changed over time. New solutions resulted in the drive to develop more difficult codes. When discussing cryptography, one must also closely analyze the circumstances surrounding a particular time period. Cryptanalysis methods and current information in one period can quickly become obsolete in only a few decades. Historical events may also cause rapid advances, such as in the Islamic golden age, or slowed progress, such as during the dark ages in Europe.

In The Code Book, Simon Singh notes that "Cryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of scholarship in several disciplines, including mathematics, statistics, and linguistics" (Singh 15). Despite this, amateur cryptanalysts today can easily begin deciphering messages thought impervious in previous times. This can make Singh's statement seem contradictory, as these individuals develop the same approach as previous crpytanalysts without being taught.

However, Singh's statement still remains true. Today's individuals enter the world surrounded by a highly sophisticated society, much different than that of the previous societies. Many factors can influence the intellectual capacity of these amateurs, such as income level, access to necessities, or even parental support. Yet one thing remains certain - today's amateurs prove much more equipped to tackle these difficult ciphers than the best of the ancient world. While young students in previous centuries worried immensely over the seemingly constant political warfare, risk of being drafted into the army, or strong possibility of suffering from diseases, today's cryptanalysts can focus their minds strictly on their studies. Thus, despite never having learned about cryptography, the mere rigor and new advances of modern education and technology equips these individuals to quickly process and develop possible solutions to decipher these codes.

Safer From Government With Privacy

In the newer technological age, cryptography is becoming more and more relevant in everyday life. Unfortunately, there is a down side to this increase in technology and encryption. Encryption helps to protect the interests and communications of criminals and terrorism. The goal is to allow the public to enjoy these cryptographic advances with out letting criminals take advantage of them. Unfortunately, this is very difficult and therefore, some people think that the US government should be given wide latitude to use electronic surveillance in the interests of national security, even if this sacrifices some privacy. In reality, the national government will overstep its bounds and take advantage of its surveillance if it has the opportunity.

Photo credit: 'Privacy' by Sean MacEntee. Flickr. Creative Commons.

Photo credit: 'Privacy' by Sean MacEntee. Flickr. Creative Commons.

Singh puts forth the example of wiretapping and the negative consequences of it in the 1960’s. Martin Luther King Jr. was wiretapped and recorded telling bawdy stories. These stories were then played in front of President Johnson and organizations that were debating supporting him. Other stories included President Kennedy wiretapping senators with the concern that they were being bribed. Although it was later determined that the senators were not being bribed, Kennedy was provided with valuable political information to win the bill. Not only does this prove that recording private conversations, whether its over the phone or via the internet, is unethical, it also shows that there is no moral way to trust a government with this power.

There's No "I" in "Team"

Photo credit: "Share" by AJ Cann via Flickr CC

Photo credit: "Share" by AJ Cann via Flickr CC

A key factor to Bletchley Park's success was the collaborative efforts that were used in order to crack Enigma time and time again. After reading Singh's chapter in The Code Book that discussed Bletchley Park, one might get the idea that Alan Turing was the key to the Allied success. Alan Turing was, no doubt, a key player in the cryptanalysis that led to the Allied success. However, there were thousands of other men and women that aided in the breaking of Enigma and deciphering German messages.

One image that stands out to me that Singh wrote of were the huts in Bletchley Park. Singh illustrates these huts as hubs of collaboration between some of the brightest minds in their given field. If a cryptanalyst was working on a cipher or encrypted message and was stumped, he would pass it to another cryptanalyst. A single message could make its way around the hut numerous times, with each cryptanalyst getting one step closer to the solution until it was solved.

Within each hut there was a clear sense of teamwork, but from hut to hut there was a similar sense as well. Each hut had a specific purpose, so once one hut had done its job with a message, it would be handed over to the next hut for the next step. This ensured that each member of Bletchley Park was doing what he or she thrived at, leading to maximized efficiency as well as an overwhelming necessity and use of communication and teamwork.

German Confidence Proves Costly

After early domination of the seas by German U-boats, Bletchley desperately needed to end the intelligence blackout. Through a series of dangerous raids on German U-boats, a German Naval codebook was captured, thus making the Naval Enigma transparent. Finally, Ally convoys could evade the deadly German vessels and British destroyers could

"German U-boat" Photo Credit: Joe Neary via Flickr

Photo Credit: "German U-boat" by Joe Neary via Flickr

go on the offensive. The Allied powers went to great lengths to not raise suspicion in Germany that their sacred Enigma machine was compromised. Fortunately for Bletchley, Germans were far too confident in the strength of their encryptions.

Although the Allies were now aware of the locations of numerous U-boats, they had to be careful not to attack all of them because this would warn Germans that they could no longer trust their communications. Therefore, they were careful to prudently attack and never risk destroying too many enemy ships at once. In one case, Bletchley became aware of a numerous amount of German tankers and decided to sink most of them, but not all as to not raise suspicion. The British destroyers successfully sank the ones they were supposed to, but then spotted the remaining German supply ships and sunk those as well because they did not know about this situation. Fortunately for the Allies, when the Germans realized about their lost ships, they thought of it as a misfortune because their Enigma was unbreakable. If the Germans had had less confidence in their encryptions, it is possible that they could have stopped the amount of information they were feeding the Allies, or even have used it against them.

Agony columns the old version of love notes

There was increased interest in cryptography and this interest still persists today. Part of the drive in this interest was the telegraph. This is due to the need to protect and hide personal or private information that would be sent over the telegraph. An example of the increased awareness and use of encryption was shown in the “agony columns” in some newspapers. Forbidden lovers used these columns quite often during the Victorian era in England. This greatly reminds me of Romeo and Juliet except quite a long time later. This would have been a more efficient and safe way of communicating for them but that didn’t happen. These columns did spark the curiosity and interest of cryptanalysis. Because lets be real who wouldn’t want to see the secret messages of forbidden lovers. These columns would be like Victorian reality TV for those who decipher the codes. Lovers did not only use these columns, they were also used to create challenging ciphers for others to solve. I guess people would do this just for funsies since there is probably nothing else do in the Victorian era. These columns were also used to criticize political figures. During this era, speaking out against public officials was greatly frowned upon so this was a way to get some freedom of expression.

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