The History and Mathematics of Codes and Code Breaking

Tag: cryptanalysis (Page 1 of 3)

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.


The Value of Mathematicians as Cryptanalysts

A variety of factors contributed to the Allied cryptanalysts’ success over German cryptographers, including espionage, determination, and cooperation. One main element that contributed to the Allied success was the employment of mathematicians and scientists in their cryptanalyst units. The Polish breakthroughs in cracking Enigma demonstrated the value of mathematicians as codebreakers. Marian Rejewski, the main Polish cryptographer working on cracking Enigma, was a mathematician. Enigma was a highly complex machine requiring much logical and mathematical thinking in order to break it. In Britain, linguists and classicists had always dominated Room 40. The addition of mathematicians and scientists to the team greatly strengthened the unit and brought in a new perspective on how to break the ciphers. Analyzing the ciphers from a mathematical lens provided valuable new insight that was necessary to break the Enigma code.

Alan Turing is known for identifying Enigma’s greatest weakness, which made it possible to crack the Enigma cipher in tough circumstances. He was a master of math, science, and logic. His advanced skills in these areas helped him think through the different layers of Enigma and figure out how to approach and tackle the haunting task of cracking the code. Turing’s unique background in mathematical machines allowed him to create his bombes. These bombes tested Enigma settings much faster than they could be tested by hand. Without mathematicians like Turing, who could conceptualize and build such machines, it’s possible that Allied cryptanalyst units would never have broken the Enigma machine ciphers.

Nowadays, when I think of a modern cryptographer, the first thing that pops into my mind is a mathematician. However, a cryptographer has to be fluent in a variety of subjects, including mathematics, science, logic, and linguistics. The ability to integrate knowledge from diverse fields when attacking a cipher is what makes an exceptional cryptographer. Although the Germans’ overconfidence in the strength of Enigma played a significant role in the success of the Allied cryptanalyst efforts, many other factors were instrumental in the cryptanalysis as well. The realization that mathematicians could be important additions to cryptanalytic staffs was vital to the Allied cryptanalysts’ successes over German cryptographers.

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Cryptographic Creativity

What I was struck most by throughout Ms. Dunin's talk was the fact that she had such a vast amount of knowledge in such a wide array of categories. She is not only an expert code breaker, but a professional code maker. She talked about her experience in the gaming industry, her understanding of steganography, and her world travels to find different pieces of cryptographic artwork. Her work experience includes not only authoring books in the above categories, but also time spent stationed in California (to which I take a particular interest) in the US Air Force. Her website brags about her personal accomplishments including her ability to speak numerous languages - which probably was supplemented by her travels to every continent. On top of all of that, she is an official administrator on Wikipedia, with over 69,000 edits.

While perusing her credentials, I was astonished by the incredible breadth of her experience. How could one woman have time for all of these things? On top of all that, where did she find time to learn about cryptography. The more I thought about it, however, I realized that her cryptographic knowledge didn't happen in spite of her educational life experience; rather the vast array of skills that she has acquired throughout her life is, more likely than not, directly correlated to her ability to decipher so adeptly.

We have talked in class numerous times about the skills that are most important in code breaking. Is it luck? Creativity? Logic? We also know from our reading that the most successful codebreaking happened when people from many different disciplines have come together to perform great feats of cryptanalysis with their combined skills. Elonka has a background in code making, a largely math based profession. She also is adept at linguistics, obvious from her ability to speak so many languages. She has had the opportunity to glean knowledge from every corner of the internet during her time at PhrekNIC and as a Wikipedia administrator. She is, undoubtedly, in the position to be the most qualified of cryptanalysts.

Elonka has accomplished incredible things during her career as a cryptanalyst. She described in class how she casually jumped into codebreaking at a conference, and then let it become a large part of her life. Is this surprising? No, rather it is inspiring. The study of cryptography is not limited. In its purest form, it is all inclusive.


Sacrifice Few to Save Many

It is extremely hard to discern whether or not Admiral Hall's decision to withhold the information contained in the Zimmerman Telegram from America is ethical or not. At first, it seems selfish to let Americans die because they are blind to the Germany and its allies' aggression towards them, especially from an American's perspective just so Britain can maintain the secret that they can decode German messages. But, sometimes I believe it is ethical to sacrifice the lives of a few to save the many. If it were not for Britain's strategic move to steal the unencrypted message that the President of Mexico received in order to conceal their cryptanalysis breakthrough, Germany may have created a different, more secure code that could have prolonged the war. This prolonging of the war would have ultimately led to more death than if Britain hid the fact that they were able to break Germany's code and use it to their advantage in thwarting Germany's advances. As an American, it is hard to accept the fact that Britain had the technology at its disposal to save some American lives during the war, but you have to look at the long term effects. Saving those American lives could have easily prolonged the war and costed the Allies many more fatalities, so I believe Britain made its decision based on the greater good of the Allies and made the ethical choice.


Ethically Relying on the Unknown

I believe that, just like beauty, ethics are in the eye of the beholder. Whether or not one finds a decision ethical arguably depends more on one’s own upbringing and personal experiences than the action itself. The wide variety of cultural responses to issues such as abortion, the death penalty, and civil liberties exemplifies the inconsistency between our perceptions of morality. Ethics often lack one right or wrong answer and instead simply show how actions can align, or not align, with one’s beliefs.

When Admiral William Hall decided not to tell President Woodrow Wilson about the immense progress of Britain cryptanalysts, he was making a decision for the future of his own country. Although the telegraph showed signs of American danger, Hall was instead thinking of the potential lives he would save by withholding the information. By letting the Germans know that their code had been broken, the British would be unable to prevent future, possibly greater attacks on both their allies and their own country.

Although both risky and difficult, Hall did what he believed was best in the long run. While he was uncertain that more attacks would be revealed through cryptanalyzing German telegraphs, he truly thought that saving the lives of those in future warfare was the right decision. Ethically, I agree with Hall. Although he withheld information that would have helped his allies, he was focused on doing what he believed would help the most people over time. Hall himself was not putting the Americans in danger; he simply did not act upon the information given. If he had shared Britain’s knowledge, he would have given away an advantage that could ultimately win them the war. While Hall’s decision was a difficult one, his intentions were ethical as he believed the withheld information would best help both countries in the end.

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A Developing Familiarity Throughout History

Fundamental development in the disciplinary topics of mathematics, statistics, and linguistics was procured from a comparative ground-level hundreds of years ago as opposed to what we have unearthed today. The advantages and resources currently available to the vast public are, of course, the most they have ever been in history. This goes without saying. "Discovering" tactics to break codes and ciphers that were once considered the most advanced techniques by exceptional cryptanalysts is certainly not as easy a task without the long history of code breaking (in the colloquial meaning of the term) that had come before us.

The ability to learn methods such as frequency analysis from a quick Google search is much less arduous a task than inventing them without any previous notion of such a possibility. Even assuming that today's amateur cryptanalysts aren't explicitly searching "how to's" from public databases, the idea of frequency analysis and any analogous general form of use is very comfortable and familiar. Perhaps teachers from grade school distributed puzzles aimed to unscramble words and phrases or your classmate used a simple cipher as a way to ask out their prom date. Experiencing or seeing a number of similar events throughout our lives inevitably ingrains the technique somewhere in the back of our minds, at least implicitly.

Noting the above, it is truly incredible to acknowledge how commonplace once incredible and cutting-edge discoveries are considered in the present day. This will always be observed, even beyond subjects regarding cryptography, as a natural progression of time.

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.

Cryptographic Darwinism

In the prologue of The Code Book, Singh introduced the “evolution of codes” and explained how codes are becoming more impactful in today’s society (Singh xiv). From encrypting simple user passcodes to concealing entire online databases, cryptographic methods are evidently becoming more and more widespread.

Along with the evolution of codes, we can also see an explosive evolution in technology and similarly in the media, which is one of the vital reasons why so many people, despite their lack of training in cryptanalysis, are able to utilize frequency analysis to solve substitution ciphers. For example, the many online resources that teach people about cryptography are easily more accessible today than they were decades ago.

Furthermore, considering the long history of cryptography, it is no surprise that methods of substitution cyphers, especially those that are elementary, are made public and passed on from generation to generation, and thus has become common knowledge to even the amateur cryptanalyst. Take The Code Book itself as an example; anyone who reads the book is exposed to, at the very least, the most basic frequency analysis approach in solving substitution cyphers. They can even be completely oblivious to what cryptography was before reading the book, but by simply comprehending the first chapter, the person has enough knowledge to create and solve simple substitution ciphers. Of course, the degree to how complex the ciphers they’ve created or can solve is probably not as high as what an expert cryptanalyst can achieve.

Nonetheless, the technology today allows even amateurs to be able to solve substitution ciphers despite their lack of a “sufficiently sophisticated level of scholarship” (Singh 15).

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