The History and Mathematics of Codes and Code Breaking

Tag: knowledge

It's What We Make of It

For this blog post I would like to introduce a rather grim prospect that I’ve been pondering about the human knowledge threshold. I was reminded of the thought after reading Marcus’ discussion on how we can wield computers and other tools of such sophistication and power with just a few “lines of code” (Doctorow 119).

The idea starts out with the outlook that humankind will continue to accumulate more and more knowledge as long as we exist, be it from discoveries in the natural world or learning it from the complex information systems that others create (ex: designing and keeping up with the expansion of the internet).

Particularly in the scientific fields, as we continue to acquire more information, we will eventually reach a point of information overload. What I mean by that is, maybe in a few centuries from now, even if someone were to start learning and specializing in one specific field from the youngest age possible, it would take them more than a lifetime to learn the information already known in that subject.

Needless to say, further expansion of knowledge within that field may be impossible to achieve by studying, which grants the scholar the awful prospect that all work that is physically possible to do in a lifetime has already been done, and a sense of futility in pursuing further scholarship in that field for greater knowledge. However, one can argue that the introduction of computers that can process all the information and sustain a method of inquiry may be able to replace us and surpass the knowledge threshold we may have.

After all, the components of such “complicated machines” have been “microminiaturized” so that “billions” of parts can now fit within the “machines,” making them more efficient overall (Doctorow 119). So who’s to say we can’t further miniaturize and compact existing computers so that they are more efficient, resulting in the possibility of synthetically attaining knowledge above a human’s threshold?

We can imagine endless possibilities as arguments against this prospect of the human knowledge threshold, and counterarguments against those arguments, but the more we try to solve this information overload, the more complex our understanding of the world becomes, the greater our fall is…when, let’s say, a terrorist group wipes out all electronic data in the world. How do we advance our quest for knowledge then?

Maybe Darwinism will have an answer for our intellectual threshold.


An additional note: the above prospect is really more focused on fields that are more scientific in nature, and that demand expansion off already existing knowledge. Thus, we will never see a “knowledge threshold” in the arts, for creativity is boundless.


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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.


Evolution of Knowledge

Isn't it strange to think that modern high schoolers undoubtedly know more about mathematics and various disciplines of sciences than ancient or even not so ancient scientists who devoted their entire lives to certain subjects? I mean, if you think about it, it's not too ludicrous. They definitely have a greater grasp on mathematics than, say, Pythagoras, who's crown jewel of a discovery is currently being taught to 6th graders around the world. Take Isaac Newton, for example, a man who appears in textbook after textbook as the late-renaissance wonder man who invented integral and differentiable calculus. He discovered the basics for physics, including the laws of motion, gravity, and optics. However, they are exactly that, the basics. Now, do not think I am bashing Newton by any means. Nor am I saying that high schoolers know all that he knew or are more intelligent than him. He is possibly the greatest thinker in the history of man; however, modern education has advanced so much so that today's teenagers now take the knowledge that past scientists and mathematicians spent their lives discovering for granted. More and more advanced knowledge and problem solving skills are being exposed to a younger and younger audience in today's education system. That is not to say that past "ground breaking" discoveries were by any means easy. It was no more easy than a scientist today discovering the secrets to the quantum world.

Because of this, it is no surprise that seeming "amateurs" use frequency analysis and other cryptanalysis strategies that took centuries to develop. Let's take the credentials of a possible "amateur" cryptanalyst into consideration. He/She probably has some sort of upper level (comparative to a few hundred years ago) mathematic training including calculus and statistics and probably multiple years of taking English courses, all of this learned from high school. According to my previous assertion, wouldn't this count as a "sufficiently sophisticated level of scholarship in several disciplines, including mathematics, statistics, and linguistics" (Singh 15)? I think so.

Standing on the Shoulders of Giants

It is curious to think of how the world was just one hundred years ago. So many things that are now obvious were unknown or shrouded in mystery. In 1915, barely anything was known about heredity and the cellular functions that were involved in it. Now, we have mapped the entire human genome and can even change DNA. In Newton’s time, gravity was a concept that hadn’t been explored. Now, it is an obvious fact, one that forms the most basic aspect of sciences that have now advanced to ever-increasing complexity. What is gravity when compared to the Higgs boson?

In this same way, the discoveries made by cryptanalysts of centuries past have now become obvious to us. This is by no fault of theirs—without civilization’s ability to analyze statistics and linguistics and apply mathematical concepts, decrypting encrypted messages could never have been attempted.

The thing is, civilization didn’t stop there. It continued to grow and make new discoveries while standing on the foundation laid by its predecessors. Discoveries of algebraic concepts that excited prominent scholars hundreds of years ago are now taught in middle school classes to unappreciative twelve-year-olds. They are no longer new and complicated and exciting, but old news, taken for granted, never thought of unless they are used for the springboard into some novel inquiry.

Another aspect to consider is the advance of technology and information. Doing statistics by hand is a painstaking process that can now easily be bypassed by calculators and software. In addition, so many more people have access to information now than they used to, whether that be in a classroom or on the Internet. Especially when considering the Internet, where any question can be answered easily in a matter of seconds, it is not all that surprising that amateur cryptanalysts can “wing it."

This is not to diminish the strategies implemented by older cryptanalysts. Rather, it is to show how far we have been able to come since their time because of the nature of their discoveries. As Isaac Newton said, "If I have seen further it is only by standing on the shoulders of giants."

The Beginning of an Era of Secrecy

Imagine for a moment that everything you've ever hidden is completely public. Everyone has access to your private emails and your bank account information, among other things. This would be life without cryptography.

Cryptography is hiding the meaning of a message, and it is typically used in most forms of modern communication. In The Code Book, the author, Simon Singh notes that secret writing has been a part of human civilization since the fifth century (Singh 4), but it was widely accepted that the most typically used cipher of ancient times, the substitution cipher (Singh 13), was impossible to crack until the 8th century when the Abbasid caliphate's place as a center of learning allowed it to become the homeplace of cryptanalysis (Singh 16).

Singh defines cryptanalysis as "the science of unscrambling a message without knowledge of the key" (Singh 15). As Singh states on page 15, cryptanalysis was only possible in the beginning due to the Muslim civilization achieving "a level of scholarship in several disciplines, including mathematics, statistics, and linguistics".

The important debate, though, is whether or not this level of scholarship is still necessary in today's society. I am of the opinion that, although our society's era of secrecy necessitated well-trained cryptanalysts, this is no longer the case. As our class demonstrated on only the second day, breaking of the more common codes is fairly simple for most modern humans. The difference, I believe, lies in the fact that in ancient times, education and widespread knowledge had not progressed to the point it has now reached. The internet, as a portal to almost all human knowledge, has made it simple for anyone to pursue any knowledge or expertise that they desire.

Without modern technology, and modern education, I am of the opinion that intense training would still be required to become a cryptanalyst. However, due to our civilization's widespread resources, it has become much easier for individuals to discover and crack codes and ciphers on their own.  Cryptology began as a secretive science, but has become an integral part of modern society, and as such we are all cryptologists in some form or another.

The Evolution of Ciphers and the Human Mind

Over two thousand years ago, Julius Caesar's methods of secret keeping were deemed groundbreaking.  His use of the substitution shift cipher was effective and secure.  Today, however, many would find his seemingly indestructible cipher to be elementary.

Like most human inventions, codes and ciphers have constantly evolved over the years to become more complicated and much more difficult to break.  Because of this advancement, what were once the world's best ciphers and codes thousands of years ago have become simple puzzles that high schoolers, even middle schoolers, can deconstruct.

According to the author of The Code Book, Simon Singh, "[c]ryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of scholarship" (Singh, 15).  The Muslim civilization achieved this heightened academic prowess due to its emphasis on being well-rounded, insightful humans.  Citizens studied a wide range of subjects, "including mathematics, statistics and linguistics" (Singh, 15).  Europeans, conversely, were stuck in the Dark Ages, unable to pursue the high scholastic level of the Islamic civilization.  While the Arabs were creating new ciphers and breaking old ones, Europe was far behind.

The Arabs had a significant advantage over the Europeans due to their overall knowledge of various subjects.  Similarly, humans today have an advantage over the Muslim civilization.  The ciphers that the Arabs were creating and breaking were much simpler than the ciphers are today, and after studying history and learning of ciphers and codes from old times, people today are able to easily decrypt old ciphers and codes.  Presently, individuals do not have to be trained in cryptanalysis because subjects such as mathematics and statistics are available to the average citizen.  Society today focuses almost entirely on “secular subjects” (Singh, 16), which is what led to the success of the Muslims.  People today also have greater opportunities to learn and have learned from history, so we are able to combat difficult problems, specifically ciphers, on our own, using past methodology, logic, creativity, and luck.

The evolution of the cipher is directly connected to the expansion of the human mind.  Substitution ciphers that were used by Julius Caesar are now commonly recognized and easy to decipher.  People today have a much more extensive knowledge of ciphers and codes, making the ciphers and codes easier to figure out.  As humans continue to advance, so will ciphers and codes and the means to breaking them.


Cryptanalysis in time

The level of knowledge required by cryptanalysts to cipher and understand codes has remained relatively the same throughout history. The difference is that this breadth of knowledge is easily developed and acquired in this day in age. Today’s society demands a higher tier of critical thinking in everyday activities due to the advancements in technology and progression of arithmetic and language. An eight year old kid nowadays has the knowledge that a seasoned cryptanalyst had at his disposal long ago. Much like the standard of life, the standard of knowledge has risen exponentially. People involuntarily and unknowingly find themselves in the midst of ciphers and codes every day, therefore peoples’ minds have become conditioned habitually to decode and decipher messages in puzzles and word games.

The knowledge and use of frequency analysis in the alphabet is a more modern practice in cryptanalysis and developed because people are exposed to puzzles, riddles, and word games at an earlier developmental stage. In the end, humans are more frequently immersed in codes and ciphers because of the advancements in thinking and technology. This allows a higher level of cryptanalysis to be performed by ordinary people only due to the fact that they have been subliminally exposed to it their entire lives. People now just have a larger pool of knowledge and experience to pull from, giving them the upper hand in cryptanalysis.

Cumulative Knowledge

There are two different types of scholarship: being able to learn and being able to discover. While almost anyone can be taught to accomplish a task, having the mental power to discover something that no one has ever thought of before takes ingenuity and a willingness to think outside the box that few people posses. Though people now might appear more intelligent than people hundreds of years ago, it is only because they have the resources to a greater wealth of knowledge and facts. This cumulative knowledge is why in the science of cryptanalysis what was once a task to be accomplished only by the finest minds of the age is now completed by common people. This occurs not because humans have evolved to become more intelligent but because it is easier and takes less time for a person to be taught how to do cryptanalysis than to have to discover how to do it. Even people who have not directly been taught to do cryptanalysis have access to a wider breadth of knowledge and experience than their ancient counterparts. Even simple things like being taught to count and recognize patterns helps people now to be able to decrypt things faster than people hundreds of years ago that never had practice in that kind of knowledge. Though humans may have greater access to the cumulative knowledge that we have amassed, it still takes the same amount of effort as before to discover new, never before thought of ideas. This is why, as in ancient times, there are only a handful of true leaders in knowledge but many followers.

Cryptography and the Availability of Information

I think that amateur cryptanalysts using methods that were impossible for some early civilizations to use demonstrates the accessibility and ubiquity of information today. For example, some puzzles are centered around ciphers and decryption. These puzzles attract the attention of novices who have little to no experience in cryptanalysis. Never the less, these amateurs utilize strategies such as frequency analysis and recognition of small or common words (a, the, and) without having ever studied them. Even on our first day of class, we were able to decrypt the cipher text presented to us by using some of these methods. Similarly, we perform other “higher-order” thinking tasks on a daily basis without giving much thought. We type rapidly, blaze the internet, estimate sale prices, and navigate Vanderbilt with (relative) ease. Of course, we utilize technology to make many of these tasks much easier, but we also must know how to use the technology and make it work for us. Thirty years ago, only serious business people and others with special training used computers. Today, most of us carry around a “tiny computer” with us at all times and know how to operate it efficiently. Basically, we do many things today that require skills that we take for granted. At the dawn of cryptanalysis, however, this knowledge simply was not there for all to benefit from. The moral of the story: when your first [insert impossible class name here] test score comes back much, much lower than you had hoped, take pride in knowing that in the Middle Ages, you would be hailed as a genius.

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