The History and Mathematics of Codes and Code Breaking

Tag: scholarship

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.

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.


Cryptography in History

After our discussion in class on chapter 1 of The Code Book, I was able to look at the history of cryptography with a new perspective. It was interesting to read about how a society would not be able to decipher the codes until it reached a certain level of scholarship which accounted for linguistics, statistics, etc. I didn’t consider the fact that one would need a strong background in several disciplines in order to contribute to the field of cryptanalysis with creativity and great insight. It makes sense that one would especially need a strong background in linguistics to be able to make connections in a grammatical sense and across various languages when deciphering a code. Another thing I learned is that since not everyone was literate at the time, only the wealthy, who had the privilege of a getting an education, were able to use cryptography. Of course, individuals in a position of power would be the ones to have important information they would want to encrypt. The common man at that time would not even need to use cryptography for day to day needs. The most important lesson from the book was that no encryption is better than a weak one. I would suggest that no matter how confident you are in your encryption, you should always be discrete with the information you share.

Blog Assignment 1: Cryptography and Scholarship

During the class discussion of Singh Chapter 1, we talked about how cryptography and cryptanalysis has developed as societies have advanced. Singh states that “Cryptanalysis could not be invented until a society had reached a sufficiently sophisticated level of scholarship in several disciplines, including mathematics, statistics, and linguistics.” Looking back, many of the ciphers once used to encrypt sensitive political messages now seem dangerously insecure. However, at the time they were unbreakable, or nearly so.

An example of this change in thinking can be seen in the way that many children pass secret messages to their friends. Although they may not know the technical name for it, they are able to understand and use a shift cipher—the sort of cipher once used by rulers and generals—even at a young age. Once they get a bit older, they are able to crack one of these ciphers fairly easily too, as our class saw from the first cryptanalysis worksheet. The reason for this is not that kids today are somehow all being born smarter. The difference is that the “scholarship” once available only to the elite has become much more ingrained in our culture. This seems obvious once you mention it, but in fact it can sometimes be overlooked, and it’s something that should be kept in mind when studying cryptography’s history.


The Appreciation of Scholarship

In chapter one of The Code Book, author Simon Singh argues that it requires a “sufficiently sophisticated level of scholarship in several disciplines,” such as Linguistics, Statistics and Mathematics, to arrive at the Frequency Analysis method in decrypting substitution ciphers. Opponents of this argument contend that mere amateurs are now intuitively using this technique, and that this is evidence against such a claim.
As Dr. Bruff has previously mentioned in class, the very popular daytime game show, “Wheel of Fortune,” is perhaps a child’s first introduction to Frequency Analysis. He/she would sit in front of the TV and enthusiastically attempt to solve the puzzle. Eventually, he/she realizes that there is a common pattern and that certain letters appear more often than others, thus effectively employing the Frequency Analysis technique. At this point, it is important to ask ourselves: does the fact that children can perform Frequency Analysis make this method any less sophisticated? The answer is no.
The simplest way to demonstrate this is by drawing an analogy. We have all, at one point in time, been in a situation similar to this one: you find yourself struggling with a Biology concept and approach your mother, who happens to be a doctor, for help. Before she goes on to explain it to you, she comments that what you are studying now is what she only began to learn in freshman year of college. Does this mean that the Biology concept has become outdated and is no longer relevant? Certainly not. Medicine and other fields of Biology would not have advanced had it not been for this seemingly trivial concept, and it still required a refined level of thought to arrive at that point. The same applies to Cryptanalysis.
Although Cryptanalysis is quickly advancing and new methods of decrypting ciphers are always being discovered, it is still important to appreciate the initial techniques that led to this progression. Therefore, when we respond to the question of whether or not it required a sophisticated level of scholarship to arrive at the Frequency Analysis method, it is important to value the skill and knowledge it involved and not take it for granted like we do with Biology concepts.

Relative Scholarship

It is not surprising to me that amateur cryptanalysts today often use an approach like frequency analysis to solve substitution ciphers without any prior training, while Singh states that a certain level of ‘scholarship’ was required for such a skill. The term scholarship is relative. This level of scholarship that Singh speaks of is much more prevalent today. Although a person may not be masterful in linguistics or statistics, he or she has most likely learned the basics through his or her childhood. The logic and problem solving techniques that set the foundation for deciphering are installed into the minds of children today at a very young age, whether it is through scholastic activities or thought provoking games. Additionally, one should keep in mind the differing levels of intellect altogether. To compare our society to one 500+ years ago is simply unfair. The level of knowledge today throughout all of society is at a significantly higher level than that of an ancient civilization. Another important factor is the overwhelming presence of technology today. Commonly used tools today, like cell phones and computers, require fundamental skills to properly navigate through them. The fact that children are able to correctly use sophisticated technology, sometimes to a greater degree than their parents, demonstrates the rising standard of knowledge for children.

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