Cryptography

The History and Mathematics of Codes and Code Breaking

Tag: frequency analysis

Cryptanalysis Evolving Over Time

In Simon Singh’s book, The Code Book, it is expressed 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.” I think this is a very true statement because cryptanalysis involves a level of mathematics and linguistics that wasn’t readily available to many people in early civilizations. The argument that amateur cryptanalysts intuitively use frequency analysis on substitution ciphers and therefore a level of scholarship isn’t needed to solve ciphers is truly invalid in my mind. One needs to realize how different modern civilization is compared to the other time periods we are comparing it to. Along with the civilization needing to reach certain levels of scholarship in mathematics, statistics, and linguistics, they also needed to have to time, energy, and willpower to sit down and try to solve ciphers. In the time of Queen Elizabeth and Queen Mary, the normal folk were illiterate and were working very hard to just have enough food to survive. If they came across a note that looked like a code, they first of all wouldn’t have enough leisure time to try to break the code if they wanted to and they also wouldn’t be literate so they wouldn’t even know where to begin.

In conclusion, the level of education in the modern era is light years ahead of what it was many hundred years ago. One example I heard in class that made it very clear to me was that a hundred years ago, a scholar that was very specialized and on a career path towards engineering or something like that would be the only person who would even considering studying physics. In today’s world, almost every high school graduate has taken a full course in physics.

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.

Cryptanalysis and Critical Thinking

Certainly, the level of scholarship experienced today is far more advanced than that of the past. Each day, each hour, each second advances are made that further expand the breadth of human knowledge; however, this knowledge stands on multiple foundations of  understood ideas,  preconceived notions, and intuitive reasoning. Cryptanalysis today can be accomplished by those of relatively common education because of the foundations set by previous eras. Thus, as Singh describes, civilizations in the past required more time, effort, and education to establish the principles of frequency analysis simply because they had not acquired the foundation of knowledge that is common today. In the era in which frequency analysis was invented, an “educated person” of the society would have the knowledge to read, write, and do arithmetic, and those skills were a great accomplishment for that era. Yet today eight-year-olds throughout the world have already acquired those skills, along with ways to collaborate with others, communicate effectively, and think critically. This advancement was only possible with a strong foundation of knowledge.

Critical thinking skills also allow ordinary cryptanalysts to intuitively use frequency analysis without training. Today’s constantly shifting society forces each person in it to think critically every day. From the rate that technology is advancing to daily medicinal miracles to constant national turmoils, each day provides an opportunity to create something new, something more effective, something no one else could conceive. In this modern society, critical thinking is vital to survival. Conversely, in the years in which frequency analysis was invented, civilizations expanded at a much slower rate, and thus critical thinking at the rate at which it occurs today was much less prevalent in earlier populations.

Frequency Analysis in a Temporal Context

Today even amateurs, given time, are intuitively predisposed to recognize otherwise “logical” patterns strewn in ciphers and codes alike. This is due to the fact that analytic methods now utilized in the realm of cryptanalysis are not products of innate understanding, but a general improvement of societal and formal education as a whole. Frequency analysis today, for example, proves a fundamental and rather elementary conceptual strategy in decrypting an enciphered message. In the wake of cryptanalysis, however, frequency analysis was a novel and unprecedented notion.

During much of cryptanalysis’ infancy, education was a luxury, largely unattainable to the masses of commoners who preoccupied themselves with self-sustaining labors specialized in practicality rather than subjects of intellect. Such individuals would find themselves entirely dumbfounded by the prospect of solving even the simplest encryptions, provided they harbor any extent of literacy. This approach accounts for the inability of the uneducated to resort to frequency analysis, thus furthering Singh’s argument. On the other end of the societal spectrum, scholars managed to stumble upon the prospect of frequency analysis – but only after a considerable amount of time and inquiry. Singh’s argument again proves sound, for frequency analysis incorporates mathematics, statistics and linguistics, itself being a development in all three fields. Therefore, it seems that “a sophisticated level of scholarship” was indeed necessary to consider frequency analysis as a viable approach for solving substitution ciphers – back then. In a temporal context, perhaps a “sophisticated level of scholarship” is not termed appropriately for the overstatement that it is. Amateur cryptanalysts, along with much of the developed world, have likely received a formal education, in which they have been exposed to the very areas of “expertise” incorporated in frequency analysis. Societal exposure similarly promotes the deciphering technique, the best example of which remains “Wheel of Fortune,” which automatically assumes the most frequently repeating English letters as common knowledge amongst contestants. Moreover, modern society in general places great emphasis on cognitive reasoning from infancy to adulthood, surely fueling the tendency to apply frequency analysis by even the most amateur of cryptanalysts.

In hindsight, the development of frequency analysis was indeed a feat of innovative intellect. Today, however, it seems only a natural inclination to attempt such a logical and practical method of deciphering.

The Ever Advancing Society

As an educated young woman in the year 2012, frequency analysis is not a hard concept to grasp. Using it as an aid to breaking ciphers, I apply fundamental knowledge to assess the frequency of certain letters and letter combinations in any given ciphertext. Because I have been reading and writing for over ten years, there is no need to be taught what letters or word combinations occur more often than others, but rather I have the ability to approach the ciphertext on my own. Back in the old days, the ubiquity of education was not as vast, thus citizens would need to be taught the theory of frequency analysis. Because most people worked on the farm and had little time to learn, scholars and highly educated people were the only ones exposed to the idea. It is interesting how these scholars would have to be thoroughly taught math, statistics, and linguistics in order to grasp the idea of frequency analysis, whereas amateurs today can use basic, elementary school logic to decipher a simple code. The fact that young people today can decipher a code using frequency analysis, without having been taught this approach (like we did in class on the first day), highlights just how advanced our society has become.

Problem Solving: Then and Now

Whether it’s Baby Einstein, Sesame Street, or even iPad apps, kids today begin problem solving at an extremely early age. They continue problem solving as they grow older, solving math problems, logic puzzles, and other intellectually stimulating activities. In contrast, when frequency analysis was first “invented,” only scholars had access to the academic resources and problem solving skills that a teenager would have in today’s time. In my opinion, the idea of frequency analysis is easy to think of once one has the ability to actually perform frequency analysis. The reason frequency analysis may have been so obscure is because there were significantly fewer people with the required level of mathematical ability. But by today’s standards, this level of ability might equate to that of a middle school student. This disparity of knowledge attests to the intellectual progress that our society has achieved over these many centuries.

Similar to most innovations, frequency analysis developed out of necessity. Only scholars thought of frequency analysis because they were the ones breaking ciphers for powerful men and women. The average amateur cryptanalyst in the present time will also be in a situation where he or she wants to decipher a text (with much lower stakes). To help them break the cipher, both history’s scholar and today’s amateur might use frequency analysis; the intellectual leap is fairly simple. The major challenge of inventing frequency analysis centuries ago was reaching the point of having the knowledge to think of this technique. Singh described the minimum level of scholarship required for cryptanalysis as “sufficiently sophisticated.” In today’s context, that same level of scholarship would best be described as sufficient – for a 12 year old.

Image: “Rubik’s Cube”, by me

Frequency Analysis Utilized by Amateurs

When Al-Kindi first developed cryptanalysis it was groundbreaking and highly advanced for his society. Today, our society is highly intellectual and focuses on stimulating problem solving abilities in young children. With the knowledge of frequency analysis, many amateur cryptanalysts can easily employ the method to successfully decrypt text.

Society today is exposed to these necessary skills early on in development. The idea of using logic to solve puzzles, riddles and other games is common starting at a very young age. What may have been considered a significant level of scholarship when cryptanalysis was first invented is now merely accounted for as common sense.

Early on in the history of cryptography people were not accustomed to the idea of codes and secret messages. This concept was so foreign that they could not begin to understand how to solve them or decrypt them. No one paid attention to what common letters were or which letters were most frequently used in their language. Today, with basic reading and common experiences such as watching word guessing game shows, people subconsciously take note of what letters most often appear in words. When an amateur cryptanalyst approaches an encrypted message they instinctively look to substitute in “e”, “t”, or “a” for example, knowing these letters form many common words. In the past, this knowledge was not considered basic knowledge and people were unaware of this crucial information. Armed with the knowledge of frequency analysis and the logical thinking our society breeds, amateur cryptanalysts can easily use frequency analysis without prior training.

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