Cryptography

The History and Mathematics of Codes and Code Breaking

Tag: education

Not So Easy Anymore

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On September 18, 2019

In Student Posts

In the previous chapter of The Code Book, Singh discussed cryptography during the time of Mary Queen of Scotts. During her time, cryptographers needed to be highly skilled and educated people who spent time dedicating themselves to the art of code breaking. The average person could not decipher encrypted messages. As I mentioned in an earlier blog post, the education level of the average person was very low. An educated person was one who was extremely privileged. Because of this, certain ciphers used during the time were generally not difficult to decode, but still required a specialist.

Cryptography became more widely used after Mary Queen of Scots, which meant that more and more people were learning the art of reading cipher text. Because of this, a more complicated form of cryptography needed to be created. Fortunately, Vigenere cipher was in the process of being perfected. Vingenere ciphers uses two or more alphabets instead of one, meaning each letter is equivalent to two (or more) cipher letters. This substitution cipher could be extremely confusing, which is why keywords were used to assist in discovering the alphabet. The addition of keywords made it so that only the people who had communicated with the author of the text had access to its cipher alphabets. 

 

Cryptography in the Modern World: Keeping a Information Secret in the Age of Computing

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On August 26, 2018

In Student Posts

In the first chapter, the examples of cryptography Singh selected were confined to the upper echelons of society: nobles, scholars, religious and military leaders. But perhaps more telling is the affluence of cryptanalysts such as Thomas Phelippes, a linguist fluent in five languages and an accomplished code-breaker; knowing five languages is a feat even in the modern world, but acquiring a new language (much less five) prior to readily accessible educational resources is nothing short of extraordinary.

Phelippes’ impressive education supports the hypothesis that cryptography and cryptanalysis are areas of study suitable for only those who have a sufficient understanding of an array of scholarly disciplines and the resources necessary to achieve it. This is perhaps more true of today’s world, as modern ciphers and cryptographic techniques are far more complex and difficult to crack than simple substitution ciphers and thus require and even more comprehensive education than was necessary centuries ago.

Fortunately, modern society provides us with the ability to attain a level of education sufficient for developing and cracking substitution ciphers by the time we graduate high school; even people who have no formal training in cryptography are capable of employing advanced classical techniques such as frequency analysis to decrypt secret messages. The ubiquity of this approach is a testament to the modern educational system’s ability to produce people capable of thinking creatively to solve new problems.

However, this amount of ingenuity entails a notable problem: it essentially renders substitution ciphers (and other ciphers with similar security levels) useless. If an enciphered message can be cracked by the average person (without the aid of a computer) in the matter of hours, a more secure method of encrypting messages is necessary to hide meaning. Although relatively secure encryption usually doesn’t present much difficulty thanks to the advent of computing, it makes securely encrypting a message or quickly decrpyting a secure message without a computer nearly impossible; furthermore, with the power of modern computing at their fingertips, cryptanalysis are constantly working to develop faster ways to decrypt information, rendering insecure techniques that were among the best we had discovered just decades earlier. Modern cryptographers are then presented with a unique challenge: creating systems of encryption that allow the intended recipient to receive the message but are strong enough to remain unbreakable for decades to come.

The Correlation Between Technology and Self-Taught Cryptography

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On August 31, 2015

In Student Posts

When the frequency analysis first emerged as a tool to decrypt substitution cyphers, it was the epitome of modern technology at the time.  Under the growing Islamic rule of the Arab nations there was, for the first time in history, the opportunity for the collection of mass amounts of diverse knowledge in one place and one time. Revolutionary at the time, in modern society this same concept of data collection is relatively commonplace. Worldwide schooling systems teach the basics of linguistics, mathematics, and statistics to children from young ages, giving them the platform upon which it is easier to compute the complicated nature of cryptography. Even more recently, information of all types has become increasingly available to any who have access to the internet. A place for data collection and collaboration of thought like no where else, the internet has revolutionized cryptography once again. No longer is a formal education entirely necessary to access the tools needed to decipher codes. One can simply study complex theories of statistical analysis taught to them through Yahoo Answers, or watch explanations of multivariable calculus on YouTube. While information is still being gathered, just as it was in ancient Arab nations, it is no longer limited to a single society, or even to formal education. There is no reason to say that the modern codebreaker is somehow inherently more adept at decryption; rather the skills which are needed to decrypt are accessible without advanced study.  Thanks to the internet, the only requirement in cryptography is the desire to seek out the tools necessary to decrypt.

Evolution of Knowledge

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On August 30, 2015

In Student Posts

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.

A Peek into Cryptography

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On August 27, 2014

In Student Posts

It’s confession time. I did not know much, if anything, about cryptography when enrolling in this class. With this lack of a background, what we read in Singh and the content that we later discussed in class were extremely fascinating to me since I hadn’t had much previous exposure to the topic.

One topic that we discussed further in class was the resources that are needed in a society in order for cryptography to be present and flourish. As societies advance mathematically, statistically, and linguistically, skills in those areas tend to be ingrained in the population of that society. As we sat down in class on the first day, we were able to figure out the cypher alphabet and then decode a message. If you had put that same coded message in front of kids our age 600 years ago, there’s not a doubt in my mind that they would struggle with it much more than we did.

While we automatically have a leg up due to our advanced society, another resource would have allowed someone our age to decode the message 600 years ago. This resource is of course the funds that would have provided an education to make up for the lack of societal knowledge. I thought it was really interesting to note how money could give you what would be more readily available in the future, just like most other commodities.

Blog Assignment #1: Security and Civilization

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On August 26, 2014

In Student Posts

In Chapter 1 of The Code Book Singh discusses the overarching issues that Mary Queen of Scots faced during and leading up to the trial for her execution. What I found most interesting, and enlightening, about the chapter were the circumstances surrounding Mary’s incrimination, and our subsequent discussion about security. I’d previously thought of codes as a fairly surefire way to communicate important information, but Mary obviously did too, and that did not turn out well for her! She was too confident in her codes, and also in the people who were helping her to communicate them. Our discussion was eye-opening in terms of thinking about doubting the codes one writes. If someone is too confident in his or her codes, he or she won’t take any more precautions, such as using vague or roundabout speech, to ensure the secrecy of a course of action, and one’s freedom from incrimination.

I also thought it was particularly interesting to discuss the implications of the development of a society as a whole on the ability of individuals to use deciphering techniques without any previous training. Children in our generation and younger use codes to gossip, and send each other messages they don’t want everyone to see. Problem solving is taught in most disciplines in schools, and children are taught to apply these techniques to everyday life, which makes amateur code breaking easier without any instruction. Since our society has achieved a particular level of sophistication in varied subjects, we are all ingrained with the basic tools to use deciphering techniques, including the ability to read, which was not widespread back in the time of Mary Queen of Scots. Techniques that seem obvious to a student today would be quite the discovery for professional cryptanalysts hundreds of years ago.

The Ease of Encryption

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On September 4, 2012

In Student Posts

Cryptanalysis has changed greatly over history in terms of difficulty and ability to be solved.  According to Simon Singh “Cryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of scholarship…” This is the case for two reasons: first, a civilization would need to have a very standardized written communication system before cyphering would even be necessary, as there is no practicality in encrypting a written language that no one understands to begin with.  Second, as written languages began to become standardized, the lack of popular education in reading and writing, left cryptography to the only greatest scholars.  Substitution cyphers could be relatively simple and still effectively conceal a message.

 

As education became more common, cyphers would need to be much more complex as more people could work on successfully decrypting.  More modernly, as education has hit new levels along with the emphasis on critical thinking, a simple substitution cypher could be analyzed for common frequency patterns easily broken by a group of college freshmen (THAT’S US!).

 

Additionally, with the development of computers, new heights of complexity are introduced to cryptography.  A simple common device such as a cell phone uses complex encryption that can ensure privacy for simple text messages, to creating secure lines for bank transactions.  Not only have the creation of codes been revolutionized by computers, but the decryption of them have been improved just as much.  Even complex substitution cyphers that would have left scholars thinking for days could be broken in seconds.

 

It is amazing how we take the complexity and convenience of encryption for granted as others in the past labored greatly to make a fraction of that security possible.

Frequency Analysis in a Temporal Context

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On September 3, 2012

In Student Posts

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.

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