Cryptography

The History and Mathematics of Codes and Code Breaking

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Yes, You're Smarter than a(n Ancient) Fifth Grader

The first chapter of Simon Singh’s The Code Book introduces the historical roots of secret writing. Steganography, the practice of hiding the existence of messages, dates as far back as to the Greco-Persian Wars in the fifth century B.C. The practice of cryptography was a novel and unchartered concept for the early Greek, Roman and Chinese civilizations. Over the centuries, military conflicts and the increasing demand for national security begged for the obscuring the meaning of messages. Without knowledge of the key, encrypted messages were effectively indiscernible until the Arab development of cryptanalysis in the first century A.D. During a millennia in which literacy was a luxury of only the aristocracy, only the finest minds were tasked with the creation and cracking of codes.

Modern cryptography, however, takes on a much different form. The current state of science and technology is infinitely more advanced than it was in medieval times, and the invention of the internet has made information vastly more accessible. Amateur cryptanalysts today are capable of employing frequency analysis without having been previously exposed to it because they have knowledge of computing and problem solving unpossessed by the early world’s most brilliant minds. Exposure to modern technology, from encryption used by computers to the teachings of a high school algebra curriculum, means that the codebreakers of today are far more equipped to solve simple codes than their predecessors.

Singh wrote 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.” Ergo, the brightest minds of the early Arabs, in their invention of the practice, proved themselves to have mastered these pillars of scholarship. Each subsequent civilization has had the opportunity to employ and build upon this knowledge; now, almost two thousand years later, even the amateur cryptanalyst is capable of this once ingenious method, which then begs the question, where else will we go from here?

Uncertain Environments Generate Safer Practices

An environment in which one knows he or she must constantly maintain precautions is safer than one where they are unaware of the dangers that potentially exist.  

This concept is exemplified in the case of Mary Queen of Scots by the simple fact that her naive belief that she was speaking in secrecy directly resulted in her death. She essentially signed up for her own funeral by openly disclosing matters of treason. If she had been living in the era in which it was common knowledge that a “codebreaker might intercept and decipher their most precious secrets,” (Singh, p.45) then it is much more likely she would have been less forthcoming with the information she provided in her encrypted messages.

The new environment created was far more advanced than anyone in her time could have predicted. Mary’s generation falls in the era of monoalphabetic substitution, whereas the new age moved on to as many as twenty-six (polyalphabetic). Furthermore, everyone in this new era of cryptography frequently changed their methods. They would not be caught dead using such a basic cipher over a prolonged period of time to transport such crucial information. Even the ciphers used for general business information transported by telegraphs was more secure than the cipher Mary trusted her life with.

The new environment of encryption even allowed for progression in the cryptography field. As ciphers became more complex, more professional codebreakers emerged that continued to prove how difficult it was to create an uncrackable code. In turn, this generated more ciphers and the loop continues from there. Progression did not just make the population more cautious, but it also generated societal growth.

The Dangers of Weak Cryptography

For one who is not well-versed in “cryptography,” hearing the word might simply bring to mind the language game Pig Latin. However, Singh is trying to convey, in layman’s terms, that cryptography is not a child’s game for all; in Mary Queen of Scots’ case, it was literally an instance of life or death. The issue at hand is that while encryption is meant to show that one's guard is up, it actually creates a false sense of security when utilized poorly.

For instance, there has been a time in every person’s life when he or she whispered something to a neighbor in the hopes of keeping the message a secret. Unbeknownst to them, spectators who speak the same language were either able to eavesdrop and hear the secret or possibly even lipread bits and pieces. Yet, to the two that were whispering in their own world, it was as if they had been speaking a foreign language. Babington and Mary were in this same little world, where they had a false sense of reality and security. As Singh stated, this was honestly an unfortunate time for Mary to be communicating through cryptography because the first true cryptanalysts were emerging. The two did little to alter their patterns and believed that only they could read what was intended for one another. The problem is, in an ever-changing world, it is naive to think that one should not have to adapt to remain undiscovered. Like two people whispering, Babington and Mary let their guard down at a critical point of their mission

By trusting her basic encoding system at an essential turning point in the history of cryptanalysis, Mary left herself vulnerable to decryption and was caught openly aligning with the rebels attempting to free her. Had she been writing without encryption, she would not have directly given her blessing for the assassination. Singh wants other cryptographers to be aware that they cannot expect to simply lay encryption over their messages like some form of a safety blanket. If a message is truly meant to be a secret, cryptographers should work to ensure that their ciphers are unbreakable.

Cryptography 1

        As the author of the code book, Simon Singh, writes, "Cryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of scholarship in several disciplines, including mathematics, statistics, and linguistics.” People’s interest and skills toward all kinds of puzzles including cryptogram are getting developed fast in this day or age . Back into my primary school time ,I saw a sukodu puzzle on the newspaper for the first time. The shape and numbers on it suddenly caught my mind. A great sense of proud came to me when I first learnt and finished the puzzle. Puzzles and cryptography, using its own beauty and sense of mystery ,attracted hundreds of thousands of fans all around the world.

       Learning how to solve these kinds of problems is not a specialization nowadays due to the advancement of the Internet and the high level of education. Higher level of education leads to more ways of creative thinking to solve the problems. For amateurs, they don’t necessarily need to learn the special methods in order to solve the basic problems. Their level of education provides them with enough knowledge to use. Such as the most used letter in the english alphabet is e or some of the most frequent conjunctions like at, or, in and so on. Even amateurs can have fun by themselves solving cryptograms, which is significantly different from the old times when people generally don’t know a lot about languages and mathematics. Getting more amateurs working on their own is a great sign, for more and more people are getting involved into cryptography and are willing to dig further.

         Despite the fact that amateurs can have great fun working on their own, Singh was never wrong about the complexity of cryptanalysis that people need to be trained to be sufficient in breaking codes. The methods of transition and substitution or even more complicated methods still needs several disciplines, including mathematics, statistics, and linguistics for perfection.

        In general, it is a great phenomenon to have so many people interested in cryptanalysis and willing to work on their own to solve it. But they still need more practice and more training to go deeper into this area.

Chapter 1 Assignment

In chapter 1 of The Code Book, Singh wrote 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." It is a reasonable comment for the reasons as below.

First of all, only if a civilization has developed mathematical methods can its code makers encrypt codes by using several mathematical algorithm like transposition or substitution. Equally, only if a civilization has developed data analysis can its cryptanalysts know how to use statistics to break codes easier. For example, to collect the frequency of each letter or symbol in a long text can lead to possible correspondence of plains and ciphers. The commonsense for an amateur cryptanalysts today is that the most frequent letter or symbol in a text may link to the character E. Some combination of letters are also critical for statistic analysis like THE or ED. Thus, frequency analysis is one of the most important methods for decryption. Finally, linguistics is also vital for a civilization to invent cryptanalysis because codes and ciphers are not only in English. Many other languages could written by letters in Latin or Spanish. Let alone that some languages can be written by their own characters but their pronunciation can be expressed by letters.

Those knowledges, in the past, are rarely related to civilian so that a cryptanalyst needed training to break codes. However, in the modern educational system, those subjects are parts of the general education that every individual has the chance to learn about some critical methods of the cryptography. Even without specific training of breaking code, amateurs can use their basic knowledge of math, stats and linguistics, like frequency analysis, to find their "own ways" to solving some of the ciphers.

You Don’t Need to Be Trained to Be Professional

With sophisticated and detailed research on statistics, al-Kindī invented his system of cryptanalysis, later known as the frequency analysis. It’s not surprised that he was considered as the greatest scientist in the ninth century when many disciplines including mathematics, statistics and linguistics that are well developed today were still in their rudimentary stages; thus his research was undoubtedly remarkable. More importantly, the public, especially amateur cryptanalysts were not educated as well as those in today’s education system; few people were likely to have the opportunity to master, or even learn mathematics. Therefore those attempting to decipher encrypted messages had to depend merely on al-Kindī’s approach. However, things have changed.

Today’s schooling system guarantees the educational opportunity for almost everyone to learn basic mathematics and statistics, and to have personal perspectives on languages. As long as we comprehend the linguistic rules, do the math and then go through the process of trial and error, all of us can crack codes in our own ways.

The easy access to various resources and information should not be understated as well. Simply searching ‘cryptography’ on the Internet, even high school students are probably capable of decrypting substitution cipher. For those who want to dedicate more time and truly dive into code breaking, thousands of books will be available if they are willing to reach them. Learning new theories and grasping the nature of any discipline without instructions are no longer the missions impossible; in other words, self-study is relatively more feasible than ever before.

Generally, the simple truth is, we are getting more knowledgeable and everything is getting more accessible. Though code breaking is hard, the actual barrier for amateur cryptanalyst today may be their willingness to reach the resources and their persistence as well as patience when deciphering codes with complex encryption.

4 Codes, 1 Sculpture: Kryptos

During the talk Elonka gave to the class on Friday, I found myself fixating on one thing, Kryptos. I was so surprised by the fact that there was a statue located on the grounds of the CIA, which has an unsolved code written on it. The CIA are supposed to be some of the greatest minds of our time, and they can't solve a cipher that is quite literally sitting right in front of them.

To give a little more information, Kryptos is a large sculpture which contains four codes. Each of these codes was placed onto the sculpture by stamping through the metal, so that the letters are holes in the metal. The four codes were created by Ed Scheidt, who at the time was the Chairman of the CIA Cryptographic Center.  The first three codes have been solved, by the public and from within the CIA, but the fourth remains a mystery.

The connection between Kryptos and our course is fairly obvious. Four encrypted messages, or codes, in a class about codemaking and codebreaking? Sounds like exactly what we're looking for I think. It's also worth mentioning that the first codes use a Vigenere cipher, something that we were discussing in class at the time Elonka came to visit. Vigenere ciphers were the code standard for quite some time, so it doesn't surprise me at all that they were used for a sculpture as famous as Krpytos.

Many famously unsolved codes were solved at a much later time. With this famous code sitting in front of some of the world's best codebreakers, I am sure that Kryptos will soon be cracked. Maybe Elonka will be the one to solve Kryptos, or maybe even one of the students of our course.

Here's a link to her Kryptos page: http://elonka.com/kryptos/

The Correlation Between Technology and Self-Taught Cryptography

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.

Changing perspectives on cryptography

It is not surprising that using frequency analysis to solve substitution required a sophisticated level of scholarship in the 9th century. It might take decades of textual study, statistics knowledge and mathematical insights for the Arabian cryptanalysts to successfully find this method. In The Code Book, Singh also suggests that the Muslim civilization provided an ideal cradle because “every Muslim is obliged to pursue knowledge in all its forms” and the scholars “had the time, money and materials required to fulfill their duty.” (Singh 16)

Today’s amateur cryptanalysts seem to still fulfill these “requirements”. Nowadays people with only a few years of education would already have certain level of knowledge in such fields. The resources are so accessible now that they no longer need to be“scholars” but indeed anyone with any intention or interest about cryptography. Undoubtedly only a small amount of people will be trained as professional cryptanalysts, but it’s incredibly easy for anyone to search about cryptography, share thoughts with others about the ciphers they write, or take an online cryptography course.

Today’s generation is a group of people that are taught to solve puzzles when little and raised with films or literature talking about cryptography often in one form or another. With the emerging technologies in hand and a broad access to the subject, people nowadays have entirely new perspective on cryptography. On the other hand, people back in time were strictly limited by the resources they had and the little exposure to the knowledge. Politics might also come into play since a large proportion of citizens interested in inventing or breaking codes might not be the best interest of a monarchical government at that time.

Easier to Learn, or Easier to Access?

I believe that, while a high level of scholarship was required to develop the frequency analysis approach, it is not critical to the use of this approach. When the world was new to this subject--when it had just discovered ciphers and keys and cryptanalysis--all of the knowledge was completely new. It was the cutting edge, so not many people understood it yet. It was essential to attain a high level of education to comprehend the mysteries of cryptology. However, with the modern education system, and modern technology, people have the information necessary more readily available. People can access the "mathematics, statistics, and linguistics" necessary to equip themselves for code making and codebreaking. Also, the easy access means that the information surrounds the human population. We have billions of pieces of data sitting at our fingertips, just waiting in that ever-present "cloud." Because of this access, and as a result of the heightened academic expectations, "amateur" cryptanalysts can use previously lengthy and difficult methods of analysis with much more ease. The civilization has reached a "sufficiently sophisticated level of scholarship in several disciplines," and therefore the people of that civilization may achieve the same accomplishments which the Islamic civilization discovered. However, as a result of the constant inundation of information prevalent in our society, and the resultant size of the body of common knowledge, amateur cryptanalysts can now use approaches such as frequency analysis, which was so arduously sought out, without any formal training.

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