The History and Mathematics of Codes and Code Breaking

Month: August 2015 (Page 1 of 2)

Bookmark Assignment #1

Interesting PinFor your first bookmarking assignment, you're invited to bookmark anything you like that's related to cryptography. Look for a news article or resource on cryptography that's interesting to you. If you're not sure where to go with this, look for inspiration in Singh Chapter 1. Give your bookmark at least two useful tags.

Your bookmark is due by 9:00 a.m. on Wednesday, September 2nd. We'll take a little time in class to share your finds. If you have any questions about using Diigo, don't hesitate to ask.

Image: "Interesting Pin," by me, Flickr (CC)

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.

Old News with a New Twist

The continuous development of the human mind and collective knowledge makes it ever more difficult to protect those thoughts and ideas we wish to keep to ourselves. The idea of privacy might seem distant or even unattainable to us today due to the prevalence of modern technologies and new advances in communication. The more information that there is out there, the more people that are trying to find it (and the more bits of information that may slip out).

They key component to understanding the evolution of cryptoanalysis is realizing that we have quite the advantage now. The fact that we know about the wax-coated balls of silk bearing Chinese messages and egg shells with hidden writing shows that we have learned from past attempts and successes of encryption and learned from them (Singh, 5).  It is always more difficult to come with a new way to go about something rather than just adapting a previous process. It took many scholars many years of training in order to figure out how to crack the codes that probably took up just as long to create in the first place.

Humans are natural-born problem solvers and as such our brains are wired to look for order. It may have required “a sufficiently sophisticated level of scholarship” to first create and crack these ciphers, but living in a society in which training in linguistics and mathematics is readily accessible gives us the same advantage that the Islamic empire had (without the years of specialized training). We have learned from the trials and errors of cryptographers long ago and will continue to develop new means of encrypting and decoding messages.

Evolution of Technology's Affect on Cryptanalysis

Information is at a premium in the 21st century. Any person of any age can discover the necessary information in seconds with the click of a button. Throughout history, as technology evolved, cryptanalysis became progressively simpler. The sophisticated level of mathematics, statistics, and linguistics required to be a good frequency analyst became more accessible with the evolution of the internet. It is so simple now for an amateur cryptanalyst to use an application such as Microsoft Word to count the frequency of each character in a ciphertext and to use Google Translate to help decrypt a message in a different language. Amateur cryptanalysts have so many useful tools to help them find shortcuts in almost any decryption methods. Codebreakers no longer have to work long, tedious hours just to verify that their theories are correct. Decryption methods that took the mathematicians days to work on now take hours, which gives amateur cryptanalysts much more time to test different theories. Now, as the new age of codebreakers begins to perfect frequency analysis which has been around for centuries, they can go forward and discover completely new ways to analyze encrypted messages. As technology evolves, so will cryptanalysis because the accessibility of information will get more efficient.

A Developing Familiarity Throughout History

Fundamental development in the disciplinary topics of mathematics, statistics, and linguistics was procured from a comparative ground-level hundreds of years ago as opposed to what we have unearthed today. The advantages and resources currently available to the vast public are, of course, the most they have ever been in history. This goes without saying. "Discovering" tactics to break codes and ciphers that were once considered the most advanced techniques by exceptional cryptanalysts is certainly not as easy a task without the long history of code breaking (in the colloquial meaning of the term) that had come before us.

The ability to learn methods such as frequency analysis from a quick Google search is much less arduous a task than inventing them without any previous notion of such a possibility. Even assuming that today's amateur cryptanalysts aren't explicitly searching "how to's" from public databases, the idea of frequency analysis and any analogous general form of use is very comfortable and familiar. Perhaps teachers from grade school distributed puzzles aimed to unscramble words and phrases or your classmate used a simple cipher as a way to ask out their prom date. Experiencing or seeing a number of similar events throughout our lives inevitably ingrains the technique somewhere in the back of our minds, at least implicitly.

Noting the above, it is truly incredible to acknowledge how commonplace once incredible and cutting-edge discoveries are considered in the present day. This will always be observed, even beyond subjects regarding cryptography, as a natural progression of time.

Cryptanalysis: From Complexity to Common Knowledge

Each an art form of its own, cryptanalysis and cryptography demonstrate opposing counterparts focused on accomplishing the same common goal—the understanding of a hidden message. These two techniques highlight the competitive battle between codemakers and codebreakers. Although cryptography requires a distinct level of skill and secrecy, the practice of cryptanalysis encounters even greater obstacles as the codebreaker must determine the meaning of the hidden message as well as the technique necessary to break it. Arguably, the mastery of one skill can lead to an expertise in the other as the making of a complex cipher derives the further logic and creativity necessary to uncover these intricate codes.

Singh cites the frequency analysis technique as an “innocuous observation” by Muslim cryptanalysts that became “the first great breakthrough in cryptanalysis” (17). Nowadays, this code-breaking method is quickly and easily used by first-time cryptanalysts with no previous instruction, almost as if by second nature. While the frequency analysis technique was undoubtedly a major breakthrough in the seventh century, the vast amount of education and technology provided to our society today allows this method to become an obvious first step towards discovering the unknown.

As time has gone on and technology has expanded, the human mind has reached a common intelligence almost unimaginable even one hundred short years ago. Education has taught us to not only focus on how to put things together, but also on how to take them apart. Practices such as cryptanalysis have become more applicable to the average man as common knowledge typically requires an understanding of both how and why things work. The fifteenth century Western world is a prime example of the human tendency to discover how something functions as immediately after cryptography was introduced “already there were individuals attempting to destroy this security” (27).

While in the past cryptanalysis was labeled as an expertise only accessible to those in higher society with the finest education, its ability to be understood by even the most amateur cryptanalyst emphasizes the incredible expansion of knowledge in our society today.

Ancient Influences On A Modern World

In a world enveloped by constant communication and endless data transfer, the necessity for privacy remains a top priority. With the aid of cryptography, society hopes to maintain secrecy in various interests, ranging from personal matters to governmental espionage. Yet how secure can we ever truly become?

As human civilizations advanced, the intricacies of cryptography drastically changed over time. New solutions resulted in the drive to develop more difficult codes. When discussing cryptography, one must also closely analyze the circumstances surrounding a particular time period. Cryptanalysis methods and current information in one period can quickly become obsolete in only a few decades. Historical events may also cause rapid advances, such as in the Islamic golden age, or slowed progress, such as during the dark ages in Europe.

In The Code Book, Simon Singh notes 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" (Singh 15). Despite this, amateur cryptanalysts today can easily begin deciphering messages thought impervious in previous times. This can make Singh's statement seem contradictory, as these individuals develop the same approach as previous crpytanalysts without being taught.

However, Singh's statement still remains true. Today's individuals enter the world surrounded by a highly sophisticated society, much different than that of the previous societies. Many factors can influence the intellectual capacity of these amateurs, such as income level, access to necessities, or even parental support. Yet one thing remains certain - today's amateurs prove much more equipped to tackle these difficult ciphers than the best of the ancient world. While young students in previous centuries worried immensely over the seemingly constant political warfare, risk of being drafted into the army, or strong possibility of suffering from diseases, today's cryptanalysts can focus their minds strictly on their studies. Thus, despite never having learned about cryptography, the mere rigor and new advances of modern education and technology equips these individuals to quickly process and develop possible solutions to decipher these codes.

Cryptographic Darwinism

In the prologue of The Code Book, Singh introduced the “evolution of codes” and explained how codes are becoming more impactful in today’s society (Singh xiv). From encrypting simple user passcodes to concealing entire online databases, cryptographic methods are evidently becoming more and more widespread.

Along with the evolution of codes, we can also see an explosive evolution in technology and similarly in the media, which is one of the vital reasons why so many people, despite their lack of training in cryptanalysis, are able to utilize frequency analysis to solve substitution ciphers. For example, the many online resources that teach people about cryptography are easily more accessible today than they were decades ago.

Furthermore, considering the long history of cryptography, it is no surprise that methods of substitution cyphers, especially those that are elementary, are made public and passed on from generation to generation, and thus has become common knowledge to even the amateur cryptanalyst. Take The Code Book itself as an example; anyone who reads the book is exposed to, at the very least, the most basic frequency analysis approach in solving substitution cyphers. They can even be completely oblivious to what cryptography was before reading the book, but by simply comprehending the first chapter, the person has enough knowledge to create and solve simple substitution ciphers. Of course, the degree to how complex the ciphers they’ve created or can solve is probably not as high as what an expert cryptanalyst can achieve.

Nonetheless, the technology today allows even amateurs to be able to solve substitution ciphers despite their lack of a “sufficiently sophisticated level of scholarship” (Singh 15).

Page 1 of 2

Powered by WordPress & Theme by Anders Norén