The History and Mathematics of Codes and Code Breaking

Tag: history

The Theatricality of Cryptography

The first chapter of Singh’s The Code Book is packed with historical examples of cryptography. The Greeks, Persians, Arabs, French, and English, to name a few, were just some of the infinite number of societies and civilizations of which cryptography was crucial to their development. However, most of the examples described did involve people in positions of power. Kings, queens, nobles, and military leaders of all types have had to use cryptography to defend or expand their nations; clearly, cryptography has been crucial to changing history.

Despite the importance of these examples, I do believe that there has been a need for cryptography since the dawn of written language. I can’t imagine that cryptography was only used by well-resourced people; there has always been a need for encryption and secrecy, even if it’s on the most rudimentary level. Perhaps these are the only examples that survived, or perhaps Singh chose to include them because of their dramatic nature – after all, he does need to entice the reader somehow. It would be foolish to say that cryptography requires exceptional resources.

Yes, the most theatrical and interesting stories usually include a plot, some characters, and a dramatic, dire consequence that will result if the code is decrypted. But we can’t discount the more simple, day-to-day interactions that may have required people to encrypt their messages, like a potter who may have needed to protect his or her recipe for glaze, or a citizen who wanted to hide the contents of a letter from their government. I can’t imagine that examples such as these, though less exciting, didn’t exist before the stories of kings, queens, armies, and wars.

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?

Cryptography Changes History

In Chapter 1 of The Code Book, author Simon Signh introduces the reader to the concept of cryptography. In this chapter, Signh gives explanations for what codes and ciphers are, examples of specific codes and ciphers, and many examples in which codes and ciphers were used. Many of the examples Signh uses in which cryptography was used are from long ago and involve political and military leaders and major events in history. This begs the question of why Signh chose these examples to talk about the concealing of messages. It seems that he used them not because they are the only examples that have survived or because cryptography requires exceptional resources. I believe that Signh used these examples because he had to start at the beginning of the history of cryptography and at the same time try to sell cryptography as an interesting concept. 

Signh’s goal in this chapter is to introduce cryptography and its history, so naturally he will start with early examples of cryptography. Yet he doesn’t just pick any early examples; he picks the ones that had the biggest impact on major events. The first example of hidden messages in history Signh uses is Demaratus and the battle between Persia and Greece. In this example, Demartus, a greek living in Persia, took the wax off of a table, wrote a message warning the Greeks of Persia’s plan to attack on the wood, rewaxed the table, and transported this table to the Greeks. The Greeks were able to find and read Demartus’ hidden message, allowing them to prepare for the attack. I believe that Signh used this example not to demonstrate that only a few examples of hidden messages throughout history have survived, nor to demonstrate that hiding messages requires advanced resources (all that was needed was a table), but because this example entices the reader into the subject of cryptography and explains how impactful it can be. Hiding messages is one thing, but hiding messages that change the outcome of entire wars, that is exciting and important. 

Signh’s use of these examples as his first examples in his book casts meaning on what he sees as the purpose of cryptography in today’s world. Sign doesn’t just value code making and code breaking for their own sake. He understands that they are, today and in the future, tools that can change history.

Standing on the Shoulders of Giants

It is curious to think of how the world was just one hundred years ago. So many things that are now obvious were unknown or shrouded in mystery. In 1915, barely anything was known about heredity and the cellular functions that were involved in it. Now, we have mapped the entire human genome and can even change DNA. In Newton’s time, gravity was a concept that hadn’t been explored. Now, it is an obvious fact, one that forms the most basic aspect of sciences that have now advanced to ever-increasing complexity. What is gravity when compared to the Higgs boson?

In this same way, the discoveries made by cryptanalysts of centuries past have now become obvious to us. This is by no fault of theirs—without civilization’s ability to analyze statistics and linguistics and apply mathematical concepts, decrypting encrypted messages could never have been attempted.

The thing is, civilization didn’t stop there. It continued to grow and make new discoveries while standing on the foundation laid by its predecessors. Discoveries of algebraic concepts that excited prominent scholars hundreds of years ago are now taught in middle school classes to unappreciative twelve-year-olds. They are no longer new and complicated and exciting, but old news, taken for granted, never thought of unless they are used for the springboard into some novel inquiry.

Another aspect to consider is the advance of technology and information. Doing statistics by hand is a painstaking process that can now easily be bypassed by calculators and software. In addition, so many more people have access to information now than they used to, whether that be in a classroom or on the Internet. Especially when considering the Internet, where any question can be answered easily in a matter of seconds, it is not all that surprising that amateur cryptanalysts can “wing it.”

This is not to diminish the strategies implemented by older cryptanalysts. Rather, it is to show how far we have been able to come since their time because of the nature of their discoveries. As Isaac Newton said, “If I have seen further it is only by standing on the shoulders of giants.”

The Beginning of an Era of Secrecy

Imagine for a moment that everything you’ve ever hidden is completely public. Everyone has access to your private emails and your bank account information, among other things. This would be life without cryptography.

Cryptography is hiding the meaning of a message, and it is typically used in most forms of modern communication. In The Code Book, the author, Simon Singh notes that secret writing has been a part of human civilization since the fifth century (Singh 4), but it was widely accepted that the most typically used cipher of ancient times, the substitution cipher (Singh 13), was impossible to crack until the 8th century when the Abbasid caliphate’s place as a center of learning allowed it to become the homeplace of cryptanalysis (Singh 16).

Singh defines cryptanalysis as “the science of unscrambling a message without knowledge of the key” (Singh 15). As Singh states on page 15, cryptanalysis was only possible in the beginning due to the Muslim civilization achieving “a level of scholarship in several disciplines, including mathematics, statistics, and linguistics”.

The important debate, though, is whether or not this level of scholarship is still necessary in today’s society. I am of the opinion that, although our society’s era of secrecy necessitated well-trained cryptanalysts, this is no longer the case. As our class demonstrated on only the second day, breaking of the more common codes is fairly simple for most modern humans. The difference, I believe, lies in the fact that in ancient times, education and widespread knowledge had not progressed to the point it has now reached. The internet, as a portal to almost all human knowledge, has made it simple for anyone to pursue any knowledge or expertise that they desire.

Without modern technology, and modern education, I am of the opinion that intense training would still be required to become a cryptanalyst. However, due to our civilization’s widespread resources, it has become much easier for individuals to discover and crack codes and ciphers on their own.  Cryptology began as a secretive science, but has become an integral part of modern society, and as such we are all cryptologists in some form or another.

Don’t Overlook the History of Seemingly Simple Things

Cryptography and cryptanalysis are two fields whose progress is intertwined; both make advances to either get an advantage over the other or to compensate for a breakthrough the other has made. As societies have progressed, the need for more complex methods of both encryption and decryption has risen along with the complexity of society.

Messages have been hidden and encrypted from prying eyes since the fifth century B.C. (Singh 4), but it wasn’t until around 800 A.D. in the flourishing Arab empire that cryptanalysis was invented (Singh 17). Singh notes, “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). But ever since, the battle between cryptographers and cryptanalysts has employed the growing knowledge and technology of civilization, to the point where the decryption methods discovered by the greatest of Arab thinkers is now almost common sense for any elementary school child.

Why is that? Well consider for example how mathematical technology has advanced along with society. The abacus appeared in China as early as 500 B.C., followed by the invention of Arabic numerals in 1202, and just think of all the different models of TI-calculators that can be found at Target now (source). For a young child, counting with Arabic numerals is pretty simple, but the use of more complicated and advanced calculators takes more work and learning. The same goes for code-breaking: basic substitution ciphers can be easily figured out, but more complex codes and ciphers will take more time and effort.

This shows how far society has come in a couple thousand years; it shows how human knowledge builds upon itself to reach even higher. The breakthroughs by Arab cryptanalysts over a thousand years ago sparked entire industries and professions, and who knows, maybe a discovery in 2015 could change the entire future of cryptography and cryptanalysis.

Blog Post #1

I can honestly say that going into this class I had very little knowledge of what cryptology is or its implications. I had most likely heard the word in passing but never fully tried to comprehend the true meaning. The first chapter of Singh was to say the least an eye opener. I was shocked by the widespread use and history of codes and ciphers. The chapter expanded on the history of ciphers in various societies and cultures. The main example of the first chapter is Mary Queen of Scots and her cipher mishap. This situation displays the risks of ciphers. As discussed in class, sometimes a weak cipher can be worse than no cipher at all. The reasoning behind this is the false sense of security that a cipher can give the sender and recipient. Mary Queen of Scots also made the mistake of trusting someone else to deliver and keep the secrets safe. As the saying goes, “loose lips sink the ship.” Well in Mary Queen of Scots case deception, ciphers, and double agents sank that ship. The discussion in class led me to realize that Mary had no other option than to trust that her correspondences were honest since she had very limited resources. This ties into another topic that we discussed about the impact that resources has in ciphers. In Mary’s case, the limited option of resources and possible ways of communication forced her to relay on her a double agent. She had no way to change the cipher or strengthen it without him knowing so she was sort of doomed. If she was more vague and a little less trusting in the strength of the cipher she could have saved herself but that did not happen. The discussion in class aided me in seeing the scope of ciphers along with the potential drawbacks of them.

Blog Assignment 1

I had a general idea about what cryptography and code breaking was. Learning the history of the subject in the first chapter was interesting. When I was in grade school, my friends and I used to wrap pieces of paper around pencils to write small messages; similar to how the Spartans used the scytale. The idea of using the frequency to determine the letters in cipher seems logical, however tedious to do, and it appears that it would only work with the most basic of ciphers. It is fascinating that cryptanalysis can be used when the 26 symbols are not even letters of the english alphabet. The most interesting piece of the chapter was the quote on page 41, “The cipher of Mary Queen of Scots clearly demonstrates that a weak encryption can be worse than no encryption at all.” It shed some light on the actual content of the cipher rather then the means of encrypting and decrypting it. Combining the cipher with discretion would be the safest means of communication. It amazed me that some complicated ciphers have been cracked throughout history without the technology we have today. As with most branches of science, more data is better. The more a certain cipher is used, the more likely it is to be cracked because certain patterns begin to emerge. That is why cryptography is a constantly evolving field: adaptation is necessary for survival.

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