Cryptography

The History and Mathematics of Codes and Code Breaking

Tag: amateur cryptography

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.

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).

The Infinite Struggle Between Makers and Breakers

The continuous tug-of-war between cryptographers and cryptanalysts has triggered the expansion and prominence of cryptography in the world today. Just as quickly as new encryption methods are developed, new decryption strategies are implemented, creating a state of equilibrium in cryptography.

The art of secret writing dates back to Herodotus (Singh 3) and has had various uses in history, including military communication and murder plots. In more recent years, the explosion of technology has propelled the expansion and necessity of cryptography to the point where it has an effect, either direct or indirect, on every individual. Cryptography has a range of important functions, such as keeping bank account information private and ensuring that government information is kept secret.

Cryptanalysis was not invented until the Islamic golden age under the Abbasid caliphate (Singh 14). According to Singh, cryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of scholarship in several disciplines, including mathematics, statistics, and linguistics (15). The Muslim civilization provided an ideal cradle for cryptanalysis because the Muslims were educated in a variety of fields and pursued knowledge in all of its forms (Singh 15).

This breadth of knowledge associated with the Muslim civilization is valued in most modern society today. Most individuals are at least somewhat proficient in an assortment of disciplines. Primary education sets the field by educating children about a variety of different subjects in order to equip them with a large intellectual toolset. Many secondary education institutions stress a liberal education in which students obtain an educational background in the humanities as well as the math and science fields.

Because of this, it is no longer necessary to undergo formal education in cryptanalysis in order to use elementary strategies such as frequency analysis. With the broad education that modern citizens receive, combined with the availability of abundant resources, especially those on the Internet, many of the older, simpler codes can be decrypted by the layperson. However, modern encryptions are much more complex than those of the past and may require serious study.

During the past few centuries, cryptography has exploded due to the expansion of technology. Cryptography affects numerous fields ranging from government information to banking, and brings in knowledge from a variety of areas including mathematics, logic, linguistics, and statistics. Modern education allows us to engage in the world of cryptography even as the complexity and number of cryptographic techniques increase exponentially.

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.

Temptation and Treasure

Although thousands of intelligent, well-trained people have attempted to break the Beale ciphers, they remain a mystery. However, the defeats of the past do not deter the many people who still try to crack the code. Some of these people are driven by the thought of the treasure buried by Beale years ago. A potential reward of $20 million can be highly motivating. For most, though, it is likely more than that—after all, trying to break an unbreakable code is sort of terrible as a get-rich-quick scheme. Instead, it is the tale itself that is the draw. A mysterious stranger, buried treasure, coded notes—it all reads like an adventure story, and that’s something people want to be a part of.  We are surrounded by stories like this our whole lives, and as children we play at being pirates following a map to the buried chest of gold. Attempting to solve the Beale ciphers makes this childhood game a reality.

Additionally, some cryptographers reason that someone has to eventually come up with a solution—so why not them? We often think that we will be able to be the one who solves a problem even if we’ve seen many people fail at the same task. This can be commonly seen in simple everyday tasks. If one person in a group tries to open a door and gives up, saying it’s locked or stuck, often others will test the handle for themselves. Even if they don’t consciously realize it, they believe that they will be able to do better than the first person—somehow if they jiggle the handle differently or apply enough pressure the door will open for them. The Beale ciphers are a locked door behind which lies the answer to a hundred-year-old mystery. It’s just too much to resist.

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