Cryptography

The History and Mathematics of Codes and Code Breaking

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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.

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.

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.

The Importance of Privacy

jeff_golden. Flickr. Creative Commons.

jeff_golden. Flickr. Creative Commons.

The government does not have the right to infringe upon the privacy and security of United State’s citizen. The proposed idea of the government being given ”wide latitude” of surveillance breaches these privacy barriers that are protected by the Constitution. The ability to keep information secure has decreased with the increased use of technology. A face-to-face conversation is the most secure method or exchanging information but is not practical with todays growing world. “The advent of digital technology, which makes monitoring so much easier” fuels the desire to protect your information (Singh 306). This decreased ability to protect your information has led to the creation of enciphering methods on the Internet. The creation of this type of security has aided in the protection of citizen’s rights. These are ways that citizens protect their right to privacy and the government should not be allowed access to their citizen’s private information. The government should be prevented from infringing upon the security of its citizens without reasonable cause and search warrants. Giving the government ”wide latitude” would allow citizen’s rights to be violated. It is the government’s job to respect the constitution and the wishes of their constituents. The citizen’s rights are supposed to be of the utmost importance to the government and the basis of the constitution.

Power of The Great Cipher

There exists a never ending battle in the field of cryptography between those coming up with encryption methods and encrypting messages to those trying to break these ciphers. This back and forth is an ongoing and fairly quick process with each side constantly making advancements. However, the 2nd chapter of Singh discussed “The Great Cipher” which was the cipher used by Louis XIV, which remained unbroken for 200 years. The obvious question is then, what made this particular cipher so difficult and take so long to crack?

There are multiple reasons for this, starting with the complexity of the code itself. The code was comprised of 587 unique numbers with thousands of numbers altogether. This alone makes it very difficult to decipher as if you were assuming these numbers corresponded to letters or a set number of letters, as there would have to be repeated elements of the cipher text corresponding to the same thing in the plain text, which would render frequency analysis practically useless. This leads into the next reason why the cipher was so secure, which is that the numbers corresponded to syllables instead of letters or groups of letters. The majority of the ciphers up till this point revolved around changing something into individual letters, so this not being the case probably threw off many would be deciphers of the text.

Lastly, one of the main reasons this code was so secure is the technology that was available at the time. Nowadays with our computers, excel files, other programs and whatnot it is fairly simple and straightforward to do things such as frequency analysis or substituting in sequences in the cipher text for what we assume it to be in plain text. However, back in the 17th and 18th centuries performing these tasks by hand (especially with a text thousands of characters long) would be an incredibly daunting task. The sheer time commitment it would take to decipher a text of this length would be enormous and this probably discouraged many people from attempting to decipher it.

Do your research

I think the best advice for college students using the internet is to just be aware of the amount of privacy you have. I know there are many of us who think they are perfectly safe on the internet because their profiles are set as private, and they don’t post about where they are going to be and they only talk about personal issues on secure, private messages, and they don’t post their private photos onto the internet. Issues with their privacy can be found quite quickly with a little bit of research. The article “The 5 Biggest Online Privacy Threats of 2013”, for examples, tells us that your phone stores the location each picture is taken on, and unless you turn this off or remove this information, anyone on the internet can get this information from the photos you post. Also, as we have seen recently with the big celebrity leak, even the data on your phone can be retrieved without access to your phone, as this information is stored in a cloud database. Emails and your messages on social media, as private as they seem, can be accessed by the NSA and if they see fit. While I know the average college student isn’t really doing anything on their email that would be of interest to the NSA, the fact that they have access shows that other people could gain access if they really wanted to. The article “5 Essential Privacy Tools for the Next Crypto War” is a great resource for college students as it gives simple, more secure encrypted alternatives for file sharing, emailing, and messaging services that you don’t need to be tech savvy or computer whizzes to use. These small steps could help all of us avoid embarrassing leaks of personal information or stealing of data from our computers.

Technology and Cryptography

After the class discussion, I began thinking about the concept that cryptography and cryptanalysis is dependent on exceptional resources. Upon first reading the chapter, I had considered the cryptanalysis that was done at the time as super basic due to the lack of technology such as computers. However, after further reflection upon the concept of resources during the discussion, I now believe that the people of means did have computing power at their disposal. The people that worked under them were their computers. It is true that a computer can easily brute force a simple dictionary password, but that does not mean humans cannot brute force as well. The time differences may be very different but in the end both processes will yield the password.

Every day our computers get more powerful and capable. It is hard to believe, but probably true, that future generations will be discussing the same topic and thinking about our technology in the same way we view that of previous generations. The discussion made me realize that maybe in a few years our level of cryptanalysis will be considered primitive. Cryptanalysis has evolved so rapidly over the past few years, due in part to the advent of the Internet, and it is hard to imagine what advances are bound to occur.

Blindly Building

The most interesting passage from Cryptonomicon that relates to a discussion earlier in the course is found on page 89. Here, Lawrence describes the most intriguing machine found at Station Hypo: at machine built by Commander Schoen and designed to break Japan’s INDIGO cipher. According to the book’s description, INDIGO was similar to ENIGMA, in that it was enciphered using a machine. However, unlike ENIGMA, none of the cryptanalysts had seen the INDIGO machine, so they had no idea how to tackle it. Amazingly, Schoen was able to reverse-engineer the cipher machine simply by analyzing the encoded messages and finding patterns in the numbers.

Of course, this section directly relates to our discussion of ENIGMA and its downfall. The main difference between the two, though, seems to be where the bulk of the security was. With ENIGMA, cryptanalysts struggled to break the code, even with the machine in front of them. According to the book, the major breakthrough with INDIGO was creating a copy of the machine.

After reading the passage, I was convinced that Stephenson had fabricated this part of the story. I found it highly unlikely that any person could reverse-engineer an elaborate mechanism by simply searching for patterns in encrypted knowledge. However, after a quick Wikipedia search, I found that this instance was actually based off of a real-life occurrence.

The actual cipher was named PURPLE (INDIGO was a great name for Stephenson to pick) and the main storyline remains the same: a machine was being used to encipher messages and no one knew what it looked like. The biggest difference between reality and the fictionalized story is that multiple people worked together to create the PURPLE machine, compared to the lone Commander Schoen in Cryptonomicon. Nevertheless, creating a complex machine by analyzing the numbers it output is still genius.

Image: “COBOL Rube Goldberg” by Phil Manker

The Availability of Ingenuity

I’m a staunch supporter of sharing information. In fact, I believe that patents should have a quicker expiration date (especially in fields where innovation moves very rapidly). Consider this: a patent filed in 1993 for a particular style of trackball mouse would still be in effect until next year. However, the vast majority of us do not utilize such hardware anymore.

What does this have to do with the NSA restricting the strength of encryption available to businesses? Without equal access to innovations and information, there is a lag between discovery and improvements. If everyone has equal access to information, there is a greater chance that breakthrough ideas will emerge. This simple principle is demonstrated by Singh’s description of the development of our modern encryption techniques. Because information was shared among different groups, a team tackled one security problem (key distribution) while another group on the other side of the United States worked on another issue (one-way encryption functions).

by Nick CarterBeyond this fact, there is the consideration that the NSA was effectively lying to the public about security. The NSA wanted to promote DES as a universal standard of secure communication. However, they made provisions to keep it from being as secure as it could be. In effect, the NSA was convincing businesses that DES offered adequate protection of corporate secrets. This sort of repression of information brings to mind “Big Brother” and “doublethink” in a realization of George Orwell’s intrusive government.

I can see no rationale adequate enough to justify the NSA’s paranoia. Their attempt to keep  the public’s secrets under their thumb was a bad idea.

Photo: Broken Rusty Lock by Nick Carter

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