The History and Mathematics of Codes and Code Breaking

Author: Felix T

Sharing Is Caring – Or Is it?

In It’s Complicated, author danah boyd writes “In a world in which posting updates is common, purposeful, and performative, sharing often allows teens to control a social situation more than simply opting out. It also guarantees that others can’t
define the social situation” (boyd 75). boyd points out that by sharing small snippets of one’s life, they can effectively partition off a section of their life to remain private. I never realized this as an alternative to simply opting out of social media, and this solution proves much more useful than staying off the internet.

boyd shares a situation in which a teen girl posted embarrassing photos of herself on her profile. When questioned, the girl pointed out that it was far safer that the photos be posted on her own terms. Since her friends also possessed embarrassing photos, posting them before they had a chance “undermined her friends’ ability to define the situation differently” (boyd 75). Not only could she avoid being publicly embarrassed, this gave her an extensive amount of privacy. “Her apparent exhibitionism left plenty of room for people to not focus in on the things that were deeply intimate in her life” (boyd 75).

boyd also draws a comparison to the practice of steganography. By hiding messages in plain sight through “countless linguistic and cultural tools,” (boyd 66) teens can avoid surveillance by their parents. This “social steganography” also relates to the previous situation, in regards to the girl posting her photos online. By putting them out there, she draws attention away from her actual personal life, essentially hiding it in plain sight under the veil of her photos.

Overall, boyd notes that “where people share to maintain privacy, they do because they do not want someone to have power over them” (boyd 75). By selectively choosing what to share, people can form pictures of their life that appear true, but actually only define a small portion of their life. This allows people to maintain their privacy in an ever increasingly invasive society. Although I’ve always desired privacy, I never thought of it concretely as maintaining power over myself. boyd has essentially redefined privacy in a meaningful way that truly captures its essence in today’s world.

The False Positive Paradox

While I had previously worked with false positives in various statistic problems, I never considered the implications behind it. Cory Doctorow addresses this “false positive paradox” in his book Little Brother.

In the story, the narrator, Marcus, talks about a “99 percent accurate” test for “Super-AIDS” (Doctorow 47). However, this means the test is one percent inaccurate. One percent of one million is 10,000. Only one of those people will actually have the disease, and thus, the “99 percent accurate test will perform with 99.99 percent inaccuracy” (Doctorow 47).

This was extremely interesting, as I had never considered how inaccurate these tests really were. The statistics and numbers had always seemed solid. It made sense, and 99% seemed like an extremely high percentages. But Doctorow makes an intriguing analogy. Pointing at a single pixel on your screen with a sharp pencil works. However, pointing at a single atom with a sharp pencil would be extremely inaccurate. This essentially highlights the flaws in any test that could potentially produce false positives. Whether detecting diseases or terrorism, these tests could result in large wastes of resources, such as time and money.

This could also be connected to the process of cracking ciphers. For example, when searching for cribs in an Enigma deciphered message, a crib may make sense in a particular context but could turn out to be an incorrect decipherment for the whole message . Even in general cryptanalysis, you could potentially make progress on deciphering a message. After hours of working on a message, you could realize that you made a mistake originally and your previous progress had simply been a “false positive”. Clearly, false positives can be quite dangerous and misleading. The false positive paradox further magnifies the huge effect these false positive readings can have on carrying out important tests or examinations, and the consequences could be devastating. Imagine administering a drug thought to combat a certain disease to a patient who really didn’t have the disease. Because the patient was perfectly fine, this drug actually resulted in the patients’ children having birth defects. A simple false positive could cause tragic repercussions.

The Power Of The Individual

One of the main reasons the cryptanalysts at Bletchley Park were successful could be contributed to the German overconfidence in the Enigma machine. Their hubris blinded them, and this blinding trust in the strength of Enigma ultimately led to the German downfall. However, certain individuals also contributed to the ultimate defeat of the Germans – Hans-Thilo Schmidt and Marian Rejewski. These individual contributions would prove invaluable throughout the war.

Schmidt’s story shows the effects of the negative German culture. Because he was deemed unworthy, he was forced to leave his position on the army. In addition, his failed business and his descent into poverty left him resentful toward Germany. Had the Germans simply decided not to cut him from their ranks, they could have potentially avoided the Allies’ cracking of Enigma. Disillusioned with his country, he sought revenge. Without Schmidt’s treachery, the Allies would never have obtained a functioning Enigma machine that could function similarly to the German military machines.

Rejewski’s work at the Biuro Szyfrow introduced the importance of mathematics and logic into cryptanalysis. With his famous Rejewski Chains, he was able to crack the earlier version of Enigma before the Germans added more scramblers and plugboards to make it more difficult. His work proved that mathematics and logic were extremely important once cryptography became mechanized. The work of linguists analyzing patterns was no longer enough. Despite Rejewsi’s work being essentially useless as Schmidt had given up the German keys for months, his work made it possible for the Allies in the future war efforts to crack the new and improved German Enigma machine. This crucial information gave the Allies a head start and the confidence that Enigma could be beaten.

Without these two individuals, the Allied cryptanalysts may never have achieved victory over the Germans. Although there are many factors that contribute to their victory, the influence of brilliant individuals cannot be ignored.

Hidden In Plain Sight

While almost everything on Elonka Dunin’s website seemed very interesting, the one thing that stood out the most to me was her presentation on steganography. She goes into great detail on what exactly steganography is, and whether or not terrorists were truly utilizing steganography to spread hidden messages. Elonka found that to this date, Al Qaeda’s members have never utilized digital steganography to spread messages. Although there was great speculation and some instances that pointed to this being true, Elonka found no convincing evidence that this was the case.

Elonka also goes on to show interesting examples of steganography, such as the “sekrit” page. The page had numbers that translated into an ISBN number for the book “Disappearing Cryptography, which contained information on steganography. The page also featured anagrams and steganographically hidden small files, which contained information on opening a message hidden elsewhere in the code. She also showed numerous examples of modern steganography, especially hiding messages inside pictures.

After showing examples of steganography and how it is employed, Elonka detailed ways in which to defeat steganography. She highlighted the “Three D’s of Defeating Steganography” – Detection, Decryption, and Deletion. Detection involves examining an image for irregularities or changes in patterns. Decryption involves obtaining a password or information about how the message was encrypted. Finally, deletion involves cropping an image or changing an intercepted message in some way to remove the stegonographic image. Although you won’t be able to decipher it, the intended receiver will no longer be able to find the message either.

I enjoyed going through Elonka’s presentation as it presented a lot of cool information about steganography, which we haven’t been able to cover in depth in class. She covered various forms of steganography, how to beat it, and intriguing examples of steganography in use. Especially interesting were the various sites and programs that could create steganographically hidden messages for you, with the user only needing to provide the message. While the ciphers covered in class, such as the monoalphabetic and vigenère ciphers, were difficult but not impossible to beat, steganography could be a powerful way to protect information. If you have no idea where to look or how to begin, the message may easily skip past you without you even realizing a message was present.

Victory At All Costs

The Zimmerman telegram could be described as the key leading to an allied victory and the end of the war. However, after being deciphered, Admiral William Hall decided to keep America in the dark, withholding the contents of the telegram from President Wilson. Despite the immediate danger this posed to the United States, I believe Admiral Hall made the correct decision. Disclosing the contents of the telegram would have alerted the Germans to the vulnerabilities in their encryption, leading them to create more secure ciphers and eventually cutting off British access to German information.

Essentially, this boils down to whether or not “the end justifies the means”. Although this paved the way to an allied victory, keeping the telegram a secret endangered countless american lives. One could argue Admiral Hall’s decision was extremely unethical, as it unnecessary risked peoples’ lives. Needless deaths must be avoided, even if it leads to a faster victory. The means are simply too cruel to justify the end. However, keeping the telegram a secret potentially changed the course of the war. Although American involvement was believed to ensure an allied victory, it was not guaranteed. The British access to German intelligence proved to be invaluable to their war effort, and saving more lives was not as important as keeping these intelligence lines open. With this intelligence, the British forces could always stay one step ahead of the German offensive. This aided greatly in preventing the Germans from dominating the war, and essentially allowed the allied forces to emerge victory. Thus, safekeeping this crucial line of intel proved much more important than saving more american lives. In addition, Admiral Hall’s plans to intercept the German’s telegram in Mexico would lead to President Wilson learning of the contents of the Zimmerman telegram. Although he would learn of its contents late, the effect of the telegram still stirred America to action. Thus, immediately sending the Zimmerman telegram to America was not even completely necessary. Overall, victory was the main objective, and thus the end did justify the means.

The Uncomfortable Truth

Time always progresses, despite any actions you might take. Quinn Norton points out a startling and uncomfortable reality: even after undergoing extensive security precautions or making every possible effort to remain secrecy, any information you provide on the internet will one day become public. As long as time progresses, your data is never truly secret. Time will always prevail.

In “Hello Future Pastebin Readers”, Norton effectively addresses the fact that all her private conversations and information will soon be public. This fact becomes more and more relevant every day, as we continue to rely more and more on our technology. Many of us plan out our entire daily routine on our phones, utilizing various calendar apps and social networking platforms to plan out events and communicate with others. We’ve been driven to accept that our “private” information will remain private, hidden from the prying eyes of others. Yet we struggle to realize the vulnerabilities of our security. Eventually, our information will become public, open to the scrutiny of others. As Norton notes, it doesn’t matter if you’re rich and famous or relatively unknown, this private personal data is the same for all. All people, from the average human being to the biggest celebrities, must realize that it is only a matter of time until it is all released.

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.

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