Cryptography

The History and Mathematics of Codes and Code Breaking

Tag: cryptography (Page 1 of 3)

Illegal Math: Fact not Fiction

I chose the beginning of chapter 17, when Marcus and Ange went to the journalist, Barbara Stratford, to expose the rampant abuses of power that were occurring in San Francisco. During this, they discovered that Barbara herself had covered the original ‘crypto wars’ in the 90’s. Barbara describes how the government had labeled cryptography as a munition and made it illegal to use it or export it, all in the name of national security. While I thought this was really interesting, the next sentence blew my mind. This means that we had ILLEGAL math. MATH, made illegal.

Can you imagine there being a time when certain equations and formulae were considered illegal? This interests me most because less than two decades after this illegal math, we are taking a class specifically about this illegal math. We’ve seen in class how cryptography has been used throughout history, and it always has been, and probably always will be, a part of life in government. However, it was always that it was only accessible to the wealthy, and those in government. No one else could afford the knowledge required, so we couldn’t keep secrets from the government. With the rapid spread of computers and advancement in technology, suddenly average citizens could afford to encode their messages, and it is very interesting to me that the government was so threatened by this that they felt the need to ban this knowledge.

Of course, it is also my opinion that, like Prohibition, this just proliferated the use of cryptography, but with even less government control. My favorite part of class so far has been our discussions about the intersection of cryptography, government, and privacy, which is why Little Brother, and especially this chapter hold my interest so well. With cryptography and cryptanalysis becoming ever more advanced, it will be exciting to see how the government handles all this as well.

Rejewski and Turing

One of the main reasons for the success of the Allied cryptanalysts at Bletchley Park over German cryptographers is the acquisition of the previous work of the Polish on the German Enigma. Polish cryptanalyst, Marian Rejewski, led the polish to first break Enigma in 1932, and kept up with breaking any new security the Germans implemented to strengthen Enigma, until in 1939, when the Germans increased the number of plugboard connections from 5 to 8 to 7 to 10, which made cryptanalysis extremely more difficult. This spurred the Polish to disclose all their work on Enigma to the Allies, especially as the likelihood for another war was growing. Thus, when war broke out and the need to break Enigma became of utmost importance, the Allies had a head start on breaking the codes, as they already had acquired intelligence on Enigma.

Another curious and more indirect reason why the Allies were ultimately successful was because Britain never found out that Alan Turing was a homosexual. Turing was the one of the most important men in the war in that he led the cryptanalyst team at Bletchley Park to victory in breaking Enigma. At the time, homosexuality in Britain was illegal and it was very fortunate that the state never found out about Alan Turing’s case during the war, otherwise Turing probably would never had made it to Bletchley.  Needless to say, if Turing had not been working for the Allies during the war, Enigma may never have been broken and the Germans may have won.

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The Mammoth Book of Secret Codes and Cryptograms

Not only is Elonka Dunin able to solve extremely difficult codes and ciphers, but she is also able to create them and teach others the techniques to solve them, which truly shows a mastery of the skill. She illustrates this talent in her book that was released in 2006 called The Mammoth Book of Secret Codes and Cryptograms. I really want to read this book because it includes a wide range of fun brain teasers such as secret messages, substitution ciphers, historical ciphers used by Julius Caesar or JFK, etc. She also includes tips to solve some of the most famous ciphers in history such as the fourth section of Kryptos or the Zodiac Killer ciphers.

The book seems like a fun and interactive way to extend my knowledge and cryptography, and it also relates to some of the things we have discussed in class this year. Of course, it include Kryptos which Elonka Dunin came in to teach us a little about, but we have also learned about the Caesar ciphers (substitution ciphers where the alphabet is just shifted), and we probably have the tools to solve some of the low to medium levels of ciphers that she includes in her text. Overall, I am excited to read her book because it will be an interactive way to learn how to solve more difficult ciphers and extend my knowledge on the history of cryptography.

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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.

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Odd Drawings and a Secret Script: The Voynich Manuscript

While perusing Elonka’s website, I was fascinated by her page of “Famous Unsolved Codes and Ciphers”. Like Sara stated in her blog post, it is so astonishing to think about how even with modern technology and current knowledge, there are still numerous ancient ciphers that have yet to be broken, including the Beale Ciphers and the Voynich Manuscript.

I was not surprised that the Beale Ciphers was seated at the top of the list, which was ordered in terms of “fame.” In class, we discussed how its popularity most likely stemmed from the monetary prize associated with cracking it. Both professional cryptanalysts and amateurs have taken a crack at the Beale Ciphers, motivated largely by the potential of finding $20 million worth of treasure.

Although we have discussed the Beale Ciphers at length in class, the majority of the ciphers on the list were foreign to me. I found the Voynich Manuscript to be particularly intriguing. The Voynich Manuscript, which was constructed in the early 1400s, is a staggering 232 pages long. Its uniqueness stems from the fact that it not only contains text, but that it consists of drawings as well. Eccentric drawings of plants, herbal recipes, astrological diagrams, and humans in plumbing-like contraptions dominate its pages. This makes me wonder: what role do the drawings serve? Do the drawings contain the key to decrypting the text?

In class, we talked about the advantage of having a substantial amount of encrypted text when attempting to break a cipher. The Voynich Manuscript poses no problem in this respect. However, it is written in an unknown script of which there is no known other example of in the world. The script is alphabetic in nature, but shares no letters with any English or European alphabets. While this greatly elevates the difficulty of decrypting the script, it makes the manuscript equally more intriguing as well.

The Voynich Manuscript is considered ‘The Most Mysterious Manuscript in the World.’ Although it is possible that it is just a great hoax with no true meaning, crpytanalysts continue to devote extreme amounts of time and effort towards decoding it. Not only would decryption explain the strange drawings, but it would also reveal a new language never seen before. The Voynich Manuscript is simply fascinating; how and when it will be solved still remain a complete mystery, but I eagerly await its decryption.

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The Morality of Admiral Hall's Actions

Upon learning the intended plans of the Germans from deciphering the Zimmerman telegram, it was ethical of Admiral Hall to withhold such information from the President.

 

One may argue that Admiral Hall should morally concede the information to the President so that Britain may be subsequently informed, and lives could be potentially saved during the outbreak of unrestricted submarine warfare. Yet, if America was to intervene before German acted out their plan, they would’ve “concluded that their method of encryption had been broken,” leading them to “develop a new and stronger encryption system” (Singh 113). This grants the possibility of the German’s using an extremely more complicated encryption system, one that the cryptanalysts in Britain’s Room 40 may never solve in their lifetime, to act out their unrestricted submarine warfare unopposed. This, in turn, could’ve led to a higher number of wartime casualties, especially among passenger ships. Thus, through decrypting future German telegrams without their knowledge that their encryption system had already been broken, Admiral Hall’s actions could potentially save many more lives than he would’ve had he passed on the information.

 

Furthermore, as history proved, by not informing the President, Admiral Hall ensured that the Germans did not realize the Americans had broken their encryption system, granting the Americans an advantage in decrypting any future German messages encrypted by the same system. Eventually the Mexican version of the Zimmermann telegram led America to retaliate, granting the same outcome had the Admiral actually passed on the information, but without the Germans discovering their blunder.

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The Truth Behind the Zimmerman Telegram

In 1917, during the height of World War I, the British intercepted a German telegram (the Zimmermann Telegram) that was meant for the Mexican government.  The Germans called for unrestricted submarine warfare, which violated a previous agreement with the United States, and proposed that if Mexico invaded the United States, Mexico would receive United States territory at the end of the war.

In high school history classes, we are told that as soon the British caught word of this duplicitous German telegram, the United States' government was immediately notified.  However, as Singh explains in the third chapter of The Code Book, the British initially withheld the information, at the potential cost of American lives due to unrestricted submarine warfare, in order to protect the cryptographic advancements of the British.  At first, I thought that the actions of the British were wrong.  The lives of innocent people were on the line.  Yet, I realize that from a broader perspective, the move to protect British cryptographic intelligence was ethical and necessary, because in the end, it led to the demise of the Germans and to the end of the war.

If the British had immediately informed the American government of the Zimmermann Telegram, chances are the United States would have publicly condemned Germany for its actions.  The success of the British codebreakers would have become known, and the Germans would have realized that their ciphers would need improving.  Had the Germans known this, they could have created a better, more impenetrable cipher, and the Allies would have been back at square one.  Since the Germans were unaware that their cipher had been broken (they believed that the Mexican government had handed over the telegram to the United States), the Allies had an upper hand, because they now knew the German code.

Overall, the British decision was ethical, because in the grand scheme of the war, more lives were saved by defeating the Germans than lives that would have been lost from unrestricted submarine warfare.  By protecting British cryptographic intelligence, Germany was blindsided and fell behind in their cryptographic advancements.  Because of this, Germany lost yet another advantage in the war.

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The New Normal

In Hello Future Pastebin Readers, Quinn Norton talks about how everyone who has access to technology is essentially the same in that none of their personal information and data, no matter how securely uploaded or downloaded, is actually private. This particularly interests me because today’s society is so heavily centered around the distribution of information globally, and this feeling of interconnectedness provides a false sense of security to many people, because in reality, they can have no idea what other people are possibly doing with their data.

The article also exposes readers to the idea that as we progress towards the more modern and technologically-oriented society, more people will learn how to hack, and the status quo will shift to a society where people must become comfortable knowing that privately posting anything online is the same as posting it to the public. On this topic, Norton furthermore brings up the interesting prospect that we should embrace the idea of performing as if “on stage” whenever we do anything online, which ultimately may help the world move towards a more open society, technologically speaking.

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.

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."

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