Cryptography

The History and Mathematics of Codes and Code Breaking

Tag: FYWS

Zodiac Killer on the Loose

I thought that the podcast about the Zodiac Killer was extremely interesting and very well done. I think that one of the most important aspects of this podcast was the use of music. The creator of the podcast clearly knew how dark the subject matter was and chose music accordingly. I liked how the music was not overpowering either so that the voice of the narrator was crisp and clear. I think that finding this balance is difficult, and I think they did a very good job with it.

I also really liked their use of storytelling. Nowadays, we are so used to the movies where everything is shown to us, so explaining in words the gruesomeness and eerieness surrounding the Zodiac killer's murders is a difficult task on a podcast especially. They did a very good job with the storytelling, and overall their podcast was pretty stellar.

If I had to make one small critique though, it would be that at a couple of places there were a few short pauses/ stumbles that drew away from the rather fluid nature of the podcast, if these were cleared up, I think it would be very hard for me to tell their podcast apart from the professional ones.

A comment on another student's analysis of how the enigma was broken.

(http://derekbruff.org/blogs/fywscrypto/2017/10/08/an-interdisciplinary-approach/) (link to original blog post)

In his blog post titled "An Interdisciplinary Approach," Browkm10 shows how the creativity of the minds in Bletchley park heavily contributed to the success of the team. We talked about in class how breaking a cipher involved a certain degree of logic, creativity, and skill. Browkm10 discusses how all the major players like Turing brought diverse expertise to the table. He talks about how there were chess champions, bridge builders, and machine experts all congregated together working on the same problem. He ultimately argues that it was the combination of creativity and logic that made the defeat of the German enigma possible.

I do think, however, that he/she left out an important aspect that had to take place for the enigma to be broken, which was luck. The cipher was only able to be solved because of a few key mistakes that were made by the Germans. They didn't allow switchboards to have connections to adjacent letters, which lowers the total number of combinations by a huge amount. They also had rules about scambler placement that had the same effect. It was the logic and creativity that made breaking the enigma possible, but there were a good amount of mistakes made by the Germans as well that contributed to the Enigma's demise. I think overall the blogger made some very good points, but I think that this nuance's his/her argument.

 

German Cryptography is still Human Cryptography

During WWII, Germans sent out thousands of messages encrypted using the supposedly unbreakable Enigma machine. It was discovered after the war that German intelligence knew that these messages could be captured by the Allies, but they could not think anyone would have the time or resources to possibly decipher them. This strongly held idea that Enigma was unbreakable was perhaps the greatest mistake of Germany.

Another factor, besides German overconfidence, that allowed the Allies to decipher German messages were the patterns discovered when Enigma was used. These patterns were precisely the result of non-randomness that describes human nature. Some keys were easily guessed because the letters on the Enigma keyboard were next to each other. Other keys may have been similarly predictable because they resembled German names, or they were used repeatedly. These were called "cillies." Ironically, an effort to consciously combat human un-randomness was also a mistake on Germany's part. By avoiding "obvious" plugboard settings and arranging rotors to avoid repeated positions, the amount of possible settings were drastically reduced.

Human nature in and of itself is never truly random; this is a basic fact we learn in our statistics classes. If you asked a population to randomly choose a number between 1 and 4, would a fourth of the people choose each of the numbers? Polls have shown that, instead, a clear majority would choose the number 3. In the same manner, cipher keys are not always a random garble of letters. They are often derived from meaningful words or phrases that may be pertinent to the message or the receiver/sender of the message.

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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 Process of Writing

Writing my practical cryptography paper requires a lot of time and effort. Firstly and most importantly, I have found all of the sources I need in writing this paper. This took a great amount of time to find the perfect articles on the internet to address my topic, phishing. After finding and printing out all of my sources, I then needed to figure out how to organize this paper from beginning to end. In addition, it is imperative that I organize this paper without the classic "slow wind-up" and make it interesting for the audience.

I have made good progress so far in this paper with about one-third of the word count left to go. I need to continue improving my introduction and conclusion and expand my body paragraphs to increase the word count. By far the most challenging part of completing this paper is getting to the word count. It is difficult to write a large amount about this topic without feeling like I am just rambling or repeating. Perhaps I need to add another source or two to my paper. It has been enjoyable to learn all about phishing and its impact on our society. I have enjoyed becoming familiar with the topic as a whole and even learned new steps and measures I should take to avoid being "phished".

Privacy: From Times Square to the Percent Accuracy

The overwhelming theme of the novel Little Brother concerns the privacy of an individual and a society in all aspects of life. From the moment in which Marcus is first questioned by the National Homeland Security (NHS) until the end of the novel, Marcus highlights to the reader of the many horrifying consequences of a government overstepping its boundaries. Two examples described by Marcus hit me hard about why privacy is vital in having a normal and functioning society.

The first example is after the NHS confiscates Marcus's electronic devices and receiving the passwords of those devices through brute force and intimidation. The NHS tells Marcus that if he truly has nothing to hide, then it should be no problem for them to take a look through his devices. This bothers Marcus extremely; however, he eventually gives in due to the fact that he knows that giving the NHS what they want is the only way for him to be released. Marcus compares this thinking of the NHS to forcing somebody to go to the bathroom in a clear glass room in the middle of Times Square. Although they have nothing to hide or protect, any normal person would want privacy when going to the bathroom and to not be in the public eye. This comparison was powerful in the imagery it invokes. Picturing somebody having to use the bathroom in public shows that Marcus having to give away all of his privacy and dignity is wasteful.

Secondly, as somebody who loves statistics and numbers in general, I also found the example of "false positives" and "percent accuracy" powerful. It demonstrates how problematic and inefficient the search and interrogation of almost everybody throughout San Francisco is in finding the terrorists who blew up the bridge. By displaying that even a 99% accuracy causes the government agencies and police to searching thousands and thousands of people further highlights the inefficiency of investigating people for possible terrorist suspects because in reality, their percent accuracy is closer to 50%. This example shows the reader not only how difficult it is to catch a terrorist in this manner, but also how it complicates and hurts the lives of the everyday citizens.

 

The Vigenère Cipher

For some time before the development of the Vigenère cipher, “anybody sending an encrypted message had to accept that an expert enemy codebreaker might intercept and decipher their most precious secrets.” (Singh, p. 45) How is this environment different from the one that Mary Queen of Scots experienced, where one didn’t know how likely it was that one’s encrypted message was secure?

Before the tragic execution of Mary Queen of Scots, the majority of people believed that the monoalphabetic substitution cipher would be sufficient in enciphering secrets. This is the exact reason why Mary Queen of Scots and her conspirators were extremely blunt and honest. Once the cipher was deciphered, she was immediately incriminated. However, at the same time of her death, a new polyalphabetic substitution cipher was used, the Vigenère cipher began to be involved greatly. The Vigenère cipher changed the landscape of all ciphers because it used twenty-six different alphabets for enciphering instead of only one. This made the deciphering process much more arduous or even close to impossible for the interceptor.
Back in Mary Queen of Scots time, it was not known that a number of people had figured out how to easily solve a monoalphabetic substitution cipher. Therefore, people kept using it. Once the news broke about the Mary Queen of Scots and the interceptor, mathematicians knew that it was necessary to create a much more difficult cipher in order to make sure secrets could be safe. The interceptors had made the adjustment, and it was time for the mathematicians to make their move. The Vigenère cipher was groundbreaking in that it stumped decipherers for years and years. Perhaps, had the fiasco involving Mary Queen of Scots not occurred, the advancement of cryptography as a whole could have been delayed hundreds of years. After this incident, anybody who used the simple monoalphabetic substitution cipher knew that they were under great risk of having their secret deciphered; this led to the rapid increase of technology and intelligence in the realm of cryptography.

Securing Social Media

Although I am not too informed on most measures you can take in ensuring better security online, the major step I always take is limiting the number of electronic devices you log into that requires passwords. This is an easy way all college students can increase their security, especially in terms of social media. The lower the number of computers you log into on Facebook, the better. I have heard and read a number of articles about people hacking into public computers and retrieving data from social media websites. These hackers have had great success thus far and will continue hacking. The major safety step we should all take is to not log in to social media accounts on public computers. For example, the computers at the Commons should be used for printing only, not for typing in credit card information or checking your Facebook, Twitter, etc.
Reading Christian’s article about the HTTPS now being available for Facebook interested me greatly because it has always seemed as places like Facebook had either little or no security at all. Hopefully this new added level of security will cure some of the major problems that have happened concerning hacking over the last few years. Although this might ameliorate the problem most of the time, it is still of everyone’s best interest to keep logging in to accounts on your own personal computer or “smart” phone. The chances of someone stealing your computer and accessing your information are less than a random hacker checking a public computer and gaining access to your information that way. Like always, safety is most important. I feel confident that if college students play it smart by just using their own computer for their social media accounts/bank accounts, they will significantly lower the chance of a much bigger security problem down the road.

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