Cryptography

The History and Mathematics of Codes and Code Breaking

Month: August 2012

Cryptography and the Availability of Information

I think that amateur cryptanalysts using methods that were impossible for some early civilizations to use demonstrates the accessibility and ubiquity of information today. For example, some puzzles are centered around ciphers and decryption. These puzzles attract the attention of novices who have little to no experience in cryptanalysis. Never the less, these amateurs utilize strategies such as frequency analysis and recognition of small or common words (a, the, and) without having ever studied them. Even on our first day of class, we were able to decrypt the cipher text presented to us by using some of these methods. Similarly, we perform other “higher-order” thinking tasks on a daily basis without giving much thought. We type rapidly, blaze the internet, estimate sale prices, and navigate Vanderbilt with (relative) ease. Of course, we utilize technology to make many of these tasks much easier, but we also must know how to use the technology and make it work for us. Thirty years ago, only serious business people and others with special training used computers. Today, most of us carry around a “tiny computer” with us at all times and know how to operate it efficiently. Basically, we do many things today that require skills that we take for granted. At the dawn of cryptanalysis, however, this knowledge simply was not there for all to benefit from. The moral of the story: when your first [insert impossible class name here] test score comes back much, much lower than you had hoped, take pride in knowing that in the Middle Ages, you would be hailed as a genius.

Frequency Analysis Utilized by Amateurs

When Al-Kindi first developed cryptanalysis it was groundbreaking and highly advanced for his society. Today, our society is highly intellectual and focuses on stimulating problem solving abilities in young children. With the knowledge of frequency analysis, many amateur cryptanalysts can easily employ the method to successfully decrypt text.

Society today is exposed to these necessary skills early on in development. The idea of using logic to solve puzzles, riddles and other games is common starting at a very young age. What may have been considered a significant level of scholarship when cryptanalysis was first invented is now merely accounted for as common sense.

Early on in the history of cryptography people were not accustomed to the idea of codes and secret messages. This concept was so foreign that they could not begin to understand how to solve them or decrypt them. No one paid attention to what common letters were or which letters were most frequently used in their language. Today, with basic reading and common experiences such as watching word guessing game shows, people subconsciously take note of what letters most often appear in words. When an amateur cryptanalyst approaches an encrypted message they instinctively look to substitute in “e”, “t”, or “a” for example, knowing these letters form many common words. In the past, this knowledge was not considered basic knowledge and people were unaware of this crucial information. Armed with the knowledge of frequency analysis and the logical thinking our society breeds, amateur cryptanalysts can easily use frequency analysis without prior training.

Social Bookmarking Assignment #1

For your first social bookmarking assignment, find and bookmark a credible source that provides additional information on some topic introduced in Singh Chapter 1. Tag your bookmark with "Chapter1," along with at least one other meaningful tag.

Your bookmark is due by 8:00 a.m. on Thursday, September 6th. If you have any questions about using Diigo or determining if a source is credible, don't hesitate to ask.

Image: "Interesting Pin," by me, Flickr (CC)

Problem Set #1

Here's your first problem set, available in Word and PDF formats. It's due at the start of class on Thursday, September 6th. You're welcome to turn in typeset or handwritten solutions, but please turn in a hard copy of your work. In other words, don't email me your problem set.

Also, here's an Excel file you can use to aid your decryption of the ciphertext in the first problem.

Update: Please ignore Problem #5 on this problem set. We didn't get far enough into decimation ciphers for you to be able to answer it. Look for it to reappear on the next problem set.

Singh Chapter 1 - Reading Questions

As I mentioned in class, you'll need to read the first chapter of The Code Book for class tomorrow. In case you'd like a little guidance for your reading or would like to prepare for discussion tomorrow, here are a few questions about Chapter 1 you might consider. I'm not expecting you to answer these questions (on the blog or in writing), I'm just providing them as a resource.

  1. On page 41, Singh writes, “The cipher of Mary Queen of Scots clearly demonstrates that a weak encryption can be worse than no encryption at all.”  What does Singh mean by this and what does it imply for those who would attempt to keep their communications secret through cryptography?
  2. Most of the examples of cryptography in Chapter 1 were associated with well-resourced people—monarchs, military leaders, etc.  Is that because those are the only examples that have survived or is that because cryptography and cryptography development is dependent on exceptional resources?  If the latter, do you think that has changed over time?  What implications does that have for today’s uses of cryptography?
  3. Given that Singh was presumably trying to write an interesting and engaging book, why do you think he chose these examples for Chapter 1 instead of other potential examples of classical cryptography?

Zimmerman, BlackBerry, and Poem Codes

Here are the visuals for three presentations I've given in the course thus far. Hope they're helpful!



The Advancement of Civilization's Effect on Cryptography

The reason that relatively untrained cryptanalysts are able to use frequency "on their own" is because the civilization has advanced enough for them to think in a way that allows for them to  think in complex ways. Though they are relatively untrained in the discipline of cryptography, they are well versed in the realm of linguistics, both reading and writing, and as well as at least a basic understanding of math and statistics.  This is very different from the civilizations that Singh refers to when discussing civilizations that weren't advanced enough to to preform crypt analysis, in those civilizations writing, reading, math and statistics were reserved to such a select few that new and original ideas were hard introduce. Because there were no new ideas that came into the intellectual aspect of the civilizations and the intellectual community is so small, it is hard for people to notice the patterns that is the basis of frequency analysis. In today's society, even those that are classified as "amateur" cryptanalysts still have a solid base in linguistics and at least a basis in math and statistics which allows them to be able to come up with frequency analysis "on their own."   The intellectual community is larger and because of that , there are more examples of cryptography and as Singh shows in his book, the more material there is, the easier it is to see the pattern of the encryption that hides the plain text of a message. The intellectual basis combines with the fact that the intellectual community is larger in order to create the opportunity for frequency analysis to appear naturally in today's society, as opposed to the civilization, such as Europe, who Singh classifies as not having "sufficiently sophisticated level of scholarship ".

Blog Assignment #1

For your first blog assignment, write a post between 200 and 400 words that responds to the following question:

On page 15 of The Code Book, author Simon Singh writes, "Cryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of scholarship in several disciplines, including mathematics, statistics, and linguistics."  If such a level of scholarship was required for the development of the frequency analysis approach to solving substitution ciphers, what do you make of the fact that amateur cryptanalysts today often use that approach "on their own," so to speak, without being trained in it?

Please give your post a descriptive title, and use the "Student Posts" category for your post. Also, give your post at least three tags, where each tag is a word or very short phrase (no more than three words) that describe the post's content. You're encouraged to use tags already in the system if they apply to your post.

Your post is due by 8:00 a.m. on Tuesday, September 4th. If you have any questions about sharing your first post here on the blog, don't hesitate to ask.

Update: Here are some basic instructions for posting to WordPress that you might find useful. Also, via xkcd, here's the secret to using any kind of computer technology.

Image: "Ghost Writer," by me, Flickr (CC)

Fall 2012 Edition

Welcome to the course blog for Math 115F: Cryptography, the first-year writing seminar I teach from time to time at Vanderbilt University. This semester is one of those times, and I'm looking forward to exploring the history and mathematics of codes and ciphers with another group of first-years.

Here's the syllabus for this fall's offering of the course. You'll want to read through it carefully. You'll also need to do a few other things to get started as a student in the course.

  1. Obtain copies of the three texts we'll use this semester: The Code Book by Simon Singh (Anchor, 1999), Cryptonomicon by Neal Stephenson (Avon, 1999), and Little Brother by Cory Doctorow (Tor, 2008). Please note that Little Brother is available as a free download from the author's website.
  2. Activate your account here on the course blog, which is powered by WordPress. I'll send you an email with a link to do so tomorrow after class. As noted in the syllabus, you'll be blogging regularly as part of this course. Once your account is activated, read through these instructions for authoring WordPress posts. I'll give you your first blogging assignment soon.
  3. Sign up for an account on Diigo, the social bookmarking service. Once you have an account, request to join the Math 115F Diigo group, where we'll be sharing news articles, websites, and other online resources relevant to the course. I'll let you know your first social bookmarking assignment soon, too.

Two important points about the blog and Diigo: One is that if you need any help using these digital platforms, just ask. The other is that you're welcome to use a pseudonym on either platform. Your blog posts and Diigo bookmarks will be on the open Web, meaning anyone could see them. You might want your name attached to them as a way to start building a digital footprint that represents you well. Or you might prefer a little more anonymity for your work in this course. Your choice. If you use a pseudonym, however, you'll need to tell me what it is so that I can give you credit for your blog posts and bookmarks.

Image: "Welcome" sierraromeo, Flickr (CC)

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