Cryptography

The History and Mathematics of Codes and Code Breaking

Month: September 2010

Cryptography in the Movies

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On September 10, 2010

In Resources

Sneakers (1992) isn’t the only movie to feature cryptography, although it is one of the best! Here are some other movies that feature codes and ciphers.

Did I miss any?

Reading Questions for September 16th

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On September 10, 2010

In Reading Qs

In preparation for class on Thursday, September 16th, please read pages 45 to 62 in the second chapter in the Simon Singh book and think about the following questions.

  1. 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?
  2. Can you think of any ways to improve the security of the Vigenère cipher?
  3. The Great Cipher used by Louis XIV remained unbroken for 200 years.  What were the factors that led to such a secure cipher?
  4. Why do you think that the advent of the telegraph motivated the use of a more secure cipher like the Vigenère cipher?

As a reminder, note that responding to these questions by leaving a comment here on the blog is one of the ways in which you can contribute to your participation grade in this course.

Resources for September 9th – Transposition & Keyword Ciphers

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On September 9, 2010

In Resources

Here are several useful Excel files from today’s class:

  • Keyword Cipher – This file will generate a cipher alphabet using the keyword cipher method. Enter your keyword (or keyphrase) at the top of the first worksheet in the file, and look for the resulting cipher alphabet on the lefthand side of the worksheet below. On the second worksheet, you can encipher whatever plaintext you like using the cipher alphabet constructed on the first worksheet.
  • Frequency Analysis – This file will conduct a letter frequency analysis on any ciphertext you give it. If you replace the default ciphertext, you’ll want to sort columns D, E, and F by the values in column F in order to identify the most common letters in the ciphertext. Check out the “Graph” worksheet in the file to see a bar chart comparing the ciphertext frequencies with those in standard English.
  • Cryptanalysis – Substitution – Here (once again) is the Excel file that will save you a lot of time when attempting cryptanalysis of a message enciphered using a monoalphabetic substitution cipher. Use this file in conjunction with the Frequency Analysis file when the plaintext’s original spacing isn’t preserved.

Also, here is the handout with examples from class, in Word and PDF versions.

Problem Set 2

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On September 8, 2010

In Problem Sets

Here’s Problem Set 2 in Word and PDF versions. It’s due at the start of class on Tuesday, September 14th.

Update: There was a typo in the first problem.  The Coptic alphabet has 30 letters, not 32.  I’ve corrected this in the Word and PDF files attached here.

Resources from September 7th – College Writing

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On September 8, 2010

In Resources

Thanks to the Writing Studio consultants who visited us and provided a useful introduction to college writing. Please remember that you can schedule a consultation with the Writing Studio at any time in the writing process. The handouts from yesterday’s session are available on the Writing Studio website, along with lots of other useful handouts on writing. The Writing Studio also hosts a number of events each semester, including “Dinner and Draft,” a chance to hear faculty members talk about their writing processes. The “Dinner and a Draft” line-up this fall includes two great guests, Keivan Stassun (Astronomy) and Kate Daniels (English).

We also wrapped up our discussion of decimation ciphers and relatively prime numbers yesterday, mostly drawn from the Barr textbook, Section 2.2. I’ve been meaning to tell you that I’ve placed a copy of the Barr textbook on reserve in the Science & Engineering Library (the one in the basement of Stevenson Center), so if you don’t have a copy, you now have access to one.

Speaking of Barr, here’s the theorem I didn’t write on the board yesterday since it’s in the Barr book. I’m putting it here for easier reference.

Theorem: (The Fundamental Theorem of Arithmetic) Each integer greater than 1 is either prime or the product of powers of primes.  Moreover, in the latter case, if an integer is written as a product of powers of primes, and these factors are written in increasing order of the primes, then no other factorization is possible.

Image: “pen and paper” by Flickr user LucasTheExperience, Creative Commons licensed.

Resources from September 2nd

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On September 2, 2010

In Resources

Here’s my office hour schedule between now and Tuesday’s class:

  • Today (Thursday) 4:00 to 5:00 in my office
  • Monday 8 to 9 pm in the Common Center lobby

Also, please note that you don’t need to do Question 5 on the problem set that’s due on Tuesday. We’ll defer that question to the next problem set.

I used Wolfram|Alpha a couple of times during class today, once to calculate 26! and once to calculate 254!. You might find it a handy tool in your math and science courses.

Here are my PowerPoint slides from today (in PDF format), which include the clicker questions I asked. I’ll be sure to post here on the blog any clicker questions we use in the future, so you don’t have to write them down during class.

And here are the two Excel files we saw today that use modular arithmetic: the one that handles shift ciphers and the one that handles decimation ciphers. Feel free to use these on your homework if you find them helpful.

Problem Set 1

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On September 1, 2010

In Problem Sets

Here’s Problem Set 1 in both Word (.docx) and PDF formats.  It’s due at the start of class on Tuesday, September 7th. Please note: You should ignore Question 5! We didn’t get quite far enough in class today for you to tackle Question 5. Look for it to reappear on the next problem set.

Update: You’re welcome to email me your problem or hand in a hard copy at the start of class on Tuesday–whichever is easier.

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