The History and Mathematics of Codes and Code Breaking

Category: Resources (Page 1 of 5)

World War II Cryptography

In case they're helpful, here are my sketchnotes from our guest speaker, history professor Michael Bess, earlier in the week.

Resources on Plagiarism and Academic Integrity

Some resources relevant to our discussion of plagiarism and academic integrity...

2017 Our Muslim Neighbor Conference

I wanted to invite you to attend the third annual Our Muslim Neighbor Conference on October 21, 2017, right here on campus. This event is hosted by the Faith & Culture Center, a Nashville non-profit that works to create dialog across lines of faith, race, culture, and ethnicity. I went to the Music City Iftar event they hosted in June and I really enjoyed the conversations I had there with Nashville citizens of a variety of backgrounds.

The reason I share the conference with you is that the theme of the conference touches upon key questions we're exploring in our course. The conference theme is "Security and American Muslims: National Narrative, Local Impact." Speakers include Faiza Patel, co-director of the Liberty and National Security program at the Brennan Center for Justice at New York University School of Law, and Alberto Fernandez, former coordinator of the Center for Strategic Counterterrorism Communications at the US Department of State, as well as local (Nashville) Muslim leaders.

I can't go, unfortunately. But it would be great if one or more of you could attend and report back, either during class or here on the blog. If you're interested in going, let me know, and register here. Thanks!

Little Brother Resources

Some Little Brother resources that might be useful...

And here's a photo of the debate map we constructed in class on Monday. Click on the photo for a better view.

Frequency Analysis Resources

Here are a couple of Excel files we'll use in class today:

Decimation Ciphers

Here's that proof I promised at the end of class on Monday. Read through it line by and line and see if you can follow it. Let me know if you have any questions.

Theorem: If a decimation cipher multiplier is NOT relatively prime to the alphabet length (that is, if it has a prime factor in common), then it produces an unusable cipher alphabet.

Proof: (in the case where the alphabet has length 26)

  • Suppose d has a prime factor p in common with 26 (either 2 or 13).
  • Let x be a number between 0 and 25, representing a letter in the plain text alphabet.
  • Then xd must be divisible by p, since d is divisible by p.
  • Dividing 26 into xd yields xd =26q + r for some quotient q and remainder r, where r is between 0 and 25.
  • Then r = 26qxd, which is divisible by p since p is a factor of 26 (and thus of 26q) and of xd.
  • Thus xd MOD 26 is a number between 0 and 25 that is divisible by p. There aren’t 26 such numbers, so we’re guaranteed to get repeats in the cipher alphabet.

Note that we could make the same argument for other alphabet lengths.

This theorem allows us to rule out 2, 4, 6, 8, 10, 12, 13, 14, 16, 18, 20, 22, and 24 as usable decimation cipher multipliers. That leaves 11 possible multipliers: 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, and 25. We can verify experimentally that all of these work, or we could prove the following conjecture.

Conjecture: If a decimation cipher factor is relatively prime to the alphabet length (that is, if it has no prime factors in common), then it produces a usable cipher alphabet.

I can't call this a theorem until we've proved it! I haven't proved it yet, but I suspect that it's true.


Border Dispute

Here's the @snowden tweet (well, retweet) that caught my eye:

I mentioned this after our Citizenfour screening last night: The laws governing search and seizure at US borders aren't the same as the laws that apply within the country. Specifically, searches and seizures at borders don't require warrants. The tweet above references a recent course case that pushes back on this policy. The judge in the case ruled that the US government should not have seized (and searched) a laptop belonging to a South Korean businessman while he traveled through an LA airport, since they didn't have a warrant.

Given all the time Snowden spent between borders in a Moscow airport in 2013, perhaps he has a personal interest in this story, in addition to a policy interest.

Computer Ciphers

Two resources from today's class:

  • An ASCII table, showing how to translate characters (like "a" and "@") into numbers that computers can understand.
  • Today's Computer Cipher Worksheet, which features several questions about binary numbers. We went over questions 1 through 4 during class today. See if you can make sense of question 5 before class on Monday.

Little Brother Links

A few Little Brother links for you, most of them mentioned in class...

  • Cory Doctorow blogged about my blog post about our in-class debate map activity.
  • On Twitter, I asked Cory Doctor about the terms "surveillance" and "security" as they apply to this debate. Here's what he said.
  • Here's that streamgraph showing the use of words in Little Brother from start to finish.
  • Cory Doctorow wrote a sequel to Little Brother called Homeland that describes the continuing adventures of Marcus Yallow.

Little Brother Debate Map (2015)

I snapped a photo of the debate map we constructed during class on Monday. We'll talk more about Little Brother in class tomorrow, and I thought you'd want a copy of the debate map for reference. Recall that orange Post-it notes captured pro-security arguments made by characters in the novel, while magenta Post-it notes captured pro-privacy arguments. Click on the image for a better look. And if you're really interested, check out the 2012 debate map and the 2014 debate map.

Little Brother Debate Map 2015

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