Saturday, November 24, 2007

Unplugged Project: WKDQN IXOHF for FLSKH UVHFG

The theme for this week's project is Thankful.

Have you ever played Cryptograms? A cryptogram is actually a Caesar Cipher, or a secret code. Like on a secret decoder ring. You shift the alphabet as many places left or right as you desire and replace the original message with the new letters. The Caesar Cipher that I used for my two secret words in the title of this post has a shift of 3 places to the right. Here is my cipher key (P means plain text; C means cipher):

Do you know what WKDQNIXO means?
Do you know what FLSKHUV means?

But why, in the title to this post, have I typed WKDQN IXOHF and FLSKH UVHFG? In English, there are a few one- , two- and three-letter words that we can easily decode (such as a, an, the, I, we, etc.). In order to prevent this happening (because we don't want the wrong person to read our secret code notes), codes are broken into five letter segments. If the last segment is less than five letters, two more random letters are sometimes added so that the total number of the letters is five. These random letters are called "nulls." The five-letter segments and the nulls make it more difficult to decode my message.

Julius Caesar is said to have used this same cipher key to send secret messages to his generals in war time. You can make your own code very easily (as you have probably figured out by now).

There is a mathematical way to code and decode ciphers and it uses modular arithmetic. I'm not going to go into modular arithmetic here except to say that you already know how to do modular arithmetic if you can add, subtract and convert inches to feet, days to months, seconds to minutes, weeks to months or months to years. Modular arithmetic is also called "clock arithmetic" and you can play with it in this java applet. Your family can study the discussions and help files for the instructor and learner so that you can all learn more.

When you understand clock arithmetic, move on to the Caesar Cipher I applet and make your own secret codes. Again, your family can study the discussions and help files for the instructor and learner so that you can all learn more.

Besides writing secret messages, why would anybody want to learn the mathematics behind ciphers? Ciphers are a type of encryption. And encryption rules our world now. Every time you download a zip file, use a debit or credit card, buy something online, or even send an e-mail, encryption is involved. Children who understand the value and importance of mathematics in our world will not be afraid to pursue careers in mathematics and computer science. (They'll make good money, too!)

Here are two more puzzles for you.
Each puzzle will open in its own window if you click on it.

The first uses the same Caesar Cipher key that you used above. I made it with the Caesar Cipher I applet from shodor.org (I used a multiplier of 1, and a constant of 3):

This second cipher is more difficult and will require the whole family's participation:


And don't forget: be sure to play Cryptograms often!
You can play cryptograms on this blog — down on the right sidebar.

Visit other participants of the Unplugged Project here.
Next week's project is open-ended and the theme is PAPER.
Or if you prefer — Water Paper Painting:
Wet some paper down with a paintbrush. 
Have your child (or you!) draw on it with paints or magic markers and see what happens.
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References:

Caesar cipher. (2007, November 12). In Wikipedia, The Free Encyclopedia. Retrieved 02:16, November 24, 2007, from http://en.wikipedia.org/w/index.php?title=Caesar_cipher&oldid=171008675

Caesar cipher I. In Shodor.org Interactivate Activities. Retrieved 10:12, November 24, 2007 from http://www.shodor.org/interactivate/activities/CaesarCipher/

Clock arithmetic. In Shodor.org Interactivate Activities. Retrieved 9:55, November 24, 2007 from http://www.shodor.org/interactivate/activities/ClockArithmetic/

Modular arithmetic. (2007, November 19). In Wikipedia, The Free Encyclopedia. Retrieved 02:27, November 24, 2007, from http://en.wikipedia.org/w/index.php?title=Modular_arithmetic&oldid=172507761

Malkevitch, J. and Froelich, G. and Froelich, D. 1991. Codes Galore. HistoMAP Module 18. COMAP, Inc., Lexington, MA.

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4 comments:

  1. "Last digit" arithmetic is perhaps the simplest modular arithmetic to understand. Working mod 10 means only the last digit matters.

    I've had good luck teaching with it.

    ReplyDelete
  2. It is so funny that you should have posted about this, since we were doing some ciphers a few weeks ago.

    This summer when I was at my Dad's I found an old book of mine in the attic and brought it back home with me: "Code Games," by Norvin Pallas. I just LOVED this book as a child! I am trying to interest my children in these puzzles too.

    I figured out WKDQNIXO and FLSKHUV (but I won't write the answer here so as not to spoil it for others!). The other ciphers will require more time and thought. We'll come back to those later.

    Thanks for this great idea!

    ReplyDelete
  3. Since I think in numbers, this is maddening for me to not decipher. Hahaha... I love the cryptograms. Now I have to figure them out ... :)

    ReplyDelete
  4. That is really cool. I am not to good at those type of puzzles, but my husband is so I will make sure to show him. Great idea though

    ReplyDelete

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