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--- problem:simple_shift_on_26_letters [2013/08/08 23:40]
bmwoodruff
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-Long ago, in ancient Rome, Julius Caesar is said to have used simple ciphers
-to encrypt messages that he wanted to stay secret.
-The following problems are based on a modified version of this same cipher.
-Caesar started by writing out the alphabet and pairing each letter to a number that would represent it.
-One such pairing is
-$$
-\begin{array}{c|c|c|c|c}
-a&b&c&\cdots & z\\\hline
-&1&2&\cdots & 25\\
-\end{array}.
-$$
-With this pairing, we would encode the word //defend// as 4, 5, 6,
-, 14, 4. We'll call this the trivial pairing.
-\begin{problem}
-I want them to come up with a definition for a pairing.
-Then I want them to encode a word using their pairing.
-Then I will give them a pairing (a shift right of 3 units).
-Then from the pairing I gave them, I will ask them to decode a message.
-\end{problem}
-=== Comments ===
-I would like them to realize that one of the key ideas for making a pairing work is that they need a function that has an inverse.  This should make inverses become crucial.
-They are basically starting with symmetric groups with this problem.  I might ask them how many such pairings exist (26!), but I'm not sure.

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