Some Math Examples 
 
 
 
Here are some codes that you can actually try... 
 
 
1. The Caesar Cipher 
 
 
 
The Caesar cipher encrypts messages by replacing each letter of the alphabet with the letter shown beneath it when written in two lines, as below
 
 
ABCDEFGHIKLMNOPQRSTUVWXYZ 
  DEFGHIJKLMNOPQRSTUVWXYZABC
 
 
Try following these examples:
 
       
        A. WLMVMVDFRGH
 
        B. BRXDUHVPDUW
 
        C. GUOHIFRXUWMVVPDUW
 
(FAPP)
 
 
2. The Spiral
 
 
The spiral looks complicated but is actually quite user-friendly.  It's all done using a spiral chart of valued letters, like this one:
 
                                                           
 
Each character on the spiral can be represented with a number. In the first spiral the letter A is equal to 1. B is equal to 2, etc.  As the spiral continues around the cipher clock each character is given another value that can be used in your cipher. A is also equal to the number 30, in the second spiral. Can you figure out what the value for A is on the third spiral?  Letter A is equal to values 1, 30, 59, 88, and so on. Simply add 29 to the original value of A to get the value for the next spiral. You add 29 because there are 29 characters in the entire cipher clock. Using the spiral you can write a cipher using any of the values for each character on the spiral cipher clock. Using the spiral above see if you can decipher the message:
 
 
25, 15, 21, 29, 1, 18, 5, 29, 7, 34, 20, 49, 9, 43, 7, 29, 36, 15, 44, 33, 28
 
 
Notice how some letters are represented with two different values? One can make spiral cipher clocks even harder by using non-sequenced letters and extra characters.
 
(Dunham)
 
 
 
3. Map Cipher

Maps have been used by people for centuries to aid in navigation. However, if you look closely at some maps you may be able to identify a pattern. Map ciphers are maps that look normal but have a secret cipher hidden within.

To create a map cipher one must create a set of symbols that stand for each letter in the alphabet. The example below uses tree branches and a matrix to create an alphabet of trees. The position of each letter in the matrix determines the number of branches on the left or right side of the tree. Look at letter "C", located in the matrix position of (1, 3). Place on branch on the left, 3 on the right.



Using the matrix above, can you figure out what the secret message is below?



Often, mountains, tributaries to streams, or other objects that don't give secret messages away are chosen as places to hide ciphers. The key to any good cipher is to make it look normal. If the enemy doesn't suspect anything the message will likely remain a secret.

Another successful idea is to randomly place letters into the matrix so that the cipher doesn't have such an easy pattern to decipher. Perhaps put letter "A" in (1, 4) and put letter "B" in (3, 2), etc. Maybe you'll use extra matrix locations to put in punctuation marks or distraction letters? 
 
(Dunham)
 
 
 
Solutions
1. A="This is a code"; B="You are smart."; C="Dr. Lefcourt is smart."
2. "You are getting good." 
3. "Cool cipher." 
 
 

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This page presented by Susan Floyd, Joanna Jenkins, Adrienne Mattea, and Katie Sutton for Dr. Lefcourt's M302 class at The University of Texas at Austin, Fall 1997.  Please e-mail any of us with any comments.