### Chapter 8 Number Theory

Applet 12. Affine Cipher Calculator

 This calculator enciphers and deciphers text using an affine cipher (such as the Caesar cipher) in which letters are encoded using the formula C=aP+b (mod 26) where a and b are whole numbers between 0 and 25 and a is relatively prime to 26. The calculator also supports general substitution ciphers in which each letter is replaced by a another letter in a given permutation.
 To encipher, enter plain text in the upper text box, and click on the down-arrow. To decipher, enter cipher text in the lower text box, and click on the up-arrow. Before you can encipher or decipher text, you need to set a cipher. The two columns of letters on the left show the plaintext letters (blue) and their cipher substitutions (white). To set an affine cipher, click "Affine", and enter values for the parameters a and b. The default values (a=1 and b=3) give the Caesar cipher. After you click "OK", notice how the pattern of letters in right hand colums of the main display change. To set a general substitution cipher, you need to choose letter-by-letter which substitutions to make. In the table on the right, click on a plaintext letter (blue background) to select a value, and drop that letter in a ciphertext position by clicking on a cell with a white background. Repeat until you have set up the desired substitutions. If you're trying to crack a cipher and you think you know a few of the substitutions, it often helps to "empty" the cipher and fill in only the letters you think you know. When you decipher the message with a partially-completed cipher, letters that can't be decoded are left blank (like Wheel of Fortune). Use this tool in conjunction with the Letter Frequency Analysis Calculator to experiment with cracking codes. The letter frequency analysis method illustrates the flaws of letter-substitution ciphers and, more generally, shows how hidden clues withing ciphertext can reveal weaknesses that expose it to cryptanalysis (cracking).