### Chapter 8 Number Theory

Applet 11. Letter Frequency Analysis Calculator

 A tool to help crack letter-substitution ciphers by making a table of the frequencies of the letters in a sample of ciphertext.
 Type or paste enchiphered text into the textbox on the right. A histogram to the left shows the relative frequency of each of the letters in the text. (If the histograph does not appear immediately on pasting, press the "Count" button.) If you know that the ciphertext was made using a letter-substitution cipher from English plaintext, then information about letter frequencies can help you identify key letters. Usually "E" is the most common letter in English text, with "A", "O" and "T" running next. So the chances are that "E" has been replaced by whichever letter is the most common in the ciphertext. Use the Affine Cipher Calculator to experiment with the results of various possible substitutions. Once you have identified which letters have been substituted a few key letters such as "A", "E", "O" and "T", then even a partial deciphering of the message should enable you to guess the rest.