6g4 BELL SYSTEM TECHNICAL JOURNAL 



text has been started at a random point (by opening a book and putting 

 a pencil down at random on the page). The message selected in this way 

 begins "creases to . . ." starting inside the word increases. If the message 

 were known to start a sentence a different set of probabilities must be used, 

 corresponding to the frequencies of letters, digrams, etc., at the beginning 

 of sentences. 



N = 5 



The Caesar with random key is a pure cipher and the particular key chosen 

 does not affect the a posteriori probabilities. To determine these we need 

 merely hst the possible decipherments by all keys and calculate their a 

 priori probabilities. The a posteriori probabilities are these divided by their 

 sum. These possible decipherments are found by the standard process of 

 "running down the alphabet" from the message and are listed at the left. 

 These form the residue class for the message. For one intercepted letter the 

 a posteriori probabilities are equal to the a priori probabilities for letters'" 

 and are shown in the column headed A' = 1. For two intercepted letters 

 the probabilities are those for digrams adjusted to sum to unit}- and these 

 are shown in the column X = 2. 



'» The probabilities for this table were taken from frequency tables given by Fletcher 

 Pratt in a book "Secret and Urgent" published by Blue Ribbon Books, New York, 1939. 

 Although not complete, they are sufficient for present purposes. 



